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Advantageous or Adverse Selection in Emerging Health Insurance Markets:

Evidence from a Micro Health Insurance Program in Pakistan1

Yi Yao

Joan T. Schmit

Justin R. Sydnor

1Yi Yao (corresponding author [email protected]) is a PhD candidate at School of Business, University of Wisconsin at

Madison. Joan Schmit is a professor and American Family Insurance Chair in Risk Management and Insurance at University of Wisconsin at Madison. Justin Sydnor is an assistant professor of Risk Management and Insurance at University of Wisconsin at Madison.


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Abstract

Despite widespread interest in microinsurance programs in developing countries, little is known

about the nature of information asymmetries and selection in these emerging markets. We use

data from a micro health insurance program in Pakistan to investigate the degree of adverse

selection in the program. We analyze how claim rates evolve as households renew their policies

and find that households who have larger claims during the policy period are slightly more likely

to renew their policies for the next period. Although that pattern is on the surface consistent with

adverse selection, we instead find that when compared to households joining the insurance in the

same period, renewed households have significantly lower claim frequency and total claim

amounts. Taken together these results suggest that a) households who experience claims

perceive higher value to insurance, b) that households do not seem to be acting (at least on the

margin of renewals) on private information about their risk types and c) that there are forces

affecting insurance demand that lead to advantageous selection in the policyholders that retain

coverage over time.


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I: Introduction

In recent years there has been an explosion of interest in the creation of new insurance products in

developing countries. Closely related to the growth of “microfinance,” these new “microinsurance”

programs are often created by non-profit organizations to provide insurance in the developing world. To

achieve their goals, however, these organizations must find a sustainable business model. This paper

focuses on the viability of micro health insurance in particular. Because there are generally data

limitations, high transaction costs (relative to premium and income), and low levels of education in

developing countries, insurance policies of all kinds need to be simple. That need for simplicity in both

underwriting (to limit distribution expenses) and policy language (both to limit administrative expenses as

well as to develop product demand) may be a particular challenge for the development of health insurance

because most private health insurance markets require extensive underwriting and further employ

somewhat complex policy provisions to limit both adverse selection as well as moral hazard.

Although there is a significant body of empirical literature on detecting adverse selection in health

insurance markets in developed countries (see Cohen and Siegelman, 2010 for a review), there is little

empirical evidence on the role adverse selection plays in developing microinsurance markets. The small

existing literature paints somewhat conflicting views of the potential for sustainable micro health

insurance. Pauly et.al (2008) used data from the World Health Survey for 14 developing countries to

compare the risk premium that local people would be willing to pay with likely values for the

administrative expense. Without taking adverse selection and moral hazard into consideration, they

concluded that a voluntary health insurance market might be feasible. In contrast, Biener and Eling (2009)

examined the problems and solutions for microinsurance markets using Berliner’s (1982) set of criteria to

identify significant problems discussed in existing studies on microinsurance. Based on a survey of

studies that looked at hypothetical decisions to join an insurance program, they concluded that problems

of information asymmetry were “epidemic” in micro health insurance, providing evidence ranging from

adverse selection, moral hazard to fraud in the previous literatures.

In this paper, we help address this debate about the viability of micro health insurance by examining

household renewal decisions to understand better the development of a microinsurer’s risk portfolio in its

early years of operations. The results reveal the essence of selection in the given micro health insurance

market.

Resolving this debate is important because of all the microinsurance programs being provided, micro

health insurance programs are among the most needed but least provided. Both acute and chronic

diseases are serious problems for the poor in developing countries, where poor sanitation, low nutrition,

and inadequate preventative care are widespread. As a result, the life expectancy for those living in low

and middle income countries is 20% lower than those living in high income countries. In an extreme

comparison, the life expectancy for people living in Sub-Saharan African is only 46, compared with 75.5

in high income countries2. The consequences of illness for the poor not only include reduced current

standards of living, but may also lead them to reduce investments in their future human capital. With that

backdrop, it is perhaps not surprising that people with low income also have an interest in health

2 Table 2.3 Selected mortality characteristics by sex and World Bank region in 2001, Global burden of disease and

risk factors, Oxford University Press and The World Bank, 2006.


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insurance programs. Despite that interest, however, it is estimated that only 20% have access to adequate

health insurance3 (Bockstal, 2008).

For this study we use data from the Aga Khan Agency for Microfinance (AKAM), which has run a simple

micro health insurance program in Pakistan since 2007. Testing for the nature of selection issues in

microinsurance markets presents unique challenges. Most studies of selection issues in insurance have to

overcome the inability to observe outcomes for people who do not purchase any insurance. In developed

markets, researchers typically approach the issues by using tests for adverse selection that analyze

differences in claim experience across insureds who purchase different amounts of insurance (see

Chiapporri and Salanie, 2000). In developing markets, like the AKAM product studied here, customers

are given only one option in coverage in order to hold down administrative costs and keep the products

simple for a population inexperienced in insurance purchasing. The standard “positive correlation” test

between coverage level and risk, therefore, is not feasible.

Other methods to detect adverse selection in the micro health insurance market, however, are available.

In this paper we analyze the nature of selection by measuring the development of claim experience in

renewal policies. We use a two-part model to compare the microinsurer’s new book of business to its

renewed book of business and test whether the risk pool has deteriorated over time, which could

demonstrate the existence of adverse selection. From a theoretical standpoint, the selection and evolution

of renewal policies could result in either adverse or advantageous selection. On the one hand, there are

forces leading to adverse selection in a sense that riskier people might be more likely to stay with the

insurer. One classic version of the adverse selection story here would be if policyholders have private

information about their risk type and suffer unrelated income shocks that affect whether they can afford

insurance. In that case, we would expect that those who know they are especially high risk would be less

likely to cancel insurance due to an income shock, which would result in a deteriorating book of business

when looking at renewed policies. Another possibility is that people might learn about their risk type

over time – for instance learning that they are pregnant. If people act on that new information, we would

expect adverse selection as those who have learned they are higher risk choose to renew while low risks

do not. On the other hand, there are also other forces affecting the decision to be insured that may be

unrelated to risk type and could even result in advantageous selection. In new markets, like that in

Pakistan, people start to learn about the value of insurance and how it protects their financial stability and

flexibility. People who happened to have a claim that was well-handled might be more likely to renew,

not because they are high risk but because they better understand the value of insurance. In addition,

more financially savvy people tend to be healthier ones and might be more likely to stay in the program.

Ultimately, the direction of any selection effects in this type of micro insurance market is an open

empirical question.

We analyze how claim rates evolve as households renew their policies and find that households who have

larger claims during the policy period are slightly more likely to renew their policy for the next period.

Although that pattern is on the surface consistent with adverse selection, we instead find that when

compared to households joining the insurance in the same period, renewed households have significantly

lower claim frequency and total claim amounts. Taken together these results suggest that a) households

who experience claims perceive higher value to insurance, b) that households do not seem to be acting (at

3 Bockstal, Christine. 2008, “HMIS in national social protection strategies: Experiences from francophone African

countries.” Presentation in the 4th International Microinsurance Conference.


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least on the margin of renewals) on private information about their risk type and c) that there are forces

affecting insurance demand that lead to advantageous selection in the policyholders that retain coverage

over time.

The remainder of this paper proceeds as follows. Section 2 presents a literature review highlighting work

on adverse selection generally and the small literature on micro insurance. Section 3 introduces the

AKAM micro insurance program and our data, while Section 4 discusses our models and results. We

conclude in Section 5 about our findings.

II: Literature Review

2.1 Introduction to theory of adverse selection

The theory of asymmetric information was first established in 1970s with the seminal work of Akerlof

(1970), Pauly (1974), and Rothchild and Stigliz (1976), and it was further developed by generations of

scholars (see Miyazaki 1977, Wilson 1977, Finkelstein and McGarry 2006). In the classic Rothchild-

Stigliz model, insureds were assumed to be of different risk types, and the resulting market equilibrium

was a separating one where low risk individuals bought partial insurance with reduced welfare, and high

risk individuals bought full insurance. The results of these theories motivated the need of risk

classification as a solution to overcome adverse selection, since if the insurance company could

differentiate the low risk from the high risk, it could offer different contracts to both groups and improve

the welfare of society. In addition, these theories established the rationale of testing for adverse selection

in a given market using the “positive correlation test” between risk type and insurance coverage

purchased. For example, in Puelz and Snow (1994), they used data from auto insurance market of the

United States, and found those with higher accident risk choose lower deductibles (more insurance

coverage), following the “positive correlation test.”

To alleviate the effect of adverse selection, the insurance industry has developed techniques in risk

classification; however, they are still not able to prevent adverse selection completely. Numerous

empirical studies have tested for the existence of adverse selection in different types of insurance markets

around the globe (see Cohen and Siegelman, 2010 for a review), with mixed results. In some cases,

scholars even found empirically it was the low risk individuals who bought more insurance coverage,

which has been referred to as “advantageous selection” (Finkelstein and McGarry, 2006).

2.2 Adverse selection in microinsurance markets

Though the basic predictions from insurance theory should largely function similarly for microinsurance,

the nature of the product imposes a number of challenges in developing the market (Brau et.al, 2009).

Microinsurance as an emerging product for low-income people in developing countries could suffer from

adverse selection in a vital way, in particular because of its limited ability in classifying risks. Due to the

need to reduce administrative costs while keeping the product simple, microinsurance products are often

designed to be universal, without deductible or coinsurance options. There are mainly two reasons for

that. First, it fits the financial literacy of low income individuals. Usually a microinsurance policy is the

first insurance policy that the low income individual purchases, and having deductibles and coinsurance

requires more sophisticated knowledge about insurance. Without proper education and claim handling,

there could be misunderstandings that ruin the reputation of the insurer and insurance overall before the


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market can fully develop. Second, insurers are reluctant to implement more sophisticated policy features

because they want to hold down administrative costs. Effectively administering policies with deductibles

and coinsurance requires electronic record keeping and it may be necessary to implement a system for

tracking and verify claims on site at every clinic. Most microinsurers have not yet invested in these

technologies and infrastructure.

2.3 Empirical tests for adverse selection in “traditional” insurance markets

The traditional approach of empirical tests for adverse selection is a “positive correlation test,” i.e., a

positive correlation between risk type and insurance coverage is expected with the existence of adverse

selection.

Scholars tested for adverse selection in various markets using different proxies for risk type and insurance

coverage (see Cohen and Siegelman, 2010 for a review). The most common proxies of insurance

coverage are policies with different levels of deductibles and copayments, the decision to opt in and out of

insurance, and the decision to purchase supplemental insurance. Proxies for risk type ranged from

subjective measurement (self-evaluated health condition) to objective ones (indicators such as age and

medical history) and predicted risk type (see Browne, 1992 & 2006, Gao et.al 2009).

Others (see Fang et.al 2008, Bolhaar et.al 2008, Gao et.al 2009) have found a negative, rather than

positive, relationship between risk type and insurance coverage, which indicates that low risk individuals

purchased more insurance coverage. This negative relationship observed in empirical tests was referred

to as advantageous selection, in contrast to the traditional term of adverse selection. Besides risk

preference, various other sources of advantageous selection have been proposed, including heterogeneity

in income, education, health preferences, financial planning horizons, and cognitive ability.

2.4 Empirical tests for adverse selection in micro health insurance market

Since the development of microinsurance markets remains relatively immature, and data are often

inaccessible and imperfect, the empirical studies on the topic of adverse selection in this market are still

limited. The limited range of studies using various methods, however, all found evidence to support the

existence of adverse selection in micro health insurance markets of different countries in different time

periods.

A series of studies on adverse selection have been conducted using data from a rural mutual healthcare

insurance scheme in China. Wang et al. (2006) followed a voluntary mutual healthcare insurance scheme

in a rural county in China and carried out a panel data analysis over the period of 2002 to 2006. Using

individual level data, they found strong evidence of adverse selection despite a high enrollment rate and

the requirement of having the entire household enroll as a unit. In particular, they found the pre-enrolled

medical expenditure for enrolled individuals were 9.6% higher than average expenditure of all residents.

In addition, the enrolled members of the partially-enrolled family spent 1.7 times more than those non-

enrolled members of the partial enrolled family. Zhang and Wang (2008) also observed that people with

chronic condition history, with fair or poor health were more likely to enroll in the program, showing the

existence of adverse selection. The extent of adverse selection, however, seemed to be stable over the

study period.

Similarly, Ito and Kono (2010) found evidence of adverse selection in a micro health insurance program

in India, based on the result that households with a higher ratio of sick members were more likely to


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purchase insurance. Using data from Masisi district in Zaire, Noterman et.al (1995) also found evidence

for adverse selection. They examined the null hypothesis that the increase in hospital utilization by

insureds can be attributable equally to predictable and unpredictable risk conditions and rejected the null

hypothesis.

With a historical survey data of American short-term disability microinsurance back in the early

twentieth-century, Murray (2011) found prima facie evidence of asymmetric information, with evidence

for the presence of adverse selection stronger than that of moral hazard. In addition, it was shown that the

countermeasures taken by the microinsurers, including the enforcement of a trial period and waiting

period, effectively reduced claims.

Besides the effect of adverse selection in explaining the demand for micro health insurance, there are also

other factors affecting the purchase decision which are studied empirically in numerous research studies,

including income, wealth, education, history with insurance, gender, family composition, residence

district, etc. (see Dror et.al, 2006; Ito and Kono, 2010; Bhat and Jain, 2006; Donfouet and Makaudze,

2010, Msuya and Asfaw, 2004; Rao et.al, 2009; Schneider and Diop, 2001).

III: AKAM Micro Health Insurance Program and Data Description

3.1 AKAM program background

AKAM micro health insurance program in Pakistan

The AKAM Microinsurance Initiative commenced in 2006, with support from the Bill and Melinda Gates

Foundation. AKAM is owned by the Aga Khan Development Network (AKDN) and it started its pilot

enrollment period for an annual micro health insurance policy in the Northern Area (NA)4of Pakistan in

Nov 2007. NA is the northernmost political entity located in the mountainous part of Pakistan, with an

estimated population of 1.35 million scattered across six districts. The provision of health insurance is a

milestone in that it is the first effort to make health insurance available to the poor in the area. In the

three years since the program first launched, there were over 100,000 members enrolled, which accounted

for around 7.5% of the local population.

The coverage and premium are the same for every member and the individual annual premium of 400

Pakistan Rupees (PKR) (approximately $5.60) is paid up front5. There is no individual risk classification

in underwriting. In exchange for this premium, the policy provides the following coverage: annual

hospitalization coverage (the core of the product) up to 25,000 PKR (approximately $400)6, life insurance

of 25,000 PKR (approximately $400) on the head of the family and one outpatient voucher valid for a

one-time physician visit. The hospitalization coverage and the life insurance coverage increase to 30,000

PKR for renewed insureds for the same premium, providing motivation for policyholders to renew their

policies. The average annual income per person in NA is around 50,000 PKR in 20097, so the insurance

coverage is equivalent to about half of their annual income.

4 The Northern Areas (NA) is now known as Gilgit-Baltistan(GB).

5 The premium was 350 in Nov 2007, and increased to 400 for Nov 2008, July 2009 and Nov 2009. It increased to

450 PKR for new insureds in ZADO and Danyore in July 2010, but stayed the same for all the other insureds. 6 25000PKR convert to $400 in Nov 2007, $312 in Nov 2008, and $293 in Feb 2011.

7http://www.unicef.org


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Distribution of micro insurance and provision of health service

Figure1:Flow chart for AKAM micro health insurance program

AKAM partnered with local supporting organizations (LSOs) to distribute the product to voluntary

groups. There were two purposes for selling group policies. First, the local supporting organizations

have an existing network for disseminating information and hence greatly reduce underwriting and

distribution costs. Second, as the way it works in developed markets, selling group policies helps to

address concerns of adverse selection because these groups are not formed solely for purchasing health

insurance. The major types of group are village organizations (VOs) and women’s organizations (WOs),

and their members could purchase health insurance through the VO/WO if at least 50% of the households

in the organization agreed, in the test survey, to purchase the product if it were available. In addition, the

entire household is required to enroll in the program in order to alleviate adverse selection.

AKAM initiated policies for New Jubilee Life Insurance Company (NJLI), which is a commercial insurer

based in Karachi, Pakistan, owned also by AKDN8. The LSO enters into an agreement with AKAM,

which has been appointed by NJLI to represent it in all matters pertaining to the health microinsurance

program. The LSO contracts with NJLI on behalf of their village member households.

8In regard to the reinsurance arrangement, AKAM arranged a stop loss contract with Swiss Re.

Parent organization

Policyholders

Healthcare providers

Aga Khan Agent of

Microfinance-

Microinsurance

Initiative

(AKAM-MI)

Financial institutions

Reinsurance provider:

Swiss Re

Seller of insurance policy

(insurer): New Jubilee

Life Insurance (NJLI)

Legal representative for

buyers of group contract:

Local supporting organization

(LSO)

Members of LSO: Village

organizations and women’s

organizations (VO/WOs)

Policyholder: Households in

qualified VO/WOs

Other healthcare provider:

Combined military

hospital (CMH) and

government hospital

Main healthcare

provider: Aga Khan

Health Services Pakistan

(AKHSP)

Aga Khan Development

Network (AKDN)


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AKAM chose NA to be the first area to provide health insurance because the AKDN intensity is very high.

The main health service provider (Aga Khan Health Services Pakistan, AKHSP), which is a part of

AKDN, operated in NA for over thirty years. It has three hospitals and twenty-five primary care facilities

in NA, and over 90% of the claims from AKAM micro health insurance program are handled within

AKHSP systems. In addition, there are the Combined Military Hospital (CMH) and the government

hospital located in NA, which altogether take less than 10% of the claims, mostly for emergency service.

Background of VO/WO/LSO

AKAM relies on an existing network for village organizations and women’s organizations for product

distribution. By the end of 2005, there were more than 4,000 Village Organizations (VOs) and Women’s

Organizations (WOs) in Northern Areas, covering more than 78 percent of the total households9.

VO/WOs are grass root community organizations that were first built to improve the households’ capacity

for undertaking village development initiative. For example, projects include obtaining funding and

organizing the villagers to work on infrastructure project such as minor irrigation works, flood protection,

erosion control and link roads. In addition, VO/WOs were also involved in organizing informal

community-based micro loans among their members before AKAM started its formal microfinance

service in the area. More recently, those organizations have become key players in providing supportive

networks to enlarge communities’ assets and harness individual skills to generate income in a sustainable

manner.

Local Supporting Organizations (LSOs) are large organizations working for the member organizations in

the area, which may consist of 50 or more villages. They are nonprofit organizations set up in joint effort

with the Aga Khan Rural Support Program (AKRSP) and local population, serving as registered legal

entities under the Pakistan law. LSOs are the umbrellas under whom VOs and WOs could enter into any

legal agreement as a group or sub-group since VOs and WOs are not registered organizations. Gradually,

LSOs have obtained project funding and expanded their service to a wide coverage. Currently, there are

around 40 LSOs in the region.

3.2 Data description

The empirical application utilizes a dataset comprised of household level information, including some

basic demographics on the head of the household’s age and gender, members’ age and gender

decomposition, household size, village organization and local supporting organization to which the

household belongs. It also has some policy level information such as policy limit, renewal status and

enrollment date. Moreover, it contains detailed information on claims made during the policy periods,

including diagnosis, whether it was a pre-existing condition, hospital stayed, date of admission, length of

stay, total bill and bill divided into subcategories of medicine, surgical procedure, surgical supply, bed

charge, inpatient consultation, lab test, and others.

There were in total six enrollment periods since the program first launched in November 2007. Each

policy lasts for one year, and the enrollment window was fixed to November at the beginning, so that it

helped alleviate adverse selection by not allowing people to speculate in purchasing an insurance policy

9The Aga Khan Rural Support programme, an assessment of institutional development of village and women’s

organizations, results of the AKRSP’s Institutional Development Survey 2006.


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right before a surgery was needed. In addition, it helped reduce the administrative and distribution costs.

Besides the four November waves of enrollment from 2007 through 2010, a new July enrollment window

was opened in 2009 due to the increasing demand for health insurance as well as the improved

recognition of income cycle for local households.

The first enrollment period starting in Nov 2007 was a pilot period; therefore detailed information was not

collected at the time. As a consequence, we could not include the first period into the data analysis. For

the fifth enrollment period starting from July 2010, claim data is available only through Nov 2010. Since

we only have part-year claim data for that enrollment window, for any analysis based on that period we

scale the available claim data to an annual basis.

To sum up, the data analysis is based on data from four available periods, which are Nov 2008, July 2009,

Nov 2009 and July 2010, with a total member observation of 64,29010

.

Because the two key variables we examine are claim experience (both frequency and severity) and

renewal status, we summarize detailed information over different enrollment periods on those variables in

table 1 and 2 respectively.

Table 1: Summary of household level claim information and loss ratio for all enrollment periods

Enrollment time

# of HH enrolled

# of members enrolled

# of claim total claim amount (in PKR)

total premium (in PKR)

loss ratio

2007-Nov 1,715 6,044 768 2,820,595 2,115,400 1.33

2008-Nov 5,273 19,492 3,380 15,012,412 7,796,800 1.93

2009-July 2,200 9,107 1,910 8,953,674 3,642,800 2.46

2009-Nov 5,785 23,268 3,066 15,676,527 9,307,200 1.68

2010-July11 2,932 12,423 930 9,720,866 5,157,900 1.88

Overall 17,905 70,334 11,356 52,184,074 28,020,100 1.86

Table1 shows that the claim experience and loss ratio fluctuated across different enrollment periods. On

average, each enrolled household made 0.63 claims during the policy year, and claim amounts averaged at

2,914 PKR. The overall loss ratio for five periods was 1.86.

For the three November waves of enrollment, the claim experience and its corresponding loss ratio

increased in 2009 and then decreased in 2010. While for the two July waves of enrollment, the claim

experience was very high at first and then decreased.

Since the major analysis is on the household level, and the key variable of interest is the renewal status,

table 2 summarizes the household level renewal information across periods.

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We are expecting the data from the sixth enrollment period for Nov 2010. 11

This is a partial data since the policy lasts till June 2011. The available claim data runs till the end of Nov 2010.


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Table 2: summary of household renewal information across periods

Enrollment

time total HH

new

HH #

new

HH %

renewed

HH #

renewed

HH %

% of HH choosing to renew

policy at the end of period

2007-Nov 1,715 1,715 100% 0 0 44%

2008-Nov 5,273 4,521 86% 751 14% 56%

2009-Jul 2,200 2,200 100% 0 0% 42%

2009-Nov 5,785 2,828 49% 2957 51% n.a.

2010-Jul 2,932 2,007 68% 925 32% n.a.

For the first enrollment period in both July and November waves, all households were new, while for the

other three enrollment periods, it was a combination of new households and households renewed from the

previous periods. The renewal rate, defined as the percentage of household who choose to renew their

policies at the end of the current period, shows that the program has retained about half of the enrolled

households on average. Out of those who had renewed their policies once in Nov 2008, 64.3% (483 out

of 751 households) of them renewed for a second time in Nov 2009. However, the program was

expanding rapidly from period to period, so new households still were weighed more heavily than

renewed households in general.

IV: Empirical Model and Results

4.1 Analytical model

The AKAM health insurance program uses no underwriting, and as a consequence classic models of

adverse selection would predict that high risk individuals would be more likely to purchase and renew

coverage than lower-risk individuals. On the other hand, there are a number of empirical studies in

developed insurance markets that document “advantageous selection,” in which lower risk individuals are

more likely to purchase and retain the most insurance. As such, while our initial hypothesis is that

adverse selection will be a problem in this market, theory and empirical evidence in other settings suggest

that either pattern is possible – making it all the more important to test for the nature of selection in

developing health insurance markets.

Our main focus is on the relationship between policy renewal decision and claim experience, in terms of

both frequency and severity, and we examined the relationship through three models in total.

Our first model is to test how claim experience impacts the decision to renew the policy. The regression

model takes the following form:

Model 1 (probability of renewing):

Renewal decision for period n+1=f(whether they are new at the beginning of period n, total claim amount

at period n, household level demographics)

where f( ) is a discrete-choice function, such as logit or probit.


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In addition, we include a number of control variables on the household level demographics. They are

family size, age and gender of the head of the household, the percentage of child, teenager, adult, elderly

and female in the family, LSO that the household belongs to and a renewal dummy to indicate whether

the household were new or renewed at the beginning of the period.

The other two models focus on measuring how claim experience is affected by renewal status. The first

approach (model 2) uses a two-part frequency severity model while the second approach in model 3

examines the total claim amount.

Finding a positive relationship between policy renewal and claims would be consistent with adverse

selection in the decision to retain insurance. If instead there were a negative correlation between renewal

and claims, it would suggest that there are forces of positive selection leading lower-risk insured to retain

insurance.

In summary, model 2 and 3 take the following forms:

Model 2 (two-part model):

Claim frequency=f(renewal status, HH demographics, enrollment period dummy)

Claim severity=f(renewal status, claim frequency, HH demographics, enrollment period dummy)

Model 3 (total claim amount):

Total claim=f(renewal status, HH demographics, enrollment period dummy)

Our primary measures of claim experience are claim frequency, claim severity, and the total claim

amount, which equals the product of claim frequency and severity. In the two-part model, we use claim

frequency as the dependent variable, and model it in various specifications with linear, Poisson and

negative binomial distribution in the first part. Then conditional on the household having a claim, we use

claim severity (average claim amount) as the dependent variable, and model it with a gamma distribution

using general linear model (GLM). As an alternative to, as well as a sensitivity test for the two-part

model, we also include model 3 using total claim amounts as the dependent variable. For this

specification we use a Tobit model left censored at zero to take into account that there are a large portion

of zeros in the dependent variable.

For both models 2 and 3, we start with using only renewal status and a dummy variable indicating July

cohort as the independent variables in specification [1], and then we also include the following control

variables to measure other policyholder characteristics that may affect claim experience throughout

models 2 and 3 in specification [2]. These control variables are log of family size, age of the head of the

household, gender of the head of the household, family structure (percentage of members that are children,

teenagers, adults, elderly and female) and geographical variable (LSO that insured household belongs to).


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4.2 Results

Table 3 summarizes variable description and statistics by enrollment period, and table 4 summarizes

statistics by renewal status.

Table 3: variable description and summary statistics

Variable name Description

Full sample 2008 Nov 2009 July 2009 Nov 2010 July

Demographics

HH size # of members in the HH 3.99 3.73 4.21 4.01 4.27

(1.76) (1.67) (1.70) (1.76) (1.87)

head age age of HH head 44.84 44.07 42.79 46.10 45.27

(16.62) (14.22) (13.96) (18.36) (18.49)

head male 1 if male, 0 if female 0.74 0.74 0.74 0.72 0.76

(0.44) (0.44) (0.44) (0.45) (0.43)

% renewed % of HH renewed from n.a. 0.14 0.00 0.50 0.29

last period n.a. (0.35) 0.00 (0.50) (0.45)

child % % of HH age btw 0 and 5 0.14 0.13 0.14 0.14 0.13

(0.19) (0.19) (0.18) (0.19) (0.18)

teenager % % of HH age btw 6 and 16 0.18 0.19 0.16 0.17 0.18

(0.22) (0.23) (0.21) (0.21) (0.21)

adult % % of HH age btw 17 and 0.56 0.57 0.60 0.55 0.56

59 (0.26) (0.26) (0.25) (0.26) (0.26)

elderly % % of HH age btw 60 and 0.10 0.11 0.10 0.10 0.10

99 (0.20) (0.22) (0.17) (0.20) (0.19)

over100 % % of HH age above 100 0.02 0.00 0.00 0.04 0.03

(0.10) (0.02) (0.03) (0.14) (0.13)

male % % of HH male 0.45 0.44 0.45 0.44 0.46

(0.20) (0.21) (0.19) (0.21) (0.19)

Claim

total bill total claim amount 2,685.33 2,844.51 4,053.58 2,683.50 1,374.40

(5,969.31) (5,851.72) (7,118.47) (6,173.13) (4,332.88)

loss # of claims 0.57 0.64 0.87 0.52 0.32

frequency

(0.98) (1.02) (1.23) (0.91) (0.69)

loss severity average amount of claims 4,931.89 4,734.02 4,991.18 5,307.00 4,332.30

(5,334.41) (5,090.41) (5,095.08) (5,678.66) (5,328.50)

# of obs. # of households 16,225 5,272 2,197 5,831 2,925

Notes: mean is shown on top and standard deviation is shown in brackets for each variable.


14

Table 4: summary statistics of mean by renewal status

Variables new HH renewed HH

# of CLAIM 0.60 0.51

SEVERITY 1,883.56 1,535.98

TOTAL BILL 2,814.13 2,350.37

FAMILY SIZE 3.86 4.34

HEAD AGE 44.82 44.91

HEAD MALE 0.73 0.76

CHILD% 0.13 0.15

TEENAGER% 0.17 0.19

ADULT% 0.58 0.53

ELDERLY% 0.10 0.11

FEMALE% 0.56 0.55

Observations 11,719 4,506

From table 4, it is clear that the renewal households have a better claim experience than the new

households enrolled, with lower mean in average number of claims (claim frequency), claim severity, and

the total claim amount. Also the renewed households in general are larger than those new households on

average, with more male being the head of the family, more percentage of households being child,

teenager, elderly and male. Furthermore, figure 1 shows the histogram comparison for claim frequency

and severity between new and renewed households respectively.

Figure1: Histograms comparison between new insured and renewed insured in their claim frequency and

severity (average loss per claim)

Figure 1 shows that renewed households have lower claim frequency than the newly enrolled households;

however, the claim severity differences are not as significant as it is in frequency.

022

4466

Perc

ent

0 5 10 15frequency

Not Renewed Renewed

0

5.75

11.5

17.2

5

23

Perc

ent

0 10000 20000 30000severity

Not Renewed Renewed


15

Our regression results for three models are shown in table 5, 6, and 7 respectively. In table 5, using the

enrollment data from Nov 2008 and July 2009 separately, we found that in both periods, the total bill

during the policy year was positively related to the renewal decision for the next period. Every 1000PKR

increase in current period claim increases the probability of renewing by 1%. Households with larger

claim amounts in the current period are more likely to renew their policy, and this could happen due to

multiple reasons. First, it could be a traditional “adverse selection” story in which high risk households

had private information thus chose to renew their policies. The other explanation could be that the

households which utilized more insurance coverage valued their insurance policy more, and had more

knowledge in the service and potential benefit it could provide, thus leading to their renewal decision. To

delineate between these two possibilities, we further examine the relationship in models 2 and 3, with the

results reported in tables 6 and 7 respectively.

Table 5: regression results from model 1 (probability of renewing)

Dependent variable=1 if HH renewed for the next period

Nov-08 Jul-09

OLS Logit OLS Logit

PREVIOUSLY RENEWED 0.19*** 0.18***

(0.020) (0.020)

TOTAL BILL (in thousands) 0.01*** 0.01*** 0.01*** 0.01***

(0.000) (0.000) (0.000) (0.000)

FAMILY SIZE 0.09*** 0.10*** 0.13*** 0.14***

(0.021) (0.023) (0.030) (0.031)

HEAD AGE 0.00 0.00 0.00 0.00

(0.001) (0.001) (0.001) (0.001)

HEAD GENDER 0.01 0.01 -0.01 -0.01

(0.019) (0.021) (0.029) (0.031)

CHILD% 0.05 0.05 0.07 0.07

(0.045) (0.048) (0.066) (0.069)

TEENAGER% -0.14*** -0.15*** -0.04 -0.05

(0.040) (0.043) (0.060) (0.064)

ELDERLY% 0.08** 0.09** 0.15** 0.16**

(0.040) (0.043) (0.069) (0.071)

FEMALE% -0.04 -0.05 -0.19*** -0.20***

(0.037) (0.039) (0.058) (0.062)

LSO FIXED EFFECT X X X X

R square 0.58 0.43

Observations 5,272 5,272 2,197 2,197

Notes: Coefficient values and standard errors clustered by family are presented using both OLS and Logit

regressions-marginal effects reported. The dependent variable is a dummy variable indicating whether a household

renewed for the next period.

*significant at 10 percent; **significant at 5 percent; ***significant at 1 percent


16

In table 5, we also observe that the renewal decision for the following period is positively impacted by the

renewal decision in the previous period. Those household that were renewed at the beginning of Nov 08

are 18% more likely to renew again for the Nov 09 period.

Family size is another important factor that affects the decision of renewing the policy. We used log of

the total member count in a household as a measurement of family size, in order to account the

nonlinearity between member count and decision making. We found that every 10% increase in family

size will result in an average 1% increase in the probability of renewing the policy for Nov 2008 period.

And this impact increased to 1.4% in July 2010.

As to the impact of age composition, the percentage of elderly in the family has a consistently positive

impact on the renewal decision. In Nov 2008, every 10% increase in elderly percentage, holding other

factors constant, will increase the probability of policy renewal by 0.9%. And in July 2009 this impact

increased to 1.6%. The impact of teenager percentage is negative, but it is only significant for Nov 2008.

Each 10% increase in teenager percentage decreases the probability of renewing by 1.5%, while the

children percentage doesn’t have a significant impact on renewal decision making.

Female percentage consistently yields a negative impact on renewal probability, and it was significant for

July 2009. Each 10% increases in percentage of household being female decreases the probability of

renewing by 2%.

Table 6 demonstrates the regression results for the two-part model. The analysis of claim frequency

shows that renewed households file fewer claims than new customers. That pattern is confirmed in each

of the three specifications in table 6. On average, the renewed households had about 0.07 fewer claims

than newly enrolled households.

We also found that larger families have a higher claim frequency, which is intuitive. Each 1% increase in

family size leads to a 0.008 increase in number of claims. Households where the head is male make

fewer claims than households with female heads by 0.10. One possible explanation is that households

with male head might be better off than female head financially, leading to better nutrition and fewer

claims. In addition, families with higher fractions of children, elderly and female have more claims, each

1% increase on average affect number of claim by 0.004, 0.003 and 0.002 respectively. As to time trend

in claims, compared to Nov 08 enrolled households July 09 cohort had more claims while Nov 09 and

July 10 had less claims.

In the severity model, all estimates of the coefficients are of a small scale; however, we found that

renewed households have a slightly higher claim severity than the newly enrolled households and it is

statistically significant when all control variables were included. The effects of control variables were

largely consistent with the results in the frequency model, with more family members being children and

female positively correlated to claim severity. However, the magnitude of impact both remained very

small.

The results of the two-part model are consistent with health literature on selection. We expect to find

selection problem in frequency analysis since households are making decision to seek for medical

services, but not in severity analysis because it was also driven by the decision of physician, which is

exogenous of households’ decisions.


17

Table 6: regression results from model 2 (two-part model)

Frequency Model Severity Model

Linear Poisson Negative Binomial Gamma

Effect [1] [2] [1] [2] [1] [2] [1] [2]

Intercept 0.61*** -0.49*** -0.49*** 1.97E-04*** (0.011) (0.018) (0.018) (0.000) RENEWAL -0.10*** -0.04** -0.17*** -0.07* -0.18*** -0.07** 9.87E-06 1.89E-05*** (0.016) (0.018) (0.030) (0.035) (0.030) (0.035) (0.000) (0.000) JULY COHORT -0.04** -0.07** -0.08** 1.32E-05** (0.018) (0.031) (0.032) (0.000) FAMILY SIZE 0.45*** 0.81*** 0.80*** -1.32E-06 (0.025) (0.039) (0.039) (0.000) HEAD AGE 0.00*** -0.01*** -0.01*** -3.86E-07** (0.001) (0.001) (0.001) (0.000) HEAD MALE -0.10*** -0.16*** -0.15*** -7.22E-06 (0.023) (0.038) (0.038) (0.000) CHILD% 0.28*** 0.42*** 0.42*** 1.59E-04*** (0.001) (0.075) (0.075) (0.000) TEENAGER% -0.59*** -1.12*** -1.10*** -1.82E-05 (0.001) (0.085) (0.084) (0.000) ELDERLY% 0.15*** 0.27*** 0.28*** -1.59E-05 (0.001) (0.084) (0.084) (0.000) FEMALE% 0.09** 0.16** 0.17** 4.49E-05*** (0.044) (0.077) (0.077) (0.000) Jul-09 0.09*** 0.06 0.05 -1.11E-05 (0.030) (0.038) (0.037) (0.000) Nov-09 -0.12*** -0.22*** -0.23*** -2.98E-05*** (0.019) (0.033) (0.033) (0.000) Jul-10 -0.47*** -0.95*** -0.96*** -7.62E-06 (0.022) (0.047) (0.046) (0.000) FREQUENCY 7.78E-06*** (0.000) LSO FIXED EFFECT

X X X X

Observations 16,225 16,155 16,225 16,155 16,225 16,155 5,879 5,875 R square 0.002 0.328 0.002 AIC 19.01 18.94

Notes: Coefficient values and standard errors clustered by family are presented. For the frequency model, the

dependent variable is claim frequency indicating number of claim that a household filed during the policy period,

and we ran three types of models each using two specifications: [1] with only renewal status and July cohort dummy

as independent variables, and [2] with other control variables. For the severity model, the dependent variable is

claim severity indicating average size of claim and we ran general linear model with Gamma family, again with the

same two specifications.


As a sensitive test, we also run a model for the total claim amount. The results for both OLS and Tobit

model are shown in table 7. The results are consistent with the two-part model by and large, showing that

renewal households have a lower total claim amount than that of newly enrolled households. The

renewed households on average have around 500PKR less in total claim amount than that of newly

enrolled households.


18

Table 7: regression results from model 3 (total loss amount model)

Dependent variable: total claim

OLS Tobit

[1] [2] [1] [2]

intercept 2,931.18***

-4,065.34***

(66.431)

(180.683)

RENEWAL -520.15*** -507.70*** -1,896.38*** -1,407.17***

(101.348) (117.175) (267.289) (303.826)

JULY COHORT -321.16***

-1,116.25***

(99.524)

(253.080)

FAMILY SIZE

1,955.85***

5,458.34***

(145.813)

(351.819)

HEAD AGE

-10.97***

-57.90***

(3.211)

(8.674)

HEAD MALE

-286.22**

-700.10**

(127.356)

(311.255)

CHILD%

-686.14**

407.74

(281.388)

(673.722)

TEENAGER%

-2,894.91***

-9,588.16***

(263.321)

(706.005)

ELDERLY%

845.59***

1,677.23**

(269.641)

(702.258)

FEMALE%

44.39**

1,269.43**

(255.979)

(636.623)

Jul-09

582.38***

964.93***

(175.523)

(353.706)

Nov-09

-28.67

-790.75***

(127.448)

(303.832)

Jul-10

-1,801.61***

-6,855.28***

(127.556)

(382.940)

LSO FIXED EFFECT

X

X

R square 0.0018 0.2049 0.0004 Observations 16,225 16,155 16,225 16,155

Notes: Coefficient values and robust standard errors are presented for both OLS and Tobit regressions. The

dependent variable is total claim amount that a household incurred during the policy period. We ran it with the same

two specifications in Table 6.


The coefficients estimate for the other control variables are also consistent with the results in the previous

model. Family size has a significant positive impact on total claim, with 1% increase in family size

bringing 19.56PKR increase in total claim. The age of head and the gender of head being male both have

a negative effect on total claim amount. As to age composition, having a larger percentage of family

members being teenager decreases the total claim amount, while having more elderly in the household


19

increases the total claim amount significantly. A larger percentage of family members being female also

increases the total claim amount.

In conclusion, though households having more claims during the policy period are slightly more likely to

renew their policy for the next period, which is a likely adverse selection scenario. Interestingly, however,

we found that renewed households actually have lower claim frequency and total claim amount than those

of the newly enrolled households; therefore, it appears to be advantageous selection rather than adverse

selection in the long run.

V: Conclusion

The market with asymmetric information has been studied extensively in the insurance literature. Yet

most empirical studies focus on traditional insurance markets in developed countries, and there is little

evidence on the infant microinsurance industries in developing countries. We used data from a micro

health insurance program in Pakistan, and examined the relationship between the renewal decision and

claim history to observe the development of renewal policies. We found that though households with

more claim amount filed were more likely to renew their policies, the renewed households actually had

fewer numbers of claims and less total claim amounts than those of newly enrolled households. Thus, the

entire risk portfolio actually was getting better, instead of deteriorating as it was in a classic adverse

selection process.

In response to the need for affordable and quality health insurance for the poor, micro health insurance

programs have been established with financial aid from donors, in the hope that they will become

sustainable in the long run. Adverse selection is potentially a significant barrier to sustainability for these

programs. Our finding shed light on the possibility of a successful micro insurance program in a long run,

despite of lack of underwriting.

We expect that our analysis will help providers of microinsurance to better evaluate their performance

and by determining the degree to which adverse selection is a problem in this market will help them to

clarify the potential value to alternative program designs aimed at mitigating adverse selection.


20

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