Essays on Insurance Economics - University of St....

Essays on Insurance Economics

DISSERTATION of the University of St. Gallen,

School of Management, Economics, Law, Social Sciences

and International Affairs to obtain the title of

Doctor of Philosophy in Finance

submitted by

Ruo Jia 贾若

from

China

Approved on the application of

Prof. Dr. Martin Eling

and

Prof. Dr. Roland Füss

Dissertation no. 4526

Difo-Druck GmbH, Bamberg, 2016

The University of St. Gallen, School of Management, Economics, Law, Social Sciences and International Affairs hereby consents to the printing of the present dissertation, without hereby expressing any opinion on the views herein expressed. St. Gallen, May 25, 2016 The President: Prof. Dr. Thomas Bieger

List of contents

Summary ................................................................................................................................... 1 Introduction .............................................................................................................................. 4 Essay I Between-group adverse selection: Evidence from group critical illness insurance .... 7 1. Introduction .......................................................................................................................... 8 2. Theoretical background and hypotheses ............................................................................ 10 3. Data and insurance product ................................................................................................ 13 4. Empirical models ................................................................................................................ 19 5. Results ................................................................................................................................ 21 6. Robustness tests .................................................................................................................. 24 7. Discussion........................................................................................................................... 25 8. Concluding remarks and future research ............................................................................ 29 Essay II The structure of the global reinsurance market: An analysis of efficiency, scale, and scope ................................................................................................................................ 46 1. Introduction ........................................................................................................................ 47 2. Hypothesis development .................................................................................................... 49 3. Data and methodology ........................................................................................................ 53 4. Empirical results ................................................................................................................. 61 5. Robustness tests .................................................................................................................. 73 6. Conclusions ........................................................................................................................ 75 Essay III Internationalization and performance: The role of industry context and cost eficiency ............................................................................................................................... 100 1. Introduction ...................................................................................................................... 101 2. Literature review and hypothesis development ................................................................ 102 3. Data and methodology ...................................................................................................... 107 4. Results .............................................................................................................................. 114 5. Discussion......................................................................................................................... 118 6. Conclusions and managerial implications ........................................................................ 123 Essay IV Roles of commitment and information in multi-period insurance contracting: A comprehensive review and new empirical evidence ............................................................ 141 1. Introduction ...................................................................................................................... 142 2. Common theoretical platform .......................................................................................... 143 3. Hypotheses ....................................................................................................................... 152 4. Empirical evidence ........................................................................................................... 155 5. New empirical evidence ................................................................................................... 159 6. Concluding remarks ......................................................................................................... 173 Curriculum Vitae .................................................................................................................. 179

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Summary

This dissertation consists of four essays on insurance economies. It aims to answer questions in the fields of insurance transactions (Essays I and IV) as well as insurance operations and strategies (Essays II and III). These questions are relevant both to the insurance academic community and to the insurance industry. The methodologies explored in the dissertation are mainly empirical economics including multivariate regressions, data envenlopment analyses, among others.

The first essay, “Between-group adverse selection: Evidence from group critical illness insurance”, demonstrates the presence of adverse selection in the group insurance market even if individual choices are not allowed. It shows that group insurance alone is not effective enough to eliminate adverse selection, i.e., between-group adverse selection exists, which, however, disappears over time if the group renews with the same insurer for a certain period. The results thus indicate that experience rating and underwriting based on information that insurers learn over time are important in addressing adverse selection.

The second essay, “The structure of the global reinsurance market: An analysis of efficiency, scale, and scope”, uses a multidimensional data envelopment analysis to study economies of scale, economies of scope, and cost efficiency in the reinsurance industry. Reinsurers with total assets less than USD 2.9 billion exhibit scale economies, while those with assets greater than USD 15.5 billion do not. Large reinsurers are characterized by high cost efficiency. Small reinsurers exhibit superior efficiency when they are specialized.

The third essay, “Internationalization and performance: The role of industry context and cost efficiency”, analyzes the impact of globalization strategies (inter-regional internationalization) on insurers’ performance and show that the impact is different for life and nonlife insurers. It introduces the cost efficiency to explain the difference in internationalization-performance relationship and points out the industry idiosyncrasies between life and nonlife insurers in the liability of foreigness.

The fourth essay investigates the “Roles of commitment and information in multi-period insurance contracting”. It presents the first comprehensive review of theoretical and empirical research to uncover the roles of commitment and information in determining the type of inter-temporal pricing pattern. A novel two-sample empirical design is constructed, which excludes heterogeneity in firms, markets, and time periods, thus to isolate the impact of insurer’s commitment on its inter-temporal pricing strategy.

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Zusammenfassung

Die vorliegende Dissertationsschrift besteht aus vier Kapiteln und adressiert Kernfragen in den Bereichen Versicherungstransaktionen (Teil I und IV) sowie Versicherungsbetrieb und -strategien (Teil II und III). Die aufgeworfenen Forschungsfragen sind sowohl für die akademische Forschung als auch für die Versicherungspraxis bedeutsam. Die in dieser Dissertationsschrift verwendeten Methoden sind primär der empirischen Ökonomie zuzuordnen.

Das erste Kapitel weist das Vorhandensein adverser Selektion im Gruppenversicherungsmarkt nach. Die Arbeit zeigt, dass eine Kollektivversicherung allein nicht ausreichend wirksam ist, um adverse Selektion zu beseitigen. Die adverse Selektion zwischen Gruppen verschwindet jedoch im Zeitverauf, wenn die Gruppe ihren Vertrag mit dem gleichen Versicherer für einen bestimmten Zeitraum erneuert. Die Ergebnisse zeigen somit, dass Beurteilungen basierend auf Experience Rating und ein Underwriting basierend auf Informationen, die der Versicherer über die Zeit sammelt, zur Bewältigung der adversen Selektion wichtig sind.

Das zweite Kapitel verwendet eine multidimensionale Data Envelopment Analysis, um Skaleneffekte, Verbundvorteile und Kosteneffizienz in der Rückversicherungsbranche zu analysieren. Rückversicherer mit einem Gesamtvermögen von weniger als USD 2,9 Milliarden haben Skaleneffekte, während diejenigen mit einem Vermögen von mehr als USD 15,5 Milliarden diese nicht haben. Große Rückversicherer und kleine Rückversicherer, die spezialisiert sind, zeichnen sich durch hohe Kosteneffizienz aus.

Das dritte Kapitel analysiert die Auswirkungen von Globalisierung (interregionale Internationalisierung) auf die Performance von Lebensversicherungsunternehmen und zeigt, dass die Auswirkungen negativ sind. Der negative Zusammenhang resultiert aus einer, mit der Globalisierung einhergenden, Erhöhung der Kosteneffizienz.

Das vierte Kapitel untersucht die Rolle von Commitment und der Informationen bei der Bestimmung der Art des intertemporalen Preismusters. Die Arbeit stellt den ersten umfassenden Überblick der theoretischen und empirischen Forschung in diesem Feld dar. Darüber hinaus wird ein empirisches Zwei-Sample-Design konstruiert, das die Heterogenität der Unternehmen, Märkte und Zeiträume ausschließt, um damit die Auswirkungen des Engagements des Versicherers auf seine intertemporalen Preisstrategien zu isolieren.

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摘要

我的博士论文《保险经济学论文集》由四篇独立的小论文组成，其中第一和第四篇研

究保险交易问题，第二和第三篇研究保险运营与战略问题。我在论文中对这些问题的

分析和研究结论既有对保险学术研究的发展，也有益于保险行业实践。论文所使用的

方法包括多元回归分析、包络分析等等。

第一篇论文《团体组间逆向选择：团体重大疾病保险实证研究》主要说明：即使在个

人选择完全被排除的情况下，团体保险市场上仍然存在逆向选择；但是，被保险团体

在某个保险公司续保一段时间后，这种逆向选择现象会随之消失。团体组间逆向选择

主要是由团体本身基于自身整体风险状况作出的有利于团体成员的选择。保险人基于

历史赔付经验的定价和承保策略有助于缓解团体组间逆向选择。

第二篇论文《全球再保险市场的结构：效率、规模和业务范围的分析》，利用包络分

析的方法，研究再保险行业的规模经济、范围经济和成本效率问题。论文研究发现，

当再保险公司的总资产小于 29 亿美元时，存在规模经济效应；总资产大于 155 亿美

元时，存在规模不经济。大型再保险公司总体上成本效率较高，但小而专的再保险公

司同样可以达到较高效率水平。

第三篇论文《国际化与业绩表现：行业因素和成本效率的作用》，证实了全球化策略

对寿险公司和财险公司业绩表现的不同影响。对于寿险公司，通过成本效率因素作用，

全球化策略对利润率产生负面影响；对于财险公司，由于行业国际化成本结构不同，

全球化策略对公司利润率的负面影响被积极因素抵消。

第四篇论文《多期保险合约中承诺与信息的作用：比较综述和实证研究》。该论文首

次对多期保险合约研究进行了完整综述。论文区分了在多期动态健康险市场环境下

“前高后低“和“前低后高”两种定价定价策略，并证实了保险人对长期保险关系的

承诺是决定定价策略的关键因素。

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Introduction

Four essays on insurance economies constitute this dissertation. They aim to answer research questions in the fields of insurance transactions, operations, and strategies. These questions are important to the current insurance industry and to the worldwide insurance markets. The methodologies explored in the dissertation are mainly empirical economics including multivariate regressions, data envenlopment analyses, among others. The insurance business is investigated at two levels, the transaction (or risk, product, portfolio) level and the insurer (or group, firm) level. Essays I and IV focus on the transaction level interactions between insurers and policyholders. Essays II and III focus on the firm level operations and its implications to the management and policy makers.

Group insurance constitutes a substantial portion of global insurance markets as insurers use group insurance to mitigate adverse selection as a conventional wisdom. However, group strategic action on behalf of collective welfare may also generate adverse selection, that is, groups, like individuals, act strategically on their information advantages with high risk groups buying more coverage and low risk groups buying less coverage. This is called between-group adverse selection. The first essay in this dissertation documents the evidence that group insurance cannot eliminate adverse selection, even if individuals within a group are not allowed to choose their participation and/or coverage. Moreover, it also demonstrates the disappearance of between-group adverse selection over time by showing that in the repeated contracting setup, learning from the performance of past contracts and taking corresponding actions based on the information observed help to mitigate adverse selection problems. One implication of these results is that group insurance with no individual choice cannot be considered a market free of adverse selection, even if the group is formed for purposes other than purchasing insurance.

Reinsurers function as shock absorbers and risk bearers of last resort for the insurance industry and the global economy. Economies of scale and scope, as sources of diversification, are particularly relevant to the structure of the reinsurance market. The second essay in this dissertation estimates reinsurers’ cost efficiency using data envelopment analysis (DEA) with multiple inputs and outputs and analyzes economies of scale and scope based on DEA frontier efficiency benchmarks. It shows that the consideration of scale efficiency yields an optimal size range between USD 2.9 and 15.5 billion in total assets (inflation adjusted at 2012). The scope economies may only exist for large insurers but not for small ones. The empirical evidence explains the real-world structure of the global reinsurance market, in which large reinsurers dominate, but both diversified and specialized reinsurers play important roles. Further consolidation is expected in the global reinsurance market, not only because it

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improves cost efficiency, but also because it has the potential to lower reinsurance prices for consumers.

Internationalization has dramatically increased in both manufacturing and service industries in the past decades. However, the empirical evidence regarding the relationship between the degree of internationalization and firm performance (I-P relationship) remains inconsistent, raising more questions than answers. The third essay in this dissertation presents evidence to support the industry dependency hypothesis of I-P relationships in that both life and nonlife insurance exhibit industry idiosyncrasies in terms of their liabilities of foreignness. The life insurance industry exhibits a relatively high liability of foreignness leading to a negative impact of inter-regional internationalization on performance as opposed to the nonlife insurance industry, for which the relationship is insignificant. The results explain the disparate degrees of internationalization in different industries from the perspective of the I-P relationship. Moreover, the essay introduces a novel measure of cost efficiency and discuss its mediating and moderating roles in the I-P relationship.

Multi-period insurance relationship is appreciated by both the insured and the insurer. Thus, the majority of insurance products, either long-term or short-term with renewals, involve a multi-period relationship. The central question in multi-period insurance contracting is the type of inter-temporal pricing pattern. The fourth essay in this dissertation devotes to identify the roles of commitment and information in determining the inter-temporal pricing strategies. It presents the first piece of comprehensive review mapping extant empirical evidence with theoretical models. Moreover, it constructs a novel two-sample empirical design, which precludes heterogeneity in firms, markets, and time periods, and thus improves the credibility of insurer’s commitment-pricing strategy relationship. The results suggest that the lack of insurer’s pre-commitment to multi-period insurance relationship predicts the price lowballing strategy and its pre-commitment predicts the price highballing strategy. This conclusion may also be useful in other industries, which have similar multi-period contracting market and switching possibilities over time. One of such examples is the commercial banking industry, where loan applicants rejected by one bank can apply at other banks. This feature yields a pattern that incumbent banks keep low-risk loaners and competitors innocently attract those high-risk ones. The highballing pricing strategy has been proved to be useful to lock-in low-risk consumers, which is implemented in the insurance industry in the form of a pre-agreed premium schedule. This design may be applicable to the banking industry, where a bank charges a relatively high loan rate or a fixed amount of fees in early periods, and charges relatively low rate and no fees in later periods. The highballing pricing strategy also insures the reclassification risk, where the bank (insurer) charge additional fees (premium) to ensure the customers low rate increase in the future even if the customer’s credit (insurance) risk increases.

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The major implications and key take-aways of this dissertation lie with two folds. First, it tackles some fundamental questions in the insurance economics that are information asymmetry (Essays I and IV) and optimal risk sharing (Essays II and III). It contributes to the insurance economics with the first piece of evidence on between-group adverse selection (Essay I), with the new evidence on the inter-temporal pricing pattern of insurance products (Essay IV), with the explanation of the reinsurance market structure (Essay II), and with the globalization impact on insurance performance (Essay III). Second, it has strong managerial implications to the insurance industry practice. Particularly, it challenges a few conventional wisdoms and points out potential solutions: group insurance may not be enough to mitigate the adverse selection but experience rating is important (Essay I); globalization may not be a good solution for life insurers but a bit more favorable to nonlife insurers (Essay III); economics of scope interact with economies of scale and thus the strategic focused strategy is suitable for small reinsurers and conglomeration strategy is more likely to work for the large ones (Essay II).

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Essay I Between-group adverse selection: Evidence from group critical illness insurance

Abstract

This essay demonstrates the presence of adverse selection in the group insurance market. Conventional wisdom suggests that group insurance mitigates adverse selection because it minimizes individual choice. We complement this conventional wisdom by analyzing a group insurance scenario in which individual choice is excluded, and we find that group insurance alone is not effective enough to eliminate adverse selection; that is, between-group adverse selection exists. Between-group adverse selection, however, disappears over time if the group renews with the same insurer for a certain period. Our results thus indicate that experience rating and underwriting based on information that insurers learn over time are important in addressing adverse selection.

Keywords

Adverse Selection, Information Asymmetry, Learning over Time, Group Insurance, Health Insurance

-------------------------------------

Martin Eling, Ruo Jia, Yi Yao (2016). This essay has been accepted for publication by the Journal of Risk and Insurance.

Essay I Between-Group Adverse Selection

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1. Introduction

Group insurance constitutes a substantial portion of global insurance markets, and its importance to life and health insurance is increasing.1 Administrative efficiency and low performance volatility are strong motivations for the insurance industry to develop group insurance products (Bickelhaupt, 1983). Many policyholders also favor group insurance because it allows them to avoid the difficulty and anxiety of shopping for insurance (Pauly and Percy, 2000).

Consistent with conventional wisdom and widely accepted industry practice, insurers use group insurance to mitigate adverse selection because (1) the mixture of high- and low-risks decreases the variance of grouped losses compared to individual losses, (2) individual choice is minimized, and (3) individuals do not act strategically on information advantage regarding risk types when group insurance is tangential to other factors that influence an employment decision (Mayers and Smith, 1981; Browne, 1992). Our paper defines a group as a set of five or more people formed for reasons other than purchasing insurance, e.g., firms, unions, families, or other social groups.2 Thus, between-group adverse selection refers to the adverse selection in the group insurance market, which results from group strategic action on behalf of collective welfare, rather than from individual choice within a group (Mayers and Smith, 1981; Hanson, 2005).

Mayers and Smith (1981) predict that the group insurance market should have no adverse selection if the group insurance does not allow for individual choices within a group and if the group is formed for purposes other than purchasing insurance. Browne (1992) uses the group insurance market as the benchmark market free of adverse selection and concludes that individual insurance suffers more from adverse selection than group insurance. In contrast to Mayers and Smith’s (1981) prediction, Hanson (2005) proves that the equilibrium in the group insurance market with no individual choice is not materially different from the equilibrium in the individual insurance market. Hanson’s (2005) model implies that groups, like individuals, act strategically on their information advantages, which yields between-group adverse selection. The two competing theoretical predictions motivate us to empirically test for the existence of and, if found, the persistence of adverse selection in a group insurance market.

1 In 2012, the direct written premiums of group insurance in U.S. totaled USD 295 billion, accounting for 41.9% of total

premiums in the life and health sector; in particular, group insurance dominates the U.S. health insurance market, accounting for 53.8% of total health premiums (Insurance Information Institute, 2013). In Europe, group insurance accounted for 36% of total premiums in life insurance in 2012, whereas the percentage was 29% in 2010 and 31% in 2008 (Insurance Europe, 2014).

2 We use two datasets to test the robustness of our conclusions on different types of groups. Our core model uses employment-based groups, such as firms and unions; in a robustness test, we explore another dataset of family-based groups.


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The existing empirical evidence on adverse selection in group insurance concentrates on the U.S. health insurance market, where individual choice among competing health insurance plans is an important driver of adverse selection (see, e.g., Cutler and Zeckhauser, 2000; Handel, 2013). Simon (2005) analyzes adverse selection in the U.S. small-group health insurance market, which combines the effects of individual choice and group selection. To our knowledge, no empirical research has tested for the existence and/or persistence of adverse selection in a group insurance market in which no individual choice is allowed.

Following Mayers and Smith (1981), we split the individual choice and group decision effects in group adverse selection by differentiating within- and between-group adverse selection. We use a new and comprehensive dataset of group critical illness (CI) insurance policies.3 Our findings show that group insurance cannot eliminate adverse selection, even if individuals within a group are not allowed to choose their participation and/or coverage, supporting Hanson’s (2005) prediction. The information advantage of the group over the insurer may come from the underreporting of claim histories when the group is a new customer.

We also find evidence that between-group adverse selection, together with the group’s information advantage, disappears over time if a group renews with the same insurer for a certain period. We attribute this disappearance to insurer learning over time (Kunreuther and Pauly, 1985; D’Arcy and Doherty, 1990; Hendel and Lizzeri, 2003; De Garidel-Thoron, 2005). Once the insurer has experience with the group, it will learn the risk type and then either adjust the premium or elect not to renew the high-risk group based on each group’s claim experience. Therefore, the information advantage that the group possesses as a new client diminishes with the renewal process. The asymmetric information on which the group can act strategically disappears and thus no between-group adverse selection occurs. Cohen (2012) documents the evidence of an insurer learning over time in an Israeli automobile insurance portfolio. Cutler (1994) documents the wide existence of experience rating in the U.S. small-group health insurance market. He shows that the variation in small-group insurance premiums results not from demographic or benefit differences but from experience ratings. This paper complements the extant empirical evidence by demonstrating the disappearance of between-group adverse selection over time.

The remainder of this paper is structured as follows. First, we introduce the Theoretical Background and Hypotheses. Data and Insurance Product Section describes our sample and some background information regarding the CI insurance product and the Chinese insurance market. The remaining sections are Empirical Models, Results, Robustness Tests, Discussions and Concluding Remarks and Future Research.

3 CI insurance covers the 25 critical diseases listed in Appendix 1 and pays the insurance amount if any of these diseases

is first diagnosed during the policy period, following a predefined waiting period for first-time purchasers.


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2. Theoretical background and hypotheses

Adverse selection is the tendency of high-risks to purchase insurance or to purchase more insurance coverage than do low-risks (Cummins, et al., 1983). Adverse selection results from asymmetric information that favors the insurance buyer over the insurer (Akerlof, 1970; Rothshild and Stiglitz, 1976). The existence of adverse selection has been widely documented in many types of individual insurance (see Cohen and Siegelman, 2010, for a review).

Regarding adverse selection in the group insurance market, Cutler and Zeckhauser (2000) review 14 empirical studies that examine the selection of group health insurance with individual choices, all of which find some type of adverse selection; however, none of these studies distinguish within from between-group adverse selection. Simon’s (2005) study of the U.S. small-group health insurance market reveals the relationship between individual choice and within-group adverse selection. However, whether between-group adverse selection exists and, if so, the extent of its persistence is yet unknown. We aim to fill this gap. Table 1 summarizes the theoretical framework, empirical literature, and contribution of this paper.

Table 1 Three types of adverse selection Types of adverse selection

Insurance decisions on participation and coverage

Literature providing empirical evidence

Type I: Individual adverse selection

Individual See Cohen and Siegelman (2010) for a review of empirical studies that focus on individual insurance markets.

Type II: Within-group adverse selection

Individual and group: The participation of group members is voluntary, and/or coverage choice is allowed within a group.

See Cutler and Zeckhauser (2000) for a review of empirical studies that focus on the U.S. group health insurance market.

Type III: Between-group adverse selection

Group: The participation of group members is mandatory, and the coverage is identical within a group.

The aim of this paper, not covered by the existing literature

Two competing theoretical predictions were developed regarding between-group adverse selection, as mentioned in the Introduction. Mayers and Smith (1981) predict that if a group is formed for purposes other than purchasing insurance, the average risk for that group is less likely to deviate from the relevant population average, which solves between-group adverse selection problems. However, Hanson's (2005) theoretical model yields the opposite prediction. Hanson (2005) compares the equilibria in an individual insurance market with that in a group insurance market with no individual choice and concludes that a profit-maximizing employer4 will choose contracts off the same equilibrium contract curve as would a purchaser

4 A profit-maximizing employer is defined as an employer who wishes to maximize the sum of the benefits its employees

receive from group insurance minus the price paid for the insurance.


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of individual insurance, suggesting that group insurance cannot eliminate adverse selection. This conclusion is subject to the conditions that (1) the group insured5 makes all decisions on behalf of group members, (2) it is a uniform group insurance policy, (3) there is no wealth effect, (4) there are no administrative costs, and (5) the group is formed for purposes other than purchasing insurance. In Hanson’s (2005) model, although the pooling of high- and low-risk members reduces the variance of group losses, this effect turns out to be irrelevant to the equilibrium. Between-group adverse selection is independent of the individual choices within a group. These two competing predictions yield our first hypothesis.

• Hypothesis I: If group insurance does not allow for individual choices within a group, and if the group is formed for purposes other than purchasing insurance, group insurance eliminates adverse selection.

Under the two conditions of Hypothesis I, two explanations suggest how and why adverse selection may still exist. Mayers and Smith (1981) argue that individual insured may switch employers due to differences in health insurance coverage among similar jobs; therefore, high-risk individuals choose jobs that offer more comprehensive health insurance coverage. This explanation is unlikely to apply to our case because the expected benefit of group CI insurance is small. On average, 95% of individuals have an expected benefit6 of equal to or less than CNY 109 (USD 17) per year, which does not suggest a strong motivation for employees to switch jobs. Hanson (2005) provides another explanation for the existence of between-group adverse selection: a profit-maximizing employer behaves similarly to individual insurance buyers when choosing insurance coverage. The employer will choose coverage that is more comprehensive if its employees are high-risk and vice versa. This explanation requires that the employer, specifically the human resources (HR) or other responsible department, possesses an information advantage over the insurer; otherwise, the insurer would be able to charge a risk-adequate rate to eliminate adverse selection.

Under the condition that the group insured makes all insurance decisions, there are two potential sources of group insured’s information advantage. Cohen (2005, 2012) empirically shows that the insurer is not able to fully observe a new customer’s past claim records; thus, cannot accurately assess the risk type of a new customer because self-reporting of past claims is incomplete or inaccurate (Insurance Research Council, 1991). In other words, a client is most likely to have an information advantage when he/she is a new customer to an insurer (Cohen, 2005). This argument applies to both individual and group insurance. In our sample, most group insureds are established firms that can afford voluntary employee benefits. Their HR departments know more about their employees than does the insurer, including 5 A group insured is an employer or other type of group purchasing coverage, e.g., a union. 6 The expected benefit is calculated as the insurance amount multiplied by the average claim frequency (see summary

statistics in Table 2).


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knowledge of prior health claims and critical diseases. Thus, we will use the subsample of new policies to test Hypothesis I, the existence of between-group adverse selection.

Hanson (2005) offers another explanation for group insured’s information advantage; that is, the group insured usually knows the health condition of its employees at the individual level, but the insurer knows only the group average. In reality, the HR department usually possesses individual-level health information that the insurer does not, such as whether an employee smokes or has a history of serious diseases (e.g., heart attack). In some circumstances, the employer is aware that some of its employees have symptoms of critical diseases, and it purchases insurance based on such information (Monheit and Schone, 2004), particularly for small groups. Employers obtain their information advantage via daily interactions with employees and/or via employee health examination results consolidated by HR departments, if permitted by regulations. As many U.S. small-group health insurance studies show, small groups are expected either to have more information advantages or to make better use of those advantages than large groups do; thus, small groups will exhibit stronger between-group adverse selection (Cultler, 1994; Monheit and Schone, 2004).

Kunreuther and Pauly (1985) and Watt and Vazquez (1997) emphasize that observing the realization of a policyholder’s risk during a given period enables an insurer to update its prior beliefs concerning the risk posed by that policyholder in a future policy period. Kunreuther and Pauly (1985) and Cohen and Siegelman (2010) call this phenomenon "learning over time." Jean-Baptiste and Santomero (2000) construct a model of the reinsurance market, supported by evidence in Garven, Hilliard and Grace (2014), showing that asymmetric information between insurers and reinsurers declines over time with the tenure of the insurer-reinsurer relationship.

Insurer learning over time occurs when the insurer is able to use the observed respective insured’s claim experience to adjust the premium or reject the renewal. However, this necessary condition does not apply to many individual insurance products. For instance, individual health insurance usually includes an insurer’s commitment as a guaranteed renewable clause, which prevents a premium increase and renewal rejection based on an individual’s past claim experience with the insurer. Individual life insurance usually involves a long-term commitment from insurer, and often, policy termination by the insurer or premium rate adjustment is not allowed during the entire policy period. Thus, insurer learning over time is limited by various contractual, regulatory, and/or market conditions in individual insurance.

In contrast, an insurer that offers group insurance, of almost all lines, is free to adjust the premium rate upon renewal or to reject renewals based on each group’s past claim experience. Therefore, after a few policy periods with the same insurer, the group insured’s information


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advantage from the initial claim underreporting disappears. The group insured’s information advantage regarding its employees’ individual risk type (Hanson, 2005) also fails to persist because high-risk individuals reveal their risk type over time by making claims. The insurer can thus identify high-risk groups and adjust the premium of (or elect not to renew) high-risk groups based on their claim experience. In other words, the group-average risk type, which the insurer learns over time, is enough to accurately assess group risk.7 Mayers and Smith (1981) summarize that frequent contract renegotiation controls adverse selection as long as information is revealed over time and the insurer is able to monitor and apply that information accordingly in pricing and underwriting.

Because information asymmetry is a necessary condition for the existence and persistence of adverse selection (Akerlof, 1970; Rothshild and Stiglitz, 1976), adverse selection should cease to be a problem as soon as the insurance buyer’s information advantage over the insurer disappears. We phrase our second hypothesis as follows.

• Hypothesis II: Between-group adverse selection in the group insurance market, if there is any, will disappear if the group renews with the same insurer for a few policy periods.

There is a substantial body of empirical literature that shows informational asymmetries and adverse selection decrease over time due to repeated contracting (see, e.g., Cohen, 2012; Garven, Hilliard and Grace, 2014). This paper further documents such a process for between-group adverse selection.

3. Data and insurance product

CI insurance is a type of loss-occurrence health insurance that was offered for the first time in 1983 (Barnard, 2004). The full insurance amount is paid as long as an insurer-recognized hospital provides the first-time diagnosis of the covered disease during the policy period. Usually, there is a 30- to 90-day waiting period for first-time purchasers. The claim benefit always equals the insurance amount and is paid to the insured in a lump sum without additional benefits, such as medical service. The claim payment does not require an actual medical expenditure or hospitalization. Thus CI insurance is immunized from many common problems observed in medical expense health insurance, such as choices between private and public hospitals. The product works as a finance tool rather than a cost reimbursement tool. Cochrane (1995) proposed a time-consistent health insurance plan that provides a lump sum payment and enables those with long-term critical diseases to afford future health insurance coverage. This solution supports the provision of CI insurance as extra funding for insureds with critical diseases.

7 This argument is subject to the mandatory participation requirement, i.e., low-risk individuals cannot exit the group

simply because the premium rises while other members stay. We discuss this issue in the Discussion section.


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We obtain the dataset from a life and health insurance company in China. The company has over 15 years of nationwide operations, with a broad spatial range that covers over 90% of the Chinese population. It has ranked among the top 10 largest life insurers in China over the past 15 years in terms of premium market share and assets. Its core business comes from the open market and thus is not concentrated in any particular industry or region. Its operational model, growth path, risk portfolio, and performance are representative in the Chinese insurance market. In 2012, 68 life and health insurers and 62 property and liability insurers operated in the Chinese insurance market, and most of them are legally eligible to issue group CI insurance policies, yielding a very competitive market.

In 2007, the Insurance Association of China and the Chinese Medical Doctor Association issued guidelines that define 25 types of critical diseases. In our case, and in most cases in the Chinese CI insurance market, the insurer strictly follows the CI coverage guideline, which standardizes CI insurance products. In our sample, all group policies and insured individuals have the same coverage for the 25 critical diseases listed in Appendix 1. In 2012, the total premiums written for CI insurance was CNY 40.6 billion (USD 6.5 billion) in China, accounting for 38% of health insurance premiums and covering more than 90 million people (China Insurance Regulatory Committee, 2013; Su, 2013). Both group and individual CI insurance are available in the Chinese market. The group CI insurance market is dominated by employee benefits for which the employer pays the premium and the employee contribution is minimal. The Chinese group CI insurance market has no restrictions regarding risk classification based on age, gender, occupation, region or other possible pricing factors. The insurer has sole discretion to determine the price offered for both new and renewed contracts. The market is commercial and voluntary; thus, the concerns regarding risk reclassification, availability, and affordability of such insurance are minimal.

Our dataset includes all information that the insurer uses to make underwriting and pricing decisions, which minimizes the possibility of spurious adverse selection due to information asymmetry between insurer and researcher (Cohen and Siegelman, 2010). Claims records are also included. The dataset covers all group CI policies issued between January 2008 and June 2013 and all claims settled between January 2008 and August 2012 under the corresponding group CI policies.8 The business nature of the insurance portfolio is largely, but not restricted to, employee benefits.

The original data are at individual policy level. For each individual policy entry, the dataset provides (1) policy information, including individual policy number, group policy number,

8 The claims information is electronically recorded in real time but only retrieved and organized by the actuarial team

once per year. When we obtained our data, the claim information for September 2012 to June 2013 were not yet available. In a later analysis, to avoid a potential truncation problem, we code the claim status of polices expiring after August 2012 as missing values; thus, these observations are excluded from our regressions.


15

insurance amount, premium, policy inception date, expiration date, and issuance date, (2) individual demographic information, including age, gender, and occupation category9, and (3) group insured’s demographic information, including group name, group location, and group size. The dataset also contains claim amounts and claim settlement dates for individual policies with claims.10

We organize the individual policy entries into group policies according to the group policy number. Because this paper focuses on between-group adverse selection, we select only those group policies with identical insurance coverage, i.e., identical insurance amounts11, for each individual insured in the group. Group policies with identical coverage, i.e., with no individual choice, account for more than 75% of the portfolio. This produces 7,784 group policy-year observations purchased by 3,453 groups 12 , representing more than 2,230,000 individual policies. Missing information is present in our dataset, particularly related to missing claims after August 2012 and missing renewal status for some policies in 2008. Our final sample is thus reduced to 3,540 group policy-year observations purchased by 1,957 groups after excluding observations with missing values. 13 As shown in Table 2, the portfolio is characterized by a low claim frequency, a relatively small insurance amount for most policies, and a mixture of different group sizes, occupations, ages, and genders.

Table 3 compares new policies with renewed policies; it also shows subsamples of policies with two or more consecutive renewals and with three or more consecutive renewals. ANOVA mean difference F-tests are reported. We observe no significant difference in claim frequency among subsamples, implying that the risk quality does not materially change over renewal times. Thus, we expect that our conclusions will not be influenced by inherent risk quality difference among subsamples. We find, however, significant trends in most demographic variables and policy features with an increase in renewal times. The portfolio with more renewal times contains groups with larger size, in richer region, with younger members, with more accident-prone occupations, and with more women. The portfolio with more renewal times has smaller average insurance amounts per person, lower premium rates,

9 The occupation category is based on the accident tendency of each occupation instead of the illness tendency. We

acknowledge that an industry classification reflecting the illness tendency would be a better indicator; however, such an indicator is available neither to the insurer nor to us.

10 We do not have the information of rejected claims, which is a common issue in empirical research that uses real market data (Cohen and Siegelman, 2010). However, because we care about the actual risk type of insureds, it is reasonable to assume that rejected claims fall outside the policy coverage and thus are irrelevant to the risk type and to our conclusions regarding adverse selection.

11 In group CI insurance, the only possible coverage difference within a group policy is the insurance amount. This product involves no deductible and all insureds are covered for the same 25 critical diseases.

12 All groups are recognized as independent entities and assigned a unique group reference code by the insurer. The majority of groups in our sample are independent firms. The rest include subsidiaries, branches or other types of operating units but purchase insurance policies independently. We follow the insurer’s practice in treating all entities as independent decision-making units because they buy group policies separately from their affiliates.

13 We also exclude policies that are rejoined, i.e., the group insured came back to the insurer after a gap period (496 observations).


16

and shorter policy durations. The policy duration decreases with renewal times because short-term policies renew more times than long-term policies during a certain observation period. The observed trends highlight the importance of controlling for policy and demographic features or premium rates14 in later regression analyses.

Our CI insurance portfolio is a good approximation of the mandatory participation of group members. According to the insurer’s underwriting guidelines, for small groups of no more than 50 people, the participation ratio must be 100% to issue a group policy. For larger groups, the participation ratio can be reduced to a minimum of 75%15. Employee family participation is sometimes offered and voluntary; however, because the employer pays the premiums, such participation is also very high if the contract is open to family members. The insurer’s underwriting guidelines forbid offering group insurance policies to groups formed for the purpose of purchasing insurance. We expect that groups in our sample pool different types of risks and different levels of risk attitudes. Groups may vary in levels of risk aversion; however, we find no reason to sustain a systemic pattern. As mentioned above, our sample excludes the possibility of within-group adverse selection by ensuring identical coverage for every individual insured in a group, thus any group adverse selection identified is between-group adverse selection.

14 The premium rate is defined as the policy premium divided by the insurance amount. 15 It is unlikely that large firms use this advantage to exclude high-risk members from group coverage to keep premiums

low. Group CI coverage is provided as an employee benefit voluntarily offered by the employer, and it is hard for an employer to justify internally offering such benefits to low-risk employees but not to high-risk employees who actually need it more. The employer can stop providing such benefits to all employees at any time if the premium is too high. The voluntary and employee benefit nature of group CI product also minimize the incentive of claim underreporting, aiming at avoiding premium increases.


17

Table 2 Summary statistics: Insurance portfolio overview Variables Descriptions Obs. Mean Min p5 Median p95 Max ClaimDummy 1 if any claim(s) under the group policy 3,540 0.086 0 0 0 1 1 ClaimCount Number of claims under the group policy 3,540 0.17 0 0 0 1 60 d ClaimFrequency Average number of claims per insured, i.e.,

the fraction of insureds making a claim 3,540 0.00064 0 0 0 0.0026 0.11

InsuranceAmount Insurance amount per insured in CNY 3,540 62,231.4 1,900 3,000 50,000 170,000 1,000,000 PolicyDuration Group policy duration in days 3,540 284.2 15 30 362 366 485 e GroupSize Number of individual insureds in the group 3,540 305.7 5 7 60 1,094 28,691 PremiumRate Annualized premium rate per insured 3,540 0.0024 0.000033 0.00036 0.0016 0.0066 0.066 Areaa Indicator of relative wealth and level of

insurance market development of the group’s location

3,540 1.68 1 1 1 3 4

Sex Fraction of women in the group 3,540 0.42 0 0.072 0.40 0.83 1 Age Average age in the group 3,540 33.4 0 c 23.1 32.5 45.4 57.6 Workb Group average occupation accident tendency 3,432 1.96 1 1 1.91 3 6 N Total number of group policies 3,540

Notes: a. 1 represents the most developed regions in China, while 4 represents the least developed regions. The area is based on the insurer’s branch categories, which consider not only regional wealth level but also regional insurance development level. It is a better control variable than pure wealth measurement. b. 1 represents the safest occupations, while 6 represents the most dangerous. The work is measured by the accident tendency of an occupation, e.g., office workers are 1, while coal mine workers are 6. c. Only one group policy has a minimum age of zero. Our results are robust if we exclude this policy. d. Only one group policy has 60 claims, and only two policies have more than 20 claims. Our results are robust if we exclude these policies. e. Only 19 group policies have policy durations longer than 366 days. Such policies reflect negotiated conditions for special clients. Our results are robust if we exclude these policies.


18

Table 3 Comparison between subsamples

Variables

New Policies Renewed Policies Policies renewed two or more times

Policies renewed three or more times

ANOVA F-Test for Mean

Difference

Mean Median Obs. Mean Median Obs. Mean Median Obs. Mean Median Obs. F-Value

P-Value

avClaimDummya 0.0000019 0 1,690 0.0000016 0 1,850 0.0000012 0 1,088 0.0000010 0 745 1.29 0.275 avClaimCounta 0.0000020 0 1,690 0.0000018 0 1,850 0.0000013 0 1,088 0.0000010 0 745 1.71 0.163 InsuranceAmount 64,204.6 50,000 1,690 60,428.8 50,000 1,850 59,717.0 50,000 1,088 55,483.5 50,000 745 5.64 0.001 PolicyDuration 334.9 365 1,690 237.8 333 1,850 171.5 31 1,088 107.8 31 745 670.57 0.000 GroupSize 240.3 40 1,690 365.5 95 1,850 395.4 104 1,088 378.8 113 745 4.02 0.007 PremiumRate 0.0026 0.0020 1,690 0.0021 0.0013 1,850 0.0018 0.0012 1,088 0.0015 0.0012 745 61.17 0.000 Area 1.92 2 1,690 1.45 1 1,850 1.32 1 1,088 1.20 1 745 248.59 0.000 Sex 0.41 0.39 1,690 0.42 0.40 1,850 0.44 0.42 1,088 0.46 0.44 745 10.80 0.000 Age 34.1 33.7 1,690 32.6 31.6 1,850 31.2 30.0 1,088 29.7 28.7 745 83.69 0.000 Work 1.93 1.67 1,597 1.98 2 1,835 2.19 3 1,079 2.41 3 739 49.07 0.000 N 1,690 1,850 1,088 745

Notes: a. av represents the average per insured per day. It scales claim performance indicators to a comparable level.


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4. Empirical models

To identify adverse selection, we use the classical risk-coverage correlation model shown in Equation (1) (Cohen and Siegelman, 2010). A positive correlation between risk and coverage is the necessary condition of adverse selection, implying that high risks buy more insurance coverage. An insignificant correlation between risk and coverage suggests no adverse selection. Alternatively, Chiappori and Salanié (1997, 2000) suggest the reduced form model shown in simultaneous Equations (2.1) and (2.2) to detect adverse selection. A positive correlation between the residuals 𝜀𝜀𝑖𝑖 and 𝜔𝜔𝑖𝑖 is the necessary condition of adverse selection, implying that the coverage choice and claim occurrence are not independent phenomena after controlling for observables. An insignificant correlation between 𝜀𝜀𝑖𝑖 and 𝜔𝜔𝑖𝑖 suggests no adverse selection.

Both models have advantages and limitations. Chiappori and Salanié (1997, 2000) suggest that the reduced form model may be more robust but less efficient than the classical approach. Chiappori and Salanié (2013) argue that the advantage of the reduced form model is that it does not require the estimation of the insurer’s pricing policy, which, in our case, is not a problem because we know and control for the actual prices charged for each group policy. Cohen and Siegelman (2010) summarize that the two models are equivalent under general conditions, and the major differences between them depend on the distributional assumptions made conditional on the explanatory variables. Therefore, we use the classical model as our core model (Table 4) and the reduced form as a robustness test (Appendix 2.1).

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 = 𝛼𝛼 + 𝛽𝛽𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖 + 𝛾𝛾𝑋𝑋𝑖𝑖 + 𝜀𝜀𝑖𝑖 (1)

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 = 𝐶𝐶(𝑋𝑋𝑖𝑖) + 𝜀𝜀𝑖𝑖 (2.1)

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖 = 𝑓𝑓(𝑋𝑋𝑖𝑖) + 𝜔𝜔𝑖𝑖 (2.2)

We measure the actual Risk of a group insured by its ex post claim performance in group policy i. The claim performance is measured by three claim indicators commonly used in existing literature: (1) ClaimDummy, which equals 1 if there is any claim under group policy i; (2) ClaimCount, which records the total number of claims under group policy i; and (3) ClaimFrequency, which equals the total number of claims divided by the number of individual insureds under group policy i. We do not use the total claim amount or claim severity as claim performance indicators because the claim severity of CI insurance always equals the insurance amount on an individual basis. The claim amount thus adds no additional information to ClaimFrequency.

We measure the insurance Coverage for group policy i as the natural logarithm of the insurance amount per insured. The insurance amount under group policy i is identical for every individual insured in the group. In our sample, group CI insurance always has a zero


20

deductible and covers the same 25 critical diseases for all group policies and individual insureds. There are concerns that the insurer may price discriminate clients with different insurance amounts, i.e., provide discounted premium rates for groups buying higher insurance amounts and/or for large groups. However, we find no indications in the insurer’s underwriting guidelines that such a pricing strategy exists. Moreover, we control for both group size and premium rate in our model to minimize the potential effects of a price discrimination strategy.

Xi is a vector of control variables that includes policy features, risk classification, and time effects. We control for policy features such as duration and group size. Risk classification refers to the use of observable characteristics by insurers to compute the corresponding premiums and thereby reduce asymmetric information (Dionne and Rothschild, 2014). Thus, any appearance of adverse selection in the market must reflect residual asymmetric information after controlling for risk classification. There are two alternative ways to control for risk classification: (1) observable demographic features and (2) premium rates computed based on observables. The premium rate is preferred to demographic features because it not only incorporates all demographics but also reflects the insurer’s reaction to the respective group’s claim experience (Finkelstein and McGarry, 2006). The premium rate represents the insurer’s up-to-date best estimation of risks; therefore, we use the average annualized premium rate per person, PremiumRate, to control for risk classification. We use demographic features in a robustness test (Appendix 2.2). We use year dummies to control for time effects.

We use logistic regression to estimate the model with ClaimDummy as the dependent variable and estimate a probit model as a robustness test (Appendix 2.3). We estimate a negative binomial regression with ClaimCount as the dependent variable, legitimated by the likelihood ratio tests shown in Table 4, and use Poisson, zero-inflated negative binomial, and zero-inflated Poisson models as robustness tests (Appendix 2.5). We estimate a Tobit model to fit the zero-censored dependent variable ClaimFrequency. We use cross-sectional models to test our hypotheses because one group usually has only one new policy and one nth time renewed policy, but use panel data models as robustness tests where applicable (Appendix 2.5).

We examine the potential issues of multicollinearity, endogeneity and heterogeneity. The variance inflation factors (VIF) of the independent variables range from 1.13 to 1.51 for the new policy portfolio and between 1.14 and 1.63 for the renewed policy portfolio. All VIFs are below 5, suggesting that multicollinearity is not a problem. We test for potential endogeneity of the primary explanatory variable, lnInsuranceAmount, using the instrumental variable (IV) approach. The IVs used are demographic features (age, work, sex, and area) that determine the demand for insurance and thus correlate with lnInsuranceAmount. These demographic features are exogenous, and their effects on Risk are captured by another control


21

variable, lnPremiumRate; thus, are not related to the error term of Equation (1). Wald tests of endogeneity (see Wooldridge, 2002, pp. 472-477 for a detailed discussion) are conducted for nonlinear models. For the subsample of new (renewed) policies, the p-values of Wald tests are 0.84 (0.31) for probit16 regression with ClaimDummy as the dependent variable and 0.79 (0.09) for Tobit regression with ClaimFrequency as the dependent variable. Durbin-Wu-Hausman (DWH) tests of endogeneity are conducted using a two-stage least square (2SLS) model17with ClaimCount as the dependent variable. The DWH tests yield p-values of 0.25 for the new policy portfolio and 0.64 for the renewed policy portfolio. All tests suggest the acceptance of the null hypothesis of the exogenous lnInsuranceAmount at the 95% confidence level. The use of simple, linear functional forms, such as logit or probit models, should be restricted to homogeneous populations (Chiappori and Salanié, 2000). Our dataset approximates homogeneity because (1) the business nature of our sample is largely the same as employee benefits, (2) the insurer sources its business nationwide in China, (3) we control for potential heterogeneity among different group insureds using either premium rates or demographic features, and (4) we use robust standard errors clustered by group insureds in all specifications to further control for heterogeneity.

5. Results

Table 4 presents the results for Equation (1). The three panels show estimations with three different claim indicators, i.e., ClaimDummy, ClaimCount, and ClaimFrequency. The six columns show specifications with different subsamples.

To test Hypothesis I, we use the subsample of new policies because new customers are most likely to have information advantages over the insurer (Cohen, 2005). The results in Column 1 of Table 4 show that the insurance amount positively and significantly correlates with all three claim indicators conditional on premium rate. We interpret the coefficients as follows: if the insurance amount per person increases by 1%, the probability that the group will make a claim increases by 0.85% (Panel A) and the group claim frequency increases by 0.34 percentage points (Panel C). The positive correlation between risk and coverage suggests the existence of between-group adverse selection.18 This evidence is against Hypothesis I. Group insurance cannot eliminate adverse selection, even if it does not allow for individual choices and even if the group is formed for purposes other than purchasing insurance. Such adverse

16 We use a probit model to perform the Wald test with ClaimDummy as the dependent variable because the error term of

the logit model is not normally distributed. 17 We use a 2SLS model to perform the DWH test with ClaimCount as the dependent variable because the counted number

of claims approximates continuous; thus, the DWH test for linear model applies. 18 The finding in cross-sectional data that coverage is correlated with risk does not suffice to tell us whether it is caused

by adverse selection alone, moral hazard alone, or both (Cohen and Siegelman, 2010). We address this issue in the Discussion section.


22

selection is, by definition, between-group adverse selection. The results support Hanson's (2005) prediction.

To test Hypothesis II, we use subsamples of renewed policies to examine the extent of persistence (or lack thereof) of between-group adverse selection. We structure our sample in two alternative ways: (1) three layered sub-portfolios of renewed policies, i.e., all renewed policies, policies renewed two or more times, and policies renewed three or more times (Columns 2-4, Table 4); and (2) three exclusive sub-portfolios of renewed policies, i.e., first-time renewed policies, second-time renewed policies (Columns 5-6, Table 4), and policies renewed three or more times (Column 4, Table 4). The results in Columns 2 and 5 of Table 4 show positive and significant risk-coverage correlations in first-time renewed policies for all three claim indicators19. The results in Columns 3, 4, and 6 show that for policies renewed two or more times, the positive risk-coverage correlation disappears. The results suggest that there exists between-group adverse selection in new policies and that it persists for the first-time renewal, but disappears for policies renewed two or more times. Because the risk-coverage correlation is a necessary condition of adverse selection20 (Chiappori and Salanie, 2000), we conclude that between-group adverse selection disappears over time as group insured renews with the same insurer for a certain period. The evidence supports Hypothesis II. The disappearance of between-group adverse selection can be explained by insurer learning over time21, that is, insurer experience rating and underwriting based on a group’s claim experience mitigate the group insured’s information advantage, and thus mitigate between-group adverse selection.

The control variables indicate that there are more claims with longer policy durations and larger groups. Group size positively correlates with claim frequency, suggesting that large groups have a higher claim frequency than small groups. Premium rates positively correlate with number of claims and claim frequency, suggesting that the insurer successfully captures the group risk quality with premium. High-risk groups must pay higher premiums due to observables and poor claim experience.

19 We conduct Z-statistic tests to compare the claim-coverage coefficients of the new policy portfolio in Column 1 with

the claim-coverage coefficients of the (first-time) renewed policy portfolio in Column 2 (Column 5). All of them are not statistically different from each other at the 95% confidence level.

20 Finkelstein and McGarry (2006) argue that the positive risk-coverage correlation may be neither a necessary nor a sufficient condition for the presence of asymmetric information about risk type, but instead, indicates a risk preference (attitude). We address this issue in the Discussion section.

21 We discuss alternative explanations in the Discussion section.


23

Table 4 Core model results (1) (2) (3) (4) (5) (6)

Subsamples New Policies

Renewed Policies

Policies Renewed 2 or More Times

Policies Renewed 3 or More Times

1st-time renewed policies

2nd-time renewed policies

Panel A Dependent Variable: ClaimDummy, Model: Logistic lnInsuranceAmount 0.00853*** 0.00463* 0.00116 0.00160 0.0194*** 0.00115

(0.00286) (0.00246) (0.00145) (0.00117) (0.00665) (0.00651) lnPremiumRate 0.0127*** 0.00603* 0.00145 0.00169 0.0246*** -0.00165 (0.00393) (0.00321) (0.00164) (0.00126) (0.00869) (0.00907) lnGroupSize 0.0293*** 0.0165** 0.00712 0.00438** 0.0541*** 0.0332*** (0.00379) (0.00647) (0.00453) (0.00189) (0.00739) (0.0128) lnPolicyDuration 0.0671*** 0.0369*** 0.0166** 0.00774*** 0.165*** 0.174*** (0.0226) (0.00711) (0.00731) (0.00270) (0.0427) (0.0403) Pseudo R2 0.307 0.362 0.440 0.427 0.279 0.419 Panel B Dependent Variable: ClaimCount, Model: Negative Binomial lnInsuranceAmount 0.00863*** 0.00539*** 0.00105 0.0000658 0.0211*** -0.00293 (0.00236) (0.00196) (0.00147) (4.37e-05) (0.00570) (0.0107) lnPremiumRate 0.0127*** 0.00924*** 0.00372** 0.000135*** 0.0305*** 0.00653 (0.00352) (0.00254) (0.00163) (4.68e-05) (0.00692) (0.00991) lnGroupSize 0.0284*** 0.0201*** 0.00953*** 0.000220*** 0.0599*** 0.0455*** (0.00432) (0.00416) (0.00258) (4.07e-05) (0.00955) (0.00951) lnPolicyDuration 0.0776*** 0.0380*** 0.0209*** 0.000293*** 0.150*** 0.140*** (0.0223) (0.00494) (0.00475) (9.07e-05) (0.0441) (0.0341) Pseudo R2 0.319 0.312 0.364 0.396 0.259 0.310 P-value of LR test a 0.000 0.000 0.055 0.059 0.019 0.500 Panel C Dependent Variable: ClaimFrequency (scaled up by 1,000), Model: Tobit lnInsuranceAmount 3.439** 1.292* 0.901 2.402 1.822* 0.0203 (1.510) (0.708) (0.802) (1.768) (1.016) (0.848) lnPremiumRate 5.108** 2.134*** 1.875** 3.213* 2.240* 0.777 (2.054) (0.780) (0.937) (1.646) (1.250) (1.200) lnGroupSize 10.45*** 4.925*** 3.840*** 4.828*** 5.629*** 3.220*** (1.415) (0.487) (0.592) (1.026) (0.587) (0.725) lnPolicyDuration 26.91*** 11.25*** 8.625*** 7.519** 19.19** 16.33*** (10.11) (2.670) (2.182) (3.035) (8.884) (4.757) Pseudo R2 0.091 0.124 0.182 0.211 0.072 0.128 Intercepts and year

Yes Yes Yes Yes Yes Yes

Observations 1,690 1,850 1,088 745 762 343 Notes: We present the marginal effects of logistic and negative binomial models at the means of the independent variables and present the estimated coefficients of Tobit model. Robust standard errors clustered by group insureds are presented in parentheses. We also present *, **, ***, indicating significant differences of coefficients from zero at the 10 percent, 5 percent, and 1 percent levels, respectively. a. The log-likelihood ratio test discriminates negative binomial model (H1: alpha≠0) from Poisson model (H0: alpha=0).


24

6. Robustness tests

We conduct six robustness tests, the results of which are listed in Appendix 2. First, we estimate the reduced form model (Chiappori and Salanié, 1997, 2000) and monitor the correlation coefficients of the residuals from Equations (2.1) and (2.2). There are in total six specifications with both separate and system estimations of the two equations and with three claim indicators, respectively (Appendix 2.1). We allow for potential error term correlations between the two equations when doing system estimation with the full information maximum likelihood (FIML) method. Alternatively, we use the three-stage least squares (3SLS) method to replace FIML, the results of which are very similar. In five of six specifications (except system estimation with claim frequency), the residual correlations are positive and significant for the subsamples of new and renewed policies; and insignificant for the subsamples of policies renewed two or more times. The results suggest that between-group adverse selection occurs with new customers but not with customers who renew for a certain period.

Second, we use demographic features (age, sex, work and area) to replace lnPremiumRate as the risk classification control. We introduce dummies area1 to area4 to control for regional differences in levels of wealth and insurance market development. We use fraction variables of different age ranges to reflect the age mixture within one group and the fraction variables of occupation categories work1 to work6 to reflect the mixture of occupations within a group22. For both dummy and fraction control variables, we omit the largest category to avoid collinearity. Appendix 2.2 shows similar results to our core models.

Third, we consider the potential effect of group size on between-group adverse selection. The literature on U.S. group health insurance suggests that between-group adverse selection may only exist or be more problematic for small groups because small firms may seek coverage simply because an employee or dependent is ill; large groups may have less of an information advantage, if any (Monheit and Schone, 2004). We test whether between-group adverse selection exists for large groups and, if so, whether small groups have stronger adverse selection than large groups. Our dataset contains both small groups with 50 or fewer members and large groups with more than 50 members. 23 We thus introduce the interaction term lnInsuranceAmount*small to test these arguments. The results in Appendix 2.3 show (1) the same existence and persistence pattern of between-group adverse selection for large groups and (2) insignificant coefficients of interaction terms for all specifications (except the negative binomial model with policies renewed two or more times), suggesting that the level of

22 Other studies also consider schooling, income, or number of dependents as control variables; however, that information

is not captured by the insurer and thus is not considered in pricing CI risks. Moreover, these variables are more determinants of insurance demand, but relatively less influence the risk of critical illness.

23 The 50-person cutoff point for small and large groups has been adopted by most states in U.S. (Simon, 2005) and is used in many group health insurance studies (e.g. Cutler, 1994; Monheit and Schone, 2004).


25

between-group adverse selection for small groups is not materially different from that of large groups.

Fourth, we consider the potential nonlinear effects of our primary explanatory variable, lnInsuranceAmount. Dionne, Gouriéroux, and Vanasse (2001) show that the significant risk-coverage correlation may disappear after adding the projected primary explanatory variable to the classic model. We mirror their methodology by (1) regressing lnInsuranceAmount on other policy features, risk classification, and year dummies; (2) predicting the projected lnInsuranceAmount from the step 1 regression; and (3) including the projected lnInsuranceAmount as an additional control variable in Equation (1). The risk-coverage correlation remains positive and significant for new policy portfolio, suggesting the existence of between-group adverse selection is robust (Appendix 2.4).

Fifth, we show in Appendix 2.5 that our conclusions hold when estimating alternative econometric models, including a probit model on ClaimDummy; Poisson, zero-inflated Poisson, and zero-inflated negative binomial models on ClaimCount; and panel random effects models for renewed portfolios, which contain multiple continuous policies for one group insured.

Sixth, we consider the potential model misspecification risk of our core linear models; thus, we adopt a semiparametric approach (Robinson, 1988) as shown in Equation (3). We test whether a semiparametric model is significantly different from our core models using Hardle and Mammen's (1993) specification tests. The results in Appendix 2.6 suggest that the model misspecification risk of our core linear models is minimal, i.e., for subsamples of new and renewed policies, the semiparametric model is equivalent to the linear model with first-order lnInsuranceAmount; and for subsamples of policies renewed two or more times, the semiparametric model is equivalent to the linear model without lnInsuranceAmount (zero order). We also provide an example semiparametric estimation, which illustrates that the risk-coverage correlation is positive for new and renewed portfolios but less significant for policies renewed two or more times (Appendix 2.6).

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 = 𝛼𝛼 + 𝛿𝛿(𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖) + 𝛾𝛾𝑋𝑋𝑖𝑖 + 𝜀𝜀𝑖𝑖 (3)

7. Discussion

7.1. Adverse selection vs. moral hazard

A critical issue to the positive risk-coverage correlation test is disentangling adverse selection from moral hazard. Both concepts predict that insured (fully insured) should have a higher probability of accident than do uninsured (partially insured) (Richaudeau, 1999). The positive correlation found in cross-sectional models does not suffice to tell whether the relationship is caused by adverse selection alone, moral hazard alone, or both (Cohen and Siegelman, 2010).


26

We thus disentangle between-group adverse selection from moral hazard from statistical, theoretical and product design perspectives.

Statistically, we use longitudinal data to conduct the disentangling test introduced by Abbring et al. (2003). They suggest that moral hazard should lead to a negative correlation between historical claims and claims in the subsequent period under the experience rating system because the insured’s behavior changes corresponding to experience rating and insurance coverage. In contrast, adverse selection should result in a positive correlation between past and future claims because claims are determined by the insured’s risk type. We show in Appendix 3 that new policy claims and first-time renewed policy claims are positively related to each other, which is consistent with adverse selection. Theoretically, the disappearance pattern of risk-coverage correlation itself provides direct evidence that at least some new customers have private information about their risk type, which cannot be explained by moral hazard (Cohen and Siegelman, 2010).

Moreover, we consider potential risk-bearing and claim-reporting moral hazard in group insurance (Butler and Worrall, 1991; Ruser and Butler, 2010; Butler, Gardner and Kleinman, 2013). Previous research explains the pattern of risk-coverage correlation in workers’ compensation (WC) with moral hazard and argues that the incentives of employers and employees under experience-rated group insurance coverage are different. Employees tend to care less and report more claims than employees with no insurance, where the moral hazard story holds. Employers, however, face incentives to improve safety and report fewer claims to keep the premium low in the following year. The employer’s incentive, termed risk-bearing moral hazard, mitigates any moral hazard and claim-reporting moral hazard of employees, which may also show a disappearance pattern of risk-coverage correlation. This explanation was developed in the WC context, in which adverse selection is minimal due to compulsory insurance. However, in group CI insurance, neither the employer nor the employee is likely able to systemically influence the frequency of CI incidents and the market is commercial and voluntary. Thus, the moral hazard in WC market may not apply.

The product design of group CI insurance also minimizes moral hazard because the insurer pays the full insurance amount once the covered critical disease is diagnosed, which avoids the over-utilization problem commonly observed in medical expense insurance (i.e., ex post moral hazard). Moreover, considering the very small expected benefit, the insured’s incentive to change his/her lifestyle due to CI coverage is minimal. Wang et al. (2011) find adverse selection in Taiwan’s cancer insurance market, which is similar to our CI insurance product. They conclude that purchasing extended cancer insurance does not reduce insureds’ efforts to prevent cancer. We also note the potential for claim fraud. However, the claim payment is subject to the verification procedure that the claimant is always asked to obtain a second


27

opinion on the diagnosis from a different hospital approved by the insurer, which significantly reduces the risk of claim fraud. In general, group CI insurance is much less affected by moral hazard and claim fraud than is medical expense health insurance.

7.2. Alternative explanations for adverse selection disappearance

Our explanation for the disappearance of adverse selection is insurer learning over time. We discuss alternative explanations below. First, the disappearance of risk-coverage correlation could be driven by risk quality changes or selections of the group. The covered individuals may drop their coverage in the subsequent period when their groups renew, due to death, dismissal from the group, or other reasons (Yao, 2013). We thus compare the reason for coverage drop-offs between claimants (individuals filing a claim) and nonclaimants (individuals not filing a claim). For claimants, 65% of drop-offs are due to group drop-offs, and 35% are standalone drop-offs when their groups renew in the subsequent period. For nonclaimants, 62% of drop-offs are due to group drop-offs, and 38% are standalone. Clearly, most individual drop-offs are attributable to group drop-offs, and claimants are not more likely to leave the portfolio on a standalone basis than are nonclaimants. Moreover, we examine whether claimants are more likely to leave the portfolio under the condition that the group renews in the subsequent period. For claimants, 28% leave the portfolio when their groups stay; for nonclaimants, 25% leave. At the 95% confidence level, claimants are not more likely to leave the portfolio than are nonclaimants when their groups stay, subject to a binomial probability test. We find no evidence on group risk quality change over time or risk selection by the group insured. The disappearance of adverse selection is unlikely to be driven by risk quality changes within a group.

Another explanation is multidimensional information advantages. Finkelstein and McGarry (2006) argue that there are multiple dimensions of private information related not only to insureds’ risk types but also to their risk attitudes (or risk preferences). They suggest that empirical studies based on risk-coverage correlations should control for insureds’ risk attitudes because risk-averse insureds are often associated with low levels of risk, which will blur the positive risk-coverage correlation test due to “advantageous selection” (De Meza and Webb, 2001; Fang, Keane, and Silverman, 2008). However, it is hard to argue that such a correlation between risk attitudes and risk coverage applies to group insureds. It has been noted that risk aversion provides much less of a motivation for corporate insureds to purchase insurance, particularly for stock companies, because stakeholders could instead manage idiosyncratic losses through diversified portfolios (Mayers and Smith, 1982, 1990). For Chinese corporate insurance, Zhu, Kui, and Fang (2011) find that risk aversion is not a significant factor in insurance demand. In our analysis, group insureds are largely corporations and decision makers are usually in HR departments; therefore, we assume that


28

group insureds’ risk attitudes are not the major driver of insurance demand and will not distort the risk-coverage correlation.24

7.3. Generalizability of low loss frequency portfolio and of Chinese market

Medical expense health insurance and automobile insurance are common types of insurance products used to test for adverse selection. The high loss frequency of such products enables econometricians to detect adverse selection more easily than do low loss frequency products, partially because the small number of claims in a dataset may bias the measurement of actual risk when using ex post losses and partially because the insured’s perception of risk types is biased when the event probability is low (Cawley and Philipson, 1999). We thus discuss the potential effect of loss frequency on between-group adverse selection.

Theories of adverse selection do not distinguish between predictions of high and low probability risks. However, some theories suggest that people exhibit biases in judgments about risks and probabilities when the probabilities of events are small (Camerer and Kunreuther, 1989). In the context of group CI insurance, the insurance decision maker, such as the HR department of the group insured, usually has experience purchasing insurance and possesses relevant information about employee health.

Empirically, in our sample, there is one loss in every six group-year policies or every 1,500 individual-year policies, as shown in Table 2. This loss frequency is lower than in automobile and health insurance but not materially different from many common insurance products, such as fire or term life insurance. There are also empirical studies that detect adverse selection in low loss frequency markets where longitudinal data increase the power of detection (He, 2008). We perform a robustness test using a bootstrap resampling method (200 replications) to correct for potential bias in estimated standard errors (Efron and Tibshirani, 1993) due to a low loss frequency. The bootstrap resampling method constructs a number of resamples of the observed dataset and thus provides a way to account for distortions caused by a small sample that may not be fully representative of the population. The results in Appendix 4 confirm our conclusions.

In addition to the evidence drawn from Chinese group CI insurance, the U.S. small-group health insurance market provides another example of between-group adverse selection, in which high prices and low coverage resulting from adverse selection are notorious (Simon, 2005). However, two major obstacles jeopardize the empirical conclusions pertaining to between-group adverse selection in the U.S. small-group health insurance market. First, it is

24 In addition, Chiappori and Salanié (2013) suggest that risk preference alone should have negligible consequences on

the positive risk-coverage correlation in competitive markets because insureds of all types of risk aversion prefer full coverage in a competitive market. The Chinese group CI insurance market can be considered as a competitive market with standardized coverage and no rate regulation.


29

difficult to separate the effect of individual choices from group strategic actions; second, small-group reforms in the early 1990s restricted insurer experience rating and redlining. In contrast, the Chinese group CI insurance market provides almost laboratory conditions to test between-group adverse selection, considering 1) standardized products with competing prices, 2) voluntary purchase and renewal for both buyers and insurers, and 3) commercial markets without considerations of broad availability and affordability.

In principle, any group insurance arrangement without individual choices is suitable to test between-group adverse selection. 25 For example, we expect to find similar results from employer-provided group health insurance in the U.S., if policies that allow individual plan choices are excluded, from crop insurance at the village- or county-level, and from motor fleet insurance including both liability and own damage coverage. We might also find between-group adverse selection in the supplementary coverage of social insurance. However, we do not argue for the universality of between-group adverse selection. Product lines with little adverse selection in the individual insurance market may not exhibit between-group adverse selection in the group insurance market, e.g., life insurance.

8. Concluding remarks and future research

We find evidence for the existence of between-group adverse selection. Our dataset allows us to separate the effect of individual choice within a group from the effect of group strategic actions. The empirical findings complement conventional wisdom and support Hanson's (2005) theoretical prediction that adverse selection may well exist in a group insurance market even if no individual choices are allowed and even if the group is formed for purposes other than purchasing insurance. This paper also complements empirical works based on U.S. (small-) group health insurance, where the individual choice within a group is an important driver of adverse selection. In addition, we find that between-group adverse selection disappears over time as the group insured renews with the same insurer for a certain period. This evidence is consistent with the explanation of insurer learning over time. The combination of two pieces of evidence suggests that group insurance alone is not necessarily sufficient to mitigate adverse selection; in the repeated contracting setup, learning from the performance of past contracts and taking corresponding actions based on the information observed help to mitigate adverse selection problems (Dionne, 1983).

As discussed in the section of generalizability, we expect our conclusions to hold for multiple group insurance products in various markets of a similar nature, e.g., U.S. small-group health insurance. Our results may also shed light on markets other than insurance characterized by

25 We use another health insurance portfolio from Pakistan to generalize our conclusions regarding Hypothesis I. The

results confirm that between-group adverse selection exists (1) in the high loss frequency portfolio, (2) when the group insureds are families. The dataset cannot be used to test Hypothesis II due to the limited number of policy periods. These results are available from the authors upon request.


30

information asymmetry, where the existence and persistence of adverse selection are also relevant (see, e.g., Chari, Shourideh, Zetlin-Jones, 2014).

One implication of our results is that group insurance with no individual choice cannot be considered a market free of adverse selection, even if the group is formed for purposes other than purchasing insurance. Our results thus also have important business implications. Insurers must be aware that group insurance policyholders strategically act on their information advantages and should therefore monitor group claim experience over time, first to learn and then to apply that knowledge to their renewal underwriting and pricing decisions. The more efficiently insurers acquire and use such knowledge, the sooner they will overcome adverse selection.

Our dataset does not allow us to compare the level of group adverse selection to the level of individual adverse selection. An interesting next step would be to compare the magnitude and/or the persistent time of adverse selection between group and individual insurance. Moreover, there is, to date, limited theoretical work on why and how between-group adverse selection is generated via internal group processes. It would be useful to know how group insurance decision processes differ from individual insurance decisions. Finally, we recommend additional empirical studies to explore other eligible group insurance products in other markets to verify our empirical results.


31

Appendices

Appendix 1 Critical diseases covered by the group CI policy

The complete list of 25 critical diseases covered under the group CI policy is shown below. The list is recommended by the Insurance Association of China and the Chinese Medical Doctor Association and has been adopted by most players in the Chinese CI insurance market. The standard and binding definitions of these diseases can be found in Insurance Association of China and Chinese Medical Doctor Association (2007).

1. Malignant Tumor 2. Acute Myocardial Infarction 3. Sequelae of Stroke 4. Major Organ / Hematopoietic Stem Cells Transplant 5. Coronary Artery Bypass Graft 6. End Stage Renal Disease (Chronic Kidney Failure) 7. Loss of Limbs 8. Acute or Subacute Severe Hepatitis 9. Benign Brain Tumor 10. Chronic Liver Failure (End Stage) 11. Encephalitis Sequelae or Meningitis Sequelae 12. Deep Coma 13. Deafness in Both Ears 14. Blindness in Both Eyes 15. Paralysis 16. Heart Valve Surgery 17. Severe Alzheimer's Disease 18. Major Head Trauma 19. Severe Parkinson's Disease 20. Major Third Degree Burn 21. Severe Primary Pulmonary Hypertension 22. Severe Motor Neuron Disease 23. Loss of Speech 24. Severe Aplastic Anemia 25. Aorta Surgery


32

Appendix 2 Robustness tests

Appendix 2.1 Reduced form model in equations (2.1) and (2.2) Correlation coefficients between residuals of risk and residuals of coverage

Subsamples New policies Renewed policies

Policies renewed two or more

times


Panel A: Separate Estimation ClaimDummy 0.0577 (0.018) 0.0371 (0.111) 0.0236 (0.436) 0.0412 (0.262) ClaimCount 0.0631 (0.010) 0.0484 (0.037) 0.0319 (0.293) 0.0463 (0.207) ClaimFrequency 0.0636 (0.009) 0.0508 (0.029) 0.0380 (0.210) -0.0067 (0.855) Panel B: System Estimation (FIML) ClaimDummy 0.0817 (0.001) 0.0731 (0.001) 0.0494 (0.104) 0.0606 (0.098) ClaimCount 0.0638 (0.009) 0.0753 (0.001) 0.0217 (0.475) 0.0186 (0.612) ClaimFrequency 0.0337 (0.166) 0.0206 (0.375) 0.0290 (0.340) 0.0463 (0.207) Observations 1,690 1,850 1,088 745

Notes: P-values measuring significant differences from zero are presented in parentheses.


33

Appendix 2.2 Demographic control variables New policies Renewed policies Policies renewed two or more times Policies renewed three or more times

Variables Claim Dummy Claim Count Claim

Frequency Claim

Dummy Claim Count Claim Frequency

Claim Dummy Claim Count Claim

Frequency Claim

Dummy Claim Count Claim Frequency

lnInsuranceAmount

0.00853*** 0.00672*** 3.783*** 0.00435* 0.00330** 0.790 0.00207 0.00147 0.736 0.00160 0.0000198* c 1.861 (0.00265) (0.00226) (1.430) (0.00235) (0.00163) (0.754) (0.00168) (0.00114) (0.756) (0.00113) (1.18e-05) (1.186)

lnGroupSize 0.0246*** 0.0239*** 10.01*** 0.0175*** 0.0182*** 4.936*** 0.00791** 0.00712*** 3.843*** 0.00576** 0.0000659*** 6.162*** (0.00355) (0.00335) (1.387) (0.00573) (0.00266) (0.515) (0.00384) (0.00181) (0.490) (0.00242) (1.92e-05) (2.181)

lnPolicyDuration

0.0352** 0.0437** 17.07** 0.0319*** 0.0262*** 9.617*** 0.0152*** 0.0115*** 7.253*** 0.00386** 0.0000510*** 4.218*** (0.0158) (0.0185) (7.599) (0.00525) (0.00414) (2.406) (0.00493) (0.00241) (1.971) (0.00177) (9.22e-06) (0.823)

area2 0.00429 -0.000854 1.301 0.000327 -0.000942 -0.179 0.00121 0.00208 0.812 -0.00146 -0.0000181 -1.984 (0.00794) (0.00568) (3.638) (0.00421) (0.00350) (1.627) (0.00318) (0.00237) (1.838) (0.00134) (2.10e-05) (2.789)

area3 0.0116 0.00232 2.695 0.00433 0.00104 -0.451 0.00207 0.00339 -1.005 0.00172 0.0000255 1.320 (0.0108) (0.00700) (4.525) (0.00626) (0.00463) (2.153) (0.00474) (0.00349) (2.305) (0.00388) (4.58e-05) (3.605)

area4 0.0548 0.0226 12.51* -0.0212*** -71.94 -0.00885*** -43.99 0.00122 -2.13e-06 1.481 (0.0368) (0.0183) (6.816) (0.00363) (0) (0.00240) (0) (0.00454) (6.34e-05) (6.324)

sex -0.0215* -0.0198* -10.28 0.00556 -0.00132 4.273 0.00135 0.00170 0.730 -0.00570 -0.0000773 -5.821 (0.0126) (0.0107) (6.783) (0.0110) (0.0105) (4.499) (0.00729) (0.00588) (4.431) (0.0118) (0.000148) (9.467)

age0to15 -0.0186 0.0204 -25.51 -0.00869 -0.0334 -13.26 -0.00912 -0.0274* -24.70 0.00495 0.0000833 6.176 (0.0346) (0.0193) (28.12) (0.0336) (0.0225) (13.15) (0.0116) (0.0148) (22.57) (0.00434) (5.54e-05) (5.468)

age31to45 0.0464*** 0.0402*** 23.16** 0.0183 0.0191** 6.579 0.00942 0.00828 7.838* 0.00763 0.000141*** 6.893 (0.0146) (0.0128) (9.995) (0.0132) (0.00904) (4.431) (0.00875) (0.00573) (4.119) (0.00485) (4.24e-05) (4.847)

age46to60 0.0748*** 0.0811*** 42.11*** 0.0417** 0.0526*** 13.76*** 0.0182 0.0208*** 11.06** 0.0534* 0.000567** 131.9*** (0.0173) (0.0161) (13.78) (0.0174) (0.0115) (3.990) (0.0111) (0.00705) (4.333) (0.0322) (0.000224) (34.56)

age61over a 0.0504 0.107*** 8.785 0.0402 0.0539** 28.76 0.0418 0.0349 56.15** 0.000903 0.0000132 -3.441 (0.0611) (0.0408) (29.36) (0.0466) (0.0257) (20.95) (0.0411) (0.0229) (27.48) (0.00292) (2.17e-05) (3.747)

work2 -0.00315 0.00680 -0.00108 0.000558 0.000750 -0.465 -0.00119 0.00283 -2.417 -0.000130 -0.0000152 -0.0773 (0.00889) (0.00564) (5.479) (0.00596) (0.00393) (2.563) (0.00399) (0.00246) (2.484) (0.00169) (2.54e-05) (2.763)

work3 -0.000855 0.000118 -1.926 -0.00865* -0.0103** -2.874 -0.000127 -0.00380 -0.103 -0.00158 -0.0000587 -2.740 (0.00676) (0.00503) (3.551) (0.00507) (0.00430) (2.000) (0.00276) (0.00254) (1.977) (0.00442) (4.84e-05) (5.631)

work4 -0.00188 0.00521 -7.535 -0.00696 -0.0126** -4.061 -0.00149 -0.00422 -1.976 -0.0247*** -1,135 (0.0110) (0.00985) (5.969) (0.00826) (0.00511) (2.985) (0.00602) (0.00344) (3.176) (0.00643) (0)

work5 b -0.0311 -0.00760 -15.16 0.0333 0.0145** 6.321* -12.19*** -3,181 0.00160 0.0000198* 1.861 (0.0301) (0.0220) (14.83) (0.0226) (0.00605) (3.419) (4.232) (0) (0.00113) (1.18e-05) (1.186)

Pseudo R2 0.354 0.364 0.109 0.382 0.347 0.134 0.463 0.410 0.204 0.481 0.467 0.262 Observation 1,597 1,597 1,597 1,835 1,835 1,835 1,079 1,079 1,079 739 739 739

Notes: We present the marginal effects of logistic and negative binomial models at the means of the independent variables and present the estimated coefficients of Tobit model. Robust standard errors clustered by group insureds are presented in parentheses. We also present *, **, ***, indicating significant differences of coefficients from zero at the 10 percent, 5 percent, and 1 percent levels, respectively. Intercepts and year dummies are included in models but not reported. a. Only 0.7% of individual insureds are older than 60 in the portfolio, thus the coefficients become insignificant and unstable. b. work6 is omitted due to too few observations in subsamples. c. We believe this significant effect could be the spurious positive risk-coverage correlation, due to incomplete controlling for risk classification, as suggested by Cohen and Siegelman (2010). The premium rate captures more information than demographic features, leaving less residual private information for adverse selection.


34

Appendix 2.3 Large vs. small groups

Subsamples New policies

Renewed policies

Policies renewed two or more times


Panel A Dependent Variable: ClaimDummy, Model: Logistic lnInsuranceAmount 0.00865*** 0.00439* 0.00103 0.00163

(0.00293) (0.00235) (0.00132) (0.00119) lnInsuranceAmount*small 0.000644 -0.000510 -0.000408 0.0000900 (0.00107) (0.000646) (0.000529) (0.000390) lnPremiumRate 0.0128*** 0.00564* 0.00124 0.00174 (0.00406) (0.00304) (0.00150) (0.00130) lnGroupSize 0.0313*** 0.0151** 0.00613 0.00456** (0.00520) (0.00605) (0.00383) (0.00200) lnPolicyDuration 0.0699*** 0.0355*** 0.0156** 0.00779*** (0.0237) (0.00697) (0.00672) (0.00270) Pseudo R2 0.307 0.363 0.441 0.427 Panel B Dependent Variable: ClaimCount, Model: Negative Binomial lnInsuranceAmount 0.00883*** 0.00487*** 0.000693 0.0000818 (0.00243) (0.00183) (0.00119) (5.56e-05) lnInsuranceAmount*small 0.000521 -0.000913 -0.00104* 0.0000251 (0.000873) (0.000653) (0.000611) (2.27e-05) lnPremiumRate 0.0131*** 0.00811*** 0.00259* 0.000168** (0.00369) (0.00240) (0.00151) (6.56e-05) lnGroupSize 0.0301*** 0.0175*** 0.00688*** 0.000274*** (0.00525) (0.00397) (0.00231) (6.73e-05) lnPolicyDuration 0.0815*** 0.0348*** 0.0175*** 0.000362*** (0.0246) (0.00510) (0.00439) (0.000112) Pseudo R2 0.320 0.314 0.370 0.396 Panel C Dependent Variable: ClaimFrequency (scaled up by 1,000),

lnInsuranceAmount 3.218** 1.279* 0.847 2.411 (1.452) (0.707) (0.812) (1.780) lnInsuranceAmount*small 0.461 -0.243 -0.382 0.162 (0.433) (0.247) (0.303) (0.584) lnPremiumRate 4.888** 2.020** 1.641 3.348* (1.983) (0.822) (1.050) (1.906) lnGroupSize 11.40*** 4.444*** 3.111*** 5.144** (2.022) (0.816) (0.989) (2.013) lnPolicyDuration 27.33*** 11.29*** 8.680*** 7.437*** (10.37) (2.659) (2.146) (2.859) Pseudo R2 0.092 0.125 0.184 0.212 Observations 1,690 1,850 1,088 745

Notes: We present the marginal effects of logistic and negative binomial models at the means of the independent variables and present the estimated coefficients of Tobit model. Robust standard errors clustered by group insureds are presented in parentheses. We also present *, **, ***, indicating significant differences of coefficients from zero at the 10 percent, 5 percent, and 1 percent levels, respectively. Intercepts and year dummies are included in models but not reported.


35

Appendix 2.4 Potential nonlinear effects Subsample New policies Models Logistic Negative binomial Tobit

Variables ClaimDummy ClaimCount ClaimFrequency (scaled up by 1,000)

lnInsuranceAmount 0.00853*** 0.00672*** 3.783*** (0.00265) (0.00226) (1.430) Projected lnInsuranceAmount

0.322 0.276** 163.0* (0.206) (0.120) (98.91)

lnGroupSize 0.0489*** 0.0447*** 22.34*** (0.0161) (0.00971) (7.752) lnPolicyDuration 0.112* 0.110*** 56.01** (0.0601) (0.0406) (28.01) Area, Age, Sex, and Work Yes Yes Yes

Pseudo R2 0.354 0.364 0.109 Observations 1,597 1,597 1,597



36

Appendix 2.5 Alternative econometric models


Renewed policies



Panel A Dependent Variable: ClaimDummy, Model: Probit lnInsuranceAmount 0.0104**

0.00633* 0.00199 0.00195

(0.00355

(0.00326) (0.00208) (0.00147) lnPremiumRate 0.0154**

0.00854** 0.00256 0.00221

(0.00480

(0.00428) (0.00237) (0.00159) lnGroupSize 0.0363**

0.0243*** 0.0104* 0.00505**

(0.00437

(0.00824) (0.00593) (0.00241) lnPolicyDuration 0.0775**

0.0453*** 0.0200** 0.00737**

(0.0245) (0.00760) (0.00829) (0.00306) Pseudo R2 0.303 0.353 0.426 0.411 Panel B Dependent Variable: ClaimCount, Model: Poisson lnInsuranceAmount 0.00876*

0.00601*** 0.000800 8.44e-05

(0.00302

(0.00187) (0.00143) (5.95e-05) lnPremiumRate 0.00879*

0.0105*** 0.00402** 0.000190**

(0.00316

(0.00232) (0.00172) (7.63e-05) lnGroupSize 0.0217**

0.0210*** 0.00988*** 0.000311***

(0.00422

(0.00368) (0.00225) (7.21e-05) lnPolicyDuration 0.0839**

0.0384*** 0.0221*** 0.000400**

(0.0158) (0.00518) (0.00447) (0.000162) Pseudo R2 0.624 0.427 0.426 0.478 Panel C Dependent Variable: ClaimCount, Model: Zero inflated Poisson lnInsuranceAmount 0.00690*

0.00605*** 0.000800 5.21e-05

(0.00212

(0.00193) (0.00143) (6.35e-05) lnPremiumRate 0.0112**

0.0109*** 0.00402** 0.000146**

(0.00341

(0.00246) (0.00172) (6.38e-05) lnGroupSize 0.0240**

0.0212*** 0.00988*** 0.000238***

(0.00434


0.0385*** 0.0221*** 0.000296***

(0.0210) (0.00501) (0.00447) (0.000111) Log-

-447.68 -526.00 -213.94 -85.07

Panel D Dependent Variable: ClaimCount, Model: Zero inflated negative lnInsuranceAmount 0.00847*

0.00539*** 0.00105 6.35e-05

(0.00228

(0.00196) (0.00147) (4.22e-05) lnPremiumRate 0.0134**

0.00923*** 0.00372** 0.000130***

(0.00355

(0.00254) (0.00163) (4.52e-05) lnGroupSize 0.0283**

0.0201*** 0.00953*** 0.000212***

(0.00424


0.0380*** 0.0209*** 0.000283***

(0.0228) (0.00494) (0.00475) (8.75e-05) Log-

-438.34 -519.02 -212.66 -84.30

Observations 1,690 1,850 1,088 745


37

Appendix 2.5 (continued) Alternative econometric models

Subsamples Renewed Policies Policies Renewed Two or More Times

Policies Renewed Three or More Times

Panel E Dependent Variable: ClaimDummy, Model: Logistic with random

lnInsuranceAmount 0.00395** 0.000745 0.00161 [0.00194] [0.00110] [0.00142] lnPremiumRate 0.00511* 0.000926 0.00169 [0.00272] [0.00145] [0.00172] lnGroupSize 0.0144*** 0.00509 0.00438** [0.00482] [0.00409] [0.00214] lnPolicyDuration 0.0327*** 0.0123 0.00775** [0.00862] [0.00880] [0.00369] Log-likelihood -366.30 -155.73 -68.43 Panel F Dependent Variable: ClaimCount, Model: negative binomial with

lnInsuranceAmount 0.00541*** 0.000851 3.06e-06 [0.00196] [0.00141] [1.679] lnPremiumRate 0.00914*** 0.00345* 5.90e-06 [0.00286] [0.00199] [3.240] lnGroupSize 0.0201*** 0.00889*** 1.03e-05 [0.00434] [0.00313] [5.646] lnPolicyDuration 0.0376*** 0.0206*** 1.47e-05 [0.00502] [0.00528] [8.068] Log-likelihood -520.07 -212.65 -84.54 Panel G Dept. Variable: ClaimFrequency [scaled up by 1,000], Model: Tobit

lnInsuranceAmount 1.220* 0.670 1.795 [0.711] [0.907] [2.055] lnPremiumRate 1.946* 1.545 1.644 [0.999] [1.139] [2.727] lnGroupSize 4.882*** 3.726*** 4.174*** [0.630] [0.743] [1.513] lnPolicyDuration 12.36*** 9.998*** 9.099*** [2.096] [2.037] [3.152] Log-likelihood -941.28 -395.74 -155.35 Observations 1,850 1,088 745 No. of Groups 788 352 157

Notes: We present the marginal effects of logistic and negative binomial models at the means of the independent variables and present the estimated coefficients of Tobit model. Robust standard errors clustered by group insureds are presented in parentheses. Standard errors are presented in brackets for random effects models. We also present *, **, ***, indicating significant differences of coefficients from zero at the 10 percent, 5 percent, and 1 percent levels, respectively. Intercepts and year dummies are included in models but not reported. We use random effects instead of fixed effects because the residual information asymmetry, after controlling for premium rate, is exactly what we would like to detect. Firm fixed effects further control the firm-specific information that is not observed by the insurer, which thus changes the scope of residual information tested in the model. Moreover, it is reasonable to assume (1) that the group insureds in our portfolio comprise a random sample of the nationwide population, and (2) that the uncontrollable firm heterogeneity is random and not correlated with the error terms. Thus the random effects model fits better than the fixed effects model (Greene, 2011; Gujarati, 2010). In addition, the fixed effects models cannot incorporate independent variables with small or no within-group variations over time, thus many observations will be dropped if using fixed effects models. Zhang and Wang (2008) discuss why and how to apply random effects models to study adverse selection in a dynamic insurance market.


38

Appendix 2.6 Semiparametric model Hardle and Mammen’s (1993) specification test

Order of lnInsuanceAmount in the parametric models

New policies

Renewed policies

Policies renewed two or more

times

Policies renewed three or more

times 0 (lnInsuranceAmount is not included) 0.02 0.20 0.20 0.22

1 (linear as in Equation (1)) 0.38 0.30 0.06 0.12 Notes: Approximate p-values from Hardle and Mammen's (1993) specification tests are presented in the above table. The null hypothesis is that parametric and non-parametric fits are not different from each other. The results suggest that for new and renewed policy portfolios, linear models in Equation (1) are not statistically different from the Robinson’s (1988) semiparametric model in Equation (3). For policies renewed two or more times, the zero order structural model (i.e. no significant risk-coverage correlation) is not statistically different from the semiparametric model, and the linear relationship was rejected. The results confirm our conclusions to both hypotheses. The results suggest that the model misspecification risk of our core-linear model is minimal. A standard 0.05 trimming is applied for semiparametric estimations.


39

Appendix 2.6 Semiparametric model (continued)

Notes: The four charts show semiparametric estimations (Robinson, 1988) for four subsamples, respectively, as the alternative to logistic regressions on ClaimDummy. The gray shade suggests the 95 percent confidence intervals. The upper two charts indicate the positive relationship between lnInsuranceAmount and ClaimDummy for subsamples of new policies and renewed policies. The bottom two charts indicate that such relationship becomes weaker in policies renewed two or more times. The results confirm both of our conclusions. A standard 0.05 trimming is applied for semiparametric estimations.


40

Appendix 3 Disentangle adverse selection from moral hazard Subsample First-time renewed policies

Models Logistic Negative binomial Tobit

Variables ClaimDummy ClaimCount ClaimFrequency

(scaled up by 1,000)

Claim Indicators in Corresponding New Polices

0.0993** 0.0126*** 0.221* (0.0401) (0.00345) (0.130)

lnInsuranceAmount 0.0200*** 0.0171*** 1.759* (0.00726) (0.00604) (1.014) lnPremiumRate 0.0203** 0.0273*** 2.016 (0.00922) (0.00665) (1.224) lnGroupSize 0.0492*** 0.0591*** 5.659*** (0.00662) (0.00771) (0.591) lnPolicyDuration 0.149*** 0.142*** 19.00** (0.0387) (0.0411) (8.822) Pseudo R2 0.301 0.281 0.074 Observations 762 762 762



41

Appendix 4 Bootstrapping standard errors


Renewed policies



Panel A Dependent Variable: ClaimDummy, Model: Logistic lnInsuranceAmount 0.00853*** 0.00463* 0.00116 0.00160

(0.00284) (0.00239) (0.00238) (0.00347) lnPremiumRate 0.0127*** 0.00603* 0.00145 0.00169 (0.00385) (0.00349) (0.00320) (0.00368) lnGroupSize 0.0293*** 0.0165** 0.00712 0.00438 (0.00404) (0.00706) (0.0136) (0.00880) lnPolicyDuration 0.0671*** 0.0369*** 0.0166 0.00774 (0.0217) (0.00832) (0.0212) (0.0123) Pseudo R2 0.307 0.362 0.440 0.427 Panel B Dependent Variable: ClaimCount, Model: Negative Binomial lnInsuranceAmount 0.00863*** 0.00539** 0.00105 0.0000658 (0.00265) (0.00251) (0.00128) (8.64e-05) lnPremiumRate 0.0127*** 0.00924*** 0.00372 0.000135 (0.00378) (0.00347) (0.00232) (0.000155) lnGroupSize 0.0284*** 0.0201*** 0.00953** 0.000220 (0.00631) (0.00676) (0.00423) (0.000241) lnPolicyDuration 0.0776*** 0.0380*** 0.0209*** 0.000293 (0.0244) (0.00597) (0.00736) (0.000304) Pseudo R2 0.319 0.312 0.364 0.396 Panel C Dependent Variable: ClaimFrequency (scaled up by 1,000), Model: Tobit lnInsuranceAmount 3.439** 1.292* 0.901 2.402 (1.450) (0.730) (0.790) (1.836) lnPremiumRate 5.108** 2.134*** 1.875* 3.213* (2.121) (0.807) (1.022) (1.926) lnGroupSize 10.45*** 4.925*** 3.840*** 4.828*** (1.359) (0.430) (0.580) (0.941) lnPolicyDuration 26.91** 11.25*** 8.625*** 7.519* (12.00) (3.064) (2.779) (4.165) Pseudo R2 0.091 0.124 0.182 0.211 Observations 1,690 1,850 1,088 745

Notes: We present the marginal effects of logistic and negative binomial models at the means of the independent variables and present the estimated coefficients of Tobit model. Bootstrapping standard errors with 200 replications are presented in parentheses. We also present *, **, ***, indicating significant differences of coefficients from zero at the 10 percent, 5 percent, and 1 percent levels, respectively. Intercepts and year dummies are included in models but not reported.


42

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Essay II The structure of the global reinsurance market: An analysis of efficiency, scale, and scope

Abstract

We estimate economies of scale and scope as well as cost efficiency to explain the structure of the global reinsurance market, where large reinsurers dominate, but both diversified and specialized reinsurers play important roles. The costs and benefits of size and product diversification play significant roles in the reinsurance industry as risk diversification is at the heart of the industry’s business model. We find that reinsurers with total assets less than USD 2.9 billion exhibit scale economies, while those with total assets greater than USD 15.5 billion do not. Large reinsurers are characterized by high cost efficiency; small reinsurers exhibit superior efficiency only when they are specialized. The evidence is in line with the efficient structure hypothesis and suggests an optimal size range for reinsurance firms from which the current market structure results.

Keywords

Insurance, Data Envelopment Analysis, Cost Efficiency, Market Structure, Economies of Scale, Economies of Scope

-------------------------------------

Christian Biener, Martin Eling, Ruo Jia (2016).

This paper was presented at the World Risk and Insurance Economics Congress (WRIEC) 2015 in Munich and has been submitted to the Journal of Banking and Finance.

Essay II Global Reinsurance Market

47

1. Introduction

Reinsurers function as shock absorbers and risk bearers of last resort for the insurance industry and the global economy. They also provide real services to primary insurers, including underwriting, pricing, claim management, and consultancy, and thus enable primary insurers to protect individuals and institutions against risks such as natural catastrophes, terrorism, and longevity. It has been indicated that reinsurance performs an important strategic function in insurance markets, supporting primary insurers to grow and to increase market share (Upreti and Adams, 2015). Moreover, reinsurers, with large and long-term investment portfolios, are a reliable source of alternative capital to primary insurers and to the global economy.

The reinsurance industry has undergone significant change in the 21st century, preceded by a number of large-scale catastrophes, the 2008 financial crises, new competition from alternative risk transfer schemes, and new sources of capital from hedge funds and pension funds (Butt, 2007; Cummins and Weiss, 2009). All of these factors have resulted in consolidation (Cummins and Weiss, 2000; Cole and McCullough, 2006) and structural change in the global reinsurance market.

Economies of scale and scope, as sources of diversification, are particularly relevant to the structure of the reinsurance market. The advantages offered by scale economies motivate market consolidation because large firms tend to be more scale efficient than small firms. Scope economies come into play when more product diversified firms exhibit cost efficiency advantages relative to specialized firms (Clark, 1988; Elango, Ma, and Pope, 2008; Panzar and Willig, 1977, 1981). Borch (1960, 1962) takes a different perspective and argues that the global reinsurance market should be structured around optimal risk allocation. He predicts that, in the market equilibrium, all reinsurers hold a proportional share of the “market portfolio” that pools all risks. Borch’s equilibrium implies complete diversification of risks with the market portfolio. The theories involving economies of scale and scope, as well as Borch’s equilibrium, focus on two key features of the reinsurance business—size (scale) and product diversification26 (scope)—and thus provide a basis for analyzing their empirical validity as well as the consequences for market structure.27

To date, academic research on reinsurance has been focusing on reinsurance demand, contract design, pricing (see Bernard, 2013 for a review), and reinsurance decisions (see e.g. Kader, Adams, and Mouratidis, 2010). However, the reinsurance market itself, especially the

26 This paper focuses on product diversification, an aspect not to date studied in the context of the global reinsurance

market. Regarding geographical or international diversification in the reinsurance market, we refer to, e.g., Cole, Lee, and McCullough (2007) and Outreville (2012a).

27 Reinsurance is a persuasive context to analyze the market structure, not only because of the variety of recent corporate strategic changes (Klarner and Raisch, 2013), but also because of the industry-specific features, such as the risk allocation problem (Borch, 1960, 1962), which motivates diversification, and the intangible and regulated nature, which may serve as entry barrier and limit the options for diversification.


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performance and efficiency of reinsurers, has not yet received sufficient attention. Most literature on reinsurance performance applies traditional accounting indicators, such as ROE, ROA, or underwriting ratios (see, e.g., Chen and Hamwi, 2000; Cole, Ferguson, Lee, and McCullough, 2010; Cole and McCullough, 2008; Outreville, 2012a, 2012b). Cummins and Weiss (2000) provide the first piece of evidence on reinsurers’ efficiencies regarding the tradeoff between mean and standard deviation of ROE. Their approach sits in between the accounting performance measurement and the frontier efficiency performance measurement, because they include only one input and one output. In our view, the research gap in reinsurance partially attributes to the difficulty to consistently identify reinsurers and to combine different datasets to get a complete picture of the global reinsurance market. Moreover, the efficiency study in financial service business is in general difficult and has attracted less attention than manufacturing industries in which output is easier to quantify.

This paper makes four primary contributions. (1) We estimate reinsurer cost efficiency using data envelopment analysis (DEA) with multiple inputs and outputs. (2) We analyze economies of scale and scope based on DEA frontier efficiency benchmarks, thus explaining the real-world structure of the global reinsurance market. (3) We derive an optimal size range for reinsurers by uncovering thresholds at which scale economies are exhausted. (4) We test the efficient structure (ES) hypothesis in the global reinsurance market, under which efficient firms are expected to be more competitive because they charge lower prices without sacrificing profitability. To our knowledge, none of these analyses have been conducted previously.

Our empirical results suggest that the consideration of scale efficiency yields an optimal size range between USD 2.9 and 15.5 billion in total assets (inflation adjusted at 2012). Scale diseconomies of the largest reinsurers are offset by their strong positions in X-efficiency (i.e., the part of cost efficiency that cannot be explained by scale efficiency); hence, the largest reinsurers are, in general, most cost efficient. Some small reinsurers are also able to employ the best available technology and exhibit high pure technical efficiency in their specialized fields, thus partially offsetting their scale inefficiencies. Product diversification (scope) decreases X-efficiency and cost efficiency for small reinsurers. Our finding supports the ES hypothesis, in the sense that cost-efficient reinsurers can charge lower prices without sacrificing their profitability, which, as a byproduct, also sheds lights on the relationship between the frontier efficiency and traditional accounting measurements. Our results explain the current structure of the global reinsurance market, in which large reinsurers dominate, but both diversified and specialized reinsurers play important roles.

We contribute to finance and insurance research by showing how the global market for risk transfer is organized. The results illustrate the tradeoff between scale diseconomies and gains


49

in X-efficiency, which is relevant for mergers and acquisitions as well as decisions about firm growth not only in the reinsurance industry, but also in other industries that are becoming more global. Hence, our work contributes to the ongoing discussions around performance and efficiency of insurance companies (Eckles, Hoyt, and Miller, 2014), cross-country insurance studies (Pasiouras and Gaganis, 2013), and systemic relevance of the reinsurance sector (Cummins and Weiss, 2014; Park and Xie, 2014).

The paper is organized as follows. In Section 2, we discuss the theories and derive our hypotheses. Section 3 describes our data and methodology. In Section 4 and 5, we present the empirical results and robustness tests, respectively. We conclude in Section 6.

2. Hypothesis development

2.1. Economies of scale

The theory of economies of scale implies a possible optimal firm size and thus an optimal market structure. Scale economies (diseconomies) occur when a marginal proportional increase in the scale of all inputs leads to a more (less) than proportional increase in the outputs produced (Clark, 1988; Mansfield, 1970). Hence, competition is Pareto efficient if scale economies become exhausted at a level of output that is a small portion of the market. However, when scale economies are significant and unexhausted at the full extent of the market, a monopoly firm may be able to minimize industry costs and prevent market entry (Panzar and Willig, 1977).

Economies of scale may exist in the reinsurance industry due to expensive IT systems, claim settlement operations, and risk management activities (Cummins and Xie, 2013), thus motivating market consolidation (Cummins, Tennyson, and Weiss, 1999; Lonkevich, 1995). However, large firm size can also lead to inefficiencies in the reinsurance industry due to agency conflicts, communication costs, and duplication efforts (Cummins and Weiss, 2013). Therefore, scale diseconomies may be present when the disadvantages of scale exceed its advantages. This tradeoff leads to our first hypothesis as follows.

• Hypothesis 1A: Reinsurer size 28 has an inverse-U shaped relationship to scale efficiency.

Alternatively, H1A can be stated as small reinsurers are more likely to operate under increasing returns to scale (IRS), medium-sized reinsurers are more likely to operate under constant returns to scale (CRS), and the largest reinsurers are more likely to operate under decreasing returns to scale (DRS). Such a relationship between firm size and scale efficiency (returns to scale) is found in many industries (see, e.g., Bikker and Gorter, 2011; Cummins

28 We capture the reinsurer’s size by its real value of total assets. As a robustness test, we alternatively use the real value

of net premiums written.


50

and Xie, 2013; Katrishen and Scordis, 1998 for primary insurance; Berger and Humphrey, 1991; Noulas, Ray, and Miller, 1990 for banking). Furthermore, we look for evidence on the optimal size range, if the inverse-U shaped relationship between reinsurer size and scale efficiency exists.

2.2. Scale impact on cost efficiency

Cost efficiency involves other aspects that cannot be explained by the economics of scale (scale efficiency). To capture these other aspects, we introduce the concept of X-efficiency29 (Berger, 1995; Cummins, Weiss, Xie, and Zi, 2010; Weiss and Choi, 2008), defined as cost efficiency divided by scale efficiency or as pure technical efficiency multiplied by allocative efficiency. Therefore, the scale impact on cost efficiency manifests via two channels, i.e., economies of scale (scale efficiency) and X-efficiency. The scale impact on X-efficiency is important to the reinsurance industry because (1) larger scale enables reinsurers to attract qualified managers and experts to develop and maintain state-of-the-art technologies for assessing and pricing risks, and (2) large reinsurers are closer to the conditions to apply the law of large numbers, which reduces loss volatility and, thus, enables the use of less capital to manage more risks. Large reinsurers potentially have superior resources for developing and using state-of-the-art technology and thus for being more X-efficient (Cummins and Weiss, 2000). Therefore, we derive our second hypothesis as follows.

• Hypothesis 1B: Large reinsurers’ strong X-efficiency offsets their scale diseconomies and results in an overall positive correlation between reinsurer size and cost efficiency.

Complexity theory suggests that X may relate to Y positively, negatively, and not at all within the same set of data, which is contingent on various antecedents and configurations (Woodside, 2014). We thus also test whether the relationship between reinsurer’s scale and efficiency is contingent on reinsurer’s scope. The results are presented in the analyses of returns to scale (see Table 6) and interaction terms between scale and scope (see robustness test 10).

2.3. Economies of scope

Panzar and Willig (1977, 1981) extend the concept of economies of scale to economies of scope. They suggest that firms become more cost efficient by extending their output from only one to two or more products. Economies of scope explain the existence of multi-product

29 Cost efficiency can be decomposed into scale efficiency and X-efficiency. The concept of X-efficiency was proposed

by Leibenstein (1966) to capture all sources of unspecified inefficiencies that are not allocative efficiency. Berger (1995) follows the original intention of X-efficiency and defines it as the differences in costs that cannot be explained by differences in scale or other observable characteristics. Cummins et al. (2010) and Weiss and Choi (2008) further define X-efficiency in the insurance DEA efficiency context as the part of cost efficiency that cannot be explained by scale efficiency, i.e., the product of pure technical efficiency and allocative efficiency. We notice the significant changes in definition over time and apply the last definition in the context of insurance DEA efficiency.


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firms in a competitive environment. Therefore, in addition to economies of scale and the scale impact on cost efficiency, any examination of market structure must also consider the economies of scope.

Economies of scope are particularly important to the reinsurance industry because not only can certain inputs—such as IT systems, policy services, and underwriting know-how—be used recurrently for multiple product lines, as in other industries (Teece, 1980); but also a more diversified product portfolio reduces underwriting volatility (Cummins and Weiss, 2013), allowing for higher leverage and less equity capital (Lewellen, 1971). Product diversification may also negatively influence efficiency. For example, more specialized firms may develop core competencies in their core business, leading to decreasing managerial and agency costs (Berger, Cummins, Weiss, and Zi, 2000). Moreover, life and nonlife insurance require different underwriting and pricing techniques, meaning that any benefits from sharing underwriting may be negligible. Furthermore, reinsurers engaged in both primary and reinsurance business may be subject to conflicts of interest with themselves because its primary insurance line will be competing for primary insurance business with customers of its reinsurance line.

Berger et al. (2000) and Cummins et al. (2010) develop an empirical framework for economies of scope in the insurance industry by testing the conglomeration hypothesis and the strategic focus hypothesis. Berger et al. (2000) suggest that conglomeration is the dominant strategy for some types of insurers, e.g., larger insurers focusing on personal lines and having a vertically integrated distribution system; whereas the strategic focus is preferred by small insurers focusing on commercial lines and having a nonintegrated distribution system. Therefore, it is important to examine whether the impact of product diversification (scope) varies by type of reinsurer. Given that reinsurance is a pure B2B business and that, typically, reinsurers’ distribution systems are not integrated, i.e. reinsurance brokers play an important role, we expect that strategic focus strategies prevail in the reinsurance industry, particularly for small reinsurers, which yields our third hypothesis below.

• Hypothesis 2A: Specialization (diversification) improves (reduces) X-efficiency and thus the cost efficiency of small reinsurers.

Distribution systems of large reinsurers are usually more integrated than those of small reinsurers, i.e. through own client manager teams handling large primary insurers in order to avoid high brokerage costs on large transactions. Moreover, large insurers may have incentives to develop more lines of business in order to fully deploy its advanced and expensive IT system. Large reinsurers also have larger management teams than small reinsurers. The members of these teams usually have different backgrounds and areas of expertise and thus enable large reinsurers to expand across different lines of business.


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Therefore, large reinsurers may reap additional benefits from scope economics, which yields the conglomeration hypothesis for large reinsurers below.

• Hypothesis 2B: Diversification (specialization) improves (reduces) X-efficiency and thus the cost efficiency of large reinsurers.

2.4. Efficient Structure

The efficient structure (ES) hypothesis (Berger, 1995; Choi and Weiss, 2005; Weiss and Choi, 2008) explains the market structure from an efficiency perspective (Demsetz, 1973; Peltzman, 1977). More efficient firms have superior management, better production technology, or simply more efficient scales than others, and thus have a lower cost (Berger, 1995). Therefore, they can charge lower prices than inefficient firms without sacrificing profitability, which yields the efficient structure hypothesis below.

• Hypothesis 3: Cost-efficient reinsurers can charge lower prices without sacrificing profitability.

Market consolidation is an expected byproduct of efficiency differences, with more efficient reinsurers gaining higher market shares through consolidation (Choi and Weiss, 2005; Weiss and Choi, 2008). In other words, the efficiency drives both the profitability30 (Greene and Segal, 2004) and the market structure (Berger, 1995) in the same direction. From a policymaker’s perspective, such consolidation is beneficial for both firms (which operate more efficiently) and consumers (who pay lower prices).

Choi and Weiss (2005) and Weiss and Choi (2008) develop an empirical framework for the ES hypothesis in the context of the U.S. nonlife insurance market following Berger (1995). A negative price-efficiency correlation and a positive profit-efficiency correlation support the ES hypothesis. They find that efficient insurers can charge lower prices while generating higher profits than inefficient insurers and thus have higher market shares. Berry-Stoelzle, Weiss, and Wende (2011) support the ES hypothesis in the European nonlife insurance market. Two alternative theories offer explanations for the market structure. Positive correlations between market share, price, and profit support the relative market power (RMP) hypothesis.31 Positive correlations between market concentration, price, and profit support

30 An important question in frontier efficiency studies is how the efficiency measure is related to the traditional measures

of firm profitability (Greene and Segal, 2004). We observe, as a corollary of ES hypothesis tests, a significant and positive correlation between cost efficiency and firm’s underwriting profit, but a much weaker positive correlation between cost efficiency and firm’s returns on equity. This finding is in general consistent with the findings for the U.S. life insurance industry (Greene and Segal, 2004).

31 The RMP assumes that consumers rely on a firm’s position in the market as an indicator of quality, thus predicting that larger firms have market power simply by virtue of their position in the market, which allows them to earn rents (Rhoades, 1985).


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the structure-conduct-performance (SCP) hypothesis. 32 We also test the RMP and SCP hypotheses.

The scale impact on cost efficiency (H1B) and the efficient structure hypothesis (H3) may be interconnected because: 1) the large size yields high cost efficiency via two channels that are scale and X-efficiency; 2) cost- efficient firms can charge a lower price without sacrificing profitability and thus attract more clients than inefficient firms can; and 3) the cost-efficient firms will increase in size either by natural growth or by acquiring less efficient firms. We introduce the Granger test to verify this potential interconnection.

In summary, the three hypotheses set out above have important implications for the structure of the global reinsurance market. If an industry’s technology allows for economies of scale (scope), the industry will tend to be made up of large (diversified) firms; alternatively, if technology does not allow such economies, small (specialized) firms will tend to dominate (Clark, 1988). Extant scale and scope economies indicate potential for market consolidation from the production perspective, and the competitive pricing advantages of cost-efficient firms also lead to this expectation.

3. Data and methodology

3.1. Data and summary statistics

Like Cummins and Weiss (2000), we found it difficult to discover a single coherent data source that contains all the information necessary to conducting a global reinsurance efficiency study. We thus use four sources: (1) Best’s Insurance Reports (A.M. Best, 2002–2012) database, which includes general and financial information on all non-U.S. reinsurers; (2) Standard and Poor’s Global Reinsurance Highlights (Standard and Poor’s Rating Services, 2003–2013), which includes a global reinsurance survey for each year and contains the most complete list of active reinsurers worldwide. We use them to identify U.S. reinsurers and fill in information missing from Best’s Insurance Reports; (3) annual reports of reinsurers (2002–2012), which is our major source for number of employees and financial information of U.S. reinsurers; and (4) the Best’s Special Report on Global Reinsurance (A.M. Best, 2013), from which we use the list of top 50 reinsurers to fill in missing values.

The global reinsurance market is dominated by professional reinsurers 33 (Holzheu and Lechner, 2007). Different approaches are taken in differentiating professional reinsurers from primary insurers (Beaver, McNichols, and Nelson, 2003; Cole and McCullough, 2006; Cummins and Weiss, 2000). Cole and McCullough (2008) find that the criteria used to

32 The SCP suggests that market concentration may foster collusion among firms in the market. Higher concentration

lowers the cost of collusion, resulting in monopoly rents (Weiss, 1974). 33 A professional reinsurer is a firm for which open market reinsurance is the major business. Primary insurers may also

engage in reinsurance business as a sideline.


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identify reinsurers significantly influences empirical outcomes–a standard empirical selection bias problem–and that efforts to unify the definition of reinsurer are inconclusive. Whether a company is a reinsurer or a primary insurer is much less clear-cut than whether a company is a life or a nonlife insurer. This is because some insurers sell both primary and reinsurance, and because the reinsurance transactions often cover a significant share of transactions between affiliated firms (e.g., subsidiaries reinsure their portfolios with their headquarters). This paper does not aim to solve the reinsurance definition problem, but instead we control for the influence that the selection criteria could have on the empirical results.

We follow a four-step algorithm to generate our sample of professional reinsurers. First, an insurer’s reinsurance premiums written must account for more than 50% of its total premiums written34 (Beaver, McNichols, and Nelson, 2003). Second, we eliminate multiple reinsurers within one reinsurance group and identify one unique operating entity that reflects the reinsurance business of the group. We focus on the reinsurance business share,35 setting the cut-off threshold at 50%. Only those entities above the threshold are considered as representative of the reinsurance group. Third, if multiple entities meet the representation criterion within a group, we select the one that is used as the A.M. Best Rating Unit, which separates out the entity best representing the reinsurance group’s operation and eliminates reinsurance transactions within a group or among affiliates. Fourth, we exclude Lloyd’s syndicates, captives, reinsurance pools, and “bridge reinsurers” that retain less than 20% of their gross premiums written.36 We employ year 2012 data for our identification procedure, and due to data limitations, assume consistency back to earlier years. Reinsurers that existed before 2012, but were not active in 2012, were usually bought by one of the other reinsurers in our sample, instead of going bankrupt.37 The poor performance of acquired reinsurers becomes an integral part of the acquiring reinsurers. Thus, we consider survivorship bias to be minimal. Our dataset is at the firm-year level, and thus we are not able to allocate firm-specific resources (e.g. firm assets) to its reinsurance and primary business separately, if the reinsurer operates both. However, this problem is mitigated by our reinsurer selection process,

34 In most cases, gross premiums are considered; if these are not available, we take net premiums. 35 Gross reinsurance premiums written of the identified entity divided by gross reinsurance premiums written of the group.

If gross premiums are not available, we take net reinsurance premiums. 36 Lloyd’s syndicates usually operate only core functions (e.g., underwriting) by themselves and outsource supporting

functions (e.g., HR, IT) to Lloyd’s market services. This practice leads to these firms having a very small number of employees. Thus, we cannot consider Lloyd’s syndicates as stand-alone firms. Only one-third of the business done by Lloyd’s market as a whole is reinsurance and thus they do not meet the criteria of professional reinsurer. Captives, reinsurance pools, and “bridge reinsurers” have operating models different from those of traditional reinsurers, and their financial results are not fully comparable to those of traditional reinsurers. Thus, we do not include them in our analysis.

37 We identified 14 cases that the professional reinsurers existed before 2012, but were not active in 2012, by reviewing the top 40 reinsurers each year in Global Reinsurance Highlights (2003–2012). All of them were bought by other reinsurers in our sample, e.g., GE insurance solutions was bought by Swiss Re. Cummins and Weiss (2000) also indicate that mergers and acquisitions of reinsurers usually happen within the reinsurance industry, with a purpose of risk diversification.


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where we ensure that the major business of the reinsurer is reinsurance and we select the operating entity that mostly reflects the firm’s reinsurance business.

Our final sample contains 116 professional reinsurers and 841 firm-years.38 The total net reinsurance premiums written by our sample in 2012 is USD 164 billion, representing 91% of the professional reinsurance market and 71% of the total global reinsurance market.39 The reinsurance business in our sample varies from treaty to facultative reinsurance and from proportional to non-proportional reinsurance; however, detailed information regarding the product mix is not available. The dataset covers the period from 2002 to 2012. We exclude observations with extreme values (i.e., outside the 1 and 99 percentiles) in operating expense ratio and business services ratio.40 These reinsurers with extreme values are mostly startups that do not yet underwrite reinsurance or runoff reinsurers, which are not comparable to and not in competition with regular reinsurers.

Table 1 presents the sample summary statistics and Appendix B presents the geographical and yearly distribution of our sample. 45% of reinsurers engage in both life and nonlife reinsurance; 16% of professional reinsurers write significant amounts of primary insurance business, having a reinsurance premium share between 50% and 95%; 25% of reinsurers operate as unaffiliated single firms, while the remaining firms operate as groups or affiliates with others. The average leverage ratio is 2.75, which is slightly higher than the leverage ratio of 2.13 found a decade ago by Cummins and Weiss (2000). The reinsurer studies must be conducted on the global (i.e., cross-country) level, because reinsurance risks must be shared across borders and the reinsurance market, by its nature of risk diversification, requires a global business portfolio. Even national reinsurers (e.g., China Re) assume significant portion of European, American, and South East Asia exposures and cede a significant portion of Chinese exposures through retrocessions. We thus assume that reinsurers operate in a global market and calculate a one-world frontier. Still the global reinsurers are heterogeneous in their size, geographical locations, product specialization, underwriting risk, and returns. It is thus important to manage potential heterogeneity problems in cross-country studies (Pasiouras and

38 Some values are missing from our dataset due to the unavailability of some inputs and outputs from any of our four

data sources. The most common missing values are number of employees. We fill in the missing information using predicted values that we extrapolated based on the observed information, e.g., using operating expenses to predict number of employees. We perform a robustness test by using only observed data, i.e. excluding observations with missing values, the results of which are consistent with our main analyses.

39 We use the total net reinsurance premiums written (USD 179.22 billion) from SandP Global Reinsurance Survey 2012 as the size of the global professional reinsurance market (Standard and Poor’s Rating Services, 2013). We use Swiss Re’s estimation of USD 230 billion in global reinsurance premiums in 2012 as the size of the global reinsurance market, which includes reinsurance assumed by both professional reinsurers and primary insurers (Swiss Re, 2013).

40 The operating expense ratio is defined as operating expenses divided by net premiums written. The business services ratio is defined as cost of materials and business services divided by total operating expenses. This trimming procedure excludes 4% firm-year observations from our sample. The business service ratio captures the tradeoff between using employees and using independent contractors, we thus exclude those firms operating under extreme outsourcing models.


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Gaganis, 2013). We thus always control for the market (or the firm) fixed effects through the analyses. Moreover, in a robustness test, we show a DEA specification that uses regional frontiers instead of one world frontier. The results are consistent with our conclusions.

3.2. Data envelopment analysis

We use input-oriented data envelopment analysis (DEA), assuming constant (CRS), variable (VRS), and non-increasing returns to scale (NIRS) to estimate efficient production frontiers separately for each year between 2002 and 2012 (Cook and Zhu, 2014; Cummins and Weiss, 2013), an empirical approach frequently employed in finance and insurance research (Leverty and Grace, 2010; Curi, Lozano-Vivas, and Zelenyuk, 2015).41 The model allows computing the Shephard (1970) input-oriented distance functions, which are reported as the reciprocal of Farrell’s (1957) input efficiency measures. The resulting measures of cost (CE), allocative (AE), pure technical (PTE), and scale (SE) efficiency represent the firm’s distance from the respective best-practice efficient frontier and are bounded between 0 and 1. Moreover, we estimate X-efficiency (XE) as CE divided by SE or as the product of PTE and AE (Cummins et al., 2010; Weiss and Choi, 2008). Table 2 summarizes the definitions of DEA terms.42

41 Regarding the process of the DEA linear programming methods, we refer to Eling and Luhnen (2010) and Cummins

and Weiss (2013) for the detailed discussion. 42 We focus on cost efficiency and exclude revenue efficiency from our analyses, because the revenue efficiency becomes

important when consumers are willing to pay for the extra convenience of one-stop shopping (Berger et al., 2000) for multiple products and/or for large quantity of one product. However, the one-stop shopping effects are minimal in the reinsurance market because (1) commercial buyers are more interested in tailored specialized services (Berger et al. 2000); (2) reinsurance buyers usually have a specialized team to handle reinsurance cessions (e.g. reinsurance department or actuarial department) and to compare the reinsurance products and providers in the reinsurance market; (3) the deep involvement of reinsurance brokers reduces the cost of shopping around; (4) the risk diversification considerations are also against one-stop shopping.


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Table 1 Summary statistics Unit Mean Std. Dev. Min. 10th PTCL Median 90th PTCL Max. Panel A: Input Quantities Number of employees 1 538.5 1,572.5 2h 38 122 1,038 11,702 Quantity of materials and business services 1,000 539,130 2,008,515 166.5 7,838 94,785 707,956 19,888,900 Equity capital and surplus a 1,000 1,919,850 4,845,149 626.7 44,592 416,072 4,223,843 39,919,200 Panel B: Input Prices Wage a 1 47,215.6 26,137.7 1,394 13,782 48,642 71,741 138,017 CPI with base year of 2012 % 88.5 12.1 32.2 76.1 91.5 100 101.3 PPI with base year of 2012 b % 87.4 13.2 32.2 70.7 91.2 100 112.8 ROE 1 0.099 0.17 -2.27 -0.011 0.099 0.23 1.69 MSCI yearly rates of equity total returns 1 0.14 0.15 -0.058 0.011 0.11 0.25 1.48 Panel C: Output Quantities Total invested assets a 1,000 8,332,645 33,878,375 926.0 71,407 844,445 11,022,524 277,719,424 Smoothed loss a 1,000 1,467,686 5,055,169 730.5 17,791 241,395 2,351,311 43,623,480 Net premiums written a 1,000 2,110,135 7,197,933 945.7 27,166 369,349 3,613,961 66,319,992 Panel D: Others Total assets a 1,000 11,581,832 44,005,533 2,149.8 96,468 1,276,144 15,440,389 342,956,544 Composite c,d dummy 0.45 0.50 0 0 0 1 1 Conglomerate c,e dummy 0.16 0.37 0 0 0 1 1 Unaffiliated c,f dummy 0.25 0.43 0 0 0 1 1 Leverage ratio 1 2.75 3.23 0.054 0.56 1.77 5.84 34.4 Loss ratio % 67.0 25.0 1.20 43.2 65.1 88.6 284.5 Smoothed loss ratio g % 65.9 6.87 44.5 57.3 65.7 74.6 96.8 Operating expenses ratio % 30.6 11.1 2.70 17.3 29.8 43.8 82.1 Smoothed underwriting profit ratio (1-smoothed loss ratio) % 3.44 11.1 -59.1 -7.23 3.92 15.6 40.0 Market growth % 6.72 8.38 -8.10 -2.90 7.30 14.4 33.1 Price of reinsurance (inverse of smoothed loss ratio) 1 1.53 0.16 1.03 1.34 1.52 1.75 2.25 Number of firm-year observations 841 Number of Firms 116

Notes: a In USD and inflation adjusted at 2012. b For the following countries or regions, PPIs are not available, and are thus replaced by CPIs: Barbados, Bermuda, Cayman Islands, Dominican Republic, Ghana, Kenya, Lebanon, and Nigeria. c Information is only available for the year of 2012, and we assume the status is unchanged for one firm over our sample period. d Composite equals 1 if the reinsurer engages in both life and nonlife business. e Conglomerate equals 1 if the primary insurance premium takes more than 5% and less than 50% of the total premium written. f Unaffiliated equals 1 if the reinsurer is an unaffiliated single firm. g The smoothed loss ratios are calculated based on the actual loss ratios following the procedure in Cummins and Xie (2008), described in Appendix A. h The small number of employees is a result of estimated employee number (see footnote 14), where the actual number of employees is missing.


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Table 2 DEA efficiency terms Abbreviation Description Components Cost Efficiency CE Minimum (optimal) costs / observed (actual) costs SE*PTE*AE

or SE*XE Scale Efficiency SE Equals 1 if constant returns to scale, less than 1 if

various (increasing or decreasing) returns to scale N.A.

X-Efficiency XE The part of cost efficiency that cannot be explained

by scale efficiency CE/SE or PTE*AE

Pure Technical Efficiency

PTE

Technical efficiency on various returns to scale, capturing the relative production technology the firm explores (the part of technical efficiency that cannot be explained by scale efficiency)

N.A.

Allocative Efficiency AE Efficiency to allocate resources among different

inputs N.A.

We exploit the variation of efficiency estimates for the different production frontiers of a reinsurance firm to make inferences about scale economies (Aly, Grabowski, Pasurka, and Rangan, 1990), that is, to discover whether a firm operates under increasing (IRS) or decreasing (DRS) returns to scale if it is scale inefficient.43 By definition, the scale efficient firms operate under constant returns to scale (CRS). Simar and Wilson (2000) suggest a bootstrapping bias-correction procedure for DEA analysis. This approach, however, leads to bootstrapping bias for different frontiers (i.e., CRS, VRS, and NIRS) and the results cannot be easily used to make inferences about returns to scales. This is why we present the original efficiency estimates throughout the paper and show results subject to the bootstrapping bias-correction procedure as a robustness test, which support our conclusions.

Compared to accounting performance measures (e.g., ROE, ROA), the advantage of DEA is that the resulting cost efficiency measure can be decomposed into several components, shedding light on the process through which scale and scope affect cost efficiency. This is particularly useful in analyzing the market structure. The decompositions can directly explain the paradox that on the one hand, microeconomic theory predicts that firms failing to attain cost efficiency will not survive in the market in the long-run; and on the other hand, many firms are relatively cost inefficient. As we will show later, the decomposition of DEA cost efficiency has a strong power to explain this empirical fact. The peer comparison concept of DEA is informative and important, as managers have to measure their performance against the best practice in the industry. Moreover, the DEA decompositions inform the management

43 According to Aly et al. (1990), if a firm’s technical efficiency against the VRS frontier is smaller than its technical

efficiency against the NIRS frontier, then it operates under IRS; if a firm is scale in efficient and its technical efficiency against VRS frontier equals to that against NIRS frontier, then it operates under DRS.


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as to which direction or component the firm should improve (scale, techniques, or resource allocation), in order to catch up with the best practice.44

For DEA input quantities, we use labor (number of employees), materials and business services45, and total equity capital (in real values at 2012), following the common practice in the insurance DEA studies (Cummins and Weiss, 2013). The number of employees is from annual reports of the respective reinsurers. We use the annual average wages for the insurance sector (banking, if insurance is not available) in respective country-years as the price of labor. The wage information is obtained from the ILO Main Statistics and October Inquiry databases. 46 The total employee costs are therefore equal to the product of number of employees and the annual average wage in respective countries. The quantity of materials and business services is calculated as operating expenses minus employee costs, following the procedure in Cummins and Weiss (2013). We proxy the price of materials and business services by the consumer price indices (CPI) of respective country-years. Production price indices (PPI) are used as a robustness test. We approximate total equity capital by capital and surplus in Best’s Insurance Reports (A.M. Best, 2002–2012). We use the average realized ROE of respective years as the price of equity capital. The yearly rates of total return from Morgan Stanley Capital International (MSCI) Indices in respective countries are used as a robustness test.47 Some insurance efficiency studies also use debt capital as an additional input, accounting for insurers raising debt capital by issuing insurance policies and “intermediate” the debt capital into invested assets. However, Cummins and Weiss (2013) argue that it is improper to use debt capital as an input, because insurance reserves, the major part of debt capital, have characteristics of both inputs and outputs. We include debt capital in one of our robustness tests, in response to the concern for DEA sensitivities to the number of inputs. In fact, we observe some changes in our findings which support Cummins and Weiss’s (2013) argument that the mixed character of debt capital as input and output limits its usability.

44 The DEA frontier efficiency measures also have limitations that restrict their application in practice. First, DEA is a

relative measurement, which changes with the development of the industry every year. The dynamic nature on one side captures the full picture of changes in a firm, but on the other side may not meet the static requirement of regulations. Second, the complication in inputs and outputs of DEA method limit its use in daily management decisions. However, these limitations underscore the urgency of having researchers carefully practice the DEA method through the full range of robustness tests on inputs and outputs, statistical methodologies, and sample selections. We address these aspects in the section “Robustness tests.”

45 Materials and business services are usually combined together in insurance DEA studies to represent the remaining part of insurer’s operating expenses other than employee expenses. It is includes items like travel, communications, and advertising (Eling and Luhnen, 2010) and usually not further subdivided due to data limitation. There is a tradeoff between using own employees and outsourcing functions. A part of the materials and business services captures outsourcing expenses and the input of labors capture the employee expenses. We thus expect the tradeoff has no significant influence on our estimated DEA efficiency scores.

46 Wage is not available for all country-years, so we proxy the price of labor by adjusting the nearest available data point to the previous or later year using CPIs.

47 A rolling window of 10-year averages is used. The remaining negative values are censored at 0. The MSCI Indices are obtained from the Thomson DataStream database.


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For DEA output quantities, we use smoothed losses and total invested assets (both in real values at 2012). These represent a reinsurer’s two major functions: risk pooling (risk bearing) and financial intermediation. Reinsurers also act as think tanks and serve as consultants to primary insurers; however, they do not usually charge for such services, but offer them as a door to acquiring new business. Therefore, the consulting function is integrated into, and reflected by, the output of loss. The loss reflects the quantity of risks that the insurer pools together and redistributes. More losses indicate more risks. Thus, loss measurements are widely used in insurance DEA studies as the output (Cummins and Weiss, 2013). We calculate the smoothed losses with the loss-smoothing procedure in Cummins and Xie (2008), described in Appendix A. This procedure is particularly well-suited for the highly volatile losses of PandC and reinsurance, because it corrects the potential “error in variables” problem due to the randomness nature of losses (Cummins and Xie, 2013). Premiums are sometimes used as an alternative output to loss, since premiums represent the business volume produced, although Yuengert (1993) points out that premiums represent price times quantity, instead of just quantity. We include a Robustness test relying on net premiums written, instead of smoothed losses, as the output, the results of which are consistent with our core models. We approximate total invested assets by total investments in Best’s Insurance Reports (A.M. Best, 2002–2012).

After deriving the DEA efficiency scores, we perform DEA second stage regressions48 as shown in Equation (1) (Cooper, Seiford, and Zhu, 2011). As we hypothesized, we explain the differences in efficiencies by the firm’s scale and scope. Hypotheses predict nonlinear relationship between firm size and efficiency. Therefore, we use the natural logarithm of real total assets and its squared term to capture the nonlinear size effects. Each lnAsset is centered at the mean of all firm-year lnAsset values to avoid multicollinearity between size and its square. l𝑛𝑛𝑛𝑛𝑅𝑅𝑅𝑅𝐶𝐶𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐 = lnAsseti,t − lnAsset��, where lnAsset�� is the average of all firm-

years, and all asset values are inflation adjusted at 2012. We capture the scope of a reinsurer by two dummy variables. The dummy variable composite measures a reinsurer’s product diversification across life and nonlife business. The dummy variable conglomerate measures the reinsurer’s product diversification across reinsurance and primary insurance. X is a series of control variables, including leverage ratio (total liabilities divided by total equity and surplus), affiliation status (1 if the reinsurer is an unaffiliated single firm), headquarter

48 There is a debate on whether DEA second stage regressions are appropriate. One of the concerns is that the factors used

to derive the efficiency scores should not appear again as the explanatory variable in the second stage regressions. We comply with this requirement. We refer to Cooper, Seiford, and Zhu (2011) for the detailed discussion regarding the DEA second stage regression.


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location dummies (market fixed effects), and year dummies (time fixed effects). 49 After controlling for the market and year fixed effects, we use random effects panel regressions legitimated by Hausman and log-likelihood ratio tests. 50 We conduct firm fixed effects regressions, as well as the Tobit and Truncated (Simar and Wilson, 2007) regressions as robustness tests, the results of which are consistent with our core models. We also include the interaction term between scale and scope in a robustness test, the results of which are consistent with our conclusions.

𝐸𝐸𝑓𝑓𝑓𝑓𝑅𝑅𝐸𝐸𝑅𝑅𝐶𝐶𝑛𝑛𝐸𝐸𝐸𝐸𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + 𝛽𝛽1𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶𝑖𝑖,𝑐𝑐 + 𝛽𝛽2𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶𝑖𝑖,𝑐𝑐2 + 𝛽𝛽3𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶𝑖𝑖 + 𝛽𝛽𝑗𝑗𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (1)

Based on the IRS, CRS, and DRS differentiation, we conduct a multinomial logistic regression (Greene, 2012) to assess drivers of returns to scale (RTS) as specified in Equation (2) (Cummins and Xie, 2013). The explanatory variables used in Equation (2) are the same as those in Equation (1). This additional analysis further demonstrates the robustness of our economics of scale hypothesis (H1A).

𝑅𝑅𝑅𝑅𝑆𝑆𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + 𝛽𝛽1𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶𝑖𝑖,𝑐𝑐 + 𝛽𝛽2𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶𝑖𝑖,𝑐𝑐2 + 𝛽𝛽3𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶𝑖𝑖 + 𝛽𝛽𝑗𝑗𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (2)

4. Empirical results

4.1. Efficiency estimations

Table 3 reports the estimated DEA efficiency scores. We show the average efficiency scores by year and by size (i.e., small, medium, and large).51 In the two right-hand columns of the table, we present the average efficiency scores for all firm-years in aggregate and the number of efficient firm-years (the efficient score equals 1). The results suggest that small reinsurers are significantly less scale-efficient than medium and large reinsurers in all years. For PTE, both small and large reinsurers are more efficient than medium reinsurers; this is true for six out of eight significant results and true for all firm-years in aggregate. The AE trend by size categories is largely insignificant. XE has the same pattern as PTE: small reinsurers are more (less) X-efficient than medium (large) reinsurers; this is true for seven out of eight significant results and true for all firm-years in aggregate. Combining the results of SE and XE, we observe that CE scores increase with firm size in all years, indicating initial support for Hypothesis 1B.

49 In Appendix 2, we present the distribution of our sample over years and by geographical regions. We group the

domiciled locations of reinsurers into four reinsurance hubs and six additional regional markets. The reinsurance hubs are Western Continental Europe, North America, Bermuda, and London (Holzheu and Lechner, 2007). The additional regional markets include Asia Developed, Asia Emerging, Africa, Eastern Europe, Latin America, and Middle East.

50 The Hausman test discriminates fixed from random effects models and gives the Chi-square statistic of 11.71 (p-value of 0.63). The log-likelihood ratio test discriminates random effects models from pooled OLS regressions and gives Chi-bar-square statistic of 94.52 (p-value of 0.00).

51 We rank all firms by their total asset in each year and define the largest one-third as large, the smallest one-third as small, and the rest as medium (Biener, Eling, and Wirfs, 2015; Luhnen, 2009).


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Table 3 DEA efficiency scores Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 All b E=1c Observations 46 52 50 50 80 81 81 97 105 101 98 841 Panel A: SE

All 0.867 0.920 0.946 0.709 0.652 0.789 0.841 0.876 0.763 0.873 0.885 0.826 95 Small 0.712 0.851 0.871 0.438 0.389 0.544 0.660 0.755 0.567 0.693 0.747 0.648 14 Medium 0.954 0.976 0.984 0.812 0.689 0.848 0.904 0.958 0.861 0.950 0.964 0.899 24 Large 0.946 0.938 0.984 0.888 0.888 0.975 0.960 0.917 0.863 0.978 0.944 0.931 57 P-value a 0.000 0.007 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Panel B: PTE All 0.740 0.685 0.722 0.631 0.560 0.656 0.625 0.658 0.533 0.702 0.693 0.648 157 Small 0.666 0.550 0.646 0.698 0.692 0.626 0.638 0.680 0.610 0.708 0.703 0.657 44 Medium 0.781 0.736 0.723 0.509 0.420 0.569 0.529 0.595 0.438 0.613 0.644 0.582 28 Large 0.778 0.778 0.803 0.691 0.570 0.773 0.710 0.700 0.553 0.789 0.734 0.704 85 P-value a 0.215 0.010 0.073 0.056 0.000 0.002 0.012 0.125 0.013 0.004 0.203 0.000 Panel C: AE All 0.830 0.818 0.873 0.792 0.667 0.659 0.543 0.804 0.624 0.515 0.852 0.706 19 Small 0.870 0.876 0.903 0.806 0.631 0.744 0.565 0.781 0.571 0.483 0.833 0.771 2 Medium 0.772 0.750 0.812 0.763 0.700 0.595 0.543 0.814 0.639 0.440 0.869 0.687 4 Large 0.844 0.825 0.906 0.809 0.672 0.638 0.520 0.817 0.663 0.627 0.855 0.731 13 P-value a 0.144 0.024 0.034 0.630 0.489 0.007 0.640 0.652 0.142 0.006 0.676 0.060 Panel D: XE All 0.601 0.546 0.625 0.487 0.348 0.418 0.325 0.514 0.304 0.362 0.575 0.445 19 Small 0.565 0.481 0.579 0.545 0.410 0.451 0.337 0.504 0.328 0.338 0.566 0.444 2 Medium 0.595 0.532 0.576 0.371 0.264 0.317 0.275 0.477 0.249 0.260 0.541 0.385 4 Large 0.645 0.628 0.725 0.548 0.369 0.485 0.362 0.562 0.334 0.493 0.619 0.506 13 P-value a 0.433 0.079 0.023 0.010 0.005 0.000 0.070 0.159 0.018 0.000 0.193 0.000 Panel E: CE All 0.520 0.499 0.593 0.335 0.211 0.325 0.268 0.447 0.219 0.319 0.507 0.368 19 Small 0.388 0.400 0.503 0.220 0.143 0.231 0.207 0.374 0.170 0.234 0.419 0.281 2 Medium 0.571 0.519 0.569 0.311 0.179 0.270 0.248 0.458 0.214 0.245 0.523 0.353 4 Large 0.610 0.584 0.714 0.483 0.315 0.474 0.349 0.512 0.274 0.485 0.581 0.471 13 P-value a 0.001 0.013 0.004 0.000 0.000 0.000 0.001 0.004 0.000 0.000 0.001 0.000 Notes: We present arithmetic means of respective efficiency scores; the standard deviations of each mean values are available from the authors upon requests. a We perform mean difference F-tests to examine whether the average efficiency scores in different size categories are equal to each other. b We acknowledge the concerns regarding whether the efficiency scores across years can be aggregated and/or compared, when the efficiency frontier is estimated for each year separately. However, the aggregation of yearly results is prevalent in previous insurance DEA studies (see e.g. Cummins and Xie, 2013; Biener et al., 2015). This paper does not discriminate the two practices, but shows both the yearly and the aggregate results, which yield very similar patterns. c This column show the number of efficient firm-years (i.e. efficiency score=1) in respective size categories.


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4.2. Economies of scale

We follow Aly et al. (1990) to determine whether scale-inefficient firms operate under IRS or DRS. Firms with a SE score of 1 operate under CRS. The results in Table 4 show that 68% of reinsurers operate under IRS, 11% under CRS, and 21% under DRS. Large reinsurers are more likely to exhibit CRS and DRS, and small reinsurers have a higher proportion of IRS entities. We follow Cummins and Zi (1998) and Cummins and Xie (2013) to identify the size thresholds at which scale economies are exhausted. All firm-year observations are split into ten size deciles according to their real total assets, so that each decile contains an equal number of observations. To get a more detailed picture, we further separate our sample into 20 size vigintiles.

The results in Columns 1 to 6 of Table 4 suggest two critical points for total assets: below USD 4.3 billion, over 74% of reinsurers operate under IRS; none of the insurers with assets above USD 15.5 billion operate under IRS, but 71% of these operate under DRS. This finding supports Hypothesis 1A in the sense that small reinsurers are more likely to operate under IRS and the largest reinsurers are more likely to operate under DRS. In looking at the means of SE scores (Columns 7 and 8), we observe one significant jump from the 15th vigintile (2.04B-2.90B) to the 16th vigintile (2.90B-4.30B) in Panel B of Table 4, and one significant drop from the 9th decile (7.60B-15.50B) to the 10th decile (>15.50B) in Panel A of Table 4. Thus, we extend the optimal size range downwards to include the 16th vigintile as USD 2.9 – 15.5 billion52. The existence of a size range with significantly higher scale efficiency scores again confirms our Hypothesis 1A. Comparing our reinsurance results with the primary insurance industry, we note that the asset size at which reinsurer scale economies are exhausted is much larger than that of life insurers (USD 1 billion; see Cummins and Zi, 1998) and that of nonlife insurers (USD 137.1 million; see Cummins and Xie, 2013). The global nature of the reinsurance business may explain these differences.

We are not able to show the decile and vigintile analyses by year but in the aggregate of all years due to the small number of observations. We acknowledge the concerns regarding whether the efficiency scores across years can be aggregated and/or compared, when the efficiency frontiers are estimated for each year separately. We address this deficiency with regression analyses shown in Equation (1) and (2). The regression incorporates control variables, particularly the year fixed effects, which thus controls for the differences resulting from the yearly frontiers.

52 The range of USD 12.6 billion (2.9-15.5 billion) is a wide one in terms of absolute value; however, it is only 28.6% of

one standard deviation (USD 44.0 billion) of our sample reinsurers’ total assets. It is thus a relatively accurate range considering the whole size spectrum of reinsurers.


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Table 4 Returns to scale and mean scale efficiency scores (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Total Assets IRS CRS DRS IRS CRS DRS Mean of SE

Std. of SE

Firm-Years

Firms

Panel A: Size Deciles Firm-Years Percentage < 97 M 81 4 0 95% 5% 0% 0.545 (N.A.) 0.237 85 17

97M–237M 78 3 3 93% 4% 4% 0.679*** 0.228 84 22 237M–435M 75 5 4 89% 6% 5% 0.682 0.207 84 29 435M–795M 79 4 1 94% 5% 1% 0.809*** 0.174 84 28 795M–1.28B 79 4 1 94% 5% 1% 0.897*** 0.124 84 28 1.28B–2.04B 66 11 7 79% 13% 8% 0.911 0.114 84 25 2.04B–4.30B 62 10 12 74% 12% 14% 0.951*** 0.062 84 23 4.30B–7.60B 32 16 36 38% 19% 43% 0.966* 0.046 84 22 7.60B–15.5B 20 14 50 24% 17% 60% 0.963 0.051 84 17

> 15.5B 0 24 60 0% 29% 71% 0.858*** 0.151 84 12 Total 572 95 174 68% 11% 21% 0.826 0.207 841 116 b

Panel B: Size Vigintiles a 2.04B–2.90B 31 6 5 74% 14% 12% 0.939 0.067 42 17 2.90B–4.30B 31 4 7 74% 10% 16% 0.963* 0.056 42 17

Notes: *, **, *** denote significance levels at 10%, 5%, and 1% of mean difference t-tests between two adjacent size classes. The first SE mean has no smaller category to compare with, and thus is marked as N.A. a We show the vigintile results that are critical to identify the optimal size range. The complete results are available from the authors upon request. b The total number of firms does not equal to the sum of firms in each sub-category because one firm could fall into different categories in different years.

We apply the DEA second-stage regression to SE scores, as defined in Equation (1). The results in Column 1 of Table 5 show that SE increases with firm size at a decreasing rate, then reaches optimal size, and subsequently decreases with firm size. The pattern confirms H1A. Next, we obtain the predicted SE scores from this regression and extract top 10% scale-efficient firm-year observations to visualize the optimal asset range as shown in Figure 1. A similar approach is found in Berger and Humphrey (1991) and McAllister and McManus (1993). The two vertical lines with USD 2.9 billion and 15.5 billion mark the asset range identified by the decile and vigintile analyses. The box plots in Figure 1 show that for the top 10% scale-efficient observations, total asset values within the 25th and 75th percentiles fall into the two vertical lines, i.e., into the identified optimal size range. The histogram in Figure 1 suggests that around 60% of the top 10% scale-efficient observations have total assets within the identified optimal size range. The inspection of the visualized kernel density distribution serves as a further indicator of the robustness of the identified optimal size range.


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Table 5 Determinants of efficiencies (1) (2) (3) (4) (5) Variables SE PTE AE XE CE lnAsset 0.0355*** -0.0202* 0.0359*** 0.0173* 0.0314*** (0.00652) (0.0112) (0.00856) (0.00937) (0.00926) lnAsset2 -0.00956*** 0.00741*** -0.000356 0.00573** -0.000743 (0.00159) (0.00244) (0.00204) (0.00237) (0.00201) Composite 0.0135 0.0100 -0.0758*** -0.0456** -0.0271 (0.0151) (0.0329) (0.0233) (0.0218) (0.0199) Conglomerate 0.0185 0.0108 -0.0350 -0.0363 -0.0272 (0.0184) (0.0479) (0.0358) (0.0350) (0.0301) Leverage ratio 0.00466*** 0.0161*** -0.00233 0.00922** 0.0108** (0.00151) (0.00218) (0.00409) (0.00449) (0.00478) Unaffiliated -0.0273 0.0330 0.00617 0.0214 0.00848 (0.0276) (0.0451) (0.0277) (0.0277) (0.0268) Market fixed effects /year FE /constant Yes Yes Yes Yes Yes

Overall R2 a 0.577 0.353 0.380 0.454 0.562 Observations/number of reinsurers 841/116

Notes: We present the results of random effects panel regressions with robust standard errors clustered at firm level provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


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(a) Box plots

(b) Histogram and kernel density distribution

Figure 1 Optimal size range

Notes: The box plots show the lnAsset distribution for the top 10% scale-efficient firm-years compared with the 90% non-scale-efficient firm-years. The histogram and estimated kernel density show the lnAsset distribution for the same top 10% scale-efficient observations. The two vertical lines in both figures show the optimal size range obtained from the decile and vigintile analyses. The asset values used are in thousand U.S. dollars.


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We apply the multinomial logistic regression on Equation (2) to verify our results concluded from returns to scale analyses controlling for the firm-specific characters, market-fixed effects, and year- fixed effects. The results in Table 6 show that, the probability of operating under IRS negatively relates to firm size and the probability of operating under CRS and DRS positively relates to firm size. The impact of size on the probability of operating under DRS is significantly larger than its impact on CRS, subject to a T-test. This additional evidence again supports our H1A in the sense that small reinsurers are more likely to operate under IRS, medium-sized reinsurers are more likely to operate under CRS, and the largest reinsurers are more likely to operate under DRS.

Table 6 Determinants of returns to scale Variables IRS CRS DRS lnAsset -0.163*** 0.0199** 0.143*** (0.0511) (0.00801) (0.0501) lnAsset2 -0.00564 0.00341** 0.00222 (0.00922) (0.00172) (0.00838) Composite 0.0467 -0.0106 -0.0361 (0.0337) (0.0156) (0.0279) Conglomerate 0.0807** -0.0164 -0.0643* (0.0366) (0.0140) (0.0331) Leverage ratio 0.01000 0.00540*** -0.0154* (0.00839) (0.00153) (0.00839) Unaffiliated -0.0165 0.0294 -0.0128 (0.0416) (0.0364) (0.0401) Market FE/year FE/constant Yes Yes Yes Pseudo R2 0.451 Observations/number of reinsurers 841/116

Notes: We present the marginal effects of multinomial logistic regressions with robust standard errors clustered at firm level provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.

4.3. Scale impact on cost efficiency

To assess the scale impact on the overall cost efficiency and X-efficiency, we estimate Equation (1) with PTE, AE, XE, and CE scores, as shown in Columns 2 to 5 of Table 5. The results in Column 5 confirm Hypothesis 1B by showing that reinsurers’ cost efficiency scores increase along with firm size. The PTE results in Column 2 suggest a U-shaped relationship between firm size and PTE. Both small and large reinsurers are more likely to employ the best technologies than are medium-sized reinsurers. The results in Columns 3 suggest a positive linear relationship between firm size and AE. The X-efficiency results in Columns 4 show the combined effects of PTE and AE.

Large reinsurers are indeed the most cost efficient because they define the best-practice technology frontier and best allocate their costs among different inputs. Their advantages in XE offset the extant scale inefficiencies (scale diseconomies). Small reinsurers are also able


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to exploit the best-practice technologies (Sui and Baum, 2014); the superior PTE of some small reinsurers may result from their expertise in special segments (a focused strategy), which we will test in a later section of this paper. With respect to the control variables, there is a positive correlation between leverage and efficiency, and no significant correlation between firm affiliation type and efficiency. Reinsurers based in Western Continental Europe, the world reinsurance center, are more cost efficient than reinsurers in other regions.

4.4. Economies of scope

We follow an approach similar to that of Cummins et al. (2010) in assessing the scope impact on efficiencies so as to make inferences about economies of scope.53 The results in Column 5 of Table 5 show that product diversification, both composite (life/nonlife) and conglomerate (primary-/reinsurance), do not have a significant impact on reinsurer cost efficiency. However, the results in Columns 3 and 4 suggest that composite strategies (i.e., underwriting both life and nonlife business) increase the difficulty of cost allocation of multiple inputs, and thus decrease AE as well as XE.

We further examine economies of scope for different sizes of reinsurers (Berger et al., 2000) by sorting our sample into small, medium, and large reinsurers as in Table 2. We focus on X-efficiency, which excludes economies of scale and thus allows assessing the pure economies of scope (Cummins et al., 2010) and on cost efficiency. The results in Column 1 (Column 6) of Table 7 suggest that the negative impact of product diversification on XE (CE) only holds for small reinsurers, for which specialized strategies are more X-efficient (cost-efficient) than composite strategies. The observation supports Hypothesis 2A in the sense that small reinsurers are better off when specialized (Sui and Baum, 2014). The results in Columns 2, 3, 7, and 8 show that for medium and large reinsurers, the impact of product diversification is insignificant. Alternatively, we test Hypothesis 2 by adding dummy indicators for small-specialized and large-diversified reinsurers, as shown in Columns 4 and 5 (Column 9 and 10) of Table 7. The results confirm that small specialized reinsurers are more X-efficient and more cost-efficient. These observations again confirm H2A and explain why both specialized and diversified reinsurers can co-exist in the global reinsurance market. Concerning Hypothesis 2B, for large reinsurers, we find no significant evidence to support a conglomeration strategy, however, we are also not able to conclude a favor for strategic focus strategy. In a robustness test, we include the interaction term between scale and scope, the results become less significant due to multicollinearity but suggest the same direction of our conclusions.

53 An alternative way of analyzing economies of scope is to show that the cost of jointly producing multiple outputs is

smaller than the cost of separately producing these outputs (Berger et al., 2000). We cannot adopt this approach because our data do not allow the separation of losses between life and nonlife business, nor between primary and reinsurance. This approach furthermore requires specifying a cost function, yielding model misspecification risk.


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Based on the above findings, we argue that the scope and scale of a reinsurer’s operation need to be compatible with each other in order for the firm to be efficient. The small reinsurers are better to be specialized; while the large ones may consider to diversify the scope of business. Our findings do not support Borch’s (1962) prediction that full diversification is optimal for all types of reinsurers. We show, however, that significant cost scope diseconomies prevent small reinsurers from reaching full diversification.

Looking at the scope impact in Table 6, we note that product-diversified reinsurers are in general more likely to operate under IRS than are specialized reinsurers, and are less likely to operate under DRS. This is particularly true if considering the product diversification across primary and reinsurance business. Similar patterns are also found in primary insurance (Cummins and Xie, 2013). One explanation is that product diversification increases the size required for a firm to become scale efficient, such that firms that expand their scope need time to grow to the new size optimal for their broader scope (Cummins and Xie, 2013). The more diversified a firm, the larger it needs to be to reach scale efficiency. Firms originally operating under DRS become IRS or CRS after increasing scope, and firms originally operating under CRS become IRS. This also explains the insignificant impact of diversification on the probability of operating under CRS and on scale efficiency. The finding is also consistent with the rationale that the scope and scale of a reinsurer must match with each other.


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Table 7 Scope impact on reinsurers (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Subsamples Small Medium Large Full Sample Small Medium Large Full Sample Variables XE XE XE XE CE CE CE CE Small*Specialized 0.0882*** 0.0574*** (0.0219) (0.0198) Large*Composite 0.0420 0.0120 (0.0341) (0.0297) Small*Focused 0.0760*** 0.0468** (0.0204) (0.0184) Large*Conglomerate 0.0404 -0.00497 (0.0585) (0.0382) Composite -0.109*** -0.0100 -0.0752 -0.0256 -0.0403* -0.0518** 0.00719 -0.0843 -0.00906 -0.0232 (0.0263) (0.0381) (0.0620) (0.0259) (0.0213) (0.0225) (0.0394) (0.0616) (0.0254) (0.0200) Conglomerate -0.00687 -0.0348 -0.0668 -0.0350 -0.0315 -0.0582 -0.0325 -0.0562 -0.0248 -0.0184 (0.0440) (0.0413) (0.0637) (0.0360) (0.0387) (0.0510) (0.0401) (0.0601) (0.0309) (0.0337) lnAsset -0.125** 0.0192 -0.0480 0.0270*** 0.0273*** 0.0266 0.0439* -0.0766 0.0367*** 0.0368*** (0.0506) (0.0220) (0.0778) (0.00992) (0.0100) (0.0367) (0.0238) (0.0824) (0.00992) (0.00985) lnAsset2 -0.0134* 0.0345 0.0156 0.00456** 0.00454* -0.000311 0.00538 0.0172 -0.00149 -0.00154 (0.00696) (0.0372) (0.0144) (0.00229) (0.00235) (0.00545) (0.0352) (0.0145) (0.00192) (0.00194) Leverage ratio 0.0410*** 0.00323 0.0172*** 0.00927** 0.00965** 0.0276** 0.00321 0.0207*** 0.0106** 0.0110** (0.0110) (0.00384) (0.00478) (0.00424) (0.00411) (0.0112) (0.00408) (0.00481) (0.00462) (0.00453) Unaffiliated -0.0266 -0.0328 0.0671 0.0153 0.0125 -0.00163 -0.0377 0.123 0.00564 0.00279 (0.0271) (0.0335) (0.106) (0.0262) (0.0274) (0.0259) (0.0370) (0.0893) (0.0264) (0.0276) Market FE/year FE /constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Overall R2 0.496 0.518 0.531 0.466 0.461 0.607 0.561 0.564 0.566 0.561 Observations 281 280 280 841 841 281 280 280 841 841 Number of reinsurers 54 54 38 116 116 54 54 38 116 116



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4.5. Efficient structure

Following Berry-Stoelzle, Weiss, and Wende (2011), Choi and Weiss (2005), and Weiss and Choi (2008), we estimate reinsurers’ price and underwriting profit based on the model in Equations (3a) and (3b). As Berger (1995) suggests, we include the direct measurements of scale- and X-efficiency in the regression, together with market share and concentration measurements. This equation is shown to be a valid reduced form for the ES hypothesis as well as its competing RMP and SCP hypotheses (Berger, 1995).

We measure the reinsurance unit price as the inverse of the smoothed loss ratio (for detailed discussions on defining insurance price, see Cummins and Danzon, 1997; Winter, 1994). The underwriting profit is defined as one minus the smoothed loss ratio minus the expense ratio (Choi and Weiss, 2005; Weiss and Choi, 2008). We use ROE to measure the overall profitability of a reinsurer. Instead of the smoothed loss ratios, in a robustness test, we also use the actual loss ratios for the price and profit measurements. CE, SE, and XE approximate firm efficiency. Other independent variables include the market share of each firm in a given year, the reinsurance market growth rate per year, and the market concentration, measured by the market shares of the 10 largest reinsurers in respective years. X is a series of control variables, including leverage ratio, affiliation status, headquarter location dummies (market fixed effects). Different from Equation (1) and (2), year dummies are not included in Equation (3) due to the multicollinearity with market growth and market concentration.54 We perform a Robustness test with firm and year fixed effects regressions.

𝑃𝑃𝐶𝐶𝐶𝐶𝑓𝑓𝑅𝑅𝑡𝑡𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + 𝛽𝛽1𝑋𝑋_𝐸𝐸𝑓𝑓𝑓𝑓𝑅𝑅𝐸𝐸𝑅𝑅𝐶𝐶𝑛𝑛𝐸𝐸𝐸𝐸𝑖𝑖,𝑐𝑐 + 𝛽𝛽2𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶 𝐸𝐸𝑓𝑓𝑓𝑓𝑅𝑅𝐸𝐸𝑅𝑅𝐶𝐶𝑛𝑛𝐸𝐸𝐸𝐸𝑖𝑖,𝑐𝑐 + 𝛽𝛽3𝑀𝑀𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝑆𝑆ℎ𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖,𝑐𝑐 +𝛽𝛽4𝑀𝑀𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝐶𝐶𝐶𝐶𝑛𝑛𝐸𝐸𝐶𝐶𝑛𝑛𝑡𝑡𝐶𝐶𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑐𝑐 + 𝛽𝛽5𝑀𝑀𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝑀𝑀𝐶𝐶𝐶𝐶𝑀𝑀𝑡𝑡ℎ𝑐𝑐 + 𝛽𝛽𝑗𝑗𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (3a)

𝑃𝑃𝐶𝐶𝑅𝑅𝐸𝐸𝐶𝐶𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + 𝛽𝛽1𝑋𝑋_𝐸𝐸𝑓𝑓𝑓𝑓𝑅𝑅𝐸𝐸𝑅𝑅𝐶𝐶𝑛𝑛𝐸𝐸𝐸𝐸𝑖𝑖,𝑐𝑐 + 𝛽𝛽2𝑆𝑆𝐸𝐸𝐶𝐶𝑆𝑆𝐶𝐶 𝐸𝐸𝑓𝑓𝑓𝑓𝑅𝑅𝐸𝐸𝑅𝑅𝐶𝐶𝑛𝑛𝐸𝐸𝐸𝐸𝑖𝑖,𝑐𝑐 + 𝛽𝛽3𝑀𝑀𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝑆𝑆ℎ𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖,𝑐𝑐 +𝛽𝛽4𝑀𝑀𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝐶𝐶𝐶𝐶𝑛𝑛𝐸𝐸𝐶𝐶𝑛𝑛𝑡𝑡𝐶𝐶𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑐𝑐 + 𝛽𝛽5𝑀𝑀𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝑀𝑀𝐶𝐶𝐶𝐶𝑀𝑀𝑡𝑡ℎ𝑐𝑐 + 𝛽𝛽𝑗𝑗𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (3b)

The results in Table 8 show that CE and its components (XE and SE) negatively correlate with price, positively correlate with underwriting profit, and have no significant impact on overall profitability. The results support Hypothesis 3 in the sense that cost-efficient reinsurers can charge lower prices without sacrificing profitability. The correlations between market share (market concentration) and both price and profit are insignificant, a finding which rejects the RMP (SCP) hypothesis.

54 We examine multicollinearity by estimating VIFs of each independent variable in Equations (1) to (3). All values are

below 5, suggesting that multicollinearity is not much of a problem.


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Table 8 Test for efficient structure hypothesis

Variables Price UW Profit ROE Price UW

Profit ROE

CE -0.131*** 7.508*** 0.0550 (0.0229) (2.105) (0.0462) SE -0.0764** 5.859** -0.0565 (0.0327) (2.440) (0.0376) XE -0.108*** 5.777*** 0.0816* (0.0230) (1.986) (0.0461) Market share 0.00109 26.32 0.899 0.00301 26.27 0.839 (0.437) (32.58) (0.665) (0.432) (32.17) (0.655) Market concentration

0.0569 0.175 -0.157 0.0700 -1.543 -0.0945 (0.0888) (7.762) (0.102) (0.0900) (8.066) (0.0894)

Market growth 0.000332 -0.0529 0.000834 0.000335 -0.0554* 0.000924 (0.000230) (0.0346) (0.000637) (0.000235) (0.0335) (0.000620) Leverage ratio -0.00849*** -0.373** -0.0212 -0.00840*** -0.387** -0.0210 (0.00286) (0.156) (0.0198) (0.00267) (0.164) (0.0196) Unaffiliated 0.0146 -2.449 -0.00568 0.0135 -2.241 -0.0145

(0.0311) (2.774) (0.0255) (0.0317) (2.781) (0.0275) Market FE Yes Yes Yes Yes Yes Yes Year FE No No No No No No Overall R2 0.314 0.057 0.051 0.315 0.065 0.054 Observations/number of reinsurers 841/116


4.6. Granger causality test

Our hypotheses suggest that large scale results in high cost efficiency; high cost efficiency yields lower price; lower price may potentially attract more clients and thus increase the firm scale. The empirical evidence presented here is consistent with these predictions. However, a significant coefficient does not necessarily give information regarding the causality between the left and right hand side variables. The Granger Causality Test offers a way to discriminate whether a reinsurer’s scale drives its cost efficiency (Berger and DeYoung, 1997; Casu and Girardone, 2009) and/or vice versa. Granger test demonstrates the causality from the statistical perspective and thus strengthens our empirical analyses with an additional piece of evidence. The use of Granger causality test is also an innovative element in insurance frontier efficiency analyses.

Based on Equation (4), we test the null hypothesis (H.A0) that size does not Granger cause55 cost efficiency, i.e. β1,1 = β1,2 = ⋯ = β1,n = 0. Based on Equation (5), we test for reverse causality (H.B0) that cost efficiency does not Granger cause size, i.e. β3,1 = β3,2 = ⋯ =

55 Granger causality has two important ideas: (1) if A Granger causes B, then A must happen earlier than B; (2) A must

contain useful information that can predict B. Granger (1969) explains the test in detail.


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β3,n = 0 . We perform nested F-tests for each regression with n=1,2,…8 and show the resulting p-values in Table 9, where n represents the number of lagged Size and CE variables included in the equations, respectively. The results reject H.A0 for all n except n=8 at the 95% confidence level and accept H.B0 for all n.56 Therefore, we conclude that size Granger causes cost efficiency; we do not find evidence showing the reverse causality. We explain this by the long-term nature of high cost efficiency-low price-larger scale process. It takes time for the cost-efficient reinsurer to significantly grow and/or to find a proper acquisition target, particularly considering the reinsurance market competition is fierce and corporate clients prefer stable and long-term relationships. However, our sample can only capture maximum 8-year lags, which is relatively short for this process.

𝐶𝐶𝐸𝐸𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + ∑𝛽𝛽1,𝑐𝑐𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑖𝑖,𝑐𝑐−𝑐𝑐 + 𝛽𝛽2𝐶𝐶𝐶𝐶𝐶𝐶𝑆𝑆𝐶𝐶𝑅𝑅𝑅𝑅𝑡𝑡𝐶𝐶𝑖𝑖 + 𝛽𝛽3𝐶𝐶𝐶𝐶𝑛𝑛𝐶𝐶𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡𝐶𝐶𝑖𝑖 + ∑𝛽𝛽3,𝑐𝑐𝐶𝐶𝐸𝐸𝑖𝑖,𝑐𝑐−𝑐𝑐 +𝛽𝛽𝑗𝑗𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (4)

𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + ∑𝛽𝛽1,𝑐𝑐𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑖𝑖,𝑐𝑐−𝑐𝑐 + 𝛽𝛽2𝐶𝐶𝐶𝐶𝐶𝐶𝑆𝑆𝐶𝐶𝑅𝑅𝑅𝑅𝑡𝑡𝐶𝐶𝑖𝑖 + 𝛽𝛽3𝐶𝐶𝐶𝐶𝑛𝑛𝐶𝐶𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡𝐶𝐶𝑖𝑖 + ∑𝛽𝛽3,𝑐𝑐𝐶𝐶𝐸𝐸𝑖𝑖,𝑐𝑐−𝑐𝑐 +𝛽𝛽𝑗𝑗𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (5)

Table 9 Granger causality test n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 P-Values of Nested F-Tests H.A0 in Equation (2) 0.000 0.002 0.050 0.003 0.003 0.101 0.050 0.204 H.B0 in Equation (3) 0.678 0.355 0.322 0.343 0.234 0.549 0.753 0.231 No. of observations 706 586 474 373 289 214 149 108 Number of reinsurers 109 104 97 84 75 65 41 39

5. Robustness tests

We conducted 16 tests to check the robustness of our conclusions. The results are listed in Appendix C (Supplementary Materials). All results are consistent with our conclusions, unless otherwise stated below.

The robustness tests 1-10 analyze alternative specifications of DEA first- and second-stage models. First, we use reinsurers’ real net premiums written as an alternative output of the smoothed loss to represent the risk pooling function (Cummins and Weiss, 2013). Second, we consider alternative input prices, using (1) the MSCI yearly total return indices to replace the average realized ROE as the equity capital price and (2) the Producer Price Indices (PPI) to replace the CPI as the price for materials and business services. Third, as suggested by Simar

56 We consider the optimal lag length for both equations by using the AIC/BIC criteria. The results suggest that AIC/BIC

is minimized at n=1 for Equation (4) and at n=2 for Equation (5). We also consider whether size and cost efficiency are stationary in the panel sample. We perform Fisher-type unit root test for our unbalanced panel, the results reject the null hypothesis that all panels contain unit roots and support the alternative hypothesis that at least one panel is stationary. We also reduce our sample to balanced panel by removing firms with missing years, and then perform Harris-Tzavalis (Im-Pesaran-Shin) unit-root tests, the results again reject the null hypotheses that (all) panels contain unit roots and support the alternative hypothesis that (some) panels are stationary.


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and Wilson (2000), we use the double bootstrapping procedure in both the first- and the second-stage DEA analyses with 2,000 replications. Fourth, we consider two sets of alternative model specifications for DEA second-stage regressions: (1) the truncated regression, proposed by Simar and Wilson (2007), and (2) the Tobit regression. Fifth, we use firm and year fixed effects models to replace the random effects models (with market and year dummies) for DEA second-stage regressions. We have to omit the time-invariant variables in the firm fixed effects regressions, for example, firm affiliation status. Sixth, we use three different regional frontiers for reinsurers domiciled in matured markets, developing markets, and offshore locations. The results support our H1 in the sense that it shows an inverse U-shaped relationship between size and scale efficiency, and the largest reinsurers remain the most cost-efficient. It also consistent with our H2, however, rather than showing small and focused firms have superior X-efficiency, it shows that large and diversified firms have superior X-efficiency (H2B). The regional frontier results support H3. Seventh, we include one additional input as the debt capital and obtain the efficiency scores again. As suggested by Cummins and Weiss (2013), debt capital should not be included as the input because it contains largely the reserves for policy holders, which has also the nature of output. Therefore, consistent with our expectation, the results change significantly if debt capital is used. Eighth, we use a subsample that includes only the observations without missing values. We do this because missing values for the number of employees were imputed for some data points in our core models. We generate a new set of DEA efficiency scores and re-perform all DEA second-stage regressions. Ninth, we consider Armstrong’s (2012) and Woodside’s (2013) suggestion to include only significant control variables in the regressions to limit the number of independent variables to not more than five. Tenth, we include the interaction term between scale and scope for our efficiency analysis. The results suggest that the U-shaped (positive) relationship between reinsurer’s scale and its scale (cost) efficiency exists for both diversified and focused reinsurers, indicated by insignificant coefficients of the interaction terms and the significant coefficients of the size variables. However, this consistency does not conflict with our hypothesis 2 because composite reinsurers do have some additional positive size impact on pure technical- and X-efficiencies, supporting the conglomeration hypothesis for large insurers (H2B).

Robustness tests 11 to 14 are alternative analyses for Hypothesis 1. First, we take the top 10% scale-efficient firms in each year and then obtain the 25th and 75th percentiles of total assets in each year. Similar to the firm-year pooled analyses in Table 4, we obtain an optimal asset range of USD 5.8 to 14.5 billion (inflation adjusted at 2012), which is slightly narrower than the optimal range obtained previously. Second, we separate our sample into two time periods, i.e., before the financial crisis (2002–2007) and after (2008–2012). The decile and vigintile analyses, similar to those in Table 4, suggest that there is no structural change regarding


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optimal size range before and after the financial crisis. Third, we separate our sample by region into mature markets (West Continental Europe, London, Bermuda, North America, and Asia Developed) and emerging markets (Africa, Asia Emerging, Eastern Europe, Latin America, and Middle East). The decile and vigintile analyses suggest that in emerging markets, the most cost-efficient reinsurers are concentrated in a smaller total asset range (between USD 4.3 and 7.6 billion) and that all reinsurers with total assets above USD 7.6 billion operate under DRS. Mature markets demonstrate a pattern similar to that of the global market (see Table 4). The superior management expertise and underwriting experience of reinsurers based in mature markets may enable them to manage large and globalized firms more efficiently, thus explaining the difference between emerging and mature markets. These analyses confirm the robustness of our optimal asset range of between USD 2.9 and 15.5 billion. Fourth, we use reinsurers’ net premiums written to replace total assets as the scale measure and test Hypothesis 1. The results suggest that there is an optimal size range between USD 0.91 to 3.65 billion in net premiums written (inflation adjusted at 2012). Our results are comparable to the optimal premium income range USD 2.3 to 4.9 billion found for multinational primary insurers (Katrishen and Scordis, 1998).57 The analyses of efficiency determinants again confirm the inverse-U shaped size-SE relationship and the positive and linear size-CE relationship.

Robustness tests 15 and 16 are alternative analyses for Hypothesis 3. We use the actual loss ratio to replace the smoothed loss ratio when calculating the reinsurance price and the underwriting profit ratio (Robustness test 15). Since the actual loss ratio is very volatile in reinsurance, we only use values within the 5th and 95th percentiles in conducting the test. The results support the efficient structure hypothesis but not the alternative RMP and SCP hypotheses. In Robustness test 16, a firm and year fixed effects model is employed, in which we would have to omit all time invariant independent variables.

6. Conclusions

Our paper contributes to the finance and insurance literature by making four original conclusions. (1) Scale-efficient reinsurers exhibit an optimal size range between USD 2.9 and 15.5 billion in total assets, beyond which the scale economies are exhausted. These thresholds are larger than those found for the primary insurance market or other financial service industries. (2) The high cost-efficiency levels of large reinsurers are partially a result of their size. (3) A strategic focus strategy is appropriate for small reinsurers, whereas product

57 Katrishen and Scordis (1998) focus on multinational primary insurers, apply a different empirical approach to identify

economies of scale, and investigate a different sample period. The results thus are not fully comparable. Our optimal range for reinsurers is not significantly larger than Katrishen and Scordis’s (1998) range for primary insurers may be because they focus on international insurers that have already a large scale.


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diversification requires larger firm size. (4) Cost-efficient reinsurers can charge lower prices without sacrificing their profitability.

Our results provide new insights into the effects of economies of scale and scope on the global reinsurance market structure. The overall cost efficiency of large reinsurers explains their dominating position in the global market (Outreville, 2012b). The high pure technical efficiency of small and specialized reinsurers explains why both product-diversified and specialized firms appear to be competitively viable in the long run (Berger et al., 2000). These results explain inefficient firms’ paradoxical ability to survive for many years. Some of these firms, particularly small firms, may be cost inefficient, but hold a strong position in pure technical efficiency in their specialized field, and thus become viable over the long term.

Our findings have both regulatory policy and managerial practice implications. Further consolidation is expected in the global reinsurance market, not only because it improves cost efficiency, but also because it has the potential to lower reinsurance prices for consumers. Therefore, policymakers should be cautious about adopting anti-concentration measures in the global reinsurance market, as doing so may have the unintended consequence of raising the price of reinsurance and reducing industry cost efficiency. However, from the firm management point of view, consolidation is not without its drawbacks, especially when considering limitations in economies of scale. Although scale diseconomies are offset by advantages in X-efficiency for the largest reinsurers, they become more problematic with further growth of those largest reinsurers. At this point, we cannot guarantee that technology and management progresses will adapt fast enough to offset greater scale diseconomies in future consolidation. Thus, we do not argue for a natural monopoly in the global reinsurance market; rather, we suggest the reinsurance management carefully evaluate the tradeoffs between scale diseconomies and gains in X-efficiency, especially for reinsurers beyond the optimal size range, when considering merger and acquisition opportunities. Reinsurers should also be careful when evaluating conglomerate versus focused strategies. Specifically, small reinsurers need to be cautious about product diversification (i.e., adding life to nonlife business or vice versa) because doing so could significantly reduce the cost efficiency. The results are also important to catastrophe management discussions where reinsurers provide a significant portion of risk capacity.

These findings contribute to the recent discussion on systemic risk in the insurance and reinsurance industry (Cummins and Weiss, 2014; Park and Xie, 2014) in that we analyze the extent to which size and diversification can be justified by efficiency considerations. The way in which we analyze efficiency is not considered in the current systemic risk discussion and might therefore provide an alternative line of reasoning. If regulators, for example, require large reinsurers to hold more equity capital, this would deteriorate their cost efficiency


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advantages and affect the market structure. These results are important not only for the reinsurance industry, but also for other financial services firms where complex interactions between scale, scope, and cost efficiency are present (for similar interactions in the banking market, see, e.g., Berger, Hanweck, and Humphrey, 1987).

The empirical research on global reinsurance markets is far from conclusive. Future research may provide more detailed guidance to reinsurers and policymakers as to, for example, which inputs (outputs) reinsurers can reduce (increase) to be more cost efficient. The impact of geographic and international diversification is also under-researched, due to data limitations. The inefficiencies of certain firms are not fully explained by firm-specific characteristics. The literature suggests that tax and/or other regulatory differences may play an important role in the presence of inefficiencies (Garven and Louberge, 1996), providing yet another fruitful direction for empirical investigation.


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Appendices

Appendix A Loss smoothing procedure

We smooth the output of the loss, following the two-step procedure proposed by Cummins and Xie (2008). First, we rank the reinsurers by their net premiums written in each year. Reinsurers who rank in the top 80% are considered representative companies. The remaining 20% are the smallest companies. We then determine the 25th and 75th percentiles of the loss ratio of those representative reinsurers in each year. For reinsurers with loss ratios between the 25th and 75th percentile, we use their actual loss ratio to calculate the output quantity of the loss. For reinsurers with loss ratios below the 25th percentile or above 75th percentile, we use the 25th and 75th percentile loss ratios, respectively, to calculate the output quantity of the loss. The first step is a winsorising process on representative reinsurers. Second, for each firm in the sample, we fit a linear time trend to the new series of the loss ratios obtained in the first step and then calculate a smoothed loss ratio series. The linear trend regression for each firm-year is 𝐿𝐿𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑖𝑖,𝑐𝑐 = 𝛽𝛽𝑖𝑖 + 𝛽𝛽𝑖𝑖𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑐𝑐 , where i represents the reinsurer and t represents the year. We then use the predicted loss ratio values as smoothed loss ratios and use the smoothed loss ratio multiplied by the net premiums written of respective firm-years to generate the smoothed loss.


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Appendix B Geographical and yearly sample distribution Panel A: Geographical Distribution Panel B: Yearly Distribution

Domiciled Location Firm-years % Year Firms % (Western) Continental Europe 208 24.7 2002 46 5.5 Bermuda 160 19.0 2003 52 6.2 Africa 77 9.2 2004 50 5.9 Asia Developed 65 7.7 2005 50 5.9 East Europe 64 7.6 2006 80 9.5 North America 63 7.5 2007 81 9.6 Middle East 60 7.1 2008 81 9.6 Asia Emerging 54 6.4 2009 97 11.5 London 54 6.4 2010 105 12.5 Latin America 36 4.3 2011 101 12.0 2012 98 11.7 841 100 841 100

Continental Europe hosts the largest proportion of reinsurers, whereas Bermuda has the second largest share. London, traditionally one of the major reinsurance hubs, hosts only 6.3% of reinsurers, because we exclude Lloyd’s syndicates from our sample. In addition, London market suffered huge losses during the liability crisis in 1980s and natural catastrophes in recent years. Hence, many London players were merged with other reinsurers (Holzheu and Lechner, 2007). The relative small portion of North American reinsurers is due to: (1) American primary insurers preferring to reinsure with foreign reinsurers, due to diversification concerns (Chen and Hamwi, 2000); and (2) the strong emergence of Bermuda market. The Canadian reinsurance market is underdeveloped, because large state-owned insurers rarely use reinsurance (Holzheu and Lechner, 2007).


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Appendix C Robustness tests Robustness test 1: Net premiums written as an alternative output Variables SE PTE AE XE CE XE XE IRS CRS DRS lnAsset 0.0295*** -0.0216** 0.0349*** 0.0155* 0.0274*** 0.0240** 0.0241** -0.195*** 0.0223** 0.173*** (0.00635) (0.0102) (0.00834) (0.00914) (0.00890) (0.00968) (0.00973) (0.0381) (0.00877) (0.0363) lnAsset2 -0.00831*** 0.00716*** -0.000661 0.00525** -0.000541 0.00420* 0.00415* -0.0120 0.00476** 0.00726 (0.00159) (0.00232) (0.00197) (0.00234) (0.00194) (0.00226) (0.00232) (0.0109) (0.00195) (0.00998) Composite 0.0171 0.0180 -0.0690*** -0.0362* -0.0184 -0.0165 -0.0312 0.0229 -0.00236 -0.0206 (0.0150) (0.0314) (0.0226) (0.0217) (0.0200) (0.0262) (0.0213) (0.0347) (0.0178) (0.0280) Conglomerate 0.0239 0.0124 -0.0333 -0.0325 -0.0214 -0.0307 -0.0247 0.105*** -0.0162 -0.0885*** (0.0165) (0.0478) (0.0348) (0.0359) (0.0312) (0.0370) (0.0392) (0.0392) (0.0167) (0.0319) Leverage ratio 0.00426*** 0.0153*** -0.00262 0.00854* 0.0101** 0.00854** 0.00894** 0.0132* 0.00592*** -0.0191** (0.00149) (0.00192) (0.00392) (0.00448) (0.00479) (0.00430) (0.00416) (0.00730) (0.00159) (0.00748) Unaffiliated -0.0268 0.0205 0.0122 0.0173 0.00508 0.0123 0.00932 -0.0129 0.0302 -0.0173 (0.0264) (0.0431) (0.0264) (0.0279) (0.0270) (0.0265) (0.0276) (0.0508) (0.0364) (0.0510) Small*Specialized 0.0799*** (0.0224) Large*Composite 0.0330 (0.0340) Small*Focused 0.0688*** (0.0205) Large*Conglomerate 0.0182 (0.0597) Market FE /Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Overall R2 0.538 0.352 0.391 0.465 0.575 0.476 0.471 0.411 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of random effects panel regressions (Col 1-7) and the marginal effects of multinomial logistic regressions (Col 8-10). Robust standard errors clustered at firm level are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


81

Appendix C (Continued) Robustness test 2: PPI and MSCI total return indices as alternative input prices Variables SE PTE AE XE CE XE XE IRS CRS DRS lnAsset 0.0352*** -0.0183 0.0236** 0.00435 0.0190** 0.0126 0.0122 -0.183*** 0.0210*** 0.162*** (0.00662) (0.0113) (0.00956) (0.00996) (0.00927) (0.0105) (0.0106) (0.0416) (0.00708) (0.0409) lnAsset2 -0.00969*** 0.00736*** -0.00223 0.00315 -0.00344 0.00218 0.00216 -0.00771 0.00364** 0.00408 (0.00161) (0.00247) (0.00240) (0.00255) (0.00217) (0.00251) (0.00254) (0.00962) (0.00169) (0.00892) Composite 0.0170 0.00739 -0.0396 -0.0178 0.000904 -0.00933 -0.0127 0.0509 -0.0144 -0.0365 (0.0153) (0.0325) (0.0258) (0.0253) (0.0237) (0.0294) (0.0254) (0.0327) (0.0150) (0.0281) Conglomerate 0.0195 0.0104 -0.00974 -0.00444 0.00409 -0.00506 0.00471 0.0784** -0.0128 -0.0656** (0.0185) (0.0479) (0.0380) (0.0374) (0.0315) (0.0379) (0.0427) (0.0340) (0.0148) (0.0285) Leverage ratio 0.00489*** 0.0160*** 0.000843 0.0125*** 0.0139*** 0.0128*** 0.0129*** 0.0141 0.00471*** -0.0188** (0.00151) (0.00216) (0.00318) (0.00298) (0.00305) (0.00291) (0.00285) (0.00870) (0.00162) (0.00856) Unaffiliated -0.0273 0.0456 0.0539 0.0747** 0.0476 0.0680** 0.0664** -0.0620 0.0312 0.0308 (0.0281) (0.0439) (0.0328) (0.0336) (0.0321) (0.0324) (0.0329) (0.0572) (0.0366) (0.0629) Small*Specialized 0.0651** (0.0259) Large*Composite 0.0521 (0.0410) Small*Focused 0.0657** (0.0259) Large*Conglomerate 0.00983 (0.0536) Market FE /Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Overall R2 0.584 0.355 0.236 0.401 0.500 0.404 0.403 0.445 Obs./No. of Reinsurers

841/116 841/116 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of random effects panel regressions (Col 1-7) and the marginal effects of multinomial logistic regressions (Col 8-10). Robust standard errors clustered at firm level are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


82

Appendix C (Continued) Robustness test 3: Double bootstrapping procedure (2,000 replications) Variables SE PTE AE XE CE XE XE lnAsset 0.0408*** -0.0151* 0.0350*** 0.0139* 0.0281*** 0.0226*** 0.0230*** (0.00706) (0.00867) (0.00831) (0.00734) (0.00747) (0.00804) (0.00822) lnAsset2 -0.00653*** 0.00402** -0.00105 0.00284 -0.000711 0.00175 0.00176 (0.00192) (0.00187) (0.00218) (0.00192) (0.00173) (0.00189) (0.00184) Composite 0.0117 0.00670 -0.0660*** -0.0316* -0.0190 -0.0108 -0.0270 (0.0171) (0.0261) (0.0234) (0.0187) (0.0168) (0.0224) (0.0186) Conglomerate 0.0105 0.00231 -0.0242 -0.0270 -0.0248 -0.0247 -0.0225 (0.0199) (0.0380) (0.0339) (0.0282) (0.0254) (0.0291) (0.0308) Leverage ratio 0.00352* 0.0105*** 0.000252 0.00735* 0.00830** 0.00734* 0.00773** (0.00202) (0.00246) (0.00432) (0.00390) (0.00411) (0.00387) (0.00391) Unaffiliated -0.0203 0.0225 0.00850 0.0189 0.00835 0.0140 0.0110 (0.0301) (0.0358) (0.0289) (0.0246) (0.0237) (0.0225) (0.0240) Small*Specialized 0.0824*** (0.0213) Large*Composite 0.0316 (0.0313) Small*Focused 0.0683*** (0.0200) Large*Conglomerate 0.0347 (0.0655) Market FE /Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Overall R2 0.547 0.348 0.433 0.484 0.593 0.497 0.492 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of random effects panel regressions. Bootstrapping standard errors with 2,000 replications are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


83

Appendix C (Continued) Robustness test 4: Truncated and Tobit models

Truncated Regression Tobit Regression Variables SE PTE AE XE CE XE XE SE PTE AE XE CE XE XE lnAsset 0.0861*** -0.0156 0.0519*** 0.0195** 0.0405*** 0.0284*** 0.0288*** 0.0385*** -0.00978 0.0273*** 0.0156* 0.0325*** 0.0247** 0.0250** (0.0238) (0.0105) (0.0121) (0.00879) (0.00752) (0.00961) (0.0101) (0.00706) (0.0152) (0.00759) (0.00920) (0.00824) (0.0101) (0.0104) lnAsset2 -0.0187*** 0.0142*** -0.00194 0.00794*** 0.000156 0.00633** 0.00664*** -0.0103*** 0.0206*** -0.00150 0.00682*** 5.76e-05 0.00529** 0.00557** (0.00704) (0.00383) (0.00329) (0.00250) (0.00166) (0.00249) (0.00247) (0.00188) (0.00383) (0.00215) (0.00244) (0.00178) (0.00242) (0.00238) Composite 0.0395 0.00831 -0.107*** -0.0356* -0.0196 -0.00642 -0.0312* 0.0131 0.000742 -0.0715*** -0.0452** -0.0300 -0.0233 -0.0415* (0.0531) (0.0246) (0.0370) (0.0188) (0.0173) (0.0229) (0.0189) (0.0163) (0.0364) (0.0234) (0.0228) (0.0218) (0.0295) (0.0231) Conglomerate 0.115 0.000544 -0.0332 -0.0515* -0.0418 -0.0437 -0.0489 0.0186 -0.0321 -0.0241 -0.0552* -0.0435 -0.0497 -0.0558 (0.110) (0.0352) (0.0550) (0.0308) (0.0265) (0.0312) (0.0351) (0.0202) (0.0474) (0.0321) (0.0323) (0.0281) (0.0332) (0.0368) Leverage ratio 0.00102 0.0327*** -0.00841 0.00839* 0.00853** 0.00754* 0.00847** 0.0106*** 0.0362*** 0.00286 0.0181*** 0.0189*** 0.0176*** 0.0181*** (0.0183) (0.00711) (0.00561) (0.00436) (0.00406) (0.00411) (0.00421) (0.00396) (0.00814) (0.00536) (0.00668) (0.00677) (0.00667) (0.00653) Unaffiliated -0.0464 0.0150 0.0160 0.0426 0.0240 0.0388 0.0345 -0.0238 0.0440 0.00968 0.0429 0.0228 0.0386 0.0351 (0.0656) (0.0297) (0.0445) (0.0274) (0.0280) (0.0261) (0.0273) (0.0298) (0.0538) (0.0260) (0.0288) (0.0287) (0.0280) (0.0286) Small*Specialized 0.0965*** 0.0876*** (0.0283) (0.0281) Large*Composite 0.0159 0.0274 (0.0320) (0.0305) Small*Focused 0.0668*** 0.0640*** (0.0236) (0.0217) Large*Conglomerate 0.0479 0.0701 (0.0549) (0.0557) Market FE /Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Log-pseudo-likelihood

803.92 329.88 426.74 450.09 588.81 459.95 455.38 313.49 -48.50 234.61 332.84 415.23 340.14 337.66

Obs./No. of Reinsurers 746/110 684/106 822/115 822/115 822/115 822/115 822/115 841/116 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of random effects panel regressions. Robust standard errors clustered at firm level are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


84

Appendix C (Continued) Robustness test 5: Fixed effects models a Variables SE PTE AE XE CE IRS CRS DRS lnAsset 0.0390* -0.0499 0.0552* -0.00253 0.0237** -0.000899** 2.73e-6 0.000896** (0.0201) (0.0359) (0.0292) (0.0163) (0.0110) (0.00035) (0.00001) (0.00035) lnAsset2 -0.00997** 0.00234 0.00229 0.00348 -0.00556** 0.000021 1.86e-6 -0.000023 (0.00493) (0.00468) (0.00459) (0.00439) (0.00276) (0.00006) (0.00000) (0.00006) Leverage ratio 0.00475** 0.0158*** -0.00505 0.00698 0.00756 0.000115* 1.99e-6 -0.000117* (0.00217) (0.00328) (0.00461) (0.00469) (0.00506) (0.00006) (0.00000) (0.00006) Firm FE /Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Yes R2 0.355 0.198 0.419 0.444 0.546 0.701 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of the firm and year fixed effects panel regressions (Col 1-5) and the marginal effects of the fixed effects multinomial logistic regressions (Col 6-8). Robust standard errors clustered at firm level are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively. a Fixed effects models are not applicable to include variables with little variation over time, such as small*specialized and large*composite.


85

Appendix C (Continued) Robustness test 6: Regional frontiers Variables SE CE XE CE Price UW Profit ROE Small*Focused -0.0212 -0.0109 (0.0378) (0.0345) Large*Conglomerate 0.179*** 0.160** (0.0627) (0.0716) lnAsset 0.0205*** -0.0539*** -0.0660*** -0.0507*** (0.00783) (0.0145) (0.0150) (0.0153) lnAsset2 -0.00440** 0.00656** 0.00979*** 0.00673** (0.00217) (0.00304) (0.00293) (0.00304) Composite 0.00398 0.0604 0.0560 0.0566 (0.0103) (0.0386) (0.0378) (0.0383) Conglomerate -0.00743 0.00810 -0.0169 -0.0271 (0.0308) (0.0492) (0.0389) (0.0413) Leverage ratio 1.09e-05 -0.0146*** -0.0146*** -0.0149*** -0.0110*** -0.345** -0.0200 (0.00143) (0.00409) (0.00411) (0.00404) (0.00266) (0.150) (0.0201) Unaffiliated 0.0170 -0.0413 -0.0440 -0.0386 0.0213 -2.550 -0.00557 (0.0161) (0.0463) (0.0459) (0.0454) (0.0329) (2.900) (0.0249) CE -0.0724** -2.723 -0.0184 (0.0325) (2.381) (0.0429) Market growth -0.000399* -0.00854 0.00115* (0.000208) (0.0362) (0.000627) Market share -0.0637 31.07 0.906 (0.504) (32.06) (0.706) Market concentration 0.0146 -3.209 -0.179 (0.0901) (7.550) (0.125) Market FE /Constant Yes Yes Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes No No No Overall R2 0.104 0.394 0.444 0.408 0.256 0.026 0.047 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116 841/116



86

Appendix C (Continued) Robustness test 7: Debt capital as the fourth input Variables SE CE XE CE Price UW Profit ROE Small*Focused 0.0173 0.0199 (0.0346) (0.0349) Large*Conglomerate 0.00413 0.00953 (0.0312) (0.0282) lnAsset 0.0114** -0.0313*** -0.0330*** -0.0289** (0.00485) (0.0113) (0.0110) (0.0114) lnAsset2 -0.00450** 0.00199 0.00285 0.00166 (0.00198) (0.00204) (0.00175) (0.00201) Composite 0.00570 0.0143 0.0149 0.0159 (0.00816) (0.0339) (0.0341) (0.0342) Conglomerate 0.00877 -0.0426 -0.0387 -0.0409 (0.00988) (0.0317) (0.0324) (0.0321) Leverage ratio -0.000307 -0.0113*** -0.0112*** -0.0112*** -0.00973*** -0.230 -0.0183 (0.00109) (0.00317) (0.00324) (0.00321) (0.00277) (0.149) (0.0206) Unaffiliated -0.00434 -0.0212 -0.0208 -0.0237 0.0179 -2.783 -0.00627 (0.0153) (0.0417) (0.0410) (0.0418) (0.0324) (2.931) (0.0255) CE 0.00319 5.080 0.0519 (0.0598) (4.256) (0.0869) Market growth -0.000423** -0.0109 0.00112* (0.000215) (0.0358) (0.000628) Market share -0.0725 32.12 0.901 (0.524) (32.36) (0.709) Market concentration 0.0741 -1.469 -0.169* (0.0939) (8.047) (0.103) Market FE /Constant Yes Yes Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes No No No Overall R2 0.263 0.286 0.296 0.289 0.251 0.030 0.055 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116 841/116



87

Appendix C (Continued) Robustness test 8: Subsample of observations without missing values Variables SE PTE AE XE CE XE XE IRS CRS DRS lnAsset 0.0161 -0.0163 0.0549*** 0.0405*** 0.0464*** 0.0438** 0.0469*** -0.0110 0.00876 0.00223* (0.0109) (0.0286) (0.0150) (0.0133) (0.0161) (0.0170) (0.0143) (0.0153) (0.0152) (0.00117) lnAsset2 a -0.0104*** 0.0170** 0.00365 0.0160*** 0.00659 0.0141** 0.0132** (0.00328) (0.00670) (0.00526) (0.00488) (0.00543) (0.00639) (0.00566) Composite 0.00873 -0.0161 -0.0567 -0.0546* -0.0387 -0.0435 -0.0578 0.0227 -0.0256 0.00288 (0.0292) (0.0573) (0.0391) (0.0330) (0.0370) (0.0380) (0.0355) (0.0463) (0.0460) (0.00233) Conglomerate -0.0132 -0.102** -0.0203 -0.0962** -0.0827** -0.0882** -0.106** 0.0300 -0.0286 -0.00132 (0.0223) (0.0469) (0.0474) (0.0383) (0.0340) (0.0412) (0.0422) (0.0270) (0.0269) (0.00107) Leverage ratio 0.00831** 0.00781 0.000255 0.00527 0.0117** 0.00502 0.00536 -0.0194** 0.0205** -0.00107*** (0.00334) (0.00750) (0.00599) (0.00627) (0.00590) (0.00635) (0.00646) (0.00915) (0.00920) (0.000360) Unaffiliated -0.0770* 0.0621 0.0685** 0.112* 0.0523 0.106 0.106* -0.729** 0.732** -0.00211** (0.0430) (0.0903) (0.0338) (0.0635) (0.0807) (0.0660) (0.0626) (0.345) (0.345) (0.000908) Small*Specialized 0.0693* (0.0400) Large*Composite 0.0293 (0.133) Small*Focused 0.0341 (0.0509) Large*Conglomerate 0.137 (0.0880) Market FE /Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Overall R2 0.675 0.391 0.431 0.632 0.652 0.629 0.630 0.508 Obs./No. of Reinsurers 295/47 295/47 295/47 295/47 295/47 295/47 295/47 295/47

Notes: We present the results of random effects panel regressions (Col 1-7) and the marginal effects of multinomial logistic regressions (Col 8-10). Robust standard errors clustered at firm level are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively. a. We do not include the squared size for returns to scale analyses, due to small number of observations.


88

Appendix C (Continued) Robustness test 9: No more than five independent variables Variables SE CE XE XE IRS CRS DRS Price UW Profit ROE lnAsset 0.0486*** 0.0246*** 0.00722 0.00724 -0.196*** 0.0687*** 0.128*** (0.00584) (0.00692) (0.00969) (0.00971) (0.0370) (0.0217) (0.0312) lnAsset2 -0.00883*** 0.00108 0.00601*** 0.00585** -0.0220** 0.0169*** 0.00513 (0.00195) (0.00177) (0.00224) (0.00236) (0.0105) (0.00466) (0.00893) Composite -0.0197 -0.0367* 0.0420 -0.0308 -0.0112 (0.0196) (0.0219) (0.0542) (0.0510) (0.0251) Conglomerate 0.0185 -0.0105 0.128** -0.0755 -0.0528* (0.0252) (0.0271) (0.0567) (0.0474) (0.0270) Leverage ratio 0.00523*** 0.0139*** 0.0123** 0.0123** -0.00611 0.0213*** -0.0152** -0.00860*** -0.363** -0.0207 (0.00195) (0.00517) (0.00512) (0.00501) (0.00952) (0.00654) (0.00734) (0.00283) (0.152) (0.0200) Small*Specialized 0.0583* (0.0307) Large*Composite 0.00919 (0.0397) Small*Focused 0.0418a (0.0285) Large*Conglomerate 0.0279 (0.0877) CE -0.135*** 7.625*** 0.0628 (0.0226) (2.093) (0.0477) Market growth 0.000361 -0.0540 0.000772 (0.000229) (0.0343) (0.000644) Market share -0.198 33.13 0.926 (0.403) (30.30) (0.759) Market concentration 0.0610 -0.00158 -0.153 (0.0873) (7.685) (0.105) Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Overall R2 0.364 0.235 0.177 0.169 0.372 0.212 0.037 0.019 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of random effects panel regressions (Col 1-4, 8-10) and the marginal effects of multinomial logistic regressions (Col 5-7). Robust standard errors clustered at firm level are provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively. a. p-values equals 0.14.


89

Appendix C (Continued) Robustness test 10: Interaction terms between scale and scope Variables SE PTE AE XE CE lnAsset*composite -0.00975 0.0710*** -0.0264** 0.0213* 0.0102 (0.00901) (0.0182) (0.0119) (0.0126) (0.0121) lnAsset2*composite -0.000975 0.00818 -0.00833** -0.00526 -0.000586 (0.00308) (0.00515) (0.00382) (0.00410) (0.00400) lnAsset*conglomerate 0.0124 -0.0169 0.0139 -0.00169 0.00188 (0.0146) (0.0340) (0.0246) (0.0237) (0.0190) lnAsset2*conglomerate -0.00187 -0.00170 -0.00597 -0.00538 -0.00541 (0.00446) (0.00668) (0.00554) (0.00558) (0.00442) lnAsset 0.0402*** -0.0593*** 0.0558*** 0.0116 0.0288** (0.00837) (0.0175) (0.0116) (0.0131) (0.0139) lnAsset2 -0.00852*** 0.000343 0.00727** 0.00961*** 0.000391 (0.00208) (0.00456) (0.00296) (0.00355) (0.00379) Composite 0.0173 -0.0111 -0.0490* -0.0247 -0.0242 (0.0181) (0.0393) (0.0284) (0.0250) (0.0238) Conglomerate 0.00946 0.0620 -0.0362 -0.00385 -0.00327 (0.0197) (0.0614) (0.0410) (0.0376) (0.0332) Leverage ratio 0.00468*** 0.0167*** -0.00322 0.00864* 0.0106** (0.00149) (0.00217) (0.00362) (0.00454) (0.00479) Unaffiliated -0.0292 0.0464 -0.00508 0.0194 0.00755 (0.0284) (0.0406) (0.0281) (0.0255) (0.0257) Market FE /Year FE /Constant Yes Yes Yes Yes Yes Overall R2 0.579 0.344 0.380 0.464 0.566 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116



90

Appendix C (Continued) Robustness test 12-13 a: Subsample analyses for optimal size range

Total Assets IRS CRS DRS IRS CRS DRS SE Mean SE Std. Dev N IRS CRS DRS IRS CRS DRS SE Mean SE Std. Dev N Subsample Before financial crisis (2002-2007) After financial crisis (2008-2012)

Panel A: Size deciles Firm-years Percentage Firm-years Percentage < 97 M 40 3 0 93% 7% 0% 0.503 0.268 43 41 1 0 98% 2% 0% 0.587 0.194 42

97M – 237M 29 1 1 94% 3% 3% 0.612* 0.257 31 49 2 2 92% 4% 4% 0.719*** 0.201 53 237M – 435M 30 1 4 86% 3% 11% 0.677 0.243 35 45 4 0 92% 8% 0% 0.686 0.180 49 435M – 795M 37 2 0 95% 5% 0% 0.770* 0.203 39 42 2 1 93% 4% 2% 0.843*** 0.137 45 795M – 1.28B 30 3 0 91% 9% 0% 0.843* 0.162 33 49 1 1 96% 2% 2% 0.931*** 0.076 51 1.28B – 2.04B 27 8 2 73% 22% 5% 0.871 0.143 37 39 3 5 83% 6% 11% 0.944 0.072 47 2.04B – 4.30B 23 4 7 68% 12% 21% 0.955** 0.069 34 39 6 5 78% 12% 10% 0.948 0.058 50 4.30B – 7.60B 10 9 20 26% 23% 51% 0.971 0.046 39 22 7 16 49% 16% 36% 0.963 0.047 45 7.60B – 15.5B 8 3 21 25% 9% 66% 0.949* 0.056 32 12 11 29 23% 21% 56% 0.973 0.045 52

> 15.5B 0 11 25 0% 31% 69% 0.876*** 0.144 36 0 13 35 0% 27% 73% 0.845*** 0.156 48 Total 234 45 80 65% 13% 22% 0.798 0.235 359 338 50 94 70% 10% 20% 0.847 0.181 482

Panel B: Size vigintiles b 2.04B – 2.90B 6 3 3 50% 25% 25% 0.953 0.078 12 25 3 2 83% 10% 7% 0.934 0.062 30 2.90B – 4.30B 17 1 4 77% 5% 18% 0.957 0.066 22 14 3 3 70% 15% 15% 0.970** 0.044 20

Subsample Matured market Emerging market Panel C: Size deciles Firm-years Percentage Firm-years Percentage

< 97 M 10 4 0 71% 29% 0% 0.718 0.268 14 71 0 0 100% 0% 0% 0.511 0.216 71 97M – 237M 14 1 1 88% 6% 6% 0.809 0.245 16 64 2 2 94% 3% 3% 0.649*** 0.214 68

237M – 435M 22 3 2 81% 11% 7% 0.747 0.215 27 53 2 2 93% 4% 4% 0.652 0.198 57 435M – 795M 41 2 0 95% 5% 0% 0.814 0.155 43 38 2 1 93% 5% 2% 0.804*** 0.193 41 795M – 1.28B 55 3 1 93% 5% 2% 0.891*** 0.126 59 24 1 0 96% 4% 0% 0.909** 0.122 25 1.28B – 2.04B 54 11 7 75% 15% 10% 0.916 0.113 72 12 0 0 100% 0% 0% 0.886 0.123 12 2.04B – 4.30B 62 10 12 74% 12% 14% 0.951** 0.062 84 0 0 0 0 4.30B – 7.60B 31 15 30 41% 20% 39% 0.969** 0.043 76 1 1 6 13% 13% 75% 0.943 0.067 8 7.60B – 15.5B 20 14 45 25% 18% 57% 0.969 0.043 79 0 0 5 0% 0% 100% 0.871* 0.073 5

> 15.5B 0 24 56 0% 30% 70% 0.866*** 0.144 80 0 0 4 0% 0% 100% 0.692 c 0.204 4 Total 309 87 154 56% 16% 28% 0.902 0.140 550 263 8 20 90% 3% 7% 0.682 0.235 291

Panel D: Size vigintiles b 2.04B – 2.90B 31 6 5 74% 14% 12% 0.939 0.067 42 0 0 0 0 2.90B – 4.30B 31 4 7 74% 10% 16% 0.963* 0.056 42 0 0 0 0

Notes: *, **, *** denote significance levels at the 10%, 5%, and 1% of mean difference t-tests between two adjacent size classes. a The results of Robustness test 11 are included in the main body of the paper. b We only show the vigintile’s results critical to the identification of the optimal size range. The full analyses are available from the authors upon request. c P-value equals 0.11.


91

Appendix C (Continued) Robustness test 14: Use net premiums written to replace total assets as the size measure

Net Premiums Written IRS CRS DRS IRS CRS DRS Mean of SE Std. Dev. of SE N Size deciles Firm-years Percentage

< 27.3 M 78 6 1 92% 7% 1% 0.558 0.229 85 27.3M-61M 77 4 3 92% 5% 4% 0.630** 0.219 84 61M-117M 75 7 2 89% 8% 2% 0.712** 0.210 84 117M-215M 74 8 2 88% 10% 2% 0.818*** 0.185 84

215M-369.5M 77 4 3 92% 5% 4% 0.896*** 0.104 84 369.5-565M 71 6 7 85% 7% 8% 0.915 0.125 84 565M-910M 59 9 16 70% 11% 19% 0.948** 0.082 84 910M-1.66B 35 14 35 42% 17% 42% 0.964 a 0.059 84 1.66B-3.65B 26 12 46 31% 14% 55% 0.954 0.073 84

>3.65B 0 25 59 0% 30% 70% 0.868*** 0.146 84 Total 572 95 174 68% 11% 21% 0.826 0.207 85

Notes: *, **, *** denote significance levels at the 10%, 5%, and 1% of mean difference t-tests between two adjacent size classes. a P-value equals 0.13.

Variables SE PTE AE XE CE lnNPW 0.0370*** -0.0230** 0.0236** 0.00693 0.0226** (0.00994) (0.0116) (0.0107) (0.00919) (0.0105) lnNPW2 -0.00905*** 0.0144*** -0.00190 0.00872*** 0.00268 (0.00290) (0.00287) (0.00274) (0.00237) (0.00296) Composite -0.00287 0.0221 -0.0665*** -0.0314 -0.0240 (0.0148) (0.0332) (0.0246) (0.0242) (0.0230) Conglomerate 0.0194 0.00179 -0.0156 -0.0274 -0.0198 (0.0195) (0.0425) (0.0360) (0.0366) (0.0325) Leverage/Unaffiliated/Market FE/Year FE/Constant Yes Yes Yes Yes Yes

Overall R2 0.582 0.381 0.367 0.451 0.547 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116



92

Appendix C (Continued) Robustness test 15: Use the actual loss ratio to replace the smoothed loss ratio Variables Price Profit ROE Price Profit ROE CE -0.300*** 3.095 0.0550 (0.0546) (2.174) (0.0462) SE -0.225*** 0.198 -0.0565 (0.0694) (3.006) (0.0376) XE -0.242*** 3.080 0.0816* (0.0505) (2.348) (0.0461) Market share 0.441 43.74* 0.899 0.416 42.67* 0.839 (0.493) (23.72) (0.665) (0.482) (23.79) (0.655) Market concentration 0.0914 -0.384 -0.157 0.155 0.554 -0.0945 (0.168) (9.045) (0.102) (0.170) (9.161) (0.0894) Market growth 0.00283*** 0.0440 0.000834 0.00296*** 0.0463 0.000924 (0.00101) (0.0471) (0.000637) (0.00100) (0.0462) (0.000620) Leverage ratio -0.0342*** -1.982*** -0.0212 -0.0337*** -1.967*** -0.0210 (0.00570) (0.362) (0.0198) (0.00539) (0.361) (0.0196) Unaffiliated 0.0407 -1.583 -0.00568 0.0344 -1.711 -0.0145 (0.0579) (3.075) (0.0255) (0.0575) (3.116) (0.0275) Market FE/ Constant Yes Yes Yes Yes Yes Yes Overall R2 0.302 0.084 0.051 0.310 0.084 0.054 Obs./No. of Reinsurers 757/111 757/111 841/116 757/111 757/111 841/116

Notes: We present the results of a random effects panel regression model with robust standard errors clustered at firm level, provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


93

Appendix C (Continued) Robustness test 16: Fixed effects models Variables Price Profit ROE Price Profit ROE CE -0.0921*** 17.97*** 0.0571 (0.0280) (4.080) (0.0605) SE -0.0272 14.37*** -0.0300 (0.0393) (3.339) (0.0485) XE -0.0828*** 14.72*** 0.0625 (0.0254) (3.559) (0.0551) Market growth -0.000244 0.0224 0.000842 -0.000218 0.0342 0.000737 (0.000965) (0.0758) (0.00124) (0.000977) (0.0765) (0.00123) Leverage ratio -0.00859*** -0.445*** -0.0390** -0.00867*** -0.486*** -0.0387** (0.00299) (0.156) (0.0177) (0.00286) (0.158) (0.0177) Firm FE/Year FE/Constant Yes Yes Yes Yes Yes Yes R2 0.148 0.098 0.300 0.148 0.110 0.302 Obs./No. of Reinsurers 841/116 841/116 841/116 841/116 841/116 841/116

Notes: We present the results of firm and year fixed effects panel regressions with robust standard errors clustered at firm level, provided in parentheses; *, **, *** denote the significant differences of the regression coefficients from 0 at the 10%, 5%, and 1% levels, respectively.


94

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100

Essay III Internationalization and performance: The role of industry context and cost eficiency

Abstract

A central matter of dispute in the internationalization literature is whether a systematic relationship exists between internationalization (I) and firm performance (P). We extend the understanding of context dependency of the I-P relationship based on an insurance dataset comprising two subsamples—life and nonlife insurance. We empirically show industry context and cost efficiency to be relevant drivers of the I-P relationship. The life insurance industry exhibits a relatively high liability of foreignness leading to a negative impact of inter-regional internationalization on performance as opposed to the nonlife insurance industry, for which the relationship is insignificant. Our results explain the disparate degrees of internationalization in different industries from the perspective of the I-P relationship. Moreover, we introduce a novel measure of cost efficiency and discuss its mediating and moderating roles in the I-P relationship.

Keywords

Insurance, Internationalization, Institutional Context, Industry Idiosyncrasies, Cost Efficiency, Data Envelopment Analysis

-------------------------------------

Christian Biener, Martin Eling, Ruo Jia (2016)

This paper was presented at the World Risk and Insurance Economics Congress (WRIEC) 2015 in Munich and has been submitted to the Journal of Business Research.

Essay III Internationalization and Performance

101

1. Introduction

Internationalization 58 of firms has enormously increased over the past decades in both manufacturing and service industries and generated a vast academic literature (Capar and Kotabe, 2003; Kirca, Roth, Hult, and Cavusgil, 2012). For researchers and practitioners alike, one of the fundamental topics of interest is the impact of internationalization (I) on firm performance (P) (see, e.g., Singla and George, 2013; Tsai, 2014). However, the empirical evidence, at first sight, seems inconsistent and suggests that I-P relationships display multiple stages (Contractor, Kundu, and Hsu, 2003) and is context dependent (Kirca et al., 2012).

Several contextual factors have been found to drive the I-P relationship (Kirca et al., 2012). For example, Capar and Kotabe (2003) and Contractor et al. (2003) show that the I-P relationship depends on the industry with differences between service and manufacturing firms as well as between knowledge-based and capital-intensive service firms. Rugman and Verbeke (2004; 2007) theorize and illustrate that the I-P relationship depends on the geographical scope of internationalization. Qian, Khoury, Peng, and Qian (2010) empirically observe such differences between regionalization and globalization strategies. Singla and George (2013) find that firm characteristics such as age, size, and group structure moderate the I-P relationship. Tsai (2014) empirically documents an I-P relationship dependency on a firm’s intangible assets, including learning capabilities and production technology.

We extend the understanding of context dependency of I-P relationships in two ways. Following the industry dependency rationale, we first show that differences in I-P relationships are present even between two industries that appear to be very close—i.e., life and nonlife insurance. We theorize that such differences follow from idiosyncrasies in the liability of foreignness (Zaheer, 1995), with life insurers burdening higher liabilities due to its credence good characteristics, stricter regulation, and higher costs for cultural and local adaptation. Second, we introduce an innovative measure of cost efficiency to capture liability of foreignness and firm production technology. We document its moderating role in the I-P relationship. We show that globalization strategies are particularly harmful to profitability for firms relying on high levels of cost efficiency to compete with their peers.

Insurance provides a persuasive context to analyze internationalization strategies, due to its large variation in the degree of internationalization that followed significant regulatory changes in the 1990s in many economies (Outreville, 2010; Pasiouras and Gaganis, 2013).59

58 Studies using labels such as internationalization, globalization, geographical diversification, international

diversification, international expansion, and multinationality usually refer to the same strategic management construct (Hitt, Tihanyi, Miller, and Connelly, 2006). In this paper, we use two terms as internationalization and globalization. Globalization refers to the inter-regional internationalization (Rugman and Verbeke, 2004), whereas internationalization covers both intra- and inter-regional cross-border multinationality.

59 For example, in 1994, the European insurance markets were deregulated to create a single market, which led to a wave of acquisitions and geographical expansion across borders in the late 1990s.


102

Insurance furthermore shares innovation in IT and global communication with many other industries that lead to a wide variety of corporate strategic changes (Sadhak, 2005; Klarner and Raisch, 2013). Moreover, specific costs and benefits of internationalization make insurance an especially intriguing study subject. The intangible nature of insurance products is a double-edged sword to internationalization because, on the one hand, costs of storage and transportation are nonexistent; while, on the other hand, innovations can easily be copied. The regulated nature of most insurance markets may create entry barriers, thereby limiting the internationalization options and increasing costs. The motivation to concentrate on the insurance industry is also driven by its two distinctive sub-industries: life and nonlife insurance, which provide ideal context to study the industry dependency of internationalization (Felício and Rodrigues, 2015). To our knowledge, we provide the first piece of evidence concerning the I-P relationship in the life insurance industry and for the first time present the different nature of the life and nonlife insurance industries in terms of their internationalization strategy and I-P relationships.60

Our findings show that the impact of globalization on firm performance is negative for the life insurance industry and insignificant for the nonlife insurance industry. We empirically reject the potential mediating role of cost efficiency in the I-P relationship (Wagner, 2004), but find evidence of a moderating role. Our results thus reinforce and expand the contextual arguments in the I-P relationship literature. The findings suggest that managers and regulators are well advised to adopt different internationalization strategies and regulatory policies for industries that appear to be very close, but exhibit idiosyncrasies affecting the I-P relationship.

The remainder of this paper is organized as follows. We first review the internationalization literature and develop our hypotheses in Section 2. We then describe our variables, sample, and empirical models in Section 3, followed by the presentation of the results and robustness tests in Section 4. In Section 5, we discuss the roles of cost efficiency and other potential contextual factors in the I-P relationship both theoretically and empirically. Finally, we conclude the paper with managerial implications in Section 6.

2. Literature review and hypothesis development

Internationalization has become an increasingly important strategic option available to firms seeking sustainable competitive advantages (Tallman and Fladmoe-Lindquist, 2005). However, the liability of foreignness is a considerable disadvantage resulting in extra costs of internationalization (Zaheer, 1995; Nachum and Zaheer, 2005). Ultimately, it is an empirical task to weigh the potential benefits and costs of internationalization and to identify their

60 The size and function of the global insurance industry underscores its own economic importance (Pasiouras and

Gaganis, 2013), with USD 4.6 trillion in premium volume and USD 27 trillion in managed assets, approximately 12% of global financial assets, in 2013 (Swiss Re, 2014). The insurance industry constitutes a reliable source of capital and risk transfer capacities for the global economy, making the industry relevant outside of its market domain.


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impact on firm performance under different settings. Many empirical studies have examined the relationship between the degree of internationalization (DOI) and firm performance in the past 45 years. However, the results are mixed and inconclusive (Hitt et al., 2006; Hennart, 2007), raising more questions than answers (Glaum and Osterle, 2007). A few syntheses and meta-analyses have attempted to reconcile the mixed empirical results, but arrive at different conclusions. Hitt et al. (2006) favor the inverted U-shaped I-P relationship, where firm performance increases with DOI when the DOI is low and decreases with DOI when the DOI is high. Hennart (2007) argues for no systemic relationship; Contractor (2007) supports the S-shape; and Bausch and Krist (2007) and Kirca et al. (2011) deduce a linear positive relationship based on meta-analyses. Kirca et al. (2012) suggest that the I-P relationship is moderated by various contextual factors, including firm-, industry-, and country-specific factors.

The concept of an internationalization threshold—that is, the DOI at which the costs of internationalization exceed its benefits—was used to explain the mixed I-P relationships (Hitt, Hoskisson, and Kim, 1997). Beyond a certain DOI, multinational companies may have expanded to peripheral and/or unfamiliar markets and have become too complex, leading to a faster increase in coordination and governance costs relative to incremental revenues from further expansion.61 Thus, an overall inverted U-shaped I-P relationship is expected (Hitt et al., 1997). The S-shaped three-stage paradigm allows for an initial negative relationship at low DOIs to cover the high cost and inexperience at the initial stage of internationalization, a subsequent positive relationship at intermediate DOIs, and a negative relationship at high DOIs when over-internationalization occurs (Contractor et al., 2003; Lu and Beamish, 2004). The right tail of the S-shaped relationship corresponds to the inverted U shape.62

Regionalization theory aims to explain the mixed I-P relationships by adding a further geographical dimension to the low versus high DOI by differentiating intra- and inter-regional internationalization or, in other words, regionalization versus globalization (Rugman and Verbeke, 2004, 2007; Qian et al., 2010). Rugman and Verbeke (2004, 2007) suggest that the liability of inter-regional foreignness is higher than the liability of intra-regional foreignness due to high learning costs, limited transferability of knowledge, high risk of operations, and increased physical and cultural distance, among others. Qian et al. (2010) show that a greater degree of intra-regional internationalization may positively correlate with firm performance;

61 Firms over-internationalize because (1) they rarely continuously monitor their pace of internationalization and thus

simply do not know in time when they are overextended (Contractor et al., 2003); and (2) some firms may deliberately over-internationalize for long-term strategic reasons, even though it is detrimental to medium-run returns (Hennart, 2007).

62 In stage 1, the learning and local adaptation costs are likely to exceed the incremental benefits. In stage 2, the DOI increases to establish scale economies, reputation, and diversification benefits (i.e., reduce risk or business volatility). In stage 3, the lack of knowledge of distant markets and the complexity in a large organization may again turn the cost–benefit balance, resulting in a negative internationalization impact on firm performance (Outreville, 2010).


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however, the relationship between the degree of inter-regional internationalization and performance should exhibit an inverted U shape.63 Thus, globalization is more likely to have a negative impact on firm performance than regionalization.

Oh and Contractor (2014) impose Rugman and Verbeke’s (2004, 2007) geographical scope perspective on Contractor et al.’s (2003) S-shaped three-stage paradigm. They propose that the intra-regional internationalization encompasses stages 1 and 2 (i.e., at low and medium DOIs) and the inter-regional internationalization encompasses stage 3 (i.e., at high DOIs). They support the regionalization theory with evidence showing that inter-regional internationalization generates a more negative impact on firm performance than intra-regional internationalization.

We operationalize Qian et al.’s (2010) and Oh and Contractor’s (2014) theoretical framework in the insurance industry, by incorporating both DOI and geographical scope perspectives. We focus on the inter-regional aspect of internationalization (i.e., globalization) because globalization is controversial due to the large cultural, economic, regulatory, and legal differences across regions (Qian et al., 2010; Oh and Contractor, 2014) and particularly so in the insurance industry. The cultural and economic differences across regions are much more significant than those within regions; whereas Europe, North America, Australia, and New Zealand are mostly mature insurance markets and Asia, Africa, and Latin America are largely emerging markets. The regulatory and legal gaps are also more pronounced across regions. European insurance markets are regulated under a unified scheme. Canada and the U.S. have similar regulations, as do Australia and New Zealand. The decision to focus on inter-regional internationalization is also driven by the fact that the premium distribution at the country level is not available in existing insurance databases. This leads to our first hypothesis:

• The impact of globalization (inter-regional internationalization) on firm performance in the insurance industry depicts an inverted-U shape (H1).

The industry dependency (context-based) hypothesis explains the mixed I-P relationships by industry idiosyncrasies. Service and manufacturing firms each have their idiosyncrasies resulting in different I-P relationships (Capar and Kotabe, 2003). First, the nature of service business is mostly intangible (Berthon, Pitt, Katsikeas, and Berthon, 1999); second, the production and consumption of many services occur simultaneously (Habib and Victor, 1991); third, services usually require more local presence (i.e., foreign direct investment) than the manufacturing of exportable products (Boddewyn, Halbrich, and Perry, 1986; Singla and George, 2013); fourth, services may have to be adapted more extensively than manufactured

63 The line between inter- and intra-region is typically defined at the continent level. For example, Rugman and Verbeke

(2004, 2007) consider the most relevant regions as three “broad triads”: North America (NAFTA), Europe (EU), and Asia. Qian et al. (2010) define four regions: Africa, Asia and the Pacific, Europe, and the Americas.


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products due to customers’ linguistic and cultural differences (Patterson and Cicic, 1995). These idiosyncrasies of service firms increase their liability of foreignness. Some other idiosyncrasies of service firms may generate additional benefits. For example, knowledge learning worldwide may improve competitiveness (i.e., economies of geographical scope). Service firms can also achieve economies of scale by performing activities at locations that provide the lowest cost (Capar and Kotabe, 2003). Moreover, the nonexistence of shipping and storage costs is an advantage for internationalization.

Contractor et al. (2003) further distinguish between knowledge-based (e.g., financial services, consulting, marketing) and capital-intensive (e.g., air transport, shipping, hotels, restaurants) service firms. First, knowledge-based service firms have a lower burden of tangible asset investments; thus, they are less likely to commit “irreversible resources” to foreign markets. Second, knowledge-based service firms have clients already established abroad and thus can easily adopt “follow the client” strategies. Third, knowledge-based service firms possibly exhibit greater global standardization, thereby lowering the liability of foreignness (Contractor et al., 2003). These idiosyncrasies suggest that knowledge-based service firms are easier to internationalize than capital-intensive firms. Thus, knowledge-based service firms as opposed to capital-intensive service firms are also more prone to rush foreign market expansion and over-expand, leading to poor performance (Petersen, Petersen, and Sharma, 2002; Contractor et al., 2003). Therefore, Contractor et al. (2003) hypothesize and demonstrate an S-shaped I-P relationship for knowledge-based service firms but a U-shape for capital-intensive service firms.

Following this industry dependency rationale, Hitt, Bierman, Uhlenbruck, and Shimizu (2006) investigate professional service firms (e.g., law firms, consulting firms), a sub-category of knowledge-based service firms. The idiosyncrasies of professional service firms lie with the universally applicable knowledge and the slow expansion following existing clients, which enable professional service firms to enjoy positive I-P relationships. Financial services are another sub-category of knowledge-based service firms. Outreville (2010) investigate the world’s largest financial groups to confirm Contractor et al.’s (2003) S-shaped I-P relationship. A few empirical papers have gone further down the path of industry dependency, looking at sub-industries in financial services. Hejazi and Santor (2010) investigate the Canadian banking industry and document a positive I-P relationship. Ma and Elango (2008) investigate the U.S. nonlife insurance industry. They find that nonlife insurers focusing on specific lines of business benefit from internationalization, but internationalization reduces returns if the insurer already has a diversified product range. Outreville (2012) investigate the world’s largest reinsurance groups and document an overall positive but slightly S-shaped curvy I-P relationship in terms of underwriting performance.


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The liability of foreignness concept (Zeheer, 1995) helps to determine how and why the I-P relationship in life and nonlife insurance industries are different. Liabilities of foreignness result from the increased complexities of coordination, governance, and operation among diverse operating units (Hitt et al., 1997; Capar and Kotabe, 2003), which results in extra costs of internationalization. These costs and complexities may become more prominent due to the physical distance, logistic difficulties, the cultural and linguistic distance, regulatory barriers, and currency fluctuations,64 among others (Sundaram and Black, 1992; Capar and Kotabe, 2003). We thus compare idiosyncrasies of the life and nonlife insurance industries and find that life insurance exhibits higher liabilities of foreignness in all cost components compared to nonlife insurance (see Table 1).

Table 1 Idiosyncrasies of life and nonlife insurance industries Life Nonlife Related literature Credence good Long term Short term Rejda and McNamara (2013); Cummins and

Weiss (2014) Regulation High Low Culture influence Strong Weak Hempel (1998); Chui and Kwok (2008, 2009);

Kunreuther and Michel-Kerjan (2015) Local adaptation High Low

First, life insurance is a credence good with a long contract duration, which can be lifelong for the whole life and pension coverage. Premiums are paid upfront or in early periods of the contract, and the benefits are paid after a substantial time delay; nonlife insurance contracts usually last only one year (Rejda and McNamara, 2013). Thus, it is more difficult for foreign players to operate life insurance in another region than to operate nonlife insurance because of the potential trust issue with local customers, who are concerned about the insurer being reachable to pay contractual benefits after decades. Second, life insurers typically are subject to stricter regulations than nonlife insurers due to the long-term nature of insurance policies, which requires more protection for the policyholders. Thus, the entry barrier for the life insurance industry is usually higher than it is for the nonlife insurance industry in many countries. China, for example, requires foreign life insurers to establish joint ventures with local firms, whereas nonlife insurers and other financial services are allowed to establish wholly owned subsidiaries and branches. This joint venture barrier imposed by the regulator constitutes an additional liability of foreignness for foreign life insurers. The regulation for life insurance is expected to be stricter also because life insurers are usually more leveraged than nonlife insurers and more vulnerable to systemic risks (Cummins and Weiss, 2014).

Third, national cultures have a stronger impact on life insurance consumption than on nonlife insurance consumption (Chui and Kwok, 2008; 2009). For example, Hempel (1998) emphasizes that multinational firms as life insurers’ clients must consider the national culture 64 Insurance markets, in particular, benefit from domestic currency assets in terms of asset liability matching, i.e.,

matching cash flows of expected insurance benefit or claim payments with cash flows from assets in the same currency (Kouwenberg, 2001).


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when they design employee benefit programs for employees in different countries. Thus, foreign life insurers have the additional liability of foreignness to compensate for the cultural advantages of domestic life insurers. Fourth, some country-specific institutional settings have a stronger influence on life insurance than on nonlife insurance. For example, the pre-existence of social security and/or inheritance tax systems may result in different demand patterns for life insurance (Kunreuther and Michel-Kerjan, 2015). These issues are less relevant for nonlife insurance demands. Such country-specific institutional settings limit the transferability of underwriting know-how in life insurance and require more extensive product adaptation to the local markets.

We thus operationalize the industry dependency rationale in the insurance industry and expect that the impact of globalization (inter-regional internationalization) on firm performance is different for life and nonlife insurers. Given the higher liability of foreignness for life as opposed to nonlife insurance, we hypothesize that:

• The impact of globalization (inter-regional internationalization) on firm performance is more negative for life insurers than for nonlife insurers (H2).

Cost efficiency is considered as an innovative and alternative performance measure when testing the above hypotheses, in addition to the conventional financial ratios. However, cost efficiency is more than a performance measure. In Section 5, we will disentangle the role of cost efficiency in the I-P relationship by examining whether cost efficiency mediates or moderates the I-P relationship.

3. Data and methodology

3.1. Measures

We measure an insurer’s degree of globalization (i.e., inter-regional internationalization) by its inter-regional sales entropy:

𝐶𝐶𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑖𝑖,𝑐𝑐 = ∑ 𝑅𝑅ℎ𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖,𝑐𝑐,𝑗𝑗 × ln ( 1𝑠𝑠ℎ𝑎𝑎𝑐𝑐𝑐𝑐𝑖𝑖,𝑡𝑡,𝑗𝑗

)7𝑗𝑗=1 ,

whereas sharei,t,j represents the portion of gross premiums written by firm i in year t from region j to firm i’s total gross premiums written in year t. The entropy measure based on sales across markets is widely used in international business studies (see, e.g., Sanchez-Bueno and Usero, 2014; Wu, Chen, and Jiao, 2015). Alternatively, we use the Herfindahl index (see, e.g., Cummins, Tennyson, and Weiss, 1999; Elango and Pattnaik, 2013) as a robustness test (see Section 4.2):

𝐶𝐶𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝑆𝑆𝑔𝑔𝑔𝑔𝑔𝑔𝑖𝑖,𝑐𝑐 = 1 − ∑ 𝑅𝑅ℎ𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖,𝑗𝑗,𝑐𝑐27

𝑗𝑗=1 .


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We measure an insurer’s performance by its risk-adjusted returns and cost efficiency. According to Hejazi and Santor (2010), risk inherent in internationalization must be accounted for, because a positive I-P relationship simply indicates that an increase in performance has paid off the internationalization costs; however, the increase in performance might not be sufficient to compensate for an increase in risk. Thus, any performance analysis must account for changes in risk, which is implemented by using risk-adjusted measures of firm performance in almost all I-P relationship studies of financial services (see, e.g., Ma and Elango, 2008; Hejazi and Santor, 2010; Outreville, 2010, 2012).

We follow this generally accepted practice. First, we shift all performance indicators (ROA, ROE) by adding their respective minimum values to ensure that all values are positive (Ma and Elango, 2008).65 Then, we divide the shifted performance indicators by the firm-level risk measure (Elango, Ma, and Pope, 2008; Outreville, 2010). We measure an insurer’s risk by its overall business volatility, that is, the standard deviation of a firm’s performance indicator over all available years (Lamm-Tennant and Starks, 1993; Eling and Marek, 2014). A minimum of five years of performance indicators is required to calculate the standard deviations (Pasiouras and Gaganis, 2013). Alternatively, we conduct robustness tests using (1) risk adjusted ROA and ROE before tax and (2) five-year rolling window moving standard deviations (Elango, 2010) to adjust the returns. The results of these tests confirm our conclusions (see Section 4.2).

𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑅𝑅𝑡𝑡𝐶𝐶𝑟𝑟 𝑅𝑅𝑅𝑅𝑛𝑛𝑖𝑖,𝑐𝑐 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡+0.3𝑠𝑠𝑐𝑐𝑐𝑐.𝑐𝑐𝑐𝑐𝑑𝑑.𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖

,

𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑅𝑅𝑡𝑡𝐶𝐶𝑟𝑟 𝑅𝑅𝑅𝑅𝐸𝐸𝑖𝑖,𝑐𝑐 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡+1.9𝑠𝑠𝑐𝑐𝑐𝑐.𝑐𝑐𝑐𝑐𝑑𝑑.𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖

.

We introduce data envelopment analysis (DEA) cost efficiency as a new performance measure in the context of international business research. Cost efficiency measures a firm’s ability to minimize inputs given a certain level of output. It captures the overall operational performance of a firm relative to its peers including the cost of foreignness. The measure is well established in economic theory as business firms minimize costs and maximize profits subject to existing technology and expertise constraints. Moreover, it has been shown that cost efficiency measures are, to some extent, consistent with insurers’ returns such as ROA and ROE (Greene and Segal, 2004). Therefore, cost efficiency constitutes a meaningful and alternative performance measure to profitability.

65 The calculation of risk-adjusted ROA requires a positive ROA value to keep the risk adjustments for all observations

in the same direction. Otherwise, the adjustments for negative and positive ROA may have different effects, particularly when the standard deviations vary across firms. The negative ROE or ROA accounts for 21% of the total sample. We conduct a robustness test without shifting the negative values, the results are very close to our core models and available from the authors upon request.


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We follow a standard procedure of DEA analysis to derive cost efficiency scores for each insurer in each year. A detailed discussion of the DEA methodology can be found, for example, in Eling and Luhnen (2010) and Cummins and Weiss (2013). Whereas in insurance research DEA analysis is widely applied, it remains evolutionary in international business research. To the best of our knowledge, this is the first paper to introduce a DEA cost efficiency measure at firm-level to explain the I-P relationship.66 The details of the DEA approach are presented in Appendix A.

3.2. Sample and summary statistics

We use Best’s Insurance Reports (A.M. Best, 2003–2013), which are a comprehensive source of information on insurance companies and are widely used in business research (Katrishen and Scordis, 1998; Elango, 2009; Pasiouras and Gaganis, 2013). We exclude composite insurers offering both life and nonlife insurance, because we aim to investigate industry dependency of the I-P relationship between the two sub-industries and because life and nonlife insurance is operated by separate entities in most markets. 67 We also exclude reinsurers and captive insurers, which operate different business models from primary insurers. We exclude entities such as branches, special purpose vehicles, and firms that operate insurance as a minor business (e.g., banks, manufacturers, and healthcare providers).

We trim insurers’ key ratios at the 0.5th and 99.5th percentiles for life and nonlife insurers separately in order to reduce the potential bias driven by extreme values (Barth, 2000; Kanagaretnam, Lim, and Lobo, 2011).68 The key ratios are those used in the later DEA and regression analyses: risk adjusted ROA, risk adjusted ROE, leverage ratio (total liabilities divided by total capital and surplus), liquidity ratio (liquid assets divided by total liabilities), premium retention ratio (net premiums written divided by gross premiums written), and yearly real premium growth. The complete dataset contains 1,333 life insurers with 8,497 firm-year observations and 2,323 nonlife insurers with 15,121 firm-year observations. The

66 Bunyaratavej, Hahn, and Doh (2008) present a country-level DEA analysis to examine the attractiveness of host

countries for services offshoring. 67 The proportion of composite insurers is only 12% of all firm-year observations in our sample, many of which are the

consolidation of respective life and nonlife entities that are already incorporated in the sample. We acknowledge that ideally, a continuous measure of life/nonlife premium ratio would be optimal to capture the difference of life and nonlife insurers, however, the data are not available to calculate such ratios.

68 Outliers are present in the A.M. Best dataset because of startups that do not yet underwrite business and runoff insurers that are not comparable to and not in competition with regular insurers (Biener, Eling, and Jia, 2015). We alternatively trim the key ratios at the 1st and 99th percentiles, and 2nd and 98th percentiles. The different trimming methods are consistent in their results and do not change our conclusions. The results are available from the authors upon request.


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2012 dataset covers over 50% of global insurance premiums outside of North America69 (Swiss Re, 2014).

The Best’s Insurance Reports capture insurers’ internationalization by the regional distribution of gross premiums written (i.e., Europe, Latin America, North America, Australia and New Zealand, Asia, Africa, and the rest of the world).70 Due to different disclosure requirements in different markets, our sample is limited to those firms reporting geographical distribution of premiums to A.M. Best. Thus, our final sample is an unbalanced panel consisting of 350 life insurers with 1,713 firm-year observations and 599 nonlife insurers with 2,986 firm-year observations. As shown in Appendix B in more detail, our sample covers 11 years, from 2003 to 2013, and insurers domiciled in the three major regions (i.e., Europe, Asia, and Oceania).

80% of the firm-year observations in our sample are from the member states of the European Union (EU), where cross-border barriers have been reduced to build a single insurance market since the Third Life and Non-Life Insurance Directives from 1994. It is a controversial question to determine whether EU insurers’ sales in other EU member states should be considered as foreign or domestic sales. This paper does not aim to study the geographical diversification among states within one market,71 but to investigate the internationalization in a broader geographical scope (i.e., inter-regional internationalization or globalization), where significant differences emerge in terms of regulation and culture. Internationalization is thus measured at the inter-region level instead of a cross-country level.

In Table 2, we report summary statistics of our sample of insurers covering a great variety of small and large, high and low growth, single-line and multi-line, and mature and emerging market firms. Within our sample, 48 life insurers (14%) with 220 firm-year observations (13%) and 128 nonlife insurers (21%) with 535 firm-year observations (18%) are globalized (i.e., operating in more than one region). It is necessary to keep both the globalized and non-globalized firms in the sample because we are interested in both questions: (1) whether globalization makes a difference to performance at all and (2) how sensitive performance is

69 We are not able to include U.S.-based insurers, because their geographical distributions of premiums are recorded in

aggregate as “Aggregate Other Alien,” if the premiums are written outside the U.S. and Canada. To our knowledge, the regional premium split for U.S. based insurers is also not reported in other publicly available datasets. We tried to manually collect the information to enlarge our dataset, but were unsuccessful. Oetzel and Banerjee (2008) noted the incompleteness of the A.M. Best dataset, yet insist that it remains the most comprehensive dataset available for the insurance industry. Our investigation focuses on global firms, which are less affected by the incompleteness than other applications incorporating smaller local firms.

70 According to A.M. Best, “rest of the world” is “a catch all for where a company reports perhaps key countries or country they do business in and then group the rest together as ‘rest of the world.’” We consider the rest of the world to be one standalone region; if an insurer reports sales in two regions and groups all other operations in the rest of the world, we then assume that the insurer operates in three regions. The premiums falling in the rest of the world only take 2% of total premiums in our sample.

71 Biener, Eling, and Wirfs (2015) shed light on the cross-states expansion within the European market.


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to the degree of globalization.72 We conduct the robustness test with the subset of globalized firm-years only, the results of which confirm our conclusions (see Section 4.2). Not surprisingly, various firm characteristics differ between our sample insurers and those outside of our sample. We address this issue by conducting another robustness test, where we assume that all out-of-sample insurers are not globalized (i.e., operating only in the home region). The results of this test also confirm our conclusions (see Section 4.2).

72 It would be a different case if the entropy measure starts at the cross-country level. In that case, entropy 0 means no

internationalization at all and, thus is outside the scope of DOI. In our case, even if the globalization entropy equals 0, the firm may also be internationalized, though probably to a low degree (Oh and Contractor, 2014) and focus on its home region; thus, comparing zero entropy with positive entropy is meaningful.


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Table 2 Summary statistics Life (N=1,713) Nonlife (N=2,986) Unit Mean Std. Dev. Median Mean Std. Dev. Median

Panel A: Globalization Global (1 if operates in two or more regions) Dummy 0.13 0.33 0 0.18 0.38 0 Globalization (entropy) 1 0.022 0.091 0 0.080 0.22 0 GlobalHHI (Herfindahl index) 1 0.012 0.057 0 0.048 0.13 0

Panel B: Profitability ROA 1 0.0047 0.035 0.0038 0.030 0.057 0.027 Risk-adjusted ROA 1 61.0 116.1 22.5 13.3 12.3 9.79 ROE 1 0.049 0.25 0.073 0.090 0.18 0.093 Risk-adjusted ROE 1 21.1 23.1 12.9 23.1 19.7 17.8

Panel C: Cost Efficiency scores Cost efficiency (regional frontiers) 1 0.60 0.24 0.63 0.36 0.20 0.32 Cost efficiency (global frontier) 1 0.54 0.25 0.57 0.30 0.18 0.27

Panel D: Input quantities Labor (approximate number of employees) 1 7,442 20,554 767 1,824 5,680 235 Equity capital (capital and surplus) a 1,000 561,837 14,26,412 142,444 241,552 711,142 63,047 Debt capital (total liabilities) a 1,000 7,965,671 14,825,768 2,390,283 711,134 2,298,383 151,745

Panel E: Input prices Labor price (annual wage) a 1 61,264 29,914 72,685 70,227 25,736 73,898 Equity price (MSCI yearly returns) 1 0.10 0.078 0.089 0.091 0.064 0.087 Debt price (IMF long-term govt. bond rates) 1 0.042 0.019 0.040 0.040 0.019 0.039

Panel F: Output quantities Benefits paid plus reserve changes (life) or smoothed loss (nonlife) a 1,734,010 4,604,885 438,728 182,377 431,519 36,326 Total invested assets a 1,000 7,651,891 14,082,744 2,275,642 656,598 1,968,655 140,647

Panel G: Control variables Total assets a 1,000 8,527,509 15,886,443 2,603,160 952,686 2,863,772 226,179 Real premium growth 1 0.28 1.52 0.018 0.13 0.77 0.038 Premium retention ratio 1 0.91 0.17 0.99 0.78 0.25 0.88 Leverage ratio 1 23.8 40.8 14.2 3.19 3.49 2.32 Liquidity ratio b 1 1.00 0.86 0.98 1.74 4.06 0.95 Number of lines of business (LOB) 1 2.05 1.60 1 3.51 3.46 2 Life or nonlife insurance penetration 1 0.0061 0.0030 0.0060 0.0021 0.00066 0.0023 Real GDP growth 1 0.022 0.038 0.018 0.015 0.031 0.017

Notes: a In USD and inflation adjusted for 2013. b. The liquid assets in the A.M. Best database include “cash, bonds, shares, and assets held to cover linked liabilities.” With this broad definition, liquidity ratio is thus large.


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3.3. Empirical models

We test our hypotheses by estimating the firm-year fixed effects model. The model is chosen on the grounds of log-likelihood ratio and Hausman tests.73 It is important to apply firm-year fixed effects, because the I-P relationship mostly concerns with how the DOI changes of a firm influence its performance over time. The fixed effects model controls for the unobservable firm- and year-specific characteristics and thus isolates the within-group effects.74 Alternatively, we use the random effects model as a robustness test, the results of which confirm our conclusions (see Section 4.2). The regression specification is as follows:

𝑃𝑃𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑛𝑛𝐸𝐸𝐶𝐶𝑖𝑖,𝑐𝑐 = 𝛽𝛽0 + 𝛽𝛽1𝑀𝑀𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑖𝑖,𝑐𝑐 + 𝛽𝛽2𝑀𝑀𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑖𝑖,𝑐𝑐2 + 𝛽𝛽3𝑀𝑀𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑖𝑖,𝑐𝑐 ×𝐿𝐿𝑅𝑅𝑓𝑓𝐶𝐶𝑖𝑖 + 𝛽𝛽4𝑀𝑀𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝑆𝑆𝑅𝑅𝑧𝑧𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑖𝑖,𝑐𝑐2 × 𝐿𝐿𝑅𝑅𝑓𝑓𝐶𝐶𝑖𝑖 + 𝛽𝛽5𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝛽𝛽6𝑌𝑌𝐶𝐶𝐶𝐶𝐶𝐶𝑐𝑐 + 𝛽𝛽7𝐹𝐹𝑅𝑅𝐶𝐶𝐶𝐶𝑖𝑖 + 𝜀𝜀𝑖𝑖,𝑐𝑐. (1)

Life is a dummy variable, with 1 indicating a life insurer and 0 a nonlife insurer. Life does not appear in Equation (1) as a standalone term because the fixed effects model does not allow for time-invariant independent variables.

In addition, we separately test our hypotheses with life and nonlife insurer subsamples. According to our hypotheses, the primary explanatory variables, globalization and its square term, are included in the core models; however, we present the estimations with the linear globalization term only in a robustness test75 (see Section 4.2). The entropy measure of globalization is centered to avoid multicollinearity with its squared term.76

Various organizational factors affect the performance of insurance companies (Felício and Rodrigues, 2015). We control for the following firm- and country-specific characteristics (Xi,t): firm size in terms of total assets, yearly real premium growth, premium retention ratio, leverage ratio, liquidity ratio, the level of product diversification measured by number of lines of business written by the insurer,77 life or nonlife insurance penetration (i.e., life or nonlife insurance premiums over GDP of respective country-years) capturing the maturity of firms’ home markets, and real GDP growth capturing the economic environment in firms’ home markets. Other firm- and country-specific factors may influence the I-P relationship, such as

73 Both tests yield p-values equal 0.00, supporting to use the fixed effects models. 74 The cross-sectional effects of internationalization on performance may also be of interest, which, however, require full

control over factors that influence the DOI or firm performance, for example, firm culture and the history of internationalization. These intangible factors are difficult to observe and thus the cross-sectional I-P relationship is very likely to be illusory, if any, due to omitted variables.

75 The linear and squared terms of globalization are introduced into the model in a step-by-step manner (Outreville, 2010). We do not use the cubic term of globalization because (1) our sample captures the inter-regional aspect of internationalization, which is already at the high DOI in the three-stage I-P paradigm (Oh and Contractor, 2014) and thus the right tail of the S shaped I-P relationship corresponds to an inverted U shape. In other words, the left tail of the S-shape is out of the scope of our analysis. (2) The cubic term generates serious multicollinearity with its first- and second-order terms.

76 The variance inflation factors in the base line model without fixed effects fall below 5, suggesting no multicollinearity issue.

77 These sub-lines of business include e.g., whole life, medical expense, annuity in the life insurance industry and motor, liability, property in the nonlife insurance industry.


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company age, firm culture, the management team’s international experience, R&D strength, and competition in the home market (Carpenter and Fredrickson, 2001; Wan and Hoskisson, 2003), which we are not able to control for due to data limitations. We implicitly account for these factors by firm fixed effects. We also use the year fixed effects to capture the performance dynamics over time.

When the DEA cost efficiency is used as a performance measure, we show two alternative models—Tobit and truncated regressions with upper limits at 1—in the robustness tests (see Section 4.2), following a common practice of DEA second-stage analyses (Cummins and Weiss, 2013; Cook and Zhu, 2014).

4. Results

4.1. Hypotheses tests

Columns 1-6 of Table 3 report the estimation results of Equation (1) with risk adjusted returns as performance measures. The full sample results including life and nonlife insurers in Columns 1 and 2 show positive coefficients for globalization and significantly negative coefficients for the interaction term globalization×life. Thus, the impact of globalization on risk-adjusted performance is negative for life insurers and insignificant for nonlife insurers. These results are confirmed by the subsample estimations for life and nonlife insurers separately, as shown in Columns 3 to 6. The results using risk adjusted returns as performance measure do not exhibit an inverted-U shaped I-P relationship (H1) but a negative linear relationship in the life insurance industry, capturing only the right tail of the inverted-U shape. The results fit well into Oh and Contractor’s (2014) three-stage paradigm. That is, globalization (i.e., inter-regional internationalization) encompasses stage 3 of the S-shaped I-P relationship (i.e., the negative I-P relationship at high DOIs). The results support H2 in the sense that the I-P relationship differs between life and nonlife insurers and life insurers exhibit a more negative I-P relationship than nonlife insurers.

Columns 7-9 of Table 3 report the estimation results of Equation (1) with cost efficiency as the performance measure. The full sample results in Columns 7 show a significant and negative coefficient for the interaction term globalization2×life. The impact of globalization on cost efficiency, thus, tends to be more negative for life insurers than for nonlife insurers, suggesting that a high degree of globalization is particularly harmful for life insurers and supporting H2. The results in Column 8 and 9 suggest an inverted-U shaped nonlinear I-P relationship for life insurers (supporting H1) and an insignificant impact of globalization on cost efficiency for the nonlife insurance industry.

Our results based on two distinct performance measures are consistent with predictions from the regionalization theory in the sense that inter-regional over-diversification decreases


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returns (Rugman and Verbeke, 2004; Qian et al., 2010; Oh and Contractor, 2014). Our results also support the context-based argument (Kirca et al., 2012) and the industry dependency hypothesis (Capar and Kotabe, 2003; Contractor et al., 2003) in I-P relationships, as the impact of globalization is significantly different and more negative to the performance of life insurers than to the performance of nonlife insurers. Our empirical evidence thus rationalizes the significant disparate DOIs in the life and nonlife insurance industries, where nonlife insurers are, on average, more globalized (with an average entropy of 0.080) than life insurers (with an average entropy of 0.022), subject to a mean comparison t-test (p=0.00).

Looking at the control variables, firm size is positively correlated with risk adjusted returns, suggesting strong effects of scale economies in the insurance industry and additional benefits of risk diversification for large insurers. The leverage ratio is negatively correlated with risk adjusted returns, indicating that high leverage is usually associated with high risk (i.e., volatility of returns) and thus reducing risk adjusted returns.


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Table 3 Main results (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE CE CE CE Globalization 0.538* 0.440 -0.920* -0.957* 0.470 0.500 0.00536 0.0798* 0.0365 (0.308) (0.353) (0.551) (0.580) (0.336) (0.384) (0.0393) (0.0446) (0.0344) Globalization2 0.494 0.746 -1.998 -2.910 0.600 0.892 0.0551 -0.384* 0.0649 (0.628) (0.761) (2.312) (2.164) (0.763) (0.899) (0.0709) (0.200) (0.0574) Globalization×life -1.926*** -2.145*** -0.0753 (0.628) (0.543) (0.0952) Globalization2×life -1.529 -2.968 -0.640** (2.440) (2.420) (0.300) LnAsset 0.200*** 0.259*** 0.131* 0.236** 0.319*** 0.313*** 0.0255** 0.0350* 0.00783 (0.0677) (0.0722) (0.0790) (0.0923) (0.0925) (0.0957) (0.0129) (0.0195) (0.0121) Real premium growth -0.00653 -0.00711 -0.0227 -0.00996 0.0253 0.00218 0.00270 0.00336 0.00547 (0.0167) (0.0185) (0.0185) (0.0214) (0.0315) (0.0347) (0.00336) (0.00445) (0.00339) Premium retention ratio

0.392* 0.241 -0.336 -0.105 0.600** 0.287 0.180*** 0.423*** 0.0197 (0.224) (0.234) (0.289) (0.302) (0.300) (0.321) (0.0491) (0.0664) (0.0329)

Leverage ratio -0.00812*** -0.00431** -0.00616***

-0.00322** -0.135*** -0.0797***

0.000675** 0.000582** -0.00405*

(0.00205) (0.00168) (0.00182) (0.00159) (0.0205) (0.0226) (0.000267) (0.000267) (0.00222) Liquidity ratio 0.0230 0.0179 0.280*** 0.266*** 0.0166 0.0128 0.00293* 0.0550*** 0.00224 (0.0150) (0.0135) (0.0980) (0.0963) (0.0144) (0.0139) (0.00165) (0.0166) (0.00137) Insurance penetration 4.837 20.66 -7.599 -10.65 501.0*** 606.5*** -6.100* 1.880 -79.87*** (22.06) (23.51) (23.72) (25.57) (166.1) (174.5) (3.609) (3.410) (22.01)

Real GDP growth -0.0244** -0.0162 -0.0263 -0.0149 -0.0213 -0.0181 -0.0113*** -0.0191*** -0.00527*** (0.0119) (0.0121) (0.0180) (0.0190) (0.0152) (0.0156) (0.00155) (0.00254) (0.00154)

Number of LOB Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Observations 4,699 4,699 1,713 1,713 2,986 2,986 4,699 1,713 2,986 Number of firms 949 949 350 350 599 599 949 350 599 R2 0.111 0.109 0.185 0.176 0.144 0.115 0.135 0.226 0.200 Notes: The robust standard errors clustered at firm level are provided in parentheses. *, **, *** indicate that the coefficients significantly differ from 0 at the 10%, 5%, and 1% levels, respectively.


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4.2. Robustness tests

To test the robustness of our findings, we conduct the following seven additional tests. The results are presented in Appendices C.1 through C.7 and are consistent with our conclusions, with a few exceptions discussed below. All exceptions are reductions in significance levels where the coefficient signs remain consistent with our main results.

First, we use the complete dataset by assuming that all insurers that do not report their geographical premium distribution to A.M. Best are not globalized (i.e., they operate only in the home region with a zero entropy). The results using cost efficiency as performance measures become less significant. Second, we use a sub-sample containing only globalized firms (i.e., excluding firms with a zero entropy). The sub-sample contains 48 life insurers and 128 nonlife insurers. We can thus infer the sensitivity of performance to the degree of globalization for those firms following a globalization strategy. The results using cost efficiency as performance measures become less significant.

Third, we use an alternative globalization measure—the globalization Herfindahl index (globalHHI; Elango et al., 2008), yielding consistent conclusions. Fourth, we use two alternative performance measures: risk adjusted ROE and ROA before tax and rolling window five-year moving standard deviations to adjust the returns. The impact of globalization becomes less significant in the life insurance sample using the before tax measures, however, the difference between the globalization impact in life insurance industry and that in nonlife insurance industry remain significant. Thus, our conclusion continues to hold in the sense that the globalization impact is more negative in life insurance than that in nonlife insurance. The impact of globalization becomes less significant using the ROE adjusted by five-year moving standard deviations, however, the significance levels for ROA adjusted by five-year moving standard deviations hold.

Fifth, we estimate cost efficiency based on a global cost frontier to replace the previously applied regional frontiers. The negative coefficient of the linear interaction term in the full sample and the positive coefficient of the linear term in the life insurance sample become less significant. Since the efficiency measure is upper bounded at 1, we also present the results using alternative models of Tobit regression and truncated regression with upper limit of 1, yielding consistent results. Sixth, we show results of models including only the linear globalization term, which is thus not be able to capture the nonlinear globalization-cost efficiency relationship as presented in our main results. However, all linear relationships found in our core models are confirmed. Seventh, we use the random effects model to replace the fixed effects model. The positive coefficient between globalization and cost efficiency becomes less significant in the life sample.


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5. Discussion

5.1. Does cost efficiency mediate the I-P relationship?

Wagner (2004) hypothesizes that cost efficiency is a mediator78 between internationalization and firm-level financial performance as shown in Figure 1. The DOI influences cost efficiency and cost efficiency then drives firm performance. Based on a sample of stock quoted German firms, Wagner (2004) empirically shows the first link (i.e., step (1) in Figure 1) in that cost efficiency is gained from low to medium DOIs but that high DOIs adversely affect cost efficiency. Our empirical finding in the life insurance industry (Column 8, Table 3) is consistent with Wagner’s (2004) in the sense that an inverted-U shaped relationship can be supported between the degree of globalization and cost efficiency. In the insurance literature, Greene and Segal (2004) argue that cost efficiency is of paramount importance to the profitability of life insurers and empirically document the positive correlation between cost efficiency and life insurers’ profitability (i.e., step (2) in Figure 1). However, none of the previous works has formally tested the mediating effects of cost efficiency in the I-P relationship. We fill this gap with our life insurance sample, where the relationship between globalization and cost efficiency and between globalization and risk adjusted returns are shown to be significant (Columns 3, 4, and 8, Table 3). We then formally test the mediating effect of cost efficiency using the Baron and Kenny (1986) procedure and the Sobel mediation test (Sobel, 1982; 1986).

Figure 1 Mediation conceptual framework (Wagner, 2004)

To apply Baron and Kenny’s (1986) procedure, we include cost efficiency as an additional independent variable in Equation (1) and use risk adjusted returns as performance measure. If cost efficiency were a mediator, we should observe a positive coefficient for cost efficiency and a smaller magnitude of the impact of globalization on firm returns compared to the setting excluding the cost efficiency variable (Columns 3 and 4, Table 3). This is because the impact of globalization on firm returns is partially mediated by cost efficiency, reducing the magnitude of the direct impact. However, the results presented in Columns 1 and 2 of Table 4 reject the mediating effect of cost efficiency. Although the cost efficiency is significant and

78 In statistics, a mediation model proposes that the independent variable influences the mediator variable, which in turn

influences the dependent variable (i.e., the impact of the independent variable on the dependent variable is partially or fully indirect via the mediator). Different from mediation, moderation occurs when the relationship between two variables depends on a third variable. The third variable should thus be included in the regression and interact with the independent variable. For the detailed comparison between mediation and moderation effects, we refer to Baron and Kenny (1986).

Internationalization Financial performance Cost efficiency

(1) (2)


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positively related to risk adjusted returns as in Greene and Segal (2004), the magnitude of the globalization-return correlation stays at the same level as those in Columns 3 and 4 of Table 3 (i.e., they do not become smaller as expected for mediation) after the inclusion of cost efficiency as an independent variable. Similarly, the Sobel mediation test yields Sobel coefficients of 0.085 with p-values of 0.39 for both risk adjusted ROA and ROE and thus reject the presence of a significant mediating effect. Although both Wager’s (2004) evidence on step (1) and Greene and Segal’s (2004) evidence on step (2) can be reproduced with our sample of life insurance, we cannot confirm Wagner’s (2004) conceptual framework.

5.2. Does cost efficiency moderate the I-P relationship?

Singla and George (2013) and Tsai (2014) argue for various moderating effects in explaining the complexity of I-P relationships. Singla and George (2013) document that firm characteristics such as group affiliation, firm size, and firm age moderate the I-P relationship. Tsai (2014) emphasizes that technology competence (i.e., R&D intensity) and learning capability are important moderators of the I-P relationship. The process of internationalization may endanger those life insurers relying on high cost efficiency as a core competitive advantage to earn profits. This might be owed to the difficulty of transferring state-of-the-art technology from one market to another as culture and local institutional settings play important roles in the life insurance market. Thus, internationalization decreases technical efficiency, a core component of cost efficiency. 79 Internationalization might furthermore reduce allocative efficiency, the other core component of cost efficiency, due to the increases in liability of foreignness. Since cost efficiency is of paramount importance to its profitability (Greene and Segal, 2004), we thus expect that over-internationalization will be particularly harmful to the profitability of life insurers exhibiting high cost efficiency. Figure 2 illustrates the moderating role of cost efficiency in the I-P relationship.

Figure 2 Moderation conceptual framework

The results in Columns 3 and 4 of Table 4 show significant and negative coefficients of the interaction term globalization×cost efficiency, suggesting that the negative impact of

79 Cost efficiency can be decomposed into technical efficiency and allocative efficiency. Technical efficiency measures

the production technology the firm uses in comparison to its peers in the sense of the output/input ratio. Allocative efficiency measures how cost efficient the firm can source different combination of inputs given the input prices (Cummins and Weiss, 2013).

Internationalization Financial

performance

Cost efficiency


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globalization on life insurers’ financial performance is largely driven by those firms having higher cost efficiency than their peers. In other words, globalization adversely impacts life insurers’ risk adjusted returns in general, and such adverse effects are particularly severe for those life insurers relying on high cost efficiency as core competence, but are less a problem for life insurers whose cost efficiency is far below the industry best practice anyway. Our finding is consistent with Tsai’s (2014) conclusion regarding technology competence in the sense that cost efficiency reinforces the impact of internationalization on firm performance, though the direction of impact in our sample is negative.

5.3. Further sensitivity analyses for the I-P relationship

Zhou and Wu (2014) show that the I-P relationship depends on the earliness of internationalization. The beginning years of internationalization may lead to unfavorable results due to the firm’s lack of experience and large initial investments. We follow this rationale and construct a dummy variable with 1 indicating that the insurer is in the first two years of globalization. The results in Columns 1-4 of Table 5 show insignificant coefficients for the interaction term globalization×earliness, suggesting that the I-P relationship is not sensitive to the earliness of globalization in our sample. This is probably because insurers gained experience with intra-regional internationalization before they stepped into the inter-regional internationalization, and thus suffered less from the inexperience and large invesments.

Wagner (2004) shows that the I-P relationship depends on the speed of internationalization. Rapid internationalization may lead to unfavorable results due to lack of experienced employees and rash decisions. Follow this rationale, we construct a dummy variable, expansion, with 1 indicating that the insurer is in the expansion phase of globalization and a continuous variable, change_in_entropy (i.e., entropyt-entropyt-1). The results in Columns 5-12 of Table 5 show insignificant coefficients for the interaction terms, globalization×expansion and globalization×change_in_entropy, suggesting that the I-P relationships with our sample are sensitive neither to the expansion vs. contraction phase nor to the speed of globalization. We explain this by the different characteristics of inter-regional and intra-regional internationalization. At high DOI and globalization stage, the sensitivity of I-P relationship on the speed of internationalization becomes less significant.


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Table 4 Mediator vs. moderator test (1) (2) (3) (4)

Hypotheses Mediator Moderator Samples Life Life Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE Globalization -1.027* -1.064* -0.201 -0.433 (0.559) (0.588) (0.579) (0.573) Globalization2 -1.482 -2.395 (2.335) (2.207) Cost efficiency 1.342*** 1.340*** 1.415*** 1.404*** (0.213) (0.210) (0.215) (0.213)

Globalization×cost efficiency -2.254** -1.863* (0.957) (0.984)

LnAsset 0.0844 0.189** 0.0796 0.187** (0.0743) (0.0852) (0.0739) (0.0853) Real premium growth -0.0272 -0.0145 -0.0283 -0.0154 (0.0173) (0.0208) (0.0174) (0.0208) Premium retention ratio

-0.904*** -0.672** -0.844*** -0.609** (0.294) (0.299) (0.297) (0.303)

Leverage ratio -0.00694*** -0.00400** -0.00695*** -0.00404*** (0.00185) (0.00155) (0.00182) (0.00153) Liquidity ratio 0.206** 0.192** 0.207** 0.193** (0.0922) (0.0916) (0.0927) (0.0920) Insurance density -10.12 -13.17 -9.975 -12.92 (23.85) (25.57) (24.07) (25.81)

Real GDP growth -0.000706 0.0107 0.000788 0.0122 (0.0175) (0.0181) (0.0175) (0.0181)

Number of LOB Yes Yes Yes Yes Firm-year fixed effects Yes Yes Yes Yes Constant Yes Yes Yes Yes Observations 1,713 1,713 1,713 1,713 Number of firms 350 350 350 350 R2 0.213 0.201 0.215 0.202

Notes: The robust standard errors clustered at firm level are provided in parentheses. *, **, *** indicate that the coefficients significantly differ from 0 at the 10%, 5%, and 1% levels, respectively.


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Table 5 Sensitivity analyses for the I-P relationship (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Hypotheses Earliness of internationalization Speed of internationalization Samples Life Nonlife Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE Globalization -1.511*** -1.415** 0.0521 0.119 -1.691** -1.676** -2.409*** -2.206*** 0.252 0.0448 0.414 0.355 (0.482) (0.529) (0.399) (0.460) (0.748) (0.675) (0.793) (0.753) (0.414) (0.453) (0.433) (0.465) Globalization× earlyness

-0.0276 0.00387 0.211 0.140 (0.597) (0.539) (0.305) (0.321)

Globalization× expansion

-0.252 -0.0732 0.0721 0.107 (0.622) (0.633) (0.243) (0.270)

Globalization× chang_in_entropy

-1.734 -0.259 0.0210 0.196 (1.303) (1.499) (0.380) (0.380)

Earlyness 0.302** 0.324** -0.374* -0.272 (0.137) (0.138) (0.204) (0.224) Expansion 0.201 0.101 -0.0566 0.00616 (0.142) (0.150) (0.141) (0.153) Change_in_entropy 1.797** 1.100 -0.242 -0.360 (0.752) (0.735) (0.383) (0.383) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Observations 220 220 535 535 232 232 232 232 547 547 548 548 Number of firms 48 48 128 128 48 48 48 48 129 129 129 129 R2 0.291 0.345 0.167 0.114 0.270 0.306 0.284 0.317 0.149 0.108 0.151 0.109



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6. Conclusions and managerial implications

The international business literature has generated diverse theories to explain and generalize the internationalization-performance (I-P) relationship. Overall, the I-P relationship depends on the degree of internationalization (DOI), on the geographical scope of internationalization, and is moderated by a variety of contextual factors, including firm-, industry-, and country-specific factors. We extend the discussion of the contextual dependency of I-P relationships led by Capar and Kotabe (2003), Contractor et al. (2003), Kirca et al. (2012), and Singla and George (2013) based on an insurance industry setting. We show that the impact of internationalization decisions on firm performance depends on industry idiosyncrasies such as the liability of foreignness and cost efficiency. Internationalization has a more negative impact within industries exhibiting a higher liability of foreignness and on firms relying on high cost efficiency as core competitive advantage. We fully recognize the complex business reality, arguing that the presence of contextual factors should be carefully examined when generalizing the I-P relationships. Moreover, we support predictions of regionalization theory (Rugman and Verbeke, 2004; 2007; Qian et al., 2010) in the sense that inter-regional internationalization (i.e., globalization) strategies negatively impact firm performance, which is in line with expectations for the third stage of the three-stage paradigm (Oh and Contractor, 2014).

To the best of our knowledge, this is the first work using a DEA cost efficiency measure at firm level to explain I-P relationships. This measure is particularly useful to capture differences in the liability of foreignness and in firm production technology. As a result, cost efficiency constitutes a key candidate in moderating the negative relationship between globalization and firm financial performance. Cost efficiency is, furthermore, particularly important to the profitability of those industries driven by operational costs and production efficiency, such as the life insurance industry. We identify four aspects of industry idiosyncrasies (i.e., credence good character, regulation, cultural influences, and local adaptation) of the life and the nonlife insurance industries, generating differences in its liability of foreignness and thus in its I-P relationship. Moreover, we construct an innovative two-sample empirical design to verify that the impact of globalization on the life insurance industry is negative—and more so compared to the nonlife insurance industry. We contribute to the insurance literature by providing the first piece of evidence on the I-P relationship in the life insurance industry, where we challenge the conventional wisdom that internationalization (i.e., geographical diversification) is generally beneficial for insurance companies due to risk diversification effects. In contrast, the liability of foreignness may endanger cost efficiency of life insurers and thus particularly harmful to those life insurers relying on high cost efficiency as their core competence.


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We demonstrate that the internationalization-related industry idiosyncrasies exist in a much broader scope than previous studies suggest. Industry dependency exists not only between manufacturing and service firms (Capar and Kotabe, 2003) and between knowledge-based and capital-intensive firms (Contractor et al., 2003), but also between two industries that appear to be very close—the life and nonlife insurance industries. Thus, the criteria for generalizing I-P relationships from one industry to another should be based on internationalization-related industry idiosyncrasies. For example, we would expect different I-P relationships in commercial and investment banking, because investment banking may benefit more from international risk diversification (similar to nonlife insurance); while commercial banking may benefit less from internationalization as it is heavily influenced by local culture and local regulation (similar to life insurance). We call for more contextual-based research on internationalization strategies, particularly in service industries, which remain in the evolutionary stage (Capar and Kotabe, 2003; Singla and George, 2013).

Our findings support the following managerial implications. A firm’s mere presence in foreign markets does not automatically translate into superior performance (Tsai, 2014) and its multinational efforts must be coupled with an advantageous position in the liability of foreignness and in the sensitivity of profits to cost efficiency. Managers thus need to be cautious when replicating the internationalization strategies of another industry, even though they appear to be very close. For life insurers that are already globalized, local expertise may play an important role in sales given that products, regulations, and market conditions largely differ across countries.

Our findings may also be valuable to regulators and policymakers. We suggest that different policies should be implemented for life and nonlife insurers. One example of such different policies from China is that foreign life insurers are required to establish joint ventures with local firms to operate in this market, whereas nonlife insurers are allowed to establish wholly owned subsidiaries and branches. Those rules reflect the regulators having set stricter internationalization rules for life insurers than for nonlife insurers. Future research may compare I-P relationships of wholly owned subsidiaries with joint ventures to determine whether this regulatory policy can be justified.

A limitation of this research is the lack of control over nonmarket factors (e.g., regulation, government), which have been shown to be important in international business studies (Doh and Lucea, 2013). Moreover, our analysis may not be able to capture the time dynamics and long-term benefits of globalization due to data limitations. For example, a life insurer may want to expand to an emerging market to diversify its longevity risk, which cannot be captured by our 11-year analysis. These long-term considerations are important to explain why firms keep internationalizing even when the immediate returns seem to be negative (Hennart, 2007).


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Appendices

Appendix A DEA procedure

We assume constant returns to scales (CRS) to estimate cost frontiers separately for life and nonlife insurers, for each year between 2003 and 2013 and for each of the three regions Continental Europe, UK and Ireland, and Others (including Asia, Africa, Australia and New Zealand, and Offshore)80. Cost efficiency estimates relative to a single global frontier are used as a robustness test, the results of which are consistent with our conclusions (see Section 4.2). DEA cost efficiencies are the representation of firms’ distances to the best-practice efficient frontiers and are bounded between 0 and 1 (Shephard, 1970). The best-practice frontier is defined by firms that use the minimum amount of inputs to produce certain amount of outputs. Bootstrapped bias-corrected efficiency scores are used to account for the sensitivity of efficiency measures to sampling variation (Simar and Wilson, 2000).

The inputs, outputs, and prices used to obtain the cost efficiency scores follow the common practice of DEA analyses in insurance (Eling and Luhnen, 2010; Cummins and Weiss, 2013). We use three input quantities: labor (i.e. approximated number of employees), equity capital (i.e. capital and surplus, in real values in 2013), and debt capital (i.e. total liabilities, in real values in 2013). Labor is approximated by operating expenses divided by the annual wage for the insurance sector in respective country-years. We use annual wages (in real values in 2013) for the insurance sector in respective country-years as the price for labor. The wage information is obtained from the ILO Main Statistics and October Inquiry databases.81 We use the 10-year rolling window moving averages of yearly rates of total returns of Morgan Stanley Capital International (MSCI) indices in the respective countries as the price for equity capital.82 We use the two-year rolling window averages of International Monetary Fund (IMF) long-term government bond yearly interest rates in respective countries as the price for debt capital.83 The long-term government bond rates are used to match the long duration of life

80 One important assumption of DEA efficiency estimates is that firms are employing similar technologies. The

assumption that all insurers employ similar technologies worldwide is strong. Therefore, we group insurers in our sample into three regions according to their domiciliary countries. The region categories to estimate DEA efficiency frontiers differ from the premium distribution regions that we use in the I-P relationship context. This is because we consider the operational similarities and the balance of observations in each region in the DEA context (Biener, Eling, and Jia, 2015), whereas the premium distribution regions are based on the triad concept with considerations of regionalization vs. globalization (Rugman and Verbeke, 2004, 2007).

81 If missing, we adjust the nearest available data point of ILO annual wage to the previous or later years by using changes in general price levels represented by the consumer price indices (CPI).

82 To replace negative values and impute missing values, we use the rolling window two-year averages of realized country-average ROEs in respective country-years (see Cummins and Weiss, 2013, for a discussion of capital price proxies). We use two-year moving average values because we only have the data that date back to 2002. We use country-average ROEs because many firms may have negative ROEs due to the volatile nature of the insurance business. Less than 10% of our sample is affected by this procedure.

83 If missing, we use the IMF central bank policy rate or deposit rate in respective country-years.


126

insurers’ liabilities. The MSCI indices and IMF interest rates are obtained from the Thomson DataStream database.

We use two output quantities, total invested assets and insurance benefits or losses (all in real values in 2013). The two outputs represent insurers’ two major functions— financial intermediation and risk pooling, respectively. For life insurers, the insurance benefits are captured by net benefits paid plus net reserve changes84, as reserves reflect the accumulation of unpaid cash values of life insurance policies (Cummins and Weiss, 2013). For nonlife insurers, the insurance losses are captured by the smoothed loss, which is calculated following the loss-smoothing procedure in Cummins and Xie (2008). This procedure is particularly well-suited for the highly volatile losses of nonlife insurance, because it corrects the potential “error in variables” problem due to the randomness nature of losses (Cummins and Xie, 2013). Premiums (instead of benefits or losses) are sometimes applied as an output. The rationale for using premiums is that they represent the business volume generated by insurers. However, Yuengert (1993) notes that the premiums represent price times the quantity of outputs rather than output quantity only.

84 The net benefits paid plus net reserve changes (NBPNRC) could exhibit negative values; therefore, we follow the

standard DEA practice of shifting all values by adding the minimum NBPNRC (Cummins and Weiss, 2013). This practice has no impact at all on the DEA results.


127

Appendix B Sample distribution by country and year Life Nonlife

Panel A: Sample distribution by country a Belgium 58 169 China 198 119 Denmark 120 305 France 236 352 India 69 29 Ireland 236 327 Italy 160 85 Luxembourg 49 7 Netherlands 87 225 Other 44 103 Pakistan 5 55 Portugal 32 54 Saudi Arabia N.A. 44 Sweden 43 202 Switzerland 36 142 United Arab Emirates N.A. 29 United Kingdom 340 739 Total 1,713 2,986

Panel B: Sample distribution by year 2003 101 131 2004 112 155 2005 125 174 2006 117 192 2007 151 282 2008 135 309 2009 202 385 2010 223 406 2011 209 389 2012 205 343 2013 133 220 Total 1,713 2,986

Notes: N.A. represents not available. The category of “Other” includes 18 countries (Bahrain, Norway, Bermuda, Spain, Malta, Croatia, Qatar, Australia, South Africa, Austria, Malaysia, Hong Kong, New Zealand, Slovenia, Taiwan, Thailand, Estonia, and Bulgaria). a Some important European markets are not included in our sample (e.g., Germany) because the insurers in these markets do not report their premium distributions to A.M. Best.


128

Appendix C.1 Complete dataset (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE CE CE CE Globalization 0.234 0.0500 -0.763* -0.881* 0.262 0.137 -0.00709 -0.0355 0.0125 (0.187) (0.204) (0.453) (0.492) (0.177) (0.203) (0.0173) (0.0513) (0.0162) Globalization2 0.374 0.739 0.00677 -0.627 0.491 0.788 0.0620 -0.221 0.0583 (0.522) (0.558) (1.914) (2.044) (0.546) (0.605) (0.0529) (0.223) (0.0483) Globalization×life -0.888** -0.963** -0.0824 (0.373) (0.474) (0.0674) Globalization2×life -0.0224 -1.075 -0.424 (1.945) (2.098) (0.292) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes

Observations 23,618 23,618 8,497 8,497 15,121 15,121 23,618 8,497 15,121 Number of firms 3,640 3,640 1,333 1,333 2,323 2,323 3,640 1,333 2,323 R2 0.055 0.057 0.061 0.064 0.101 0.077 0.073 0.119 0.081



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Appendix C.2 Sub-sample including only globalized firm-years (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE CE CE CE Globalization 0.262 0.235 -1.486*** -1.304** 0.210 0.266 -0.0290 -0.0247 -0.0110 (0.399) (0.458) (0.520) (0.545) (0.448) (0.518) (0.0512) (0.0664) (0.0438) Globalization2 0.261 0.322 -2.947 -4.702** 0.346 0.472 0.197** -0.332 0.191*** (0.815) (0.988) (2.003) (1.946) (0.955) (1.104) (0.0777) (0.223) (0.0629) Globalization×life -1.857** -2.511*** -0.161 (0.903) (0.913) (0.134) Globalization2×life -0.788 -2.677 -0.783** (2.226) (2.478) (0.306) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Observations 755 755 220 220 535 535 755 220 535 Number of firms 176 176 48 48 128 128 176 48 128 R2 0.127 0.120 0.285 0.345 0.157 0.109 0.233 0.365 0.256



130

Appendix C.3 Alternative globalization measure (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE CE CE CE GlobalHHI 0.854* 0.739 -1.348* -1.435* 0.718 0.794 0.00665 0.116* 0.0469 (0.440) (0.489) (0.764) (0.824) (0.452) (0.511) (0.0564) (0.0667) (0.0497) GlobalHHI2 2.384 3.615* -4.093 -5.273 2.498 3.764* 0.240 -1.213*** 0.213 (1.916) (2.089) (5.563) (5.183) (1.894) (2.158) (0.248) (0.467) (0.216) GlobalHHI×life -2.631*** -2.755*** -0.0673 (0.811) (0.719) (0.109) GlobalHHI2×life -3.995 -7.088 -1.985*** (6.092) (5.868) (0.726) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Observations 4,699 4,699 1,713 1,713 2,986 2,986 4,699 1,713 2,986 Number of firms 949 949 350 350 599 599 949 350 599 R2 0.111 0.110 0.185 0.176 0.144 0.116 0.136 0.227 0.200



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Appendix C.4 Alternative return measures (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Samples Full Life Nonlife Full Life Nonlife

Variables R.A.ROA before

tax

R.A.ROE before

tax

R.A.ROA before

tax

R.A.ROE before

tax

R.A.ROA before

tax

R.A.ROE before

tax

Moving R.A.RO

A

Moving R.A.RO

E

Moving R.A.RO

A

Moving R.A.RO

E

Moving R.A.RO

A

Moving R.A.RO

E Globalization 0.525* 0.407 -0.670 -0.736 0.464 0.490 -24.80 -6.276 -184.9** -14.33 -3.296 -2.721 (0.296) (0.338) (0.519) (0.589) (0.332) (0.370) (15.97) (8.441) (71.77) (17.20) (8.565) (8.655) Globalization2 0.516 0.928 -2.192 -2.625 0.598 1.037 7.489 -18.81 89.16 0.631 7.607 -17.95 (0.654) (0.731) (2.192) (2.309) (0.790) (0.853) (22.21) (20.75) (338.5) (71.88) (18.16) (20.89) Globalization×life

-1.732*** -1.806*** -129.1** -8.462 (0.588) (0.605) (62.87) (13.08)

Globalization2×life

-1.879 -3.003 25.14 38.39 (2.334) (2.529) (289.2) (50.28)

Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Observations 4,699 4,699 1,713 1,713 2,986 2,986 3,197 3,230 1,143 1,131 2,054 2,063 Number of firms 949 949 350 350 599 599 803 807 286 286 517 519 R2 0.115 0.115 0.184 0.183 0.150 0.117 0.048 0.043 0.083 0.070 0.048 0.029



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Appendix C.5 Alternatives of cost efficiency (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Full Life Nonlife Specifications Cost efficiency (global frontier) Tobit Truncated Globalization -0.0336 0.0541 0.0209 0.00536 0.0798* 0.0365 0.00752 0.0868* 0.0366 (0.0349) (0.0451) (0.0336) (0.0392) (0.0443) (0.0342) (0.0392) (0.0472) (0.0342) Globalization2 0.0241 -0.310* 0.0608 0.0551 -0.384* 0.0649 0.0550 -0.407** 0.0646 (0.0705) (0.184) (0.0723) (0.0706) (0.199) (0.0570) (0.0705) (0.207) (0.0570) Globalization×life -0.0428 -0.0753 -0.0780 (0.0842) (0.0948) (0.0956) Globalization2×ife -0.495* -0.640** -0.658** (0.284) (0.299) (0.305) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes

Observations 4,699 1,713 2,986 4,699 1,713 2,986 4,699 1,713 2,986 Number of firms 949 350 599 949 350 599 949 350 599 R2 or log pseudolikelihood

0.198 0.233 0.340 4595.5 1587.1 3256.7 4677.7 1671.8 3260.8



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Appendix C.6 Only linear globalization term (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE CE CE CE Globalization 0.493 0.372 -1.008** -1.085** 0.400 0.396 0.000339 0.0628 0.0290 (0.314) (0.347) (0.507) (0.514) (0.319) (0.354) (0.0394) (0.0476) (0.0344) Globalization×life -1.651*** -1.583** 0.0595 (0.623) (0.669) (0.0656) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Firm-year FE & constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Observations 4,699 4,699 1,713 1,713 2,986 2,986 4,699 1,713 2,986 Number of firms 949 949 350 350 599 599 949 350 599 R2 0.110 0.109 0.184 0.175 0.144 0.115 0.134 0.225 0.200



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Appendix C.7 Random-effects model (1) (2) (3) (4) (5) (6) (7) (8) (9)

Samples Full Life Nonlife Full Life Nonlife Variables R.A.ROA R.A.ROE R.A.ROA R.A.ROE R.A.ROA R.A.ROE CE CE CE Globalization 0.537* 0.466 -0.913* -0.933 0.474 0.532 -0.0109 0.0236 -0.00109 (0.308) (0.350) (0.551) (0.576) (0.329) (0.382) (0.0265) (0.0328) (0.0249) Globalization2 0.497 0.716 -2.000 -2.894 0.711 0.859 -0.0113 -0.363** 0.0184 (0.628) (0.761) (2.312) (2.177) (0.749) (0.905) (0.0566) (0.157) (0.0491) Globalization×life -1.907*** -2.143*** -0.145* (0.636) (0.542) (0.0819) Globalization2×life -1.544 -2.936 -0.601** (2.439) (2.429) (0.254) Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Year fixed effects/constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Observations 4,699 4,699 1,713 1,713 2,986 2,986 4,699 1,713 2,986 Number of firms 949 949 350 350 599 599 949 350 599 Overall R2 0.010 0.002 0.001 0.003 0.004 0.005 0.315 0.276 0.102



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Essay IV Roles of commitment and information in multi-period insurance contracting: A comprehensive review and new empirical evidence

Abstract

The central question in multi-period insurance contracting is the type of inter-temporal pricing pattern. Some products have a highballing (front-loaded) pattern, others are lowballing (back-loaded), and still others are flat. These patterns are sensitive to commitment and informational conditions of insurance products. This paper presents the first comprehensive review of theoretical and empirical research to uncover the roles of commitment and information in determining the type of inter-temporal pricing pattern. Moreover, a new two-sample empirical design is constructed, which excludes heterogeneity in firms, markets, and time periods, thus to isolate the impact of insurer’s commitment on its inter-temporal pricing strategy. Insurer learning is also a necessary informational condition for a lowballing pricing strategy; however whether the learning is asymmetric or symmetric turns out to be irrelevant. The paper emphasizes the control of insurance demand and supply factors in addition to the risk type when empirically examining the risk-based dynamic selection.

Keywords

Inter-Temporal Pricing Strategy, Risk-Based Dynamic Selection, Repeated (Dynamic) Contracting, Competitive Equilibrium, Insurer Learning

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Ruo Jia (2016)

This paper was presented at the 2016 annual conference of German Insurance Science e. V. (DVfVW) and has been submitted to Geneva Risk and Insurance Review.

Essay IV Multiperiod Insurance Contracting

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1. Introduction

Multi-period insurance relationship is appreciated by both the insured and the insurer. The insured is willing to pay more for long-term fixed-price coverage (Kunreuther and Michel-Kerjan, 2015); and the insurer is willing to supply more comprehensive coverage if long-term insurance relationship is sustainable85 (Crocker and Moran, 2003). Multi-period insurance contracting is also economically relevant given that the majority of insurance products, either long-term or short-term with renewals, involve a multi-period relationship.86 However, the dynamic nature of such multi-period insurance contracting increases the difficulties of theoretical modelling and empirical testing. This paper advances the multi-period insurance contracting research by providing a comprehensive review and by presenting new empirical evidence.

Academic research on multi-period insurance contracting, particularly in a competitive setup, emerged much later than that on single-period contracting. The seminal models of Kunreuther and Pauly (1985, hereafter KP), Palfrey and Spatt (1985, hereafter PS), and Cooper and Hayes (1987, hereafter CH) yield different predictions on multi-period competitive equilibriums, inter-temporal pricing (profit) patterns, and portfolio risk dynamics. These predictions are sensitive to the following informational and commitment conditions (de Garidel-Thoron, 2005): (1) the information symmetry assumption between insured and insurer(s), and between incumbent insurer and competing insurers; (2) the commitment assumption to multi-period insurance relationship from the insurer(s) and from the insured. This paper reviews 15 theoretical works in competitive multi-period insurance contracting aiming to construct a common theoretical platform (see Table 1) and to compare the roles of information and commitment conditions in respective multi-period insurance contracting predictions.

The differences in theoretical predictions particularly concern with the inter-temporal pricing strategy of highballing (front-loaded) or lowballing (back-loaded)87 (D’Arcy and Doherty, 1990), and the inter-temporal risk-based dynamic selection, i.e., high- or low-risk departures over time (Finkelstein, McGarry, and Sufi, 2005). Empirical research thus emerged to discriminate different theoretical predictions. This paper reviews 11 empirical works in multi-period insurance contracting aiming to isolate the roles of commitment and information in determining the inter-temporal pricing strategy and the risk-based dynamic selection.

85 In some markets, for example, Swiss insurers usually give a premium discount for insureds that accept three- or five-

year contracts, which indicates a strong preference in long-term coverage. 86 It is rather uncommon to see single-period insurance relationships. Even for single project-based coverage, such as

construction all risks or satellite launch protection, the project coverage is usually embedded in a multi-period insurance relationship between the insured and the insurer.

87 The highballing (lowballing) pricing strategy means that the insurer charges higher (lower) premium in early periods of the multi-period contractual relationship and charges lower (higher) premiums in later periods. The high or low premiums are measured relative to the actuarial fair premiums.


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A major deficiency of the synthesis approach is that it does not always compare apples with apples. The comparison conclusions from the existing empirical research are based on different insurers, different markets, and different time periods. Thus, it is not yet known whether the different pricing and risk selection patterns result from the strategic decision based on commitment and information conditions of different products, or simply from other characteristic differences among insurers, markets, and/or time periods. To complement this deficiency, the paper presents a pair of two samples from the same insurance company, the same market, and almost the same time period. The key difference in the two insurance products is whether the insurer is pre-committed to the long-term insurance relationship. This unique empirical design isolates the impact of the insurer’s commitment from other factors impacting the pricing strategy choice (e.g., business targets, management preferences) and thus strengthens the causal link between the insurer’s commitment and highballing pricing strategy, and between the lack of insurer’s commitment and lowballing pricing strategy. Moreover, this new evidence shows that the insurer learning is a necessary condition for the lowballing pricing strategy in a no commitment environment (Cohen, 2012), though whether the learning is asymmetric or symmetric turns out to be irrelevant.

This paper contributes to the multi-period insurance contracting research in two ways. It presents the first piece of comprehensive review mapping empirical evidence with theoretical models (see Table 1). This synthesized theoretical platform clarifies the roles of commitment and information in determining the inter-temporal pricing strategy and the risk-based dynamic selection, and thus provide theoretical structure for future empirical research. In addition, it constructs a two-sample empirical test, which precludes heterogeneity in firms, markets, and time periods, and thus improves the credibility of insurer’s commitment-pricing strategy relationship. The results expand the empirical evidence on insurer learning (Hendel and Lizzeri, 2003; Cohen 2012) and insurance commitment (Dionne and Doherty, 1994; de Garidel-Thoron, 2005). The paper also provides practical implications on insurance product management, which may serve as a basis for pricing strategy decisions.

The remainder of the paper is structured as follows. Section 2 constructs the common theoretical platform based on synthesis and comparison of extant theoretical models. Section 3 derives the hypotheses. Section 4 compares extant empirical evidence and concludes the roles of commitment and information in pricing strategy based on extant empirical evidence. Section 5 presents the two-sample empirical design, and reports the results. Section 6 concludes.

2. Common theoretical platform

The multi-period insurance contracting models are traceable to, among others, contract theories in labor (Harris and Holmstrom, 1982), procurement (Laffont and Tirole, 1990), and


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credit (Sharpe, 1990) markets. The development of contract theory leads modern insurance economics in three directions (D’Arcy and Doherty, 1990; Chiappori and Salanie, 2013). The first is the single-period contracting in competitive insurance markets, where Rothschild and Stiglitz (1976, hereafter RS) derive a separating equilibrium with different contracts for high and low risks respectively under adverse selection. Alternatively, Miyazaki (1977), Wilson (1977), and Spence (1978) demonstrate the possibility of a pooling equilibrium. The second direction is the multi-period contracting in a monopoly insurance market, where the role of experience rating is highlighted to solve the problem of adverse selection (Dionne, 1983; Dionne and Lasserre, 1985, 1987; Hosios and Peters, 1989). The third and the most recent direction is the multi-period insurance contracting in competitive markets, on which this paper will focus.

The contract(s) at the multi-period equilibrium is characterized under various commitment and informational assumptions. There are three types of commitment assumption: (1) no commitment, where neither the insurer nor the insured pre-commits to a multi-period insurance relationship; (2) semi-commitment, where the insurer pre-commits88 to a multi-period insurance relationship but the insured does not; and (3) full commitment, where both the insurer and the insured pre-commit to a multi-period insurance relationship at the beginning of the first period (Dionne and Doherty, 1994). 89 The typical form of no commitment is the annual contract (e.g., automobile insurance), which is renewable but without renewal guarantee from either side. The typical forms of semi-commitment include long-term contract (e.g., ten-year term life) and annual contract with guaranteed renewability (e.g., individual health insurance with guaranteed renewal clause). It is possible but uncommon to see full commitment insurance contracts, because insurance law in most markets allows the insured to cancel the insurance policy at any time. However, the insured can partially commit due to relationships other than insurance. For example, the employment relationship partially binds the insured to the employer sponsored group health insurance; the mortgage relationship partially binds the insured to the mortgage life insurance.

The informational assumptions in multi-period insurance contracting involve two layers: between the insured and the insurer(s) and between the incumbent (current) insurer and the competing (rival) insurers. The first layer has been extensively investigated in the single-period setup, within the context of adverse selection and moral hazard. The second issue has recently emerged from the multi-period setup: the incumbent insurer may obtain information

88 In practice, the insurer’s commitment has multiple forms, e.g., long term contracts (term life) or guaranteed renewability

(health insurance). One of the common features of these commitments is the commitment to a pre-agreed premium schedule, which can either be contingent or non-contingent on claim experience.

89 It is rarely seen in the insurance market that the insured is bound to a multi-period relationship with an insurer, while the insurer is not (Dionne and Doherty, 1994).


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advantages to its competitors, due to its learning90 from the contractual experience with the insured. Pauly (2003) constructs three information structures concerning the insured’s risk type,91 based on the two layers of informational assumptions: (1) classic adverse selection, where the insured has private information that none of the insurers knows; (2) symmetric information, where the insured and all insurers have common knowledge at every point in time; (3) asymmetric learning, where the insured and the incumbent insurer have common knowledge at every point in time but the competing insurers do not. This paper further develops Pauly’s (2003) information structures to five categories based on whether adverse selection is present in the first (early) period of contract and on the learning types in the second (later) period (asymmetric, symmetric, or no learning)92.

Table 1 structures the theoretical framework of multi-period insurance contracting in 15 assumption sub-categories by three commitment types and five risk information structures. The sub-category of full commitment and no learning is essentially single-period contracting because no change can happen across periods. All models are discussed in a two-period setup, where the long-term contract has a duration of two periods, and the short-term contract has a duration of one period. They are structured in three panels subject to whether adverse selection93 is present in period 1.

Three theoretical predictions, where available, are discussed, under each assumption sub-category. The first is the multi-period equilibrium, with a focus on whether separating contracts are offered to high and low risks or one pooling contract is offered to all risks. Second, a competitive market implies zero-profit contracts over multiple periods at the equilibrium (KP, 1985; CH, 1987). Thus, inter-temporal subsidization between young and old policies may exist in order to reach the multi-period zero-profit equilibrium.94 Thus, an inter-temporal pricing or profit pattern at the multi-period equilibrium may exist, i.e. whether young policies subsidize old policies (front-loaded, highballing), old policies subsidize young policies (back-loaded, lowballing), or no inter-temporal subsidization (actuarially-based, flat). The third prediction is on risk-based dynamic movements, i.e. if high or low risks systemically depart from the insurance portfolio in period 2.

90 Learning reflects the updates in part the initial (but unknown) differences in risks, and in part the signal (and real)

changes in risks (Pauly, 2003). 91 There are multi-dimensions in the insured’s risk information, e.g., the risk attitude, which also have an impact on

insurance contracting (Finkelstein and McGarry, 2006). However, all models discussed in this paper (implicitly) assume the risk type as the only dimension of risk information.

92 The scenario of no adverse selection and no learning is omitted, because it degenerates to general contracting theory and thus is not particularly interesting to insurance contracting studies.

93 All models discussed in this paper (implicitly) assume no moral hazard. A separate stream of multi-period contracting studies considering moral hazard can be found in e.g., Rubinstein and Yaari (1983) and Rogerson (1985).

94 All models discussed in this paper (implicitly) assume no cross subsidization among multiple products for one insured, and assume exclusive contract(s), i.e. the insured buys one type of coverage from only one insurer. The cross-subsidization between high and low risks in a multi-period setup is investigated by e.g. Ma and Browne (2005).


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Table 1 Theoretical framework of multi-period insurance contracting Commitment

Insurer learning

No commitment Semi-commitment (One-side commitment)

Full commitment (Two-side commitment)

Panel A: Adverse selection is present in period 1 Asymmetric learning

Pooling in period 1, separating in period 2, lowballing, high risks tend to departure (KP, 1985; Nilssen, 2000).

Separating; low risks choose highballing long-term contract, high risks tend to departure from the long-term contract and to choose repeated short-term contract (CH, 1987). Semi-pooling in period 1 and separating in period 2; low risks choose highballing long-term contract; high risks tend to departure from the long-term contract (Dionne and Doherty, 1994).

Separating; policies for high risks degenerate to single-period; policies for low risks are experience rated with flat pricing pattern (CH, 1987).

Symmetric learning

Pooling or semi-pooling, flat, no systemic departure (Watt and Vazquez, 1997).

Not yet covered by literature Not yet covered by literature (see footnote 12)

No learning

Separating, flat, no systemic departure (Vazquez and Watt, 1999).

Separating, flat, no systemic departure (Vazquez and Watt, 1999).

Separating, flat (RS, 1976). Pooling, flat (Miyazaki, 1977; Wilson, 1977; Spence, 1978).

Panel B: Adverse selection is NOT present in period 1 Asymmetric learning

Pooling in period 1, lowballing, high risks tend to departure (de Garidel-Thoron, 2005).

Pooling, flat, high risks tend to departure (de Garidel-Thoron, 2005).

Not yet covered by literature

Symmetric learning

Pooling, flat, no systemic departure (PS, 1985; Prendergast, 1992; Cochrane, 1995).

Pooling, highballing, low risks tend to departure (PKH, 1995; HL, 2003). Separating, undetermined pricing and risk departure pattern (Crocker and Moran, 2003).

Pooling, undetermined pricing pattern (Crocker and Moran, 2003).

Panel C: Theories connecting panel A and B Three scenarios (Pauly, 2003) Pooling, highballing, undetermined risk departure pattern (Pauly, Menzel, Kunreuther, and Hirth, 2011)


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2.1. Panel A: Adverse selection is present in period 1

CH (1987) and KP (1985) initiate the modelling of multi-period contracting in the insurance context, where adverse selection is an important feature.

Assuming no commitment, KP (1985) and Nilssen (2000) model the scenario of asymmetric insurer learning; Watt and Vazquez (1997) model symmetric learning; and Vazquez and Watt (1999) describe no learning. KP (1985) predict a pooling equilibrium in period 1, as that the insurer offers one type of short-term contract to all risks at the price reflecting the average of low and high risks in period 1. In period 2, risks who had claim(s) in period 1 (high risks), switch to competing insurers. This is because the incumbent insurer can increase the premium for the period-1 claimant; however, the competing insurers cannot tell who had a claim in period 1. Risks who did not have a claim (low risks) stay with the incumbent insurer, since the incumbent insurer shall keep their premium unchanged thus they are indifferent to switch or stay. Therefore, in period 2, the insurer can earn a positive profit by over charging the staying (low) risks. Under the zero-profit constraint, the insurer must price lower than zero-profit in period 1 to attract new customers, which is considered as the cost of acquiring knowledge about the insured’s risk type. The incumbent insurer earns an informational (monopoly) quasi rent in period 2, which competing insurers do not. This pricing and profit pattern for a sequence of short-term contracts are thus lowballing. The risk-based dynamic selection pattern is thus the high-risk departure and the low-risk locked in. Nilssen (2000) addresses two challenges to KP’s (1985) predictions. First, KP (1985) assume a myopic insured, who only considers the payoffs in period 1, but not in period 2, when making the initial decision. Nilssen’s (2000) conclusion is free of this assumption. Second, Nilssen (2000) extends RS’s (1976) and CH’s (1987) classical model, thus responding to concerns on KP’s (1985) modelling. His predictions are largely consistent with KP’s (1985) as that a pooling equilibrium is more likely to happen than the separate equilibrium, a lowballing pricing pattern prevails, and the low risks are locked in.

Watt and Vazquez (1997) assume that all insurers learn the insured’s risk type at the beginning of period 2, and thus adverse selection is only present in period 1. They prove a pooling equilibrium of full coverage if low risks are patient enough; or a semi-pooling equilibrium, where a portion of impatient low risks choose a sequence of RS’s (1976) partial coverages and all high risks and patient low risks choose a sequence of full coverages. At equilibrium, no inter-temporal subsidization is inferred, since in period 1, the insurer undercharges high risks but overcharges low risks, thus expects a zero-profit; in period 2, full information contracts are in place and thus all risks are charged at an actuarially fair rate. Vazquez and Watt (1999) assume no insurer learning over time. The model is a straightforward extension of RS’s (1976) to a multi-period setting. They conclude that the multi-period equilibrium must


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be a periodic repetition of RS’s single-period separating equilibrium. The high risks are offered with a sequence of full coverages and low risks partial coverages. Thus the profit of each period is zero and no inter-temporal subsidy is allowed.

Assuming semi- and/or full commitment, CH (1987) and Dionne and Doherty (1994) model the scenario of asymmetric insurer learning; Vazquez and Watt (1999) discuss no learning; the scenario of symmetric insurer learning has not yet been covered by literature.95 CH (1987) extend RS’s (1976) single-period adverse selection model to multi-periods and discuss both semi- and full- commitment scenarios. Semi-commitment yields a separating equilibrium, as the insurer offers experience rated long- and short-term contracts; high risks choose the repeated short-term contracts; low risks choose the long-term contract. The dynamic behavior of insurance rates is described, as that in period 1, the insurer charges low risks a higher premium than they should pay in a standard one-period contract; in period 2, the insurer gives those low risks without any period 1 claim a heavy discount, and thus charges them a lower premium than they should pay in a standard one-period contract. That is to say the pricing and profit pattern for the experience rated long-term contract is highballing. The insurer tilts payoffs towards the future to provide an incentive for insureds to remain with the firm. Full commitment yields another separating multi-period equilibrium as the insurer offers both experience rated and non-experience rated long-term contracts. High risks choose non-experience rated long-term contract, which is equivalent to a single-period contract. Low risks choose experience rated long-term contract,96 which is actuarially fair at each period, i.e. a flat pricing pattern.

Dionne and Doherty (1994) extend the semi-commitment modelling with renegotiation, which allows the insurer initially to commit to a long-term contract and to offer a revised short-term contract in period 2. The insured may stick to the long-term contract, accept the revised second-period short-term contract, or switch insurer in period 2. They conclude that the equilibrium is semi-pooling in period 1, where a portion of high risks chooses short-term full coverage, and the rest of high risks and all low risks choose long-term partial coverage. The equilibrium is separating in period 2, where high risks change to short-term full coverage (either offered by the incumbent insurer as the renegotiation or by a competing insurer); low risks stay with the long-term partial coverage. The equilibrium is similar to CH’s (1987) and is characterized by positive first-period expected profits and negative second-period expected profits for low risks, i.e. price highballing.

95 If full commitment, the asymmetric and symmetric learning maybe indifferent, because both parties pre-commit to a

long-term contract and thus competition among insurers does not exist in period 2. Thus whether the insurer learning is asymmetric or symmetric makes no difference.

96 In practice, this could be a long-term contract with a pre-agreed premium schedule/tariff contingent on the policy loss experience.


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Vazquez and Watt (1999) discuss the scenario of no insurer learning and conclude that “if commitment were a possibility, it is really just a redefinition of the term ‘period’. … Hence, multi-period contracts with commitment can be thought of as single-period contracts and so initial type revelation is possible, as was initially shown by Rothschild and Stiglitz (1976).”

2.2. Panel B: No adverse selection in period 1

Assuming no commitment, PS (1985), Prendergast (1992), and Cochrane (1995) model the multi-period insurance contracting with symmetric learning; 97 de Garidel-Thoron (2005) covers the scenario of asymmetric learning. PS (1985) predict that the equilibrium is pooled since there is no adverse selection in both periods. All policies are experience rated in period 2, based on the symmetric learning from the claims reported in period 1. The short-term policy in each period has a zero profit, implying a flat pricing pattern. This is because in period 1, no one knows the risk type, thus only a pooled premium for an average risk can be charged; in period 2, all insurers and the insured know the risk type, all risks will be charged with actuarially fair premium.

Prendergast (1992) develops a model based on Wilson’s (1977) game form. Unlike PS (1985), Prendergast (1992) assumes that the insured’s non-reported accidents98 in period 1 constitute his/her private knowledge in period 2, which no insurers would know, i.e. adverse selection is present in period 2. He proves a pooled equilibrium with small-deductible partial insurance in both periods, which relies on the asymmetric information assumption in period 2. He argues that the insurer(s) shall never offer contract to pay small losses in period 1, thus to reduce the incentive of insured’s not-to-report claims; and as long as the deductible is small enough, neither the incumbent insurer nor the competing insurers shall offer a RS’s (1976) menu contracts, but offer the partial insurance as in period 1. No inter-temporal subsidy is implied at his equilibrium.

Cochrane (1995) focuses on how to design a scheme that motivates the insurer’s commitment to offer long-term health coverage (endogenous commitment). He proves a pooled equilibrium for standard short-term health insurance with flat pricing pattern and with no insured lock-in effect. He proposes a separate coverage or separate policy accompanying by the short-term standard health insurance to insure the insured’s reclassification risk,99 which provides a lump-sum insurance payment equal to the current value of future health premium increases due to risk type changes, for example, worsening health condition. This time-

97 In this case, all parties (insured, incumbent insurer, and competing insurers) share common information at every point

in time. 98 The insureds tend not to report small accidents in period 1, since they want to establish a reputation as low risks, so that

they can get a better term in period 2. 99 Alternative terms are insurability risk, re-underwriting risk, renewability risk (Fei, Fluet, and Schlesinger, 2015), and

premium risk (Pauly, 2003). Reclassification risk refers to the insured’s risk is reclassified in later periods resulting in a significant increase of premium at policy renewals.


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consistent health package enables the insurer to offer and the insured to afford health coverage at all periods at an actuarially fair premium, even if it is expensive in later periods. In other words, the insurer endogenously commits to a long-term contractual relationship with the insured, while the insured keeps his/her flexibility to switch insurers.

De Garidel-Thoron (2005) extends the modelling from symmetric to asymmetric learning by assuming that both the insured and the incumbent insurer learn about the insured’s risk type during period 1, but competing insurers do not. Thus adverse selection arises in period 2 between the insured and competing insurers. The commitment of both insured and insurer is assumed to be endogenous, i.e. no ex ante commitment. He predicts that both the insured and the insurer may generate some commitment endogenously, the insurer will not exercise the right to modify or withdraw the contract, and thus long-term contractual relationship is the unique equilibrium. He also predicts a lowballing pricing pattern, a lock-in effect for low risks, and a tendency that high risks departure from the long-term contract to seek cheaper non-experience rated second period offer.

Assuming semi- and/or full commitment, Pauly, Kunreuther, and Hirth (1995, hereafter PKH), Hendel and Lizzeri (2003, hereafter HL), and Crocker and Moran (2003) develop models assuming symmetric learning; de Garidel Thoron (2005) covers the scenario of asymmetric learning. PKH (1995) assume that the insurer pre-commits to the long-term contractual relationship by offering guaranteed renewability100 in a sequence of short-term policies. They prove a pooled equilibrium and a highballing premium pattern. The insurer charges all risks higher than fair premium in period 1, to cover the future reclassification risk and to lock in low risks. Though the insured is legally allowed to cancel the contract, he/she would not since he/she would lose the part of front-loaded premium covering reclassification risk. PKH (1995) and Pauly, Nickel, and Kunreuther (1998) acknowledge the possibility of a level, instead of a declining, actual premium across-periods in reality, which also reflects the highballing pattern, because the health risk increases over time and thus the level premium declines relative to the risk and to the actuarially fair premium.

HL (2003) follow the same assumption as PKH (1995) and derive an equilibrium that is pooled for high and low risks, but separating for different insureds’ preference concerning the tradeoff between the level of front-loading and the degree of reclassification risk protection. That is to say some risks choose more front-loaded contract (e.g., level premium term life), and thus obtain full protection of reclassification risk; others choose a less front-loaded contract (e.g., annual renewable term life with premiums that depend on age and time elapsed since last medical examination), and thus bear some reclassification risk themselves. The 100 The guaranteed renewability does not only guarantee renewals but also guarantee to only change premium to the same

extent for all in the initial rating class (community rating) or following a pre-agreed premium schedule in subsequent periods (contingent rate).


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pricing pattern is highballing, which is an important device to lock in low risks. The model implies that low risks tend to departure from the incumbent insurer.

Crocker and Moran (2003) develop a model focusing on the relationship between the coverage and the insured’s commitment. They introduce an indicator of job switching cost to capture the insured’s commitment in the group health insurance and thus to cover the spectrum from semi-commitment to full commitment, including the insured’s partial commitment. The insurer’s ability to offer long-term contract or to cover reclassification risk is endogenous and depends the insured’s level of commitment. They prove a pooled equilibrium subject to a certain threshold of insured’s commitment. Along with the increase of insured’s commitment, the partial coverage gradually converges to full coverage. RS’s (1976) separating equilibrium is also viable when the level of commitment is below the threshold. The inter-temporal pricing is not incorporated in their model.

De Garidel-Thoron (2005) compares the semi-commitment with no commitment scenario. He predicts that if the insurer could commit to a long-term contract, the equilibrium will be pooled long-term contracts with bonus-malus type of experience rating. The low-risk insureds are locked in, as the competing insurers cannot offer them a fair premium in period 2 due to lack of information. A flat pricing pattern is implied. De Garidel-Thoron (2005) emphasizes that the asymmetric learning, where no information sharing among insurers is enforced, is strictly better off than the symmetric learning, independent of the insurer’s ability to offer long-term contract. This is because the asymmetric information between incumbent and competing insurers weakens the competing insurer’s ability to exercise a cream-off strategy, and thus improves the long-term commitment of both parties, the benefits of which outweigh the welfare loss due to asymmetric information.

2.3. Panel C: Theories connecting panel A and B

Pauly (2003) discusses three scenarios. First, he takes de Garidel-Thoron’s (2005) no commitment scenario and concludes a pooling equilibrium in period 1, lowballing pricing pattern, lock-in effects for low risks, and implying a high-risk departure pattern. Second, he discusses the semi-commitment scenario in PKH (1995) and HL (2003). A pooled equilibrium with price highballing and low-risk lock-in can be expected, implying a low-risk denaturing pattern. Third, he attempts to build the connection between the adverse selection and no adverse selection models. He argues that the presence of adverse selection (in period 1) should not change the highballing implication embedded in the insurer’s commitment (guaranteed renewability). This third aspect is formalized by Pauly, Menzel, Kunreuther, and Hirth (2011, hereafter PMKH).

PMKH’s (2011) model reconciles models assuming adverse selection with those assuming no adverse selection in period 1, and thus bridges the two panels of models in multi-period


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insurance contracting. They extend PKH’s (1995) model to allow for adverse selection in period 1 and asymmetric learning in later periods. They prove a “pseudo-pooled” equilibrium with guaranteed renewal contracts of each period, which is essentially the same as PKH’s (1995). The highballing pricing pattern remains. They argue that the incumbent insurer cannot take their information advantages to charge higher than fair premium for low risks in period 2, because it charges high front loading from all risks in period 1 and subjects to the zero-profit constraint. This prediction is against KP’s (1985) and de Garidel-Thoron’s (2005) intuition, where the incumbent insurer asymmetrically learns risk information and thus is able to systemically over charge low risks in period 2. They also discuss the potential connections with CH’s (1987) scenario, where the experience rating based on individual claim experience is allowed. They argue that such experience rating would violate the explicitly promise inherent in guaranteed renewability, thus prospective new purchasers would punish such skimping insurers by refusing to buy.

The theoretical framework in Table 1 suggests three trends: (1) no commitment associates with lowballing and semi-commitment with highballing pricing strategy; (2) adverse selection associates with a separating equilibrium; and (3) asymmetric learning associated with high-risk departure pattern. Theoretical researchers have tried to prove the existence of such trends, particularly concerning the commitment-pricing strategy relationship. For example, Dionne and Doherty’s (1994) and HL (2003) point out the commitment sensitive nature of an insurer’s pricing strategy. PMKH (2011) prove that the pricing strategy is independent of the information structure, under semi-commitment terms. These trends yield testable hypotheses and call for empirical investigations.

3. Hypotheses

The theoretical framework in Table 1 suggests that for the no commitment scenario, the pricing patterns are either lowballing or flat; for the semi-commitment scenario (including semi-commitment with renegotiation), the pricing patterns are either highballing or flat. Theoretical predictions also diverge in risk-based dynamic selection, i.e., whether high or low risks tend to departure in period 2. The theories yield two pairs of hypotheses as presented in table 2. The choice for the null hypothesis follows the “prediction tendency” summarized in Table 1 and the common practice in existing empirical research.

The intuitions are as follows. Under the no commitment scenario, the insurer uses low price to attract new clients and earns an informational quasi rent so that it can discriminate high and low risks, while the competing insurers cannot. This is termed “information monopoly rent” in economics. Thus, high risks tend to leave the incumbent insurer because he/she will be perceived as an average risk by competing insurers (KP, 1985; Nilssen, 2000). Under semi-commitment scenario, the insurer and the insured pre-agree on a premium structure at the


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beginning of the multi-period contractual relationship. The insured’s risk type develops over time or the insurer and the insured gradually learn more about the risk type. Therefore, low risks tend to depart from the incumbent insurers in search of a better premium structure when they become aware that they are low risks, because the current premium structure was agreed based on the expected risk, a mixture of high and low risks, some years ago. High risks would have no incentive to select themselves out of the original premium structure. The price highballing strategy is thus implemented with the pre-agreed premium structure aiming to lock in low risks, which, however, might not be sufficient to eliminate the low-risk departure pattern (HL, 2003; Finkelstein, McGarry, and Sufi, 2005). A renegotiation strategy may also play a role when the incumbent insurer wants to retain low risks based on its newly learned information (Dionne and Doherty, 1994).

Table 2 Hypotheses Commitment Assumption Null Hypotheses (H0) Alternative Hypotheses (H1) H1 The inter-temporal pricing pattern is H1A no commitment lowballing Flat H1B semi-commitment highballing Flat H2 The inter-temporal risk departure pattern is H2A no commitment high risks departure no pattern H2B semi-commitment low risks departure high risks departure or no pattern

The winner’s curse in the banking industry is similar to the risk-based dynamic selection problem in the insurance context. The winner’s curse results from the ability of rejected loan applicants to apply at additional banks (Shaffer, 1998) and thus the competing banks are more likely to attract higher-risk applicants. Similar to the high-risk departure pattern in H2A, the winner’s curse problem results from the asymmetric information between the incumbent bank (insurer) and its competitors (Sharpe, 1990). The incumbent bank (insurer) earns an informational monopoly quasi rent over its competitors and thus is able to select low risks.


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Table 3 Empirical evidence in multi-period insurance contracting D’Arcy

and Doherty (1990)

Cohen (2012)

Kofman and Nini (2013)

Shi and Zhang (2015)

Dionne and Doherty (1994)

Hendel and Lizzeri (2003)

Cox and Ge (2004)

Finkelstein, McGarry, and Sufi (2005)

Herring and Pauly (2006)

Pinquet, Guillen, and Ayuso (2011)

Hofmann and Browne (2013)

No Commitment Semi-Commitment Product Auto Auto Auto Auto Auto

Liability Term Life

LTC LTC Individual Health

health, life, and LTC

Individual Health

Market US Israel Australia Singapore CA, US US US US US Spain Germany Policy Duration

ST ST ST ST LT LT or GR

GR GR or LT GR GR LT or GR

Commitment Type

No No No No Semi (with renegotiation)

Semi Semi Semi Semi Semi Semi

Adverse Selection

Y Y Y Y Y N Y Y Y Y Y

Insurer Learning

Asym Asym Sym Btw asym and sym

Asym Sym Not discussed

Not discussed

Not discussed

Sym Sym

H1A Confirm Confirm Confirm Confirm / / / / / / / H1B / / / / Confirm Confirm Reject,

lowballing Confirm Confirm Confirm Confirm

H2A / Confirm Confirm Confirm / / / / / / /

H2B / / / / Rejected, high risks departure

/ / Confirm / Confirm Confirm


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4. Empirical evidence

It is ultimately an empirical task to determine what kind of product market matches with what kind of pricing strategy and of risk departure pattern, and to discriminate the roles of commitment and information structure (PK, 1985; Pauly, 2003). Policy makers and managers in insurance companies should rely not only on the theoretical research, but also on empirical analyses to develop their policy against competing insurers (Cohen and Siegelman, 2010). The extant empirical evidence concerning the two pairs of hypotheses is compared with the structure in Table 3 and reviewed in detail according to their different commitment types.

4.1. No commitment evidence

D’Arcy and Doherty (1990) start the empirical investigation in multi-period insurance contracting. They present the aggregate loss ratios by policy age cohorts of automobile insurance from seven US insurers. All seven portfolios show that loss ratios decline almost monotonically with policy age, suggesting lowballing pricing pattern and supporting H1A. They also look at three new market entrants, which have only new policies, but no private information. They found that these three new insurers’ loss ratios were indeed high (low profit) in the beginning but gradually converge to other matured firms, supporting the price lowballing pattern in H1A.

Cohen (2012) presents the first policy-level analysis for repeated short-term insurance contracting using an Israel automobile insurance portfolio. During the entire sample period, the information-sharing platform among insurers is not available, thus the asymmetric learning best captures the nature of the market. He shows that (1) profits from repeat insureds are higher than those from new insureds (i.e. a lowballing pattern); (2) the insurer reduces the price charged to repeated insureds with good claim history by less than the reduction in expected costs associated with such insureds (i.e. premium downward stickiness); (3) repeat insureds with bad claim history are more likely to switch to other insurers (i.e. high risks departure). The evidence is obtained after controlling for all risk classification factors. It directly supports H1A and H2A. Cohen’s (2012) sample matches KP’s (1985) and Nilssen’s (2000) assumptions and he argues for the role of asymmetric learning in determining the lowballing pricing strategy.

Kofman and Nini (2013) examine the Australian automobile insurance market, where a claim information sharing platform is in place to support a bonus-malus rating system. They believe that the publicly available data in Australian system capture all relevant risk type information about policyholders, with the only exception of brand new policies. Thus the market matches with Watt and Vazquez’s (1997) assumptions, (i.e. adverse selection in period 1, symmetric learning in later periods, and no commitment). The public nature of such system eliminates one important source of asymmetric learning. They document evidence of both lowballing


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pattern and high risks departure, supporting H1A and H2A. Their evidence challenges Cohen’s (2012) argument regarding the important role of asymmetric learning in determining product pricing strategy.

Shi and Zhang (2015) investigate an insurer learning scenario in between Cohen’s (2012) no information sharing market and Kofman and Nini’s (2013) complete information sharing market. The Singapore automobile insurance market has a no-claim-discount (NCD) system and a public information sharing platform. However, the platform contains only information regarding the NCD status but neither the insureds’ claim history nor their policy choice, which implies a partial information sharing among insurers (Shi and Zhang, 2015). Their conclusions again support H1A and H2A and suggest the product pricing strategy may not depend on insurer’s learning type.

4.2. Semi-commitment evidence

Dionne and Doherty (1994) examine a special automobile liability insurance portfolio from California, where two types of policies are offered: a long-term policy (semi-commitment with renegotiation) and a short-term policy (no commitment). They approximate the average policy age in a portfolio by the premium growth of that portfolio (i.e. high (low) growth indicates in average younger (old) policy age) and find a positive correlation between average policy age and loss ratio in the subsample of low risks, which is in line with the highballing prediction of semi-commitment (with renegotiation) model and thus supports H1B. Such a highballing pattern is not found in intermediate- and high-risk groups, suggesting that only the low risks choose semi-commitment long-term policies, and high risks choose flat rated short-term policies. This is in line with CH’s (1987) prediction and does not support the null but the alternative hypothesis of H2B, i.e. high risks departure.

HL (2003) present the first-piece of evidence controlling for underlying risk differences, i.e. risk classification, in multi-period insurance contracting. They look at three products of life insurance from 55 US life insurers: 20-year term life with level premium each year (TL), annual renewable term life with premiums that depend only on age (ART), and annual renewable term life with premiums that depend on age and time elapsed since last medical examination (Selection and Ultimate ART). They find that TL and ART are significant front-loaded, where the insurer pre-commits to a long-term contract (LT) or to the guaranteed renewability with a determined rating schedule (ART). The relative price to the risk almost monotonically decreases through the 20 years, supporting H1B. However, for Selection and Ultimate ART, where the premiums in later periods depend on whether the insured passed the medical reexamination (a weakened commitment with re-underwriting elements), the front-loading exists only in the first year but not in following years. They approximate the risk by the present values of premiums and find negative correlation between the front-loading and


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the risk: more front-loaded contracts insure higher proportion of low risks. They also show that more front-loaded contract (LT) has a lower lapse rate than less front-loaded contract (ART), indicating the low-risk lock-in effects associate with the highballing pricing strategy. Unfortunately, HL (2003) are not able to directly test the risk departure dynamics, which is then complemented by Finkelstein, McGarry, and Sufi (2005).

Cox and Ge (2004) present a panel data from the US long term care (LTC) insurance market and with cohort-specific information. They find a positive correlation between policy age and loss ratio, but argue that it reflects the risk changes over time and thus not a price highballing strategy. They also find a negative correlation between the square of policy age and loss ratio, and argue that it indicates a decreasing speed of loss ratio increases and thus indicates the insurer gradually increase the price relative to actuarial fair premium (i.e. a price lowballing strategy).

One way to solve this apparent theoretical (highballing, H1B) and empirical (lowballing in Cox and Ge, 2004) contradictory is to use the policy level data and control for risk classification, so that the coefficient between policy age and price/profit can directly reveal the pricing pattern. Finkelstein et al. (2005) examine the US long-term care market in such a direct way. They document pricing highballing evidence consistent with HL (2003) from the US life market, thus supporting H1B. Moreover, they examine the risk departure dynamics using the policy-year-level data controlling for risk classification. They show that insureds who let their policies lapse are indeed lower risks than those who stay. It directly supports H2B and is exactly what HL (2003) predict.

Herring and Pauly (2006) numerically develop an ideal/optimal incentive compatible premium schedule for individual health insurance with guaranteed renewability, based on PKH’s (1995) semi-commitment model. In addition, they estimate the actual market premiums for individual health insurance using Medical Expenditure Panel Survey, Community Tracking Study Household Survey, and National Health Interview Survey. They find that the actual premium schedule “does appear to be surprising consistency” with the estimated ideal premium schedule, thus supporting the highballing prediction in H1B. They conclude that the front-loaded premium is necessary for health insurers to provide a guaranteed renewability and to insure the reclassification risk, however, is mitigated because the low-risk’s expected expense increases with age, the likelihood of becoming a high-risk increases with age, and the high risk either recovers or dies.

Pinquet, Guillen, and Ayuso (2011) examine the dynamic lapse (departure) behavior in a long term package coverages of health, life, and LTC from the Spanish market. Premiums are paid annually. The experience rating on individual basis is not allowed. They find front-loaded pricing strategy (H1B) in all three coverages evidenced by the increased benefit ratios from


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younger to older groups. Moreover, they observe a continuously decreased lapse rate over insured’s age with an exception at age 65. They explain that the cost of lapse increases with the policy age and younger policyholders usually have a small policy age. Hence, younger policyholders are less locked in by the front-loading if they want to lapse for whatever reason. This result supports H2B in the sense that younger policyholders (low risks) tend to departure from the portfolio. They also discuss other possible explanations for the risk dynamics, e.g., the insured’s insufficient knowledge about insurance products, and why reclassification risk is unlikely to be a major reason for young policyholder lapse.

Hofmann and Browne (2013) present evidence from the German long-term private health insurance (semi-commitment), where the insurers commit to offer renewal at a premium rate that does not reflect revealed future information about the insured risk. They support the theoretical predictions in HL (2003): a price highballing strategy (H1B) generates the effect of insured lock-in, and a low-risk departure pattern (H2B). The evidence from the German private health market demonstrates the robustness of pricing and risk dynamic predictions, which are immunized from the strict regulation and from the existence and possible domination of social insurance program. This work also contributes to the debate how private health solutions can insure the reclassification risk. The empirical evidence shows the viability of the front-loaded premium schedule with guaranteed renewability (PKH, 1995) at least in a strictly-regulated and social insurance dominated market. In such market, the accessibility of health coverage is much less a problem than that in a private insurance driven market.

4.3. Results from synthesized evidence

Table 3 reveals the different roles of commitment and information structure in determining the inter-temporal pricing strategy. First, if the insurer offers only short-term contracts (i.e. the insurer has no commitment), the inter-temporal pricing pattern is lowballing (all four pieces of evidence support H1A); if the insurer offers long-term contracts or a sequence of short-term contracts with guaranteed renewability (i.e. the insurer commits to multi-period contractual relationship), the pattern is mostly highballing (six out of seven support H1B). The comparison results based on extant empirical evidence strongly support Dionne and Doherty’s (1994) and HL’s (2003) theoretical assertion that the product pricing strategy is sensitive to the commitment types.

Second, by the nature of insurance markets (Cohen and Siegelman, 2010), ten out of eleven products reviewed in this paper present some kind of adverse selection. Among the ten adverse selection cases, four present lowballing pricing pattern and six highballing. Comparing HL’s (2003) evidence with Pinquet et al.’s (2011), both examine a term life coverage with guaranteed renewability and symmetric learning; both conclude the same


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highballing pricing pattern. However, adverse selection is not a problem in HL’s (2003) portfolio; while Pinquet et al. (2011) acknowledge the presence of adverse selection. The comparison results show that the pricing pattern is insensitive to the presence or absence of adverse selection.

Third, eight out of eleven pieces of evidence specify or indicate the insurer’s learning type, in which three feature asymmetric learning, four symmetric learning, and one in between. Both highballing and lowballing pattern are present in both sub-categories of asymmetric and symmetric learning. Cohen (2012), Kofman and Nini (2013), and Shi and Zhang (2015) show three automobile portfolios from three markets, which have no, full, and partial information sharing systems respectively. All three papers conclude the same lowballing pricing pattern. This is a strong signal that the pricing pattern is insensitive to insurer learning types (PMKH, 2011). 101 The roles of commitment and information in risk-based dynamic selection are discussed later.

5. New empirical evidence

A major shortcoming of the results from synthesized evidence is that it does not always compare apples with apples. The comparison conclusions are based on different insurers, different markets, and different time periods, which may blur the pattern from a product pricing strategy. For example, the appeared pattern may be driven by short-term business targets or management considerations other than a product inter-temporal pricing strategy. An insurer may be under growth pressure from shareholders in some years. A product sample from this period may yield a lowballing pricing pattern due to the target of attracting new clients; however in normal periods without particular growth pressure, such a product may be flat priced. Another example is the insurance market cycle, which reflects the long-term pricing pattern of an insurance market and is mingled with the temporal pricing pattern of a product. Thus, in order to isolate the impact of product inter-temporal pricing strategy, the hypotheses are tested with two product samples from the same insurer, the same market, and almost the same period. In such two samples, if different pricing or risk selection patterns are found, it is more convincing to conclude that the patterns result from the insurer’s strategy instead of other firm-, market-, or time period-specific factors. Such an empirical design is new to multi-period insurance contracting studies and will increase the credibility of the pricing pattern found.

101 This observation does not necessarily mean the insurer learning is irrelevant in the multi-period insurance contracting.

If no insurer learning is present, the pricing pattern may not exist. Moreover, as de Garidel-Thoron (2005) suggested, the asymmetric or symmetric learning may have strong impact on the overall efficiency of the equilibrium.


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5.1. Samples

I obtain samples of two products from a Chinese life and health insurer. Tables 4 and 5 compare the two samples qualitatively and quantitatively. The insurer nationwide operations, with a broad spatial range that covers over 90% of the Chinese population. It is ranked among the top ten largest life insurers in China over the past 15 years in terms of premium volume and assets. Its core business comes from the open market and thus is not concentrated in any particular industry or region. Its operational model, growth path, risk portfolio, and performance are representative in the Chinese insurance market. In 2012, 68 life and health insurers and 62 property and liability insurers operated in the Chinese insurance market, and most of them are legally eligible to issue the two products considered here, yielding a very competitive market.

Sample A is a portfolio of Group Critical Illness (CI) insurance.102 CI insurance is a type of loss-occurrence health insurance. The full insurance amount is paid as long as an insurer-recognized hospital provides the first-time diagnosis of the covered disease during the policy period. Usually, there is a 30- to 90-day waiting period for first-time purchasers. The claim benefit always equals the insurance amount and is paid to the insured in a lump sum without additional benefits, such as medical service. The claim payment does not require actual medical expenditure or hospitalization. Thus CI insurance is immunized from many common problems observed in medical expense health insurance, such as moral hazard and choices between private and public hospitals. In 2007, the Insurance Association of China and the Chinese Medical Doctor Association issued guidelines that define 25 types of critical diseases. In this case, and in most cases in the Chinese CI insurance market, the insurer strictly follows the CI coverage guideline, which standardizes CI insurance products. In this sample, all group policies and insured individuals have the same coverage for the 25 critical diseases. Both group and individual CI insurance are available in the Chinese market. The group CI insurance market is dominated by employee benefits for which the employer pays the premium and the employee contribution is minimal. There are no restrictions regarding risk classification based on age, gender, occupation, region or other possible pricing factors. The insurer has sole discretion to determine the price offered for both new and renewed contracts. The market is commercial and voluntary. Thus, the concerns regarding risk reclassification, availability, and affordability of such insurance are minimal.

The group CI insurance falls into the no commitment category, where the insurer is free to terminate the group contract at the end of any policy period. The group insured is also free to switch or to terminate the group contract at any time. The individual insured is partially committed to the coverage due to his/her job attachment. Eling, Jia, and Yao (2015) focus on

102 Eling et al. (2015) use a different sample of the same portfolio.


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the information structure of group CI insurance and show the presence of between-group adverse selection and asymmetric learning.

Sample B is a portfolio of Loaner’s Personal Accident (PA) insurance. The borrower (insured) of a bank buys the coverage from the insurer to cover his/her accidental death and disability during the loan period. The policy beneficiary is the bank and the insurance amount usually equals the outstanding loans plus interests. The bank also serves as the sales agent of the insurer, recommends this product to its borrowers, and receives sales commission as a percentage of the insurance premium from the insurer. The bank can sell the Loaner’s PA exclusively for one insurer, or for multiple insurers. The borrowers can buy the product from the bank or from other channels. However, after consulting with the insurer, almost all borrowers buy the product from the bank channel, because they are afraid that products from other channels may not 100% meet the bank requirement, shopping products from other channels require additional efforts and knowledge, and products from other channels may be more expensive because individual borrowers may not enjoy a group discount as being insured together with all borrows from the bank. Villeneuve (2014) confirms this channel stickiness for a similar product of mortgage life in French market.

The policy period is usually one year but with an implicit guaranteed renewability until the borrowers clear all loans. This implicit guarantee is strong, because the bank, as the beneficiary, would expect the insurer to cover all its loaners as a group and thus do not accept the insurer’s cherry picking, leaving the bank itself at risk. The bank, as the sales agent, has also the market power to enforce the implicit guarantee. In the agent agreement, the insurer has in fact delegated the underwriting authority to the bank to accept all borrowers as a group. Meanwhile, a rating tariff is also delegated to the bank to insure all risks according to the tariff without further underwriting. The parameters in the tariff include age, gender, and occupation accidental categories. Premiums are not updated based on individual insured’s past claim experience (nondiscriminatory, Pauly, 2003). However, the tariff can be updated from time to time based on “community rating.” The individual insureds partially commit to the long-term coverage, because they are required to insure by the bank as long as they have outstanding loans, and they are reluctant to switch insurers (Villeneuve, 2014). The insured can terminate the coverage or significantly reduce the insurance amount at any time by early pay back (part of) his/her loans, which is very common in the Chinese market. The bank is free to terminate the agent agreement with the insurer at any time and to switch to competing insurers, which results in a considerable proportion of insureds also switching at the time of their next renewal.

The Loaner’s PA falls into the scenario of semi-commitment, where the insurer is committed to the long-term coverage by implicit guaranteed renewability and the insured is partially


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committed to the long-term coverage by his/her outstanding loans with the bank. This market presents little adverse selection, because almost all banks require all borrowers to present a Loaner’s PA for the loans, thus the product has a compulsory feature for borrowers. The product information structure features as no adverse selection with asymmetric learning.

Both samples include all information that the insurer uses to make underwriting and pricing decisions. Claims records are included. Sample A covers all group CI policies issued between January 2008 and June 2013 and all claims settled between January 2008 and August 2012 under the corresponding policies. Sample B covers all Loaner’s PA policies issued between January 2008 and December 2011 and all claims under these policies. The two samples are selected following the same procedure. First, only policies with duration between 360 and 366 days, i.e. 1-year duration, are used and thus policy age and number of renewals are aligned with each other.103 Second, policies, of which the renewal status cannot been identified, are deleted from the sample. Third, the premium rates are truncated at both the 1 and 99 percentiles to avoid the potential bias of extreme values. The final Sample A contains 5,570 group policy-year observations purchased by 3,152 groups, representing more than 1,880,000 individual policies. 104 Sample B contains more than 1,280,000 individual policy-year observations purchased by over 800,000 individual insureds. Missing information is present in both samples, particularly related to missing claims after August 2012.105

As shown in Table 4, the key differences between the two products are in the insurer’s commitment type and the presence of adverse selection in early policy periods. Other factors are either the same or largely similar such that any differences in pricing and/or risk patterns likely attributable to differences in commitment type and/or adverse selection. As shown in Table 5, both samples are characterized by a low claim frequency, a relatively small insurance amount for most policies, and a mixture of ages, genders, and occupations. The Loaner’s PA portfolio contains much more males than females, which reflect the Chinese family tradition, where the man usually manages the household’s external financial relationships, e.g., loans. It also reflects that businessmen outnumber businesswomen in China. The area distributions of the two portfolios are significantly different, where the group CI more concentrates in the developed areas, because firms that could afford the employee benefits tend to locate in more developed and affluent areas.

103 For Sample A, group policies with 1-year duration account for 62% of all policy-years; for Sample B, policies with 1-

year duration account for 82% of all policy-years. 104 The original data of Sample A are at individual policy level. The individual policy entries are then organized into

group policies according to the group policy number. 105 The claims information is electronically recorded in real time but only retrieved and organized by the actuarial team

once per year. When obtained the data for Sample A, the claim information for September 2012 to June 2013 were not yet available. In a later analysis, to avoid a potential truncation problem, the claim status of polices expiring after August 2012 are coded as missing values.


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Table 4 Qualitative comparison of samples A and B Sample A Sample B Comparison Product Group critical illness Loaner’s personal accident Insurer Anonymous LandH insurer Anonymous LandH insurer Same Market China China Same Sample period 2008-2013 2008-2011 Similar Commitment type No commitment Semi-commitment Different Insurer’s commitment 1-year short-term policy 1-year short-term policy

with guaranteed renewability Different

Bank’s or group’s commitment

Employer is free to cancel or switch insurer

Bank is free to switch insurer Similar

Individual insured’s commitment

Partially attached due to employment

Partially attached due to the loan with the bank Similar

Adverse selection

Between-group adverse selection, which diminishes after two periods (Eling et al., 2015)

No Different

Incumbent insurer’s learning

Group level experience rating Bank level experience rating Similar

Competing insurers’ learning

No information sharing system, but may observe the past claim history at group level by group declaration

No information sharing system, but may observe the past claim history at bank level by bank declaration

Similar


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Table 5 Quantitative comparison of samples A and B Sample A: Group critical illness Sample B: Loaner’s personal accident

Variables Descriptions Obs. Mean S.D. p5 Median p95 Obs. Mean S.D. p5 Median p95 Premium Rate

Annualized premium rate per insured 5,489 0.0027 0.0020 0.00066 0.0024 0.0066 1,262,082 0.0027 0.00083 0.0013 0.0028 0.0040

Departure Dummy

1 if the policy is dropped in the next period 3,884 0.39 0.49 0 0 1 803,758 0.53 0.50 0 1 1

Policy Age Count of renewal times 5,570 0.92 1.16 0 1 3 1,285,629 0.31 0.63 0 0 2

Insurance Amount

Insurance amount per insured in CNY 5,570 60,667.4 74,496.0 3,000 50,000 200,000 1,285,244 37,108.0 21,579.3 10,000 30,000 90,000

Group Size

Number of individual insureds in the group 5,570 342.0 1471.0 6 63 1248 N.A.

Policy Duration Policy duration in days 5,570 365.0 0.85 363.6 365 366 1,285,629 364.1 1.02 362 364 365

Sex (Fraction of) women 5,561 0.41 0.21 0.084 0.40 0.80 1,272,506 0.12 0.33 0 0 1 Age (Group average) age 5,568 35.7 7.21 24.7 35.8 47.1 1,285,547 40.4 9.01 26 40 56

Worka (Group average) occupation accident tendency 5,460 2.00 1.03 1 1.99 4 1,279,303 2.73 1.21 1 3 4

Areab Indicator of relative wealth and insurance market development of the policy issuance location

5,570 2.03 0.86 1 2 3 1,285,629 3.11 0.67 2 3 4

Claim Dummy

1 if any claim(s) under the policy 2,794 0.14 0.35 0 0 1 1,021,970 0.00074 0.027 0 0 0

Claim Frequency

Average number of claims per insured 2,794 0.00094 0.0050 0 0 0.0048 N.A.c

N Total number of policies 5,570 1,285,629 Notes: a. 1 represents the safest occupations, and 6 represents the most dangerous ones. The variable work represents the accident tendency of an occupation, e.g., office workers are 1, and coal mine workers are 6. The insurer accepts very few risks with occupation categories above 4. b. 1 represents the most developed regions in China, and 4 represents the least developed regions. The variable area is based on the insurer’s branch categories, which consider not only regional wealth level but also regional insurance development level. It is thus a better control variable than pure wealth measurement. c. The claim frequency is not applicable for Sample B because it is very close to the claim dummy. Almost all insureds have only one accident claim in one policy, if there is any.


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5.2. Models

The same models are applied to both samples. Equation (1) tests Hypotheses 1A and 1B with Sample A and B, respectively. The premium rate is measured by the natural logarithm of the average annualized premium rate per person, lnPremiumRate. The insurance Policy Age is measured by the number of renewals. All policies in both samples are yearly policies, and thus the renewal times fully capture the policy experience with the insurer. Xi,t is a vector of time-variant control variables, including policy features (insurance amount per person and, for Sample A, group size) and risk classification factor (age). Risk classification refers to the use of observable characteristics by insurers to compute the premiums. Yi is a vector of time-invariant control variables, including risk classification factors (gender and occupation category) and location fixed-effects. Yeart controls for the year fixed-effects.

𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑟𝑟𝐶𝐶 𝑅𝑅𝐶𝐶𝑡𝑡𝐶𝐶𝑖𝑖,𝑐𝑐 = 𝛽𝛽1 + 𝛽𝛽2𝑃𝑃𝐶𝐶𝑆𝑆𝑅𝑅𝐸𝐸𝐸𝐸 𝑛𝑛𝐶𝐶𝐶𝐶𝑖𝑖,𝑐𝑐 + 𝛽𝛽3𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝛽𝛽4𝑌𝑌𝑖𝑖 + 𝛽𝛽5𝑌𝑌𝐶𝐶𝐶𝐶𝐶𝐶𝑐𝑐 + 𝜀𝜀𝑖𝑖,𝑐𝑐 (1)

Equation (1) is estimated with OLS regressions. Random-effects and firm fixed-effects106 models are estimated as robustness tests (Zhang and Wang, 2008; Eling et al., 2015), the results of which are consistent with the core models. Chiappori and Salanie (2000) emphasize that the use of simple, linear functional forms on insurance policy-level data should be restricted to homogeneous populations. The samples approximate homogeneity because (1) the business nature is largely the same as employee benefits for Sample A and as mortgage PA for Sample B; (2) the model includes all relevant pricing factors to account for potential heterogeneity among policies; (3) Robust standard errors clustered by insureds further control for heterogeneity. However, the residual plots suggest some remaining heterogeneity in both samples, thus firm fixed-effects models are used to further reduce the heterogeneity in a robustness test, the results of which are consistent with the core models. The variance inflation factors (VIF) of the independent variables range between 1.02 and 1.63 for Sample A and 1.00 and 1.67 for Sample B. All VIFs are below 5, suggesting multicollinearity is not a problem. The Wooldridge test for autocorrelation in panel data suggests minimal autocorrelation problem in both samples with p-value of 0.67 for Sample A and with p-value of 0.15 for Sample B.

Equation (2) tests Hypotheses 2A and 2B with Sample A and B, respectively. Finkelstein et al. (2005) develop this empirical model to investigate the risk-based dynamic selection. The premium rate is used as the indicator for risk type (HL, 2003). H2A predicts that if no commitment, high risks shall depart from the portfolio over time and thus a positive coefficient is expected between the departure dummy and the premium rate (risk); H2B

106 It is acknowledged that firm fixed-effects are able to better capture the dynamics of one firm over years; however, its

costs are also significant as to omit all time-invariant variables. The results of firm fixed-effects models are present in Table 9, Section 5.5.


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predicts that if semi-commitment, low risks tend to depart from the portfolio over time and thus a negative coefficient is expected between the departure dummy and the premium rate. Xi,t is a vector of policy features (insurance amount per person and, for Sample A, group size); Locationi and Yeart represent the location and year fixed-effects, respectively. The risk classifications (i.e. the insured’s demographic features) are not included in Equation (2) because the premium rate has fully captured these information. Equation (2) is estimated with OLS regressions. The corresponding robustness tests are available upon requests.

𝐷𝐷𝐶𝐶𝑆𝑆𝐶𝐶𝐶𝐶𝑡𝑡𝑟𝑟𝐶𝐶𝐶𝐶 𝐷𝐷𝑟𝑟𝐶𝐶𝐶𝐶𝐸𝐸𝑖𝑖,𝑐𝑐 = 𝛽𝛽1 + 𝛽𝛽2𝑆𝑆𝑛𝑛𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑟𝑟𝐶𝐶𝑅𝑅𝐶𝐶𝑡𝑡𝐶𝐶𝑖𝑖,𝑐𝑐 + 𝛽𝛽3𝑋𝑋𝑖𝑖,𝑐𝑐 + 𝛽𝛽4𝐿𝐿𝐶𝐶𝐸𝐸𝐶𝐶𝑡𝑡𝑅𝑅𝐶𝐶𝑛𝑛𝑖𝑖 + 𝛽𝛽5𝑌𝑌𝐶𝐶𝐶𝐶𝐶𝐶𝑐𝑐 +𝜀𝜀𝑖𝑖,𝑐𝑐 (2)

5.3. Results on inter-temporal pricing strategy

Table 6 presents the results from Equation (1). The actual premiums are regressed against the complete risk classification control variables and claim experience, where applicable. Thus any trend found between the actual premium and the policy age reflects the inter-temporal pricing strategy controlling for the underlying risk changes. The trend observed does not necessarily reflect the actual increase or decrease of the premium rate but a relative premium increase or decrease to the actuarial fair premium, which is the inter-temporal pricing pattern (KP, 1985; PKH, 1995). The Sample A results in Panel A show positive coefficients between the premium rate and the policy age, indicating a pattern of premium lowballing (back-loaded) and supporting H1A. The Sample B results in Panel B show negative coefficients between the premium rate and the policy age, indicating a pattern of premium highballing (front-loaded) and supporting H1B.

The difference between Column 1 and 2 in Panel A is that Column 2 includes an additional independent variable, the last-period group claim frequency, to capture the experience rating at the group level for Sample A. Its coefficient is positive, as expected, meaning last-period high claim frequency associates with a higher premium rate in the current period. The positive correlation between policy age and premium rate remains. This practice is not applicable to Sample B because the loaner’s PA insurance is not experience rated at the policy level.

Looking at the subsample results of Sample A, the premium pattern is flat for the first two periods, and then continuously increases with the policy age in the 2nd, 3rd, and subsequent renewals. KP (1985), Nilssen (2000), and de Garidel-Thoron (2005) suggest that the higher profit or price is viable in later periods because the incumbent insurer can learn the insured’s risk type in early periods, and thus can over charge low risks with sticky price. Due to the low frequency nature of critical illness insurance, the insurer’s learning process may require longer time. The insured groups may have not yet revealed their risk types in claim experience in the first two periods. This is particularly true for small groups as they may simply be lucky for not having any claims. This explanation is consistent with Eling et al.’s (2015) findings,


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where they use a different subsample of the same portfolio and show that the insurer learning eliminates information asymmetry (adverse selection) after the first two periods. This flat-increase pattern implies that insurer learning is a necessary condition for the insurer adopting a price lowballing strategy, although early research has found no difference between symmetric and asymmetric learning (Cohen, 2012; Kofman and Nini, 2013, Shi and Zhang, 2015). Looking at the subsample results of Sample B, the premium rate continuously decreases with the policy age. The absolute values of coefficients between policy age and premium rate become smaller over time, suggesting that the scale of premium reduction from year to year becomes smaller and smaller.

Looking at the control variables, the actual premium rates negatively associate with the insurance amount (group size), suggesting the discount for large quantity of insurance (large clients). Women enjoy a lower rate than men because women are less likely to have critical illness and less likely to have accidents than men. Older people have a much higher critical illness risk and a slightly lower accident risk than younger people. The occupation types, by definition, reflect the propensity for accidents, instead of illness. Thus, as expected, people in the safer categories have a lower premium rate of accident insurance.

Products A and B yield the opposite inter-temporal pricing patterns, which cannot attribute to the idiosyncrasies of insurers, markets, or time periods by the two-sample constructs, but to the product differences in the insurer’s commitment type and/or in adverse selection as highlighted in Table 4. The comparison results based on synthesized empirical evidence have successfully excluded adverse selection as a determinant of the inter-temporal pricing strategy. Moreover, the adverse selection becomes minimal in Sample A after the first two contract periods (Eling et al., 2015), and thus both samples have no adverse selection when the pricing patterns are significant. Thus the opposite inter-temporal pricing patterns can reasonably attribute to the different types of the insurer’s commitment. This unique empirical design strengthens the correlation between the insurer’s no commitment and its lowballing pricing strategy and between the insurer’s pre-commitment and its highballing pricing strategy, by controlling for the differences in insurers, markets, and sample periods.


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Table 6 Results on inter-temporal pricing strategy Panel A: Group critical illness insurance Panel B: Loaner’s personal accident insurance

Full sample New-->1st renewal

1st --> 2nd

renewal 2nd-->3rd renewal

The 3rd and subsequent renewals

Full sample New-->1st renewal

1st --> 2nd

renewal

The 2nd and subsequent renewals

Variables ln(Premium Rate) ln(Premium Rate) Policy Age 0.0192* 0.0690*** -0.0244 0.0200 0.105*** 0.0876*** -0.0790*** -0.1000*** -0.00421*** -0.00149a

(0.0103) (0.0158) (0.0167) (0.0210) (0.0298) (0.0303) (0.000528) (0.000638) (0.000923) (0.00301) ln(Insurance Amount)

-0.132*** -0.138*** -0.131*** -0.146*** -0.138*** -0.0519 -0.0342*** -0.0331*** -0.0586*** -0.0620*** (0.0107) (0.0163) (0.0105) (0.0152) (0.0245) (0.0380) (0.000443) (0.000417) (0.00118) (0.00228)

ln(Group Size) -0.0859*** -0.0597*** -0.0898*** -0.0711*** -0.0667*** -0.0172 -0.0145*** -0.0145*** -0.0289*** 0.0154*** (0.00755) (0.0109) (0.00706) (0.00963) (0.0155) (0.0211) (0.00117) (0.00111) (0.00211) (0.00327)

Sex -0.207*** -0.00203 -0.274*** -0.000411 0.169 0.216 -0.000486*** -0.000338*** -0.00114*** -0.00123*** (0.0455) (0.0745) (0.0442) (0.0716) (0.125) (0.167) (3.88e-05) (3.63e-05) (7.80e-05) (0.000120) Age 0.0430*** 0.0404*** 0.0446*** 0.0438*** 0.0393*** 0.0507*** -0.106*** -0.0948*** -0.299*** -0.343*** (0.00174) (0.00262) (0.00165) (0.00230) (0.00337) (0.00428) (0.000793) (0.000752) (0.00186) (0.00388) Work2 -0.0676** -0.0946** -0.000971 -0.0715* -0.265*** -0.347*** -0.119*** -0.115*** -0.158*** -0.157*** (0.0297) (0.0464) (0.0294) (0.0383) (0.0610) (0.0762) (0.00154) (0.00146) (0.00299) (0.00488) Work3 -0.212*** -0.147*** -0.210*** -0.179*** -0.242*** -0.380*** -0.0636*** -0.0753*** -0.148*** -0.143*** (0.0278) (0.0432) (0.0270) (0.0369) (0.0608) (0.0881) (0.000975) (0.000925) (0.00219) (0.00437) Work4 -0.0493 -0.00367 -0.0683 -0.0357 -0.0154 -0.128 (0.0432) (0.0482) (0.0473) (0.0501) (0.0664) (0.104) Work5 0.0766 0.182** -0.00149 0.206 0.0267 0.0119 (0.0682) (0.0852) (0.0768) (0.132) (0.190) (0.158) Prior Claim Frequency

3.697** (1.729)

Location/Year FE /Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

R2 0.368 0.354 0.399 0.377 0.322 0.393 0.161 0.114 0.391 0.514 Observations 5,369 2,269 4,109 2,250 1,020 603 1,242,577 1,151,290 278,893 91,287

Notes: The table reports the estimated coefficients of OLS regressions. Robust standard errors clustered by insureds are presented in parentheses. It also presents *, **, ***, indicating significant differences of coefficients from 0 at the 10%, 5%, and 1% levels, respectively. a. The coefficient becomes less significant in this subsample probably due to the small number of observations.


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5.4. Results and Discussion on risk-based dynamic selection

Tables 7 presents the results from Equation (2). The Sample A (B) results in Panel A (B) show negative (positive) coefficients between the risk (measured by premium rate) and the departure dummy, indicating low (high) risks depart and high (low) risks stay in the portfolio over time, which is against H2A (H2B). The subsample results in Columns 2 and 3 confirm the same trend as the full sample in Column 1.

The question is then why? Do the observed risk dynamics result from the risk-based dynamic selection or from other factors? The demand driving factors other than the risk may provide a promising explanation. In Sample A, the insured group can cancel the policy because of bad economic environment or changes in management, which have nothing to do with whether the group is high- or low-risk. In Sample B, the insured may decide to pay back the loans because of a decrease in market interest rate, which enables him/her to access to less expensive financial resources. Moreover, the expected insurance benefits are very small in both samples. It is unlikely that the insureds would change their job or loan plan considering such small benefits. Therefore, the risk dynamics observed are very likely not risk-based but driven by other insurance demand factors. To verify this explanation, GDP growth rate for Sample A and 1-year loan interest rate for Sample B are alternatively included in the models, to replace the risk measurement (premium rate). The year fixed effects are omitted due to their multicollinearity with the macroeconomic indicators. The results in Column 4, Table 7 show that, as expected, a low GDP growth associates with high policy cancellation rate with respect to CI employee benefits; a low (current) interest rate indicates a low finance cost for the current period, thus the insured (borrower) is easier to pay back prior loans and cancel the PA policy.107

The roles of commitment and information in inter-temporal risk-based dynamic selection is more complex and less conclusive than their roles in the product pricing strategy. First, the dynamics of high and low risks in a portfolio is a two-side decision: the insurer can “select” risks by re-underwriting, experience rating, menu contracts, and by an inter-temporal product pricing strategy; the insureds also decide whether they stay or depart considering competing offers, own risk types, and other insurance demand factors. It may be easy to argue that both highballing and lowballing pricing strategies (strategy of the supply side) generate lock-in effects for low risks (Nilsson, 2000; HL, 2003; Hofmann and Browne, 2013); however, the results of such lock-in effects, combining with the force from the demand side, remain an

107 There might be an opposite incentive as that the low interest rate environment keeps the loaner paying back the loans

slowly due to reduced interest cost, while high interest rate environment speeds up the pay-back due to increased interest cost. However, the empirical evidence does not support this argument. A high interest rate usually indicates a liquidity shortage in the market and thus is a more difficult situation to pay back the loans.


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undetermined empirical question. It is still subject to the empirical examination whether high or low risks depart in a particular product portfolio.

Table 7 Results on risk dynamics Full Sample New Policies Renewed Policies Full Sample Variables Departure Dummy Panel A: Group critical illness insurance ln(Premium Rate) -0.0710*** -0.122*** -0.0155a (0.0167) (0.0227) (0.0171) Real GDP Growth -0.0135** (0.00622) ln(Insurance Amount) -0.0615*** -0.0857*** -0.0256** -0.0500*** (0.0106) (0.0150) (0.0118) (0.00951) ln(Group Size) -0.0837*** -0.0976*** -0.0425*** -0.0757*** (0.00684) (0.0108) (0.00764) (0.00656) Location FE/Constant Yes Yes Yes Yes Year FE Yes Yes Yes No R2 0.063 0.081 0.041 0.055 Observations 3,834 1,718 1,726 3,884 Panel B: Loaner’s personal accident insurance ln(Premium Rate) 0.350*** 0.412*** 0.0986*** (0.00281) (0.00307) (0.00535) Interest Rate -0.0511*** (0.00147) ln(Insurance Amount) -0.0307*** -0.0226*** -0.0344*** -0.0554*** (0.000986) (0.00119) (0.00204) (0.000922) Location FE/Constant Yes Yes Yes Yes Year FE Yes Yes Yes No R2 0.304 0.306 0.258 0.016 Observations 784,494 588,155 180,696 803,373

Notes: The table reports the marginal effects after logistic regressions at the means of the independent variables. Robust standard errors clustered by insureds are presented in parentheses. It also presents *, **, ***, indicating significant differences of coefficients from 0 at the 10%, 5%, and 1% levels, respectively. a. p value equals to 0.36.

Second, both commitment and information conditions play a role in risk-based dynamic selection. Under the no commitment scenario, re-underwriting is one of the tools to do risk-based selection, which by its nature requires the insurer update the risk type related information. Such insurer learning can either be symmetric or asymmetric, but no learning would result in no supply-side selection over multi-periods. Under the semi-commitment scenario, CH (1987) suggest that high risks depart from the long-term coverage, because the insurer can offer menu contracts of both short-term and long-term, where high risks choose the short-term and low risks choose the long-term. However, such a separating equilibrium depends on the presence of adverse selection and asymmetric learning. HL (2003) suggest low risks tend to depart from the long-term coverage, because competing insurers would apply a cream-off strategy and target at the low risks. Such an argument depends on the symmetric


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learning condition, which allows competing insurers also to distinguish low risks from high risks. Therefore, it is reasonable to conclude that the insurer learning is a necessary condition for any risk-based dynamic selection.

Empirical research, however, is limited on risk-based dynamic selection. Under the no commitment scenario, Cohen (2012), Kofman and Nini (2013), and Shi and Zhang (2015) show that the high-risk departure pattern in short-term contracts does not depend on the type of learning. Under the semi-commitment scenario, Finkelstein et al. (2005) and Pinquet et al. (2011) support HL’s (2003) prediction that the low risks tend to depart even with the highballing pricing strategy in place to lock them in. However, Dionne and Doherty (1994) show the opposite in a market with adverse selection, a menu contract could sort low risks into long-term contracts.

The contribution of this paper in respect of risk-based dynamic selection lies with the following implications. First, the observed risk type-departure pattern, even if it is significant and economically strong, it might not be the result of risk-based dynamic selection. The illusory patterns found in the two-sample empirical design are driven by the decisions of employee benefits and of early loan clearance, rather than the risk types. Second, in order to identify the risk-based selection effects, one must control for risk dynamic drivers from both supply and demand sides and thus isolate the product differences in both commitment and information structures. Third, the paper concludes that the insurer learning is a necessary condition for any risk-based dynamic selection, based on the synthesis review.

5.5. Robustness tests

First, as the pricing pattern should result in a corresponding profit pattern, D’Arcy and Doherty (1990) compare loss ratios of different policy age cohorts to identify the inter-temporal pricing strategy. This approach is less favorable to the regression with Equation (1) because (1) it does not control for the underlying risk differences, thus the profit pattern observed may result from the risk changes instead of the pricing strategy; (2) for low frequency products, as with the two samples in this paper, the volatility of actual loss ratios are significant;108 and (3) the “incurred but not reported (IBNR)” claims become significant for policies issued in later years, which further bias the loss ratio measurement. As a robustness test, Table 8 presents the loss ratio patterns over the policy age cohorts. The results for Sample A confirm the lowballing pricing pattern found in the premium rate regressions with Equation (1). However, for Sample B, it is hard to say there exists any loss ratio pattern, because there happens to be very few or no claim in policy cohorts older than 2 years,

108 Low frequency is not a problem to detect adverse selection and reflect the insurer learning as discussed in Eling et al.

(2015), however which indeed increases the randomness of the loss ratio measurement.


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indicating a strong IBNR bias in this portfolio. Therefore, as mentioned above, the regression approach to directly identify the pricing, instead of the profit, pattern seems a better choice.

Table 8 Loss ratios by policy age cohorts Sample A Sample B

Policy Age Loss Ratio Observations Loss Ratio Observations New 38.5% 2,516 23.2% 955,752

1st renewal 30.8% 1,593 12.5% 195,538 2nd renewal 24.6% 657 4.0% 83,355 3rd renewal 17.7% 363 0 5,327 4th renewal 3.8% 168 0 2,605 5th renewal 1.2% 72 N.A. N.A.

Total 31.5% 5,369 20.0% 1,242,577

Second, Equation (1) is estimated with random-effects and firm fixed-effects approach.109 The results shown in Table 9 support H1A and H2B. The advantage of firm fixed-effects is that the coefficients mostly capture the dynamics of one firm over years, i.e. the time series effects, instead of the cross- sectional effects. Thus it best identifies the pricing pattern for one firm over time. However, firm fixed-effects models have to omit all time-invariant or less variant variables, such as gender, occupation, age, insurance amount, and group size, which are important pricing factors should be controlled. Moreover, fixed-effects models may significantly reduce the estimation efficiency in a short panel as with the two samples of this paper. Random-effects models are more efficient than fixed-effects. The samples of this paper largely meet the assumptions of random-effects model: (1) the insureds can be considered as a random sample of the nationwide population, and (2) the uncontrollable firm heterogeneity is random and not correlated with the error terms (Greene, 2011; Gujarati, 2010).110 The use of panel regression approach as robustness tests instead of core models is also because one firm can buy two or more policies in nth year. All of these policies have the policy age of n, however, only one of them can be incorporated in the panel regressions. Thus, 14.8% of Sample A and 7.9% of Sample B have to be dropped from the respective samples if using the penal regression approaches, which further reduces the estimation efficiency.

109 The implications on risk-based dynamic selection (see Section 5.4) do not depend on the model specifications. Thus,

the robustness tests with Equation (2) are not present here but available upon requests. 110 Zhang and Wang (2008) discuss why and how to apply random-effects models in a dynamic insurance market.


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Table 9 Random- and fixed-effects models Sample Sample A Sample B Model RE FE RE FE Variables ln(Premium Rate) Policy Age 0.00704 0.0306*** 0.0194* -0.00297*** -0.00190*** (0.00673) (0.0104) (0.0116) (0.000136) (0.000148) Prior Claim Experience a

0.468 (0.831)

ln(Insurance Amount)

-0.142*** -0.153*** -0.0258*** (0.00869) (0.0140) (0.000424)

ln(Group Size) -0.0801*** -0.0432*** (0.00557) (0.00824)

Sex -0.184*** -0.0329 -0.0135*** (0.0407) (0.0687) (0.000952) Age 0.0376*** 0.0354*** -2.55e-05 (0.00135) (0.00202) (3.40e-05) Work1 -0.122*** (0.000729) Work2 -0.00922 -0.0367 -0.160*** (0.0182) (0.0256) (0.00115) Work3 -0.100*** -0.0678** -0.108*** (0.0179) (0.0269) (0.000790) Work4 -0.00434 0.0494 (0.0325) (0.0433) Work5 -0.0103 0.0350 (0.0643) (0.0772) Location FE Yes Yes No Yes No Year FE /Constant Yes Yes Yes Yes Yes

Overall R2 0.354 0.334 0.042 0.138 0.205 Observations b 4,803 1,999 4,916 1,149,541 1,164,759

Notes: The table reports the estimated coefficients of random- and fixed-effects regressions. Standard errors are presented in parentheses. It also presents *, **, ***, indicating significant differences of coefficients from 0 at the 10%, 5%, and 1% levels, respectively. a. Claim experience is only applicable to Sample A and to random-effects models because Sample B does not allow for experience rating and fixed-effects cannot incorporate time-invariant variables (prior claim experience is 0 for most observations due to the low frequency nature of this portfolio). b. The smaller number of observations results from that one firm buys two or more policies in nth year. All of these policies have the policy age of n, however, only one of them can be incorporated in the panel regressions. Policies signed earliest in the year are used and others are dropped. This process does not affect the conclusions.

6. Concluding remarks

This paper concludes the roles of commitment and information structure in determining the insurer’s inter-temporal pricing strategy. The results from both synthesized and new evidence confirm that the lack of insurer’s pre-commitment to multi-period insurance relationship predicts the price lowballing strategy (H1A) and its pre-commitment predicts the price highballing strategy (H1B). In addition, the insurer learning, either symmetric or asymmetric,


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is a necessary condition for the price lowballing strategy, because lowballing requires the incumbent insurer to discriminate low risks from high risks based on new information learned with policy experience. The insurer learning and the learning type are not the necessary condition for the price highballing strategy, because highballing can be implemented with a level premium or a pre-agreed premium schedule, which do not necessarily involve a price update over multi-periods. The pricing strategy is sensitive neither to the presence of adverse selection nor to the type of insured’s commitment.

This paper also discusses the determinants of risk-based dynamic selection (Finkelstein et al., 2005). The new empirical evidence shows that any risk dynamic pattern observed could be a combined result of both supply (the insurer’s selection) and demand (the insured’s self-selection) decisions, and thus explains the discrepancy in extant evidence (see Table 3). The implications are also that both commitment and informational assumptions play a role in risk-based dynamic selection and the insurer learning is a necessary condition for any risk-based dynamic selection.

The conclusions on pricing strategy and risk dynamics may also be useful in other industries, which have similar multi-period contracting market and switching possibilities over time. One of such examples is the commercial banking industry, where loan applicants rejected by one bank can apply at other banks (Shaffer, 1998). This feature yields a pattern that incumbent banks keep low-risk loaners and competitors innocently attract those high-risk ones. The highballing pricing strategy has been proved to be useful to lock-in low-risk consumers, which is implemented in the insurance industry in the form of a pre-agreed premium schedule. This design may be applicable to the banking industry, where a bank charges a relatively high loan rate or a fixed amount of fees in early periods, and charges relatively low rate and no fees in later periods. The highballing pricing strategy also insures the reclassification risk, where the bank (insurer) charge additional fees (premium) to ensure the customers no or low rate increase in the future even if the customer’s credit (insurance) risk increases.

Future theoretical work may unite the different forces driving risk dynamics in one model. Future empirical work should carefully control various sources of selection and self-selection, thus to isolate the impact of risk type and pricing strategy on risk dynamics. Ideally, the optimal dataset to test risk-based dynamic selection should be those of private term life insurance as used by Hendel and Lizzeri (2003), where the decision of purchasing insurance is more driven by the risk consideration rather than other insurance demand factors. In addition, different durations of term life insurance (e.g. yearly renewed vs. 10-year term life) naturally construct the comparison between no commitment and semi-commitment scenarios. Moreover, the meta-analysis (Kysucky and Norden, 2014) may contribute to compare the magnitude of pricing strategies, as for some products, the highballing or lowballing pricing


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pattern maybe more significant than other products. Such demand of meta-analysis also calls for more empirical samples in the field of multi-period insurance contracting. As compared to the single-period information asymmetry literature, the multi-period insurance contracting research remains at an evolutionary stage.


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Curriculum Vitae

Personal Information

Name: Ruo Jia 贾若 Date of Birth: December 4th, 1985 Place of Birth: Beijing, China Nationality: Chinese

Education

09/2013 – 07/2016 University of St. Gallen (HSG), St.Gallen, Switzerland, Ph.D. in Finance

09/2008 – 07/2010 Peking University (PKU), Beijing, China, Master of Economics in Finance

09/2004 – 07/2008 Peking University (PKU), Beijing, China, Bachelor of Economics in Insurance, Bachelor of Law in International Relationship and Foreign Affairs

06/2007 – 08/2007 Yale University, New Haven, USA, Exchange program in Finance

Work Experience

09/2016 – Department of Risk Management and Insurance, School of Economics, Peking University (PKU), Beijing, China, Assistant Professor

09/2013 – 08/2016 Institute of Insurance Economic (I.VW), University of St. Gallen (HSG), St. Gallen, Switzerland, Project Manager

08/2010 – 09/2013 Swiss Reinsurance Company Ltd., Beijing, Zurich, Singapore, Casualty Underwriter and Assistant Vice President

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