Post on 17-Jul-2018
Belief Dispersion and Investment Composition∗
Ding Ding†
Australian National University
August 15, 2015
Abstract
I analyze the effect of belief differences among investors in equity markets oncorporate investment composition. When some investors have highly optimisticbeliefs about risky projects relative to the average beliefs, firms rationally respondby allocating investment to riskier projects to exploit the belief dispersion: firmsincrease relative shares of investment in Research & Development (R&D) andMergers & Acquisitions (M&A), and decrease the investment share of physicalcapital expenditure (CAPX). A one standard deviation increase in belief dispersionraises investment shares of R&D and M&A by 4.37% and 1.31%, respectively, andreduces the share in CAPX by 5.67%. This effect remains and even becomesamplified when firms experience positive return shock to CAPX – a case in whichmore investment in CAPX would be expected. To establish a causal relationship,I use mergers of brokerage houses as an exogenous shock to analyst coverage, achange that affects belief dispersion. My results show that belief dispersion inthe financial sector can lead to risk-taking behaviour in corporate investment. Toexplain my results, I build a simple model based on Bolton et al. (2006), in whichinvestors agree to disagree and stock prices reflect the beliefs of the most optimisticinvestors. In this model, the manager-owners of firms have the option to resell theirshares to more optimistic investors, and as a result, shift investment compositiontowards riskier projects to scale up their resale option.
JEL Classification: G14, G31
Key Words: Differences in Beliefs, Corporate Investment, Resource Allocation,
Productivity Growth∗I am deeply grateful for the invaluable guidance from Xiaodong Zhu, Varouj Aivazian, and Martin Burda, and insightful
discussion and suggestions from Michael Brennan, Ing-Haw Cheng, Peter Cziraki, Phil Dybvig, Espen Eckbo, Miquel Faig,Raymond Kan, Alex Maynard, Angelo Melino, Jordi Mondria, Andreas Park, James Pesando, Shouyong Shi, Aloysius Siow,Jason Wei, Yongxin Xu, Liyan Yang, and Haoxiang Zhu, and seminar participants at the University of Toronto, the 2013Financial Management Association Meetings, and the Institute of Financial Studies at the Southwest University of Financialand Economics. All remaining errors are my own.†Email: ding.ding@anu.edu.au
1. Introduction
Belief differences among investors affect asset prices.1 Miller (1977) and Harrison and Kreps
(1978) were among the first to formalize the idea that, in financial markets with short-
sales constraints and differences in beliefs among investors,2 stock prices tend to reflect the
valuations of the most optimistic investors.3 Expanding on the earlier work, Scheinkman and
Xiong (2003) use belief differences to explain stock price build-up, such as the Internet price
bubble of the 1990s. Stock price valuations, in turn, have an impact on corporate investment
decisions. Chen et al. (2007), Chirinko and Schaller (2011), and Polk and Sapienza (2009) are
examples of recent studies that document a scale effect of investment, whereby firms invest
inefficiently in specific types of projects when market valuations are high. In this indirect
way, investor belief dispersion has an impact on corporate investment decisions. This paper
shows that in addition to the scale of investment, there is a composition effect: when belief
dispersion is high, firms change the mix of their investments.
I assemble a panel dataset of U.S. firms from the Compustat universe to analyze the
relationship between belief dispersion and the allocation of investment to projects of different
risks. The three types of investment projects investigated are physical capital expenditure
(CAPX), research and development (R&D), and mergers and acquisitions (M&A); these
categories represent the bulk of major investments undertaken by firms. In both the finance
and accounting literature, R&D and M&A are considered more risky projects compared
to CAPX, because returns from R&D and M&A are subject to greater uncertainty.4 To
1As early as the tulip mania in 1637, investors were willing to buy tulip bulbs at yet higher prices because many expectedthat the bulbs can be resold at higher prices. Mackay (1848) recorded that “Nobles, citizens, farmers, mechanics, seamen,footmen, maidservants, even chimney sweeps and old clotheswomen, dabbled in tulips.” Later, the South Sea Company’s stockprice rose by over 700% during the 1720s through advertising to investors of its potential profitable trading strategy in SouthAmerica, while making no real investments. More recently and with a musical twist, Kim and Jung (2013) attribute 800%increase in market capitalization for a Korean semi-conductor firm – owned by the father of the singer of “Gangnam Style” –in mere two months to both domestic and foreign individual investor enthusiasm about the popular song, when there was nomaterial new information about the firm’s fundamentals.
2Belief differences may arise from differential interpretations of common information (Kandel and Pearson (1995)) or asym-metric information
3Diether et al. (2002), Chen et al. (2002), and Boehme et al. (2006) are examples that provide empirical support.4For example, see Kothari et al. (2002), Berk et al. (2004), Bargeron et al. (2010), Raghavendra Rau and Vermaelen (1998),
2
measure belief dispersion across investors in the stock market, I use analyst earnings forecast
dispersion, which is a standard measure of belief dispersion in the literature; see, for example,
Diether et al. (2002), Chatterjee et al. (2012), and Choy and Wei (2012).
Belief dispersion may be jointly determined with investment composition by some unob-
served firm characteristics. Moreover, belief dispersion may change because of anticipated
adjustments in investment composition. To address concerns of endogeneity and reverse
causality and to identify the causal effect of belief dispersion on investment composition, I
use an instrumental variables approach. Specifically, I employ a sample of mergers between
brokerage houses from Hong and Kacperczyk (2010) to provide exogenous variation in ana-
lyst forecast dispersion. When two brokerage houses merge, and both brokers have analysts
covering the same firms, the merged entity will have redundant analysts. Both Hong and
Kacperczyk (2010) and Kelly and Ljungqvist (2012) show that analyst coverage for affected
firms decreases on average as redundant analysts are dismissed, and information production
as well as the quality of information decrease. I show that the reduction in coverage is asso-
ciated with an increase in belief dispersion, since such a reduction decreases the amount of
information produced and admits greater disagreement in beliefs. Given that the mergers in
my sample involve acquiring brokers who are either expanding into different business areas or
who are taking over a target in trouble, the mergers I consider are unlikely to be affected by
investment policies of the firms their analysts cover. Merger-related termination of analysts
is also unlikely to affect the forecasts of other analysts or beliefs regarding individual firms.
I find that when there is greater belief dispersion about firm value, the CAPX share of
total investment decreases while proportions of R&D and M&A increase. Specifically, a one
standard deviation increase in belief dispersion predicts increases in investment shares of
R&D and M&A by 4.37% and 1.31%, respectively, and decreases in the share of CAPX by
and Malmendier et al. (2012).
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5.67%. The change in investment composition is associated with increases of future cash flow
volatility of 180 basis point, stock return volatility of 33 basis points, and ROA volatility
of 78 basis points. The results are robust to controls for firm-specific potential growth
opportunities, profitability, and capital structure, which are determinants of investment. I
also include controls for innovative productivity and CEO characteristics of firms.
I also find that the effect on investment composition is greater when there are positive
shocks to the returns on CAPX; the latter is measured by total factor productivity (TFP)
and estimated using physical capital stock and labor as input factors. Firms with both high
levels of belief dispersion and productivity growth allocate even more investment to riskier
projects, and away from CAPX. Intuitively, when productivity increases, the expected return
to physical capital investment is higher, which would predict more investment in CAPX. My
results suggest that the effects of belief dispersion interact with productivity and dominate
the effects of standard investment determinants such as risk-adjusted returns.
Why would firms invest more in risky projects when the level of belief dispersion is high?
I develop a theoretical model based on Bolton et al. (2006) to explain my results. In a market
with heterogeneous beliefs and short-sales constraints, stock prices reflect the most optimistic
valuations. Belief dispersion then matters for investment allocation if owner-managers have
resale options in that they can sell firm shares to more optimistic investors. Since investors
disagree more on riskier projects, owner-managers will increase investment in riskier projects
to boost their resale option values. Moreover, when there is productivity growth or when
returns on CAPX increase, firms’ expected return increases and they attract more investors.
As the number of investors increases, it becomes more likely that some investors are more
optimistic and expected belief dispersion is greater; as a result, investment composition is
distorted further towards riskier projects.
My paper contributes to a growing literature that analyzes the effect of financial markets
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on real investment. In traditional finance and economic models, it is assumed firm cash
flows affect stock market valuations, but feedback effects are not considered. More recently,
there is increasing focus on investigating whether a reverse channel exists, see Morck et al.
(1990), Stein (1996), Shleifer and Vishny (2003), Jensen (2005), and Pastor and Veronesi
(2009). In the literature that examines both theoretically and empirically the impact that
the stock market has on firms’ real decisions, one strand argues that stock prices contain
new and incremental information aggregated over market participants and guide managers
in making better investment decisions; for example, see Chen et al. (2007) and Bond et al.
(2012). A second strand suggests that managers take advantage of overpriced stock prices
as a cheap source of capital to finance additional investments, see for example Chirinko and
Schaller (1996), Baker et al. (2003), and Gilchrist et al. (2005). A third strand suggests that
stock prices reflect market sentiments, and managers cater to perceived market sentiments
in order to boost short-term share prices, see representative studies by Bolton et al. (2006)
and Polk and Sapienza (2009). My work is most similar with the last strand.
Theoretical and empirical evidence showing how investor beliefs affect stock prices and
investment activities are summarized in Barberis and Thaler (2003), Baker and Wurgler
(2011), and Xiong (2013). My results are consistent with Stein (1989), which suggests that
while making investment decisions, the manager cares not only about the long-run value
of the firm, but also about the short-run stock price. Previous studies have focused on
investment levels of specific types of projects, such as physical capital expenditures in Polk
and Sapienza (2009). My results are closely related to He and Tian (2013) and the authors
show that analyst coverage reduces investment in R&D because of pressure on performance
to meet forecasts. Derrien and Kecskes (2013) also investigate the impact of analyst coverage
via an information effect on the cost of capital of investments. My paper differs from previous
work in that I examine all major investment projects undertaken by the firm, and I identify
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the effect of financial markets on relative investment allocation.
This paper’s additional contribution to the literature is that the shift in investment com-
position towards riskier projects is greater when productivity increases. My contribution
builds on Bolton et al. (2006), which first suggested that belief dispersion causes managers
with short-term horizons to shift investment towards riskier projects, because their com-
pensation schemes induce such incentives. The link between productivity growth and stock
market activity is related to Pastor and Veronesi (2009) and Hobijn and Jovanovic (2001);
these papers explore the relationship between technology advances and stock market booms
using data from the railroad and internet booms. Pastor and Veronesi (2009) employ a gen-
eral equilibrium model and suggest that a time-varying adoption of new technologies leads
to bubble-like patterns for stock prices of more innovative firms, which results from greater
uncertainty about expected returns from new technologies. They predict that there will be
higher stock prices for innovative firms, which are the quickest to adopt new technologies.
My argument involves subjective belief differences about uncertainty and posits that more
investors are attracted to the market when there are productivity advances. In this respect,
my results are supported by Kaustia and Knupfer (2011) who use Finnish data to show
that first-time stock market entry rates are five times the average during the Internet boom.
Greenwood and Nagel (2009) also find that inexperienced investors played a role in driving
the asset price boom, again, in the context of the Internet boom.
The rest of the paper is organized as follows. Section 2 discusses the construction of the
database and variables central to the empirical analysis. Section 3 describes the estimation
model, presents the results, and provides robustness analysis. Section 4 interprets the results
with a theoretical model. Section 5 concludes.
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2. Data and Definitions
The dataset merges quarterly investment and financial information of individual firms, an-
alyst forecast data, and mutual fund data from various databases. For the universe of U.S.
firms in Compustat, I obtain stock price information from CRSP, and M&A deal-level data
from SDC Platinum’s Mergers and Acquisitions database. Analyst forecast data is col-
lected from I/B/E/S and mutual fund data is from CRSP’s Survivor-Bias-Free Mutual Fund
Database. Quarterly data on R&D expenditure for Compustat firms is available from 1989
onwards, hence the data spans from 1989 to 2012.
For each firm, firm age is determined by the date of the firm’s first record on CRSP. To
determine a firm’s M&A investment, I link public firms from Compustat to deals in SDC
by the acquirer’s parent CUSIP code and company name. I also supplement the match
with CRSP’s translation tool that matches 6-digit CUSIPs from SDC with CRSP’s permno,
which is linked to Compustat’s identifier.5 Consistent with the practice in the literature,
observations with negative values for asset, capital (property, plant and equipment), or
investment are dropped. The financial services and utilities industries are excluded from the
empirical analysis, though the results are robust to the inclusion of both industries.
2.1. Investments
The investment types of interest are: CAPEX, net expenditure in PPE (property, plant, and
equipment); R&D, expenditure in research and development; M&A, expenditure on mergers
and acquisitions (excluding repurchases). Total investment is computed as the sum of the
three. To investigate investment composition, I focus on the investment shares: CAPEX’s
5I collect 113,033 M&A deals made by U.S. public firms. Approximately 50% (57367/113033) of all deals in SDC Platinumhave reported transaction values, and about 70%(78355/113033) of deals can be matched to a firm found in Compustat. Thefinal dataset contains 4121 firms with deal value data available. Deal value is defined as the total purchase price paid by theacquirer, excluding fees and expenses.
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share, R&D’s share, and M&A’s share, which are fractions of CAPEX, R&D, and M&A over
total investment, respectively. Following the literature, for firm-quarters with no observations
for R&D and M&A expenditures, values are coded to zero.6
Compared to CAPX, returns from R&D and M&A are subject to greater uncertainty.
Empirical evidence from both accounting and finance literatures suggest R&D and M&A
investments are more risky than capital expenditure. Kothari et al. (2002) find that relative
to physical capital expenditure, R&D investments generate greater future earnings variability
and have more uncertain future benefits. Berk et al. (2004), Chambers et al. (2002), and Shi
(2003) show that R&D investments bear greater uncertainty, and both equity holders and
bond holders demand higher risk premium. Coles et al. (2006) and Bargeron et al. (2010)
use higher R&D expenditure and lower physical capital investment as evidence of more risky
policy choices. On the other hand, growth strategies driven by M&A tend to provide zero
or negative average returns for long term shareholders of the acquirer, e.g., Mitchell and
Lehn (1990), Raghavendra Rau and Vermaelen (1998), and Malmendier et al. (2012). Ding
and Rahaman (2012) find that firms that make more acquisitions during booms accumulate
more firm risks and are more likely to exit inefficiently in a subsequent economic recession.
2.2. Belief Dispersion
I employ two measures of belief dispersion. The first is dispersion in analyst forecasts of
earnings per share (EPS) of a firm. Analyst EPS forecast dispersion is a widely used measure
for investor belief dispersion (e.g., Diether et al. (2002), Chatterjee et al. (2012), Choy and
Wei (2012)). While earnings forecasts are based on the subjective evaluations of firms by
the analysts who cover the equity of the firm, the forecasts are widely followed and form the
basis of investors’ valuation. Both retail and institutional investors rely on analyst forecasts
6The results are robust to if such firm-quarters are deleted.
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when they learn about an equity and make investment decisions. A voluminous literature
demonstrates analysts’ role in enhancing information efficiency and affecting equity prices.
(e.g., see Brennan, Jegadeesh, and Swaminathan (1993) and Brennan and Subrahmanyam
(1995)).
There is extensive evidence that analysts’ reports also have an economically significant
impact on stock prices (e.g., see Womack (1996), Barber, Lehavy, McNichols, and Trueman
(2001), and Jegadeesh, Kim, Krische, and Lee (2004) for recommendations, and Givoly and
Lakonishok (1979) and Stickel (1991) for earnings estimates). By producing information
about the firms that they cover, analysts also monitor these firms (e.g., see Moyer, Chatfield,
and Sisneros (1989) and Chung and Jo (1996)), and they increase the investor recognition of
these firms (see Merton (1987)). Analysts sometimes issue biased analyst reports to investors
(e.g., see Lin and McNichols (1998) and Michaely and Womack (1999)). However, analysts
are generally incentivized to produce information that is valuable to investors (e.g., see Hong
and Kubik (2003) and Mikhail, Walther, and Willis (1999). Diether et al. (2002) show that
analyst forecast dispersion predicts lower future stock returns. The relevance and impact of
forecast dispersion enables it to be a reasonable measure for belief dispersion in the wider
investor crowd.
To measure belief dispersion, I collect analyst forecast statistics from the Unadjusted
Summary file (unadjusted for stock splits) in I/B/E/S to avoid the documented rounding
bias reported by Diether et al. (2002). I define Analyst Forecast Dispersion (DISP ) as the
standard deviation of analyst forecast of quarter-ahead earnings per share, scaled by absolute
mean value of forecasts. However, when the mean forecast is very small, the dispersion
measure can be blown up, therefore, an alternative measure uses last period’s stock price to
scale the standard deviation. The results are qualitatively similar, and only the result for
the former measure is reported.
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Alternatively, I use new fund flow into sector mutual funds as a measure for belief dis-
persion. New fund flow is a used to measure the number of investors in any given sector.
The idea is that, the more investors there are in any industry, the greater the level of belief
dispersion because increase in the number of investors increases the likelihood of investors
with beliefs at either tails of the distribution. For the measure of new fund flow to sector
funds, I collect mutual fund flow data in U.S. domestic equity from CRSP’s Survivor-Bias-
Free Mutual Fund Database. I obtain fund-quarter observations on returns, total net assets
(TNA), and other fund characteristics. For the fund to be considered, it must has informa-
tion on total net asset (TNA) and monthly returns. A second screen requires the asset and
return data to be available for at least 2 years. In addition, the analysis focuses on funds
with TNA greater than $15 million.7 Fund age is computed by using the first date that
monthly return is reported for the fund.8 Funds that are less than one-year old are excluded
to address a potential upward incubation bias (Evans (2010)). The categorization of sector
funds is explained in the appendix. Following Sirri and Tufano (1998), for fund k, the net
new fund inflow in month t – i.e., new investment, or net new fund growth (Fund Flow (ff))
beyond reinvested dividends – is defined as9:
ffk,t =TNAk,t − TNAk,t−1 × (1 + rk,t)
TNAk,t−1
in which TNAk,t is the total asset under management for fund k by the end of period t, and
rk,t+1 is the return for fund k in period t. Implicitly, the definition assumes investors reinvest
dividends in the fund and new investment occurs at the end of the period. The quarterly
flows is sum of the monthly flows in the quarter.
Fund flow of all funds in the set s(j) of a particular sector j is computed as a TNA-7Elton et al. (2001) suggest that reported returns may be overstated for funds with less than $15 Million in total net assets
due to omission bias, because not all funds have a full history of monthly returns.8A fund may have reported monthly returns for many years earlier than the first offer dt variable that CRSP reports is
much later.9if there was a merger of funds, which may introduce jumps in the series, the flow is adjusted by subtracting the increase in
TNA due to mergers in time t, following Sapp and Tiwari (2004)
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weighted average of all funds in the sector:
ffj,t =
∑k∈s(j)
ffk,tTNAk,t−1∑k∈s(j)
TNAk,t−1
TNA-weighted flows may be dominated by larger funds and introduce a size bias in the
flow measure, for robustness I also calculate a net cash flow (NCF) weighted measure of fund
flow, only the equally-weighted results are reported.10
Analyst forecast dispersion and sector new fund flow are positively correlated with a
Pearson correlation coefficient of 0.1121 and statistically significant at the 10% level.
2.3. Productivity
Firm-level productivity is measured with the total factor productivity (TFP). All firms are
assumed to have access to a Cobb-Douglas production technology:
Yijt = Aijt ×KαijtL
1−αijt (1)
in which Yijt is the net sales, Kijt is the capital stock, Lijt is the number of employees, and
Aijt is the idiosyncratic total factor productivity of firm i in industry j and at time t. By
taking the natural logarithm of both sides, TFP may be estimated from the following:
yijt = aijt + αkijt + (1− α)lijt (2)
To address potential simultaneity and selection biases, I follow Olley and Pakes (1996). Olley
and Pakes (1996) use capital investment to control for unobservables in the standard Cobb-
Douglas production function. The methodology estimates a semi-parametric model and
10The net cash flow (NCF ) is defined as NCFk,t = TNAk,t − TNAk,t−1 × (1 + rk,t)
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addresses selection bias, serial correlation in firm-level productivity, and simultaneity bias.
A potential survivorship bias, which may result in overestimating the TFP , is corrected by
controlling for firm survival probability (i.e., whether the firm drops off the sample). The
survival probability is estimated with an polynomial expansion in investment and capital
stock with a full set of interactions in a probit model. Net sales is deflated at the industry
level, in which all firms in the same four-digit SIC industry use a common producer price
deflator collected from the Bureau of Labor Statistics.
Alternatively, I measure productivity changes by the idiosyncratic component of the
Hodrick-Prescott filtered net sales of the firm. The two measures are positively correlated
with a Pearson correlation coefficient of 0.1398 and is significant at the 5% level. Results
using either are qualitatively similar.
2.4. Firm-level Controls and Performance Measures
I control for a series of observable firm characteristics such as measures for investment oppor-
tunities, investment efficiency, profitability, capital structure, firm life cycle that are standard
in the investment literature, and which may affect belief dispersion. These include: Tobin’s
Q to capture investment opportunities and is computed as market value of assets divided by
book value of assets; Cash Flow to measure the firm’s financial constraint and is computed
as sum of earnings before extraordinary items and depreciation and amortization, scaled
by last period’s PPE(plant, property, and equipment); Leverage is long term debt over last
period’s total assets; ROE or return on earnings serves a proxy for firm profitability and is
computed by earnings over last period’s book equity; Size is logarithm of the firm’s total
assets; and Age is logarithm of the number of quarters since the first quarter this firm’s
debut on CRSP.
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The effect of investment policy on firm outcome is measured along two dimensions: firm
performance and risks. The performance measures include: Gross Margin [(net sales - cost
of goods sold)/net sales]; Return on Assets (ROA) (operating income before interest, taxes,
depreciation, and amortization, scaled by book value of total assets); Asset Turnover (sales
scaled by total assets); and Sales Growth (growth rate of net sales).
The proxies for firm risk are: σ(Cash), the cash flow volatility of four quarters forward
from time t and computed as ln[EBITAt−EBITAt−1] as in Shumway (2001); σ(Profitability),
the volatility of profitability by Hoberg and Phillips (2010) and obtained by regressing ROE
on lagged ROE for all firms in each industry and finding the standard deviation of the resid-
uals; σ(StockRet), standard deviation of monthly stock return; σ(ROA), standard deviation
of ROA; and σ(SalesGrowth), the standard deviation of net sales growth rates for a n-quarter
forward rolling window as in Ramey and Ramey (1995).
Table 2 presents further definition and summary statistics of firm-level variables used in
the analysis.
3. Empirical Analysis and Results
To understand how investment composition is affected by belief dispersion, I investigate
changes in relative ratios of investment in physical capital, R&D, and M&A expenditures,
respectively.
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3.1. Empirical Specification
The results of how firm investments react to productivity growth and belief dispersion are
estimated with a standard OLS framework,
Ii,t = α + β ·DISPi,t−4+γ ·DISPi,t−4 · TFPGrowthi,t−4 + δ · TFPGrowthi,t−4
+X ′i,t−4ζ + fi + yt + εi,t
(3)
Ii,t represents an investment share that makes up a firm’s investment composition of firm i at
quarter t. It is CAPX’s share, R&D’s share, and M&A’s share. DISPi,t is belief dispersion
revolving firm i at time t, and is proxied by both analyst EPS forecast dispersion and
sector new fund flow into the industry that firm i belongs to. TFPGrowthi,t is productivity
growth of firm i at time t, proxied by both its TFP and the idiosyncratic component of
Hodrick-Prescott filtered firm net sales. Xi,t−1 is a vector of firm-level controls for liquidity,
profitability, capital structure, and expected growth opportunity that are commonly found
in the investment literature. fi and yt are firm- and quarter- fixed effects to control for firm-
level and intertemporal heterogeneities that affect investments and belief dispersion, such
as changes in the macroeconomic conditions. The coefficient β measures the sensitivity of
investment share to belief dispersion and is the main focus. γ > 0 suggests that investment
share responds more to belief dispersion at a higher level of productivity growth.
All explanatory variables are lagged by 4 quarters for two reasons. First, it is common
for there to be an implementation lag between decision making in the boardroom based on
current financial characteristics and growth opportunities to the time the actual expenditure
takes place.11 Second, lagging is one way to address the issue of reverse causality. To the
extent that current level of belief dispersion may be endogenous to investment composition
and respond to observed investment or anticipated changes, it is less likely that past forecasts
11The results for lags of 2 to 4 quarters are qualitatively similar.
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or mutual fund flows are subject to the same issue.
3.2. Investment Composition to Belief Dispersion
Table 3 presents the results for regressing the different types of shares in investment on
analyst forecast dispersion (DISP ), controlling for productivity growth and a set of stan-
dard characteristics from investment models. Three sets of specifications and corresponding
results are available for each of CAPX’s share, R&D’s share, and M&A’s share. The first
specification of all three sets (Columns (1), (4), (7)) show the effect of forecast dispersion
on investment shares without adjusting for unobserved heterogeneity across the panel, while
the remaining results do. All specifications control for effects from potential growth oppor-
tunities, profitability, capital structure, and life cycle.
DISP acts differently on the investment shares. For CAPX’s share (Columns (1) to
(3)), the coefficients on DISP are consistently negative and significant at at least the 5%
level. For R&D’s share (Columns (4) to (6)), the effect from DISP is consistently positive
and signficant at the 1% level. While for M&A’s share, the overall effect is positive save
for the coefficient becoming insignificant when an interaction term between DISP and TFP
growth is added. That is, firms subject to greater forecast dispersions shift their investment
composition to R&D and M&A projects rather than making more CAPX, an effect that is
not explained by fundamental productivity differences, nor observable firm characteristics,
nor industry or time heterogeneities. The effect of an investment shift to R&D is consistent
strong and statistically significant.
Columns (3), (6), and (9) show an additional effect. By including an interaction term
between DISP and TFP growth, CAPX’s share is further depressed at both high levels of
DISP and TFP growth, while R&D’s share and M&A’s shares are higher. That is, the
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relationship between DISP and investment shares are reinforced when there is a higher
level of productivity growth. By itself, the coefficients on TFP growth suggest that greater
productivity growth should instead boost CAPX’s share (0.0043), which is more consistent
with intuition.
I repeat the estimation with new fund flow as a proxy for belief dispersion in Table 4. The
results are similar to that using DISP . The relationship between fund flow with CAPX’s
share and R&D’s share have the same signs and statistical significance as with DISP in
the previous table, while the relationship to M&A tends to be insignificant. However, the
additional reinforcement from high productivity growth to fund flow’s effect on investment
shares exist in this set of results, too. The coefficients on the interaction term between fund
flow and TFP growth remains statistically significant and negative for CAPX’s share, remain
positive and statistically significant for M&A’s share, and remains positive (but statistically
insignificant) for R&D’s share.
The results for the same specifications but uses idiosyncratic sales growth to proxy for
productivity growth are also estimated, but not reported. The signs of coefficients on DISP ,
the measure for productivity growth, and the interactions terms are generally consistent as
the previous tables.
The results are robust to using different measures for belief dispersion and productiv-
ity growth. They suggest firms that are subject to greater belief dispersions about their
prospects have higher investment compositions in riskier projects that are associated with
greater uncertainty and take longer resolution of outcome, such as R&D and M&A. They
also have lower relative investment in CAPX, which has less uncertainty about its expected
returns. As Coles et al. (2006) suggest, this shift in investment composition indicate a more
risky investment profile; one that is not explained by firm and industry fundamentals.
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The evidence also suggest that not only do firms adopt a more risky investment composi-
tion when belief dispersion is high, the effect is reinforced when there is higher productivity
growth. This is not predicted by standard theories of productivity growth. The results
suggest that productivity growth affects firm investment not only through the traditional
channel, which indicate higher productivity growth raises expected return and investment
levels in physical capital should be increased. In addition, productivity growth affects firm
investment via belief dispersion. I further explore this dimension in Section 4.
3.3. Alternative Controls
The literature provides evidence that analyst coverage affects investments. He and Tian
(2013) show analyst coverage creates pressure for firms to perform and meet forecast targets,
causing firms to invest less in R&D. On the other hand, Derrien and Kecskes (2013) explore
the information production channel and provide evidence that loss of analyst coverage leads
to reduction in investments, because less information from analysts increases cost of capital
for the firm. I therefore include control for analyst coverage (the number of forecasts for each
firm) and report the results in Column (2) in Table 5, for all types of investment shares. Both
the sign and direction of the effect through belief dispersion is consistent with the baseline
results in Column (1).
Firms may invest in more R&D if they are simply more efficient in innovative production.
To avoid confounding the relationship between investment composition and belief differences,
I add an additional control for a firm’s innovative productivity. One measure of a firm’s in-
novative output is patent ownership (Pakes and Griliches (1980), Acs and Audretsch (1988)).
I obtain firm-level patent counts, from 1980 to 2006 from the NBER Patent Data Project
developed by Hall et al. (2001), and include firm patent-R&D expense ratio (patents per $1
Million R&D, or the propensity to patent) as a control to proxy for efficiency in innovative
17
production. The results are reported in Column (3) of Table 5, for all investment shares,
show the effect of belief differences on investment composition remain robust to the inclusion
of this control.
Another important factor that affects investment allocation is CEO characteristics. The
literature of CEO tenure’s impact on investment suggests that CEOs are more likely to take
risks in the earlier periods in their tenure, when they begin to learn about the firm and are
willing to take on different initiatives to improve firm performance. As CEO tenure grows,
CEOs become entrenched and tend to prefer the status quo, e.g., Miller (1991), Berger
and Ofek (1999). The stage of CEOs life cycle appears important for decisions on firms’
investment mix. I control for the cumulative years in office of the present CEO. To do so, I
collect insider trading data from the Thompson Reuters Table One file, which records non-
derivative transactions of insiders and specifically of CEOs. I track the cumulative tenure for
each firm’s CEO since the beginning of the file. A CEO’s tenure stops when a new person
ID begins to make trades in the CEO role in lieu of the previous person ID. I estimate the
approximate time that the previous person stepped down from being a CEO and the new
person takes office to be half-way of the duration between the last trade of the previous ID
and the first trade of the new ID.
As Columns (4) in Table 5 show, CEO tenure is related positively with CAPX’s share
and negatively with R&D’s share, and is insignificant in the case of M&A’s share. The sign
is consistent with the life cycle story that as CEOs stay longer in office, they tend to avoid
more risky investments such as M&As. The effects of DISP on investment shares remain
robust as before.
To supplement the results, I also control for CEO turnover, which is an indicator variable
that takes on the value of 1 if the CEO ID changes, and zero otherwise. In the literature,
CEO turnover is considered as an event when the new management can initiate value-
18
creating investment decisions to “correct” mistakes by previous management. Weisbach
(1995), Denis and Denis (1995), and Denis et al. (1997) present evidence that associate
CEO turnovers with divesting unprofitable acquisitions, downsizing operations, or reducing
diversification. Therefore, changing investment composition to obtain a less risky profile
is expected to be associated CEO turnover. Results from Column (5) in Table 5 for all
investment shares corroborate the “reset” theory, and show CEO turnover to be associated
with less investment in the riskier projects (while the sign on CAPX’s share is negative but
statistically insignificant).
Stock market return also influences investment decisions. Higher market returns may
encourage managers to use the stock as an acquisition currency and invest in more M&A
projects, as suggested by Shleifer and Vishny (2003). I include control for excess market
return, which is stock return adjusted for the value-weighted market index. The evidence
from Column (6) in Table 5 is consistent with firms using stocks with high price appreciation
as an acquisition currency to finance acquisitions, since M&A’s share of investment is related
positively with higher stock returns, while R&D’s share is related negatively. The effect from
belief dispersion remains robust as in the baseline results.
Having adjusted for possible confounding factors as discussed above, it remains that
there may be other unobservable characteristics to the econometrician, but observed by
management that cause the change towards an investment composition that maximizes firm
performance. If this holds true, it is reasonable to expect that the change would be associated
with better future firm performance. As observed in the performance measures Table 8,
controlling for observed factors and unobserved heterogeneity across the panel that may
impact performance, firms with a higher investment composition in R&D do not have better
future performance, while they are exposed to greater firm risk.
19
3.4. Endogeneity and Instrumental Variable Analysis
The challenge of establishing a causal relationship of belief dispersion on investment com-
position is endogeneity and reverse causality. So far the results are estimated using lagged
explanatory variables, which may mitigate part of the concern if contemporaneous invest-
ment is not affected by past belief dispersion. However, investment could be persistent, so
lagged belief dispersion may be caused by lagged investment, which also explains current
investment.
In spite of the various controls I have included, it is perceivable that there remain unob-
served firm or market characteristics that determine investment decisions and belief disper-
sion jointly. It is also plausible that the direction of causality is opposite to what is supposed.
Some characteristics of the firm (unobserved by the econometrician) may dictate that the
firm should adjust its investment composition to some optimal level, such as adopting a more
risky and aggressive investment profile, thus analysts revise their expectations accordingly.
To mitigate this concern, I use merger of brokerage houses as a natural experiment
that introduces exogenous variation to the formation of forecasts and dispersion. Hong and
Kacperczyk (2010) collects a sample of thirteen brokerage mergers between 1994 and 2005
affecting 1,261 of the firms in my sample,12 and they show that the mergers resulted in a
decrease in analyst coverage because redundant analysts are let go.
The merger of two brokerages provides a reasonable identification for exogenous variation
in belief dispersion for two reasons. First, a merger considered here is likely to be an indepen-
dent event from individual firm policies or actions. As summarized in Hong and Kacperczyk
(2010), the thirteen mergers are driven by brokers expanding into different business lines
or geographic areas, or one broker is taking over another broker in trouble. Merger-related
12They identified two other mergers that are outside of my sample span.
20
termination of analysts is also unlikely to affect the forecasts of other analysts or that of
market sentiments regarding particular stocks. Other studies that use similar measures to
study the information content of forecast coverages include Kelly and Ljungqvist (2012) and
Derrien and Kecskes (2013). Second, I show that after a merger event through which analyst
coverage reduces, belief dispersion increases.
Hong and Kacperczyk (2010) find that less coverage causes analysts to make more opti-
mistic forecasts because of less competition, resulting in less accurate information production.
Kelly and Ljungqvist (2012) report that termination of analyst coverage is correlated with
increase in information asymmetry in that there is less information production. Both sets
of evidence indicate that reduction in analyst coverage should be related to greater belief
dispersion, because public signals have become more noisy. Consistent with this evidence
and theory, I first find the mergers of brokerage houses that affect the firms in my sample are
associated with reduction in analyst coverage by 1.32 analysts, an effect that is statistically
significant at the 1% level and comparable to previous work. Second, I show reduction in
coverage is associated with greater dispersion. To do so, I begin with a plot of the average
number of estimates versus forecast dispersion for different sectors over time, which is pre-
sented in Figure 1. The figure suggests that, for many of the sectors, increases in the number
of estimates, or analyst coverage, is generally accompanied by decreases in belief dispersion.
Often, the peak in the number of estimates is matched by a trough in the dispersion mea-
sure. Next, I find that increasing coverage by one analyst is associated with reducing belief
dispersion by 0.0598, statistically significant at the 1% level. The evidence is consistent with
the idea that more analyst coverage is related with less dispersion, and I will provide further
evidence in the first-stage results below.13
Specifically, I construct a dummy variable MERGER as an instrument for belief dis-
13In the limit, when the number of estimates, or analyst coverage, reaches unity, the dispersion should be zero. However, asseen in Figure 1, most industries are covered by more than 4 analysts on average.
21
persion. MERGER for a firm-quarter equals one if a brokerage merger happened and the
firm was covered by the parties involved, and equals zero otherwise. If the merger happens
at the end of the fiscal quarter for the firms, such as the case of Kidder Peabody & Co’s
merger with PaineWebber Group on December 31, 1994, I have tried a variation that assigns
MERGE to one for the quarter after, the result remains the same. Hong and Kacperczyk
(2010) also identify cases when the firm was dropped from coverage prior to the merger
date, which affected 347 firms in my sample and therefore these may not reflect exogenous
changes. I repeated the tests by dropping these observations and the results remain quali-
tatively similar. In the test, I limit the estimation sample to between 1993 and 2005 to be
within the years of the mergers. I include the same set of firm-level controls and fixed effects
as used in the baseline model.
Table 6 reports the results of the instrumental variables approach. The first column shows
the reduced form estimates of investment allocations on the instrument, MERGER, which
are significant at at least the 10% level and the estimates are of the expected signs. The
remaining columns report the first stage statistics as well as the IV estimates. For the first
stage, I regress analyst forecast dispersions on MERGER and lagged firm characteristics
that measure firm fundamentals and firm risks. Diether et al. (2002) identify that dispersion
is is positively correlated to a firm’s B/M, share turnover, trading volume, debt-to-book
ratio, earnings variability, and standard deviation of past returns, but is negatively related
to sales and size. The regression results are consistent and show that firms affected by the
merger of brokerage houses are associated with 0.0586 or 10% of standard deviation more
dispersion. The pattern is similar to the estimates in the baseline results. The measure of
belief dispersion has a positive effect on investment shares of R&D and M&A, and depresses
the CAPX’s share. The coefficients in the IV results are greater than those in the OLS
results. Since the OLS estimates contain both the causal and selection effects, the results
22
suggest that there is a negative selection effect because belief dispersion is correlated with
unobserved firm fundamental characteristics (by the econometrician) that determine firm
investment. One explanation for the negative effect can be that there is greater disagreement
or belief dispersion regarding firms with poor fundamentals.
3.5. Fractional Response Model
In any period, firms may choose to invest in any or all of physical capital, R&D, or M&A.
The investment composition in each type of project takes on the form of fractions and is
in [0, 1]. Being a bounded fractional dependent variable, the effect of explanatory variables
X may not be linear, and the variance tends to decrease when the conditional mean of
the dependent variable E(y|X) approaches its bounds. Investment shares are susceptible to
build up around either bounds, so standard OLS estimates may be biased and inconsistent.
Investment composition is not a result of censoring, so Tobit model may not be suitable.
Papke and Wooldridge (1996) address the challenge by proposing a nonlinear model for
the conditional mean of the fractional response, y, given by: E(y|X) = G(Xβ) with X
being a 1 × K vector of explanatory variables, β a K × 1 vector, and G(.) a nonlinear
function bounded between zero and one. They specify a fractional logistic link function and
estimate a consistent and asymptotically normal estimator for β using a quasi-maximum
likelihood method to maximize the Bernoulli log-likelihood function. Papke and Wooldridge
(2008) extend their earlier work for application in panel data. In this case, they use a probit
link function and obtain consistent estimates by the pooled Bernoulli quasi-MLE (QMLE)
that maximizes a pooled probit log-likelihood. To supplement the main results, I provide
alternative estimates of the specification in Equation 3 using the pooled fractional probit
estimator. Instead of having a linear specification, in the fractional model the following is
23
estimated:
E[Ii,t|DISPi,t−4, TFPGrowthi,t−4, Xi,t−4, εi,t] =
Φ(α + β ·DISPi,t−4 +X ′i,t−4ζ + εi,t)
(4)
Table 7 reports the results of this estimation. The signs of the results are consistent with
those reported in Section 3.
3.6. Investment and Performance
To gauge how investment composition is related to future firm performance, I define four
measures of firm performance with financial accounting ratios and six proxies for firm risk
as are commonly used in the literature. More specifically, the future performance and risk
measures are averages of the four-quarters forward (and repeated for eight-quarters forward).
I regress the performance measures on the investment shares, belief dispersion (using forecast
dispersion as the proxy), as well as productivity growth (TFP growth), controlling for firm-
level factors that could impact performance (such as liquidity, size, and capital structure)
and also firm- and time- fixed effects. Since the investment shares add up to one, I use
M&A’s share as the reference group and it is omitted from the estimation.
The results are summarized in Table 8. Columns (1) to (4) report the effects of analyst
forecast dispersion on performance. In general, increasing CAPX’s share is related to better
firm profitability, investment efficiency, and sales growth. Its relationship with gross margin
has a negative sign, but is insignificant. On the other hand, increasing R&D’s is associated
with worse performance across all measures.
For the risk measures, CAPX’s share is consistently related to lower risks, while increasing
R&D’s is associated with greater firm risks in the future four quarters forward. The results
24
are consistent with the literature’s stance on the relative riskiness of investment policies
through the level of investments in CAPX and R&D.
3.7. Economic Significance
Based on the identified causal effects from Table 6, a one standard deviation increase in
belief dispersion will bring about increases in R&D’s share and M&A’s share by 4.37% and
1.31%, respectively, and reduce CAPX’s share by 5.67%. To place the changes in dispersion
in perspective, there are sizable variation both cross-sectionally and across time in belief
dispersion at the firm-level (the ratio of within- over between- variations is 0.62/0.53 =
1.17).
Given Table 8, the increase in R&D’s share is thus associated with increases of 180 basis
points in cash flow volatility, 33 basis points in stock return volatility, and 78 basis points
in standard deviation in ROA, which are all averaged over the future four quarters.
4. Belief Dispersion and Corporate Investment: An Interpreta-
tion and Extension
The empirical results show belief dispersion affects firm investment allocation, and a higher
level of belief dispersion is related to relatively more investment in riskier projects, which
are related to greater firm risks. The composition effect is reinforced when a higher level of
belief dispersion is accompanied by higher productivity growth. The results are robust to
the inclusion of controls for common price-based controls such as Tobin’s Q and productivity
measure such as TFP. Taken together, the findings suggest the investment composition effect
requires an explanation when productivity and belief dispersion are considered jointly.
25
To explain the empirical results, a model can be built in the context of a market environ-
ment in which investors have resale options and there are heterogeneous beliefs and short-
sales constraints, as developed by Miller (1977), Harrison and Kreps (1978), Scheinkman and
Xiong (2003), Hong et al. (2006), and Bolton et al. (2006). In such a framework, investors
process information differently, so that firm managers-owners who have resale option in their
stakes of the firm are incentivized to invest more in riskier projects. This incentive increases
when there is productivity growth, which raises expected returns, attracts more investors,
and leads to greater expected belief dispersion.
4.1. Model
Consider a model that builds on Bolton et al. (2006) and follows similar notations. Consider
a one-period economy with three dates: d = 0, d = 1, and d = 2. There are j firms with
incumbent manager-owners. At d = 0, the manager owns 100% of the firm and makes
investment decisions. Other investors may enter the industry and buy shares of the firm at
d = 1 in the secondary market. The number of shares in the firm is normalized to one.
The firm’s investment process is as follows: the manager can choose investment by allo-
cating resources in two types of projects at d = 0 and output is realized at d = 2. Project A
produces uj, uj ∼ N(hjµj, σ2f ), in which µj is the resource allocated to operate the project or
the scale, hj > 0 measures the expected return per unit of scale, and σ2f is variance about the
return of the project that is beyond the manager’s control. Project B produces vj ≡ ωjzj, in
which ωj is the scale and zj ∼ N(0, σ2c ) is the return per unit of scale and σ2
c is the variance
on the project per unit of scale.14 In other words, scaling up investment in Project A will
increase expected long-run return without increasing the uncertainty, while project B will
increase variance of output. The firm produces total output rj = uj + vj. The remaining
14Project B is considered as the “Castle-in-the-Air” project in Bolton et al. (2006). zj has a fixed mean which is scaled tozero here. Any value of zj can be factored out and treated as a constant, so I focus on its variance-inflating aspect.
26
analysis focuses on firm j and subscript j is omitted.
At d = 1, the manager and n outside investors may trade shares in firm j on the secondary
market at d = 1 after they receive common signals about the productivity of both projects.
Each investor i is subject to a bias φi when processing the signal of Project B, that is, the
investor may overreact to the signal.15 Every investor, including the owner-manager, draws
φi i.i.d. from a publicly known, fixed and non-degenerate distribution G(.) with support
in (0,∞). Outside investors do not know φi a priori and can only make a draw after they
decide to enter the market to trade in the firm’s stock. At d = 2, the investor holding the
share in the firm receives the output and the economy ends.
Investors observe public signals s and θ about the output from projects A and B, re-
spectively. Investors update their beliefs about the firm’s output r according to the Bayes’
rule and given the manager’s optimal relative investments to the projects (µ, ω). Investors
agree on their posterior beliefs about Project A to be u = E[u|s, µ]. For Project B, however,
investors receive signal θ = z + εθ, εθ ∼ N(0, σ2θ), and differ in beliefs in the informativeness
of the signal, which is determined by their respective φi. Let τ denote the precision of a
signal, τθ = 1σ2θ. Investors, including the manager, will instead treat the precision as φiτθ,
and their subjective posteriors for Project B is given by:
vi = Ei[v|θ, ω] = λiωθ; λi ≡φiτθ
φiτθ + τz(5)
in which, φi = 1 implies the investor is not biased and φi > 1 implies the investor biases
upwards the precision of the signal, or as in Bolton et al. (2006), the investor is overconfident
about the signal.
Assuming short-sales constraints, the price of the stock at d = 1 is bid up to the highest
15A realization of φi = 1 implies the investor is not subject to the bias, whereas φi > 1 indicates the investor interprets thesignal to be more informative than it is.
27
subjective valuation of the firm (e.g., see the price-optimism models of Miller (1977), Shleifer
and Vishny (1997), etc., and empirical evidence from Diether et al. (2002), Boehme et al.
(2006)). Thus, given a set I of investors (with the manager and n outside investors), the
equilibrium price of the stock of firm j at d = 1 is the valuation of the firm is:
p1 = max{u+ vi} = u+ max∀i∈Ij{(v)i} (6)
or simply, p1 reflects the valuation of the investor who overweighs the signal θ, or analogously,
who is most optimistic.
The manager’s investment choice at d = 0 is to choose the investment scale (µ, ω) in
Projects A and B to maximize expected firm value E0[V ], given his own draw of φo and n
outside investors, and a resource constraint,
maxµj ,ωj
E0[V ]
subject to µ+ c(ω) = e
(7)
of which the resource constraint requires the total expenditure due to effort allocation into
both projects must sum up to some initial endowment e (some form of internal resources such
as the firm’s retained earnings or owner/manager’s wealth). The investment expenditure on
project A is assumed to be linear in µ, and the per unit cost is normalized to one; the
expenditure on the castle-in-the-air project is assumed to be nonlinear in ω (one can think
that such projects are subject to greater scrutiny), and is denoted by a convex function C(ω),
28
and C ′(.), C ′′(.) > 0. More precisely,
E0[V ] = E0[E(u)] + E0
[max∀i∈I{E(vi|θ, ω)}|φ0
]= hµ+ E0[max
∀i∈I{ φiτθφiτθ + τz
θω︸ ︷︷ ︸≡λiθω
}|φ0]
= hµ+ E0[max∀i∈I{λiθ}|φ0]ω
= hµ+1
2σθφ(0)
Φ(0)
E(
max∀i∈Ij{λi}|φ0
)− E
(min∀i∈Ij{λi}|φ0
)︸ ︷︷ ︸
Expected Belief Dispersion
(8)
The proof for the objective function is provided in the appendix.
4.2. Discussion
It follows from Equation 8 that the manager’s objective function contains an option com-
ponent that is increasing in the scale of variance-inflating Project B and expected investor
belief dispersion. This is also the manager’s resale option. E0[V ] is also a function of the
marginal benefits to investing in the two projects. The expected marginal return to augment
investment scale in project B for the manager is increasing in n, the number of stock market
investors. (Proved in the appendix.) When beliefs are homogeneous, the expected marginal
return to Project B is zero and no investment would be allocated to it.
As such, when the number of investors n in the marketplace increases, there is greater
expected belief dispersion. Since investors have heterogenous beliefs which bias upward their
valuations of project B, the manager optimally invest in the variance-inflating Project B to
maximize stock valuation, and in other words, the manager’s resale option value. Hence,
∂ω∂n> 0 and ∂µ
∂n< 0. In the limit, when n → ∞, this marginal benefit tends to one half the
29
inverse Mills ratio, and optimal ω is set to equate the marginal cost.
Ex-ante, investors form expectations of the firm’s output, which is a function of expected
returns on both types of projects. They will enter and participate in the market until
expected profits just offsets entry costs in the equilibrium. Intuitively, when there’s an
exogenous shock to h, which is the productivity of project A, the expected return to the firm
increases and will attract the entry of more investors. n increases.
Intuitively, if h increases, the manager should shift the investment composition to rel-
atively greater investment in project A. However, as n also increases, from the manager’s
perspective, there are two effects on the scale of project A, µ. First, the marginal return to
project A increases, so µ should be increased. Second, the option component of the man-
ager’s objective function increases with n. That is, expected belief dispersion increases and
the increasing the expected marginal benefit of Project B for the manager and ω should be
increased. If the expected marginal benefit from inflating expected belief dispersion through
ω dominates, ∂ω∂h> 0 and the investment composition is shifted to relatively more investment
in project B. In such a case, uncertainty about the firm’s output accumulates and σ(r) grows.
In Bolton et al. (2006), projects A and B are respectively referred to as “fundamental”
and “castle-in-the-air” projects, reflecting their return and risk structures. In the context of
my data and extant empirical evidence, project A can be represented by CAPX investment,
which has less uncertainty; while project B may be seen as R&D and M&A investments,
which have greater uncertainties about their expected returns.
The theoretical exercise above helps to place my results into perspective. For my first
set of results: in the presence of greater analyst forecast belief dispersion and while holding
other factors constant, the expected belief dispersion about a firm’s returns increases and
the firm maximizes firm value by changing its investment composition to favour project B’s.
30
The same holds true for when mutual fund flow in a certain sector increases, since the fund
flow is a proxy for the number of investors, an increase in n will lead to the same outcome.
Productivity growth, or a shock to h, can explain the second set of results of why a
reinforcement of the composition shift takes place. By itself, productivity growth positively
impacts CAPX’s share and generally have negative impact on R&D and M&A investments,
which is consistent with the intuition discussed previously of h’s effect on µ. At the same
time, productivity growth attracts more investors such that the option value effect dominates.
Therefore, at high levels of productivity growth and belief dispersion, there is a reinforcement
effect.
Several key assumptions drive the results. One, both heterogeneous beliefs and short-
sales constraints exist; two, the investors and owner have a resale option. The analysis also
suggests that greater information transparency will reduce excessive risk taking, because it
leads to more precise information on stochastic projects, reducing the effect from individual
bias.
Empirically, a review of the history of booms and busts shows that market investors and
sentiments have important roles in investment behaviour. As early as the tulip mania in 1637,
investors were willing to buy tulip bulbs at yet higher prices because many expected that the
bulbs can be resold at higher prices. Mackay (1848) recorded that “Nobles, citizens, farmers,
mechanics, seamen, footmen, maidservants, even chimney sweeps and old clotheswomen,
dabbled in tulips.” Later, the South Sea Company’s stock price rose by over 700% during
the 1720s through advertising to investors of its potential profitable trading strategy in South
America, while making no real investments.
Relatedly, the role of more inexperienced or individual investors in price booms is being
noted increasingly. Brennan (2004) argues the participation of first-time investors in the
31
equity markets to contribute to the technology boom in the 1990s, using aggregate U.S. data
on direct equity ownership or through mutual funds or self-directed retirement accounts.
Greenwood and Nagel (2009) find younger mutual fund managers invested heavily in tech-
nology stocks at the height of the technology boom in comparison to their more experienced
and older peers. Using data from other countries, Gong et al. (2010) attribute a continuous
inflow of new investors to be the most significant factor of price appreciation of the Baosteel
call warrants, the first derivative in China after a lengthy suspension. Kaustia and Knupfer
(2011) document new investor entry rates at five-times the average during the technology
boom, which is driven by recent gains by the investors’ peers. More recently and with a
musical twist, Kim and Jung (2013) attribute 800% increase in market capitalization for a
Korean semi-conductor firm – owned by the father of the singer of “Gangnam Style” – in
mere two months to both domestic and foreign individual investor enthusiasm about the
popular song, when there was no material new information about the firm’s fundamentals.
The idea that more investor entry to the stock market increases belief dispersion is con-
sistent with previous studies. Grinblatt and Keloharju (2001), Lamont and Thaler (2003),
and Vissing-Jorgensen (2003) provide evidence that new, unsophisticated, and overconfident
investors are more likely to enter the stock market during booms. While Barber and Odean
(2008) find that individual investors, who are limited in their ability to process informa-
tion on available stocks, tend to purchase attention-grabbing stocks. Greenwood and Nagel
(2009) document that inexperienced investors are more likely to chase the trend (for exam-
ple, loading their portfolios with technology stocks) that contribute to price appreciation.
Antoniou et al. (2012) build on the earlier results and find that asset prices to be less in
line with fundamentals during optimistic periods due to the presence of more optimistic
investors. Taken together, the evidence suggest that more investors enter the stock market
with optimistic expectations in the market during booms that are initiated by some form
32
of productivity growth, and these investors tend to flock to stocks experiencing high growth
and media exposure.
Is it possible that managers are simply at a loss with what to invest in? In my iden-
tification strategy, I conjectured and established a setting in which the loss in analysts led
to greater disagreement or belief dispersion, which I attribute to reduced information. It is
well known that analysts provide information for firm decision makers, too. The reduction
in information from the loss in analyst coverage could impact managers’ investment choices
not because they are trying to exploit disagreement, but because they themselves are not
certain which projects are best for the firm. This line of reasoning is not consistent with two
facts. First, I find a reinforcement effect of the investment composition effect when there
is productivity growth as reported earlier. In this case, the marginal return to capital has
clearly risen and it follows that more CAPX should be made relative to the other two types
of investments. Second, Derrien and Kecskes (2013) find that reduction in analyst coverage,
which increases information asymmetry and raises cost of capital, causes firms to reduce
investment levels in all projects. Therefore, firms do not appear to be investing in any ran-
dom project because they are uncertain which one to pick best as a result of losing expert
advice from analyst reduction. In sum, my results identify a different channel in which the
manager-owner changes investment composition to exploit belief dispersion.
ChapterName
5. Conclusion
This paper provides evidence that corporate investment allocation decisions are sensitive
to belief dispersion. Firms change their investment composition to include more relative
investment in riskier projects such as R&D and M&A. This relationship is robust to controls
33
for firm and industry fundamentals. The composition effect is present even when there is a
positive return shock to CAPX investment, and reinforced when greater belief dispersion is
accompanied by high return shock. To explain the empirical findings, I build a simple model
based on Bolton et al. (2006) to explain the effect that belief dispersion have on investment
composition. In a market with heterogeneous investor opinions about uncertain returns,
along with limits to arbitrage or significant short selling constraints, stock prices are bid
up to the highest subjective valuations. Investor beliefs then matter for firm investment
allocation when the manager-owner has a resale option, i.e., the manager-owner can sell firm
shares to more optimistic investors. Since investors disagree more on riskier projects and it
is more likely that someone will value riskier projects more highly when belief dispersion is
greater, the firm owner’s resale option grows in expected value as belief dispersion increases,
encouraging more investment allocation to riskier projects. Firms that are more productive
may be more incentivized to invest in riskier projects at a time of high market valuations,
because higher expected returns attract more investors, which leads to greater likelihood
of more optimistic valuations. My results then suggest a channel of how efficient capital
allocation during the boom can lead to misallocation, which can potentially explain the
phenomenon of countercyclical capital misallocation found in studies such as Eisfeldt and
Rampini (2008) and Bloom et al. (2012).
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38
A. Appendix
A.1. Data Definition
Categorization of Mutual Funds into Sector Funds To categorize a fund’s investment stylesand objectives, the database uses a combination of four indicators: the Wiesenberger Objec-tive codes prior to 1993, the Strategic Insight Objective codes between 1993 and 1998, theLipper Objective codes starting 1998, and the ”POLICY” variable whenever it is available.When there is a conflict, the fund is allocated to the sector it is most frequently associatedwith; in the case of a tie, I cross-reference the fund name and published fund prospectus todetermine the appropriate sector. The identified funds invest in the following ten sectors:Consumer Goods, Consumer Services, Finance, Gold & Precious Metals, Health, NaturalResource & Energy, Real Estate, Technology, Telecommunications, Utilities. These mu-tual fund industries are then mapped to industries identified by the SIC-code and then theFama-French 49 industry codes. The precise mapping is presented in Table 1.
A fund belongs to a particular sector if its investment objective meets the following:Wiesenberger Objective Code = ENR, FIN, GPM, HLT, TCH, UTL; Lipper Objective code=AU, CG, CS, FS, H, NR, S, TK, TL, RE, UT; Strategic Insight Objective code = ENV,FIN, GLD, HLT, NTR, RLE, SEC, TEC, UTI; Policy = Spec.
A.2. Proofs
Proof for Equation 8 and Proof of Discussion: The expected marginal benefit of allocating
effort in the castle-in-the-air project is E
[max∀i∈Ij{λiθ}|φ0
], which can be written as:
E
[max∀i∈Ij{λiθ}|φ0
]=
1
2E
[max∀i∈Ij{λi}θ|φ0, θ > 0
]+
1
2E
[min∀i∈Ij{λi}θ|φ0, θ < 0
]=
1
2E
(max∀i∈Ij{λi}|φ0
)E [θ|θ > 0] +
1
2E
(min∀i∈Ij{λi}|φ0
)E [θ|θ < 0]
and using inverse Mills ratio on θ ∼ N(0, σ2θ), we have:
E [θ|θ > 0] = σθφ(0)
1− Φ(0), E [θ|θ < 0] = σθ
−φ(0)
Φ(0), and 1− Φ(0) = Φ(0)
=1
2σθφ(0)
Φ(0)
[E
(max∀i∈I{λi}|φ0
)− E
(min∀i∈I{λi}|φ0
)]Therefore, for the manager, the expected marginal benefit to investing in the castle-in-the-airproject is a function of the expected belief divergence among investors in industry j, whichis itself an increasing function in the number of investors n in the industry.
That is, for any conditional distribution F (X|x0), and a set of i.i.d. random variables
39
X, with X = {x1, x2, ..., xn}
P (xmax < a|x0)
= P (x1 < a|x0)P (x2 < a|x0)...P (xn < a|x0)
= F n(x < a|x0)
Hence, it follows that for any n′ > n, F n(x|x0) > F n′(x|x0), and using the property of first
order stochastic dominance, E
(max∀i∈I′{λi}|λ0
)> E
(max∀i∈I{λi}|λ0
), where set I contains n
investors and set I ′ contains n′ investors, and n′ > n. Similarly, applying the above in reverse
also follows that E
(min∀i∈I′{λi}|λ0
)< E
(min∀i∈I{λi}|λ0
), where set I contains n investors and
set I ′ contains n′ investors, and n′ > n.�
40
Table 1: Mapping of Mutual Fund Sector Codes to Fama-French 49 Industry Codes
Mutual Fund Sectors Fama-French 49 Industries
1 Gold 27 Gold, Precious Metals2 Consumer Goods 9 Consumer goods3 Consumer Services 33 Personal Services4 Financial Services 45 Banking5 Health 11 Health Care
12 Medical Equipment6 Natural Resources 30 Oil, Petroleum and Natural Gas
29 Coal28 Non-Metallic and Industrial Metal Mining
7 Technology 35 Computer Hardware36 Computer Software 37 Chips Electronic Equipment
8 Telecommunication 32 Telecommunication9 Utilities 31 Utilities10 Real Estate 47 Real Estate
41
Figure 1: Number of Estimates and Analyst Forecast Dispersion
This graph plots, for each industry sector, the evolution of the average analyst quarter-ahead EPS forecastdispersion (y-axis on the left) and number of estimates (y-axis on the right) over time.
42
Table 2: Summary Statistics
Age is the number of quarters since the first quarter this firm appears on CRSP. Firm Size is ln(TotalAssets). Leverage is long termdebt over last period’s total assets. Tobin’s Q is computed as market value of assets divided by book value of assets. ROE is computedby earnings over last period’s book equity. Cash Flow is cash flow, sum of earnings before extraordinary items and depreciation andamortization, scaled by last period’s PPE(plant, property, and equipment). Gross Margin is (net sales - cost of goods sold)/net sales.ROA is operating income before interest, taxes, depreciation, and amortization, scaled by book value of total assets. Stock Return isquarterly stock return adjusted for industry average. Asset Growth growth rate of total assets. Sales Growth growth rate of net sales.σ(Sales Growth), computed as the standard deviation of net sales growth rates for a 8-quarter forward rolling window as in Rameyand Ramey (1995). Cash Flow Volatility, computed as ln[EBITAt − EBITAt−1] as in Shumway (2001).
CAPX is the ratio of physical capital expenditure to total investment expenditure (physical capital expenditure + R&D expenditure+ M&A expenditure). R&D is the ratio of research and development expenditure to total investment expenditure (physical capitalexpenditure + R&D expenditure + M&A expenditure). M&A is the ratio of mergers and acquisition expenditure to total investmentexpenditure (physical capital expenditure + R&D expenditure + M&A expenditure).
TFP Growth is quarter-over-quarter growth in TFP, and TFP is estimated using the Olley-Pakes (1996) method and is described in thedata section in the text. Idiosyncratic Sales Growth is the idiosyncratic component of Hodrick-Prescott filtered quarter-over-quarterchange in net sales. Number of Estimates is the mean number of EPS estimates recorded in I/B/E/S for the firm every quarter. MeanEstimates is the mean EPS estimate (quarter ahead) for the firm. Estimate Dispersion (DISP) is analyst forecast standard deviationover absolute mean forecast value for the firm. Industry New Fund flow is the new fund flow to a particular sector in the period,
computed as TNA-weighted industry average of ffk,t =TNAk,t−TNAk,t−1×(1+rk,t)
TNAk,t, where TNA is total net asset in fund k in the
particular sector.
Obs Mean Std. Dev. 25th 50th 75th
Firm Characteristicslog(Age) 188653 3.71 0.79 3.14 3.85 4.34log(Firm Size) 188661 6.57 1.86 5.18 6.45 7.77Leverage 187011 0.17 0.18 0.01 0.12 0.28Tobin’s Q 188661 1.77 1.99 0.82 1.25 2.05ROE 185709 0.02 0.28 0.00 0.03 0.05Cash Flow 161563 0.10 4.35 0.04 0.10 0.25Gross Margin 188661 0.18 2.80 0.22 0.36 0.55ROA 168682 0.03 0.04 0.01 0.03 0.05Market Excess Return 185717 0.01 0.31 -0.14 -0.01 0.1Asset Growth 184509 0.03 0.13 -0.01 0.02 0.05Sales Growth 106459 0.03 0.26 -0.04 0.03 0.1σ(Sales Growth) 83048 0.16 0.19 0.06 0.11 0.19σ(Cash Flow) 152226 1.22 2.06 -0.17 1.16 2.57σ(Profitability) 188065 0.06 2.72 0.00 0.01 0.04
CEO Tenure (quarters) 114756 23.16 22.52 7.00 18.00 31.00Number of Patents 45477 25.94 60.54 1.00 4.00 16.00Patent per Million R&D Expenditure 31815 3.59 32.22 0.26 0.84 2.67
Investment RatiosCAPX 182934 0.71 0.37 0.33 1.00 1.00R&D 182934 0.23 0.34 0.00 0.00 0.50M&A 182934 0.06 0.21 0.00 0.00 0.00
ProductivityTFP Growth 95234 0.01 0.25 -0.06 0.02 0.09Idiosyncratic Sales Growth 160488 0.37 84.62 -24.69 -1.75 17.03
Analyst EPS Forecast, Quarter-aheadNumber of Estimates 188661 7.50 6.13 3.00 5.00 10.00Mean Estimates 188661 1.03 1.92 0.19 0.60 1.50Estimate Dispersion (DISP) 188661 0.24 0.41 0.04 0.08 0.20
Mutual Fund FlowIndustry New Money Flow 77628 0.18 1.50 -0.01 0.03 0.10
43
Tab
le3:
InvestmentComposition
and
BeliefDispersion
(Analyst
Fore
cast
Dispersion)
This
table
rep
ort
spanel
regre
ssio
nre
sult
sof
invest
ment
com
posi
tion
on
belief
dis
pers
ion.
The
dep
endent
vari
able
sare
invest
ment
share
sin
CA
PX
,R
&D
,and
M&
A,
resp
ecti
vely
,and
const
ructe
das
the
invest
ment
ineach
typ
eover
the
tota
lin
vest
ment
exp
endit
ure
,w
hic
his
asu
mover
these
invest
ments
.T
he
measu
refo
rb
elief
dis
pers
ion
isanaly
stE
PS
fore
cast
dis
pers
ion.
All
expla
nato
ryvari
able
sare
lagged
by
4quart
ers
.E
stim
ate
Dis
persi
on
(DIS
P)
isanaly
stfo
recast
standard
devia
tion
over
abso
lute
mean
fore
cast
valu
efo
rth
efi
rm.
TF
PG
row
this
quart
er-
over-
quart
er
gro
wth
inT
FP
,and
TF
Pis
est
imate
dusi
ng
the
Olley-P
akes
(1996)
meth
od
and
isdesc
rib
ed
inth
edata
secti
on
inth
ete
xt.
Tobin
’sQ
iscom
pute
das
mark
et
valu
eof
ass
ets
div
ided
by
book
valu
eof
ass
ets
.C
ash
Flo
wis
cash
flow
,su
mof
earn
ings
befo
reextr
aord
inary
item
sand
depre
cia
tion
and
am
ort
izati
on,
scale
dby
last
peri
od’s
PP
E(p
lant,
pro
pert
y,
and
equip
ment)
.R
OE
iscom
pute
dby
earn
ings
over
last
peri
od’s
book
equit
y.
Siz
eisln
(TotalAssets
).A
ge
islo
gof
the
num
ber
of
quart
ers
since
the
firs
tquart
er
this
firm
app
ears
on
CR
SP
.L
evera
ge
islo
ng
term
debt
over
last
peri
od’s
tota
lass
ets
.
Inth
eta
ble
,“*”
denote
ssi
gnifi
cance
at
the
10%
level;
“**”
denote
ssi
gnifi
cance
at
the
5%
level;
“***”
denote
ssi
gnifi
cance
at
the
1%
level.
The
bra
ckets
beneath
coeffi
cie
nt
est
imate
sconta
int-
stati
stic
scom
pute
dfr
om
hete
rosk
edast
icit
y-r
obust
standard
err
ors
clu
stere
dby
firm
,w
here
Nu
m.
Fir
mis
identi
fied.
Tim
efixed
eff
ects
at
the
quart
er
level,
and
firm
fixed
eff
ects
are
inclu
ded.
CA
PX
’sShare
R&
D’s
Share
M&
A’s
Share
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
DIS
P-0
.0218***
-0.0
037**
-0.0
034**
0.0
179***
0.0
024**
0.0
023**
0.0
039***
0.0
013***
0.0
011***
(-3.3
9)
(-2.0
9)
(-2.0
8)
(5.4
0)
(2.5
3)
(2.5
2)
(7.3
2)
(3.6
8)
(3.6
3)
DIS
P×
TF
PG
row
th-0
.0025*
0.0
017**
0.0
008**
(-1.7
4)
(2.2
8)
(2.2
0)
TF
PG
row
th0.0
165***
0.0
054**
0.0
051**
-0.0
143***
-0.0
021*
-0.0
021*
-0.0
022
-0.0
033
-0.0
030*
(3.3
2)
(2.3
0)
(2.2
6)
(-2.9
5)
(-1.7
5)
(-1.7
8)
(-0.9
6)
(-1.3
7)
(-1.8
1)
Tobin
’sQ
0.0
215***
0.0
051***
0.0
051***
-0.0
254***
-0.0
076***
-0.0
076***
0.0
039***
0.0
025***
0.0
025***
(12.2
6)
(5.8
9)
(5.8
9)
(-10.8
2)
(-7.7
4)
(-7.7
4)
(6.0
4)
(2.8
6)
(2.8
6)
Cash
Flo
w0.0
070**
0.0
005
0.0
005
-0.0
082**
-0.0
011
-0.0
011
0.0
012*
0.0
006*
0.0
006*
(2.1
4)
(1.3
9)
(1.3
8)
(-2.2
3)
(-0.2
9)
(-0.2
9)
(1.7
9)
(1.9
5)
(1.9
5)
RO
E0.0
672***
0.0
131
0.0
133
-0.0
901***
-0.0
372***
-0.0
373***
0.0
229***
0.0
241***
0.0
240***
(5.0
6)
(1.6
2)
(1.6
3)
(-5.1
2)
(-3.8
6)
(-3.8
5)
(3.5
8)
(3.4
0)
(3.3
9)
Siz
e0.0
266***
0.0
228***
0.0
228***
-0.0
215***
-0.0
051
-0.0
051
-0.0
051***
-0.0
177***
-0.0
177***
(4.7
1)
(5.5
2)
(5.5
2)
(-6.4
1)
(-1.4
7)
(-1.4
7)
(-7.0
1)
(-5.9
6)
(-5.9
6)
Age
0.0
104
0.0
099
0.0
099
0.0
064
0.0
037
0.0
037
-0.0
168***
-0.0
136**
-0.0
136**
(0.0
6)
(1.2
0)
(1.2
1)
(1.0
7)
(0.5
4)
(0.5
4)
(-3.6
8)
(-2.4
9)
(-2.4
9)
Levera
ge
0.0
459***
0.0
497***
0.0
498***
-0.0
245***
-0.0
155
-0.0
155
-0.0
214
-0.0
342***
-0.0
343***
(17.3
6)
(3.5
4)
(3.5
4)
(-18.2
7)
(-1.4
6)
(-1.4
6)
(-0.0
4)
(-6.2
2)
(-6.2
3)
Const
ant
0.6
064***
0.6
255***
0.6
255***
0.3
585***
0.1
938***
0.1
938***
0.0
351***
0.1
807***
0.1
807***
(24.5
1)
(21.4
6)
(21.4
6)
(14.8
7)
(7.9
9)
(7.9
9)
(6.1
9)
(8.0
5)
(8.0
5)
Fir
mF
EN
oY
es
Yes
No
Yes
Yes
No
Yes
Yes
Tim
eF
EN
oY
es
Yes
No
Yes
Yes
No
Yes
Yes
R2
0.1
322
0.6
966
0.6
966
0.1
627
0.8
185
0.8
185
0.0
040
0.1
172
0.1
172
Adj.R
20.6
771
0.6
771
0.8
068
0.8
068
0.0
604
0.0
604
Num
.O
bs
76064
76064
76064
76064
76064
76064
76064
76064
76064
Num
.F
irm
s4508
4508
4508
4508
4508
4508
4508
4508
4508
44
Tab
le4:
InvestmentComposition
and
BeliefDispersion
(New
Fund
Flow)
This
table
rep
ort
spanel
regre
ssio
nre
sult
sof
invest
ment
com
posi
tion
on
belief
dis
pers
ion.
The
dep
endent
vari
able
sare
invest
ment
share
sin
CA
PX
,R
&D
,and
M&
A,
resp
ecti
vely
,and
const
ructe
das
the
invest
ment
ineach
typ
eover
the
tota
lin
vest
ment
exp
endit
ure
,w
hic
his
asu
mover
these
invest
ments
.T
he
measu
refo
rb
elief
dis
pers
ion
isnew
secto
rfu
nd
flow
.
All
expla
nato
ryvari
able
sare
lagged
by
4quart
ers
.F
un
dF
low
isth
enew
fund
flow
tom
utu
al
funds
apart
icula
rse
cto
rin
the
peri
od,
com
pute
das
TN
A-w
eig
hte
din
dust
ryavera
ge
of
ffk,t
=[TNA
k,t
−TNA
k,t
−1×
(1+rk,t
)]/TNA
k,t
,w
here
TN
Ais
tota
lnet
ass
et
infu
ndk
inth
epart
icula
rse
cto
r.T
FP
Gro
wth
isquart
er-
over-
quart
er
gro
wth
inT
FP
,and
TF
Pis
est
imate
dusi
ng
the
Olley-P
akes
(1996)
meth
od
and
isdesc
rib
ed
inth
edata
secti
on
inth
ete
xt.
Tobin
’sQ
iscom
pute
das
mark
et
valu
eof
ass
ets
div
ided
by
book
valu
eof
ass
ets
.C
ash
Flo
wis
cash
flow
,su
mof
earn
ings
befo
reextr
aord
inary
item
sand
depre
cia
tion
and
am
ort
izati
on,
scale
dby
last
peri
od’s
PP
E(p
lant,
pro
pert
y,
and
equip
ment)
.R
OE
iscom
pute
dby
earn
ings
over
last
peri
od’s
book
equit
y.
Siz
eisln
(TotalAssets
).A
ge
islo
gof
the
num
ber
of
quart
ers
since
the
firs
tquart
er
this
firm
app
ears
on
CR
SP
.L
evera
ge
islo
ng
term
debt
over
last
peri
od’s
tota
lass
ets
.
Inth
eta
ble
,“*”
denote
ssi
gnifi
cance
at
the
10%
level;
“**”
denote
ssi
gnifi
cance
at
the
5%
level;
“***”
denote
ssi
gnifi
cance
at
the
1%
level.
The
bra
ckets
beneath
coeffi
cie
nt
est
imate
sconta
int-
stati
stic
scom
pute
dfr
om
hete
rosk
edast
icit
y-r
obust
standard
err
ors
clu
stere
dby
firm
,w
here
Nu
m.
Fir
mis
identi
fied.
Tim
efixed
eff
ects
at
the
quart
er
level,
and
firm
fixed
eff
ects
are
inclu
ded.
CA
PX
’sShare
R&
D’s
Share
M&
A’s
Share
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Fund
Flo
w-0
.0072***
-0.0
024*
-0.0
022*
0.0
061***
0.0
019***
0.0
017**
0.0
011***
0.0
005*
0.0
005*
(-8.5
8)
(-1.9
5)
(-1.6
9)
(10.0
1)
(2.7
5)
(2.4
3)
(3.0
1)
(1.7
3)
(1.7
3)
Fund
Flo
w×
TF
PG
row
th-0
.0044**
0.0
038**
0.0
006
(-2.2
6)
(2.5
1)
(0.6
6)
TF
PG
row
th0.0
043
0.0
037
0.0
047
-0.0
028
-0.0
015
-0.0
023
-0.0
015**
-0.0
022**
-0.0
024**
(0.3
5)
(0.1
0)
(0.2
6)
(-1.5
6)
(-1.2
0)
(-1.6
2)
(2.4
4)
(-1.6
8)
(-1.6
6)
Tobin
’sQ
0.0
141***
0.0
039***
0.0
039***
-0.0
178***
-0.0
069***
-0.0
069***
0.0
037***
0.0
030***
0.0
030***
(11.4
4)
(6.2
9)
(6.2
7)
(-9.6
7)
(-4.3
0)
(-4.2
8)
(6.8
4)
(5.5
3)
(5.5
3)
Cash
Flo
w0.0
016*
0.0
020***
0.0
020***
-0.0
019*
-0.0
023***
-0.0
023***
0.0
003*
0.0
003*
0.0
003*
(1.7
4)
(2.9
4)
(2.9
5)
(-1.9
2)
(-3.0
6)
(-3.0
8)
(1.9
6)
(1.8
1)
(1.8
2)
RO
E0.1
094***
0.0
673***
0.0
672***
-0.1
153***
-0.0
759***
-0.0
758***
0.0
059
0.0
086*
0.0
086*
(2.9
1)
(2.7
0)
(2.7
0)
(-2.8
6)
(-2.6
6)
(-2.6
6)
(1.5
0)
(1.8
4)
(1.8
4)
Siz
e0.0
205***
0.0
126
0.0
126
-0.0
160***
-0.0
057***
-0.0
057***
-0.0
045***
-0.0
069***
-0.0
069***
(3.1
3)
(0.7
7)
(0.7
8)
(-5.4
0)
(-3.7
5)
(-3.7
6)
(-12.4
7)
(-12.0
5)
(-12.0
5)
Age
0.0
259***
0.0
264***
0.0
264***
-0.0
160**
-0.0
193***
-0.0
193***
-0.0
099***
-0.0
072***
-0.0
072***
(3.6
7)
(4.6
1)
(4.6
1)
(-2.3
0)
(-3.3
8)
(-3.3
8)
(-7.0
3)
(-4.5
1)
(-4.5
1)
Levera
ge
0.6
944***
0.2
015***
0.2
015***
-0.6
919***
-0.1
906***
-0.1
906***
-0.0
026
-0.0
109
-0.0
109
(26.2
5)
(8.1
8)
(8.1
8)
(-27.0
2)
(-8.8
5)
(-8.8
5)
(-0.3
6)
(-1.5
6)
(-1.5
6)
Const
ant
0.4
630***
0.7
817***
0.7
817***
0.5
001***
0.2
103***
0.2
103***
0.0
369***
0.0
081
0.0
081
(19.0
8)
(28.1
6)
(28.1
6)
(20.9
6)
(7.5
6)
(7.5
6)
(6.9
4)
(0.7
3)
(0.7
3)
Fir
mF
EN
oY
es
Yes
No
Yes
Yes
No
Yes
Yes
Tim
eF
EN
oY
es
Yes
No
Yes
Yes
No
Yes
Yes
R2
0.1
832
0.4
497
0.4
497
0.2
049
0.4
878
0.4
878
0.0
090
0.0
171
0.0
171
Num
.O
bs
65045
65045
65045
65045
65045
65045
65045
65045
65045
Num
.F
irm
s3555
3555
3555
3555
3555
3555
3555
3555
3555
45
Tab
le5:
InvestmentComposition
and
BeliefDispersion,Altern
ativeControls
This
table
rep
ort
spanel
regre
ssio
nre
sult
sof
invest
ment
com
posi
tion
on
belief
dis
pers
ion.
The
dep
endent
vari
able
sare
invest
ment
share
sin
CA
PX
,R
&D
,and
M&
A,
resp
ecti
vely
,and
const
ructe
das
the
invest
ment
ineach
typ
eover
the
tota
lin
vest
ment
exp
endit
ure
,w
hic
his
asu
mover
these
invest
ments
.A
ddit
ional
contr
ols
as
inth
ebase
line
specifi
cati
on
are
inclu
ded.
All
expla
nato
ryvari
able
sare
lagged
by
4quart
ers
.E
stim
ate
Dis
persi
on
(DIS
P)
isanaly
stfo
recast
standard
devia
tion
over
abso
lute
mean
fore
cast
valu
efo
rth
efi
rm.
TF
PG
row
this
quart
er-
over-
quart
er
gro
wth
inT
FP
,and
TF
Pis
est
imate
dusi
ng
the
Olley-P
akes
(1996)
meth
od
and
isdesc
rib
ed
inth
edata
secti
on
inth
ete
xt.
An
aly
stC
overa
ge
isth
enum
ber
of
analy
sts
pro
vid
ing
est
imate
sfo
rth
efirm
.P
ate
nts
per
Mil
lion
R&
Dis
the
rati
oof
pate
nts
over
R&
Dexp
endit
ure
.C
um
ula
tive
CE
OT
en
ure
isth
ecum
ula
tive
years
inoffi
ce
of
the
pre
sent
CE
O.
CE
OT
urn
over
isa
dum
my
that
takes
on
1if
anew
pers
on
isin
state
das
the
CE
O.
Sto
ck
Retu
rn
isth
efirm
’sexcess
stock
retu
rnover
the
valu
e-w
eig
hte
dm
ark
et
index.
Tobin
’sQ
iscom
pute
das
mark
et
valu
eof
ass
ets
div
ided
by
book
valu
eof
ass
ets
.C
ash
Flo
wis
cash
flow
,su
mof
earn
ings
befo
reextr
aord
inary
item
sand
depre
cia
tion
and
am
ort
izati
on,
scale
dby
last
peri
od’s
PP
E(p
lant,
pro
pert
y,
and
equip
ment)
.R
OE
iscom
pute
dby
earn
ings
over
last
peri
od’s
book
equit
y.
Siz
eisln
(TotalAssets
).A
ge
islo
gof
the
num
ber
of
quart
ers
since
the
firs
tquart
er
this
firm
app
ears
on
CR
SP
.L
evera
ge
islo
ng
term
debt
over
last
peri
od’s
tota
lass
ets
.
Inth
eta
ble
,“*”
denote
ssi
gnifi
cance
at
the
10%
level;
“**”
denote
ssi
gnifi
cance
at
the
5%
level;
“***”
denote
ssi
gnifi
cance
at
the
1%
level.
The
bra
ckets
beneath
coeffi
cie
nt
est
imate
sconta
int-
stati
stic
scom
pute
dfr
om
hete
rosk
edast
icit
y-r
obust
standard
err
ors
clu
stere
dby
firm
,w
here
Nu
m.
Fir
mis
identi
fied.
Tim
efixed
eff
ects
at
the
quart
er
level,
and
firm
fixed
eff
ects
are
inclu
ded.
CA
PX
’sShare
R&
D’s
Share
M&
A’s
Share
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
DIS
P-0
.0034**
-0.0
031***
-0.0
037**
-0.0
019*
-0.0
020*
-0.0
031***
0.0
023**
0.0
024**
0.0
021**
0.0
016*
0.0
016*
0.0
024**
0.0
011***
0.0
013**
0.0
014*
0.0
013*
0.0
019*
0.0
017**
(-2.0
8)
(-3.5
9)
(-2.2
0)
(-1.9
3)
(-1.9
5)
(-3.6
7)
(2.5
2)
(2.5
4)
(2.0
6)
(1.9
6)
(0.9
6)
(2.5
0)
(3.6
3)
(2.4
4)
(1.7
8)
(2.1
4)
(2.1
5)
(2.6
2)
DIS
P×
TF
PG
row
th-0
.0025*
-0.0
030*
-0.0
028**
-0.0
033*
-0.0
034*
-0.0
036*
0.0
017**
0.0
018**
0.0
019*
0.0
021**
0.0
023**
0.0
028*
0.0
008*
0.0
012*
0.0
009
0.0
012
0.0
012
0.0
008*
(-1.7
4)
(-1.6
9)
(-2.1
8)
(-1.8
7)
(-1.9
1)
(-1.6
7)
(2.2
8)
(2.1
2)
(1.9
6)
(2.2
0)
(2.1
7)
(1.9
5)
(2.2
0)
(1.9
4)
(1.2
7)
(1.5
8)
(1.5
7)
(1.9
1)
TF
PG
row
th0.0
051**
0.0
051**
0.0
040*
0.0
037
0.0
038
0.0
038**
-0.0
021*
-0.0
021*
-0.0
028
-0.0
008
-0.0
008
-0.0
012
-0.0
030*
-0.0
030**
-0.0
012
-0.0
029
-0.0
030
-0.0
026**
(2.2
6)
(2.1
1)
(1.8
3)
(0.8
5)
(0.8
5)
(2.1
3)
(1.7
8)
(1.7
2)
(1.3
1)
(-0.1
4)
(-0.1
3)
(1.3
8)
(-1.8
1)
(-2.2
0)
(-1.3
8)
(-0.4
5)
(-0.4
5)
(-2.0
8)
Analy
stC
overa
ge
0.0
034**
-0.0
035*
0.0
001**
(2.4
2)
(-1.6
7)
(2.1
7)
Pate
nts
per
Million
R&
D-0
.0021
0.0
037**
-0.0
016*
(-0.7
8)
(2.1
7)
(-1.6
5)
Cum
ula
tive
CE
OT
enure
0.0
004**
-0.0
005*
0.0
001
(2.3
4)
(-1.7
2)
(0.4
7)
CE
OT
urn
over
0.0
268
-0.0
172**
-0.0
096*
(0.8
3)
(-2.1
8)
(-1.7
1)
Sto
ckR
etu
rn0.0
040*
-0.0
060***
0.0
021**
(1.6
5)
(-2.9
5)
(2.1
5)
Fir
mF
EY
es
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Tim
eF
EY
es
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Adj.R
20.6
771
0.6
793
0.6
362
0.6
742
0.6
742
0.6
771
0.8
068
0.8
075
0.6
159
0.8
102
0.8
102
0.8
068
0.0
604
0.0
615
0.0
575
0.0
661
0.0
662
0.0
604
Num
.O
bs
76064
76064
10002
27854
27854
76064
76064
76064
10002
27854
27854
76064
76064
76064
10002
27854
27854
76064
Num
.F
irm
s4508
4508
1130
3300
3300
4508
4508
4508
1130
3300
3300
4508
4508
4508
1130
3300
3300
4508
46
Tab
le6:
Two-sta
geLeast-S
quare
s(2
SLS)Regre
ssion
with
Instru
mentforBeliefDispersion
This
table
rep
ort
sth
ere
sult
sfr
om
the
inst
rum
enta
lvari
able
(IV
)appro
ach
,in
whic
hb
elief
dis
pers
ion
(DIS
P)
isin
stru
mente
dw
ithMERGER
(merg
ers
inbro
kera
ge
house
s).
Both
reduced
form
panel
regre
ssio
nre
sult
sof
invest
ment
com
posi
tion
on
the
inst
rum
entMERGER
.T
he
dep
endent
vari
able
sare
invest
ment
share
sin
CA
PX
,R
&D
,and
M&
A,
resp
ecti
vely
,and
const
ructe
das
the
invest
ment
ineach
typ
eover
the
tota
lin
vest
ment
exp
endit
ure
,w
hic
his
asu
mover
these
invest
ments
.A
ddit
ional
contr
ols
as
inth
ebase
line
specifi
cati
on
are
inclu
ded.
All
expla
nato
ryvari
able
sare
lagged
by
4quart
ers
,in
clu
ded
by
not
show
nare
.T
FP
Gro
wth
isquart
er-
over-
quart
er
gro
wth
inT
FP
,and
TF
Pis
est
imate
dusi
ng
the
Olley-P
akes
(1996)
meth
od
and
isdesc
rib
ed
inth
edata
secti
on
inth
ete
xt.
Tobin
’sQ
iscom
pute
das
mark
et
valu
eof
ass
ets
div
ided
by
book
valu
eof
ass
ets
.C
ash
Flo
wis
cash
flow
,su
mof
earn
ings
befo
reextr
aord
inary
item
sand
depre
cia
tion
and
am
ort
izati
on,
scale
dby
last
peri
od’s
PP
E(p
lant,
pro
pert
y,
and
equip
ment)
.R
OE
iscom
pute
dby
earn
ings
over
last
peri
od’s
book
equit
y.
Siz
eisln
(TotalAssets
).A
ge
islo
gof
the
num
ber
of
quart
ers
since
the
firs
tquart
er
this
firm
app
ears
on
CR
SP
.L
evera
ge
islo
ng
term
debt
over
last
peri
od’s
tota
lass
ets
.
Inth
eta
ble
,“*”
denote
ssi
gnifi
cance
at
the
10%
level;
“**”
denote
ssi
gnifi
cance
at
the
5%
level;
“***”
denote
ssi
gnifi
cance
at
the
1%
level.
The
bra
ckets
beneath
coeffi
cie
nt
est
imate
sconta
int-
stati
stic
scom
pute
dfr
om
hete
rosk
edast
icit
y-r
obust
standard
err
ors
clu
stere
dby
firm
,w
here
Nu
m.
Fir
mis
identi
fied.
Tim
efixed
eff
ects
at
the
quart
er
level,
and
firm
fixed
eff
ects
are
inclu
ded.
Reduced
Form
Fir
stSta
ge
Second
Sta
ge
CA
PX
’sShare
R&
D’s
Share
M&
A’s
Share
DIS
PC
AP
X’s
Share
R&
D’s
Share
M&
A’s
Share
ME
RG
ER
-0.0
063*
0.0
049**
0.0
014*
0.0
586**
(-1.8
3)
(2.4
5)
(1.6
8)
(1.9
7)
DIS
P-0
.1669*
0.1
284*
0.0
385*
(-1.8
8)
(1.6
9)
(1.7
3)
Fir
mC
hara
cte
rist
ics
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Fir
m&
Tim
eF
EY
es
Yes
Yes
Yes
Yes
Yes
Yes
Num
.O
bs
48750
48750
48750
48750
48750
48750
48750
R2
0.6
984
0.8
057
0.0
789
0.0
315
F-S
tati
stic
8.6
9
47
Table 7: Fractional Response Model
This table reports the results of investment composition on belief dispersion, estimated with a fractional probit model. The dependentvariables are investment shares in CAPX, R&D, and M&A, respectively, and constructed as the investment in each type over the totalinvestment expenditure, which is a sum over these investments. Additional controls as in the baseline specification are included.
In the table, “*” denotes significance at the 10% level; “**” denotes significance at the 5% level; “***” denotes significance at the 1%level. The brackets beneath coefficient estimates contain t-statistics computed from heteroskedasticity-robust standard errors clusteredby firm, where Num. Firm is identified. Time fixed effects at the quarter level, and firm fixed effects are included.
CAPX’s Share R&D’s Share M&A’s Share
(1) (2) (3) (4) (5) (6)
DISP -0.0151** -0.0148* 0.0134*** 0.0120*** 0.0017*** 0.0028***(-2.12) (-1.88) (3.19) (2.84) (4.21) (3.83)
TFP Growth 0.0073* 0.0065* -0.0059** -0.0048* -0.0014 -0.0017(1.93) (1.84) (-2.01) (-1.93) (-1.53) (-1.39)
DISP × TFP Growth -0.0013* 0.0092* -0.0079*(-1.67) (1.95) (-1.77)
Firm Characteristics Yes Yes Yes Yes Yes YesNum. Observations 78807 78807 78807 78807 78807 78807
48
Tab
le8:Perform
ance,In
vestments,and
Dispersion
This
table
rep
ort
spanel
regre
ssio
nre
sult
sof
vari
ous
futu
rep
erf
orm
ance
and
firm
risk
measu
res
on
invest
ment
com
posi
tion.
The
refe
rence
invest
ment
mix
isM
&A
’ssh
are
and
isom
itte
d.
The
dep
endent
vari
able
sare
resp
ecti
vely
:th
eavera
ge
of
Gro
ssM
arg
inof
the
four
quart
ers
forw
ard
from
tim
et,
com
pute
das
(net
sale
s-
cost
of
goods
sold
)/net
sale
s.R
OA
of
the
four
quart
ers
forw
ard
from
tim
et,
com
pute
das
the
op
era
ting
incom
eb
efo
rein
tere
st,
taxes,
depre
cia
tion,
and
am
ort
izati
on,
scale
dby
book
valu
eof
tota
lass
ets
.A
sset
Tu
rn
over
of
the
four
quart
ers
forw
ard
from
tim
et,
com
pute
das
sale
ssc
ale
dby
tota
lass
ets
.S
ale
sG
row
thof
the
four
quart
ers
forw
ard
from
tim
et,
com
pute
das
gro
wth
rate
of
net
sale
s.σ
(Cash
)is
cash
flow
vola
tility
of
four
quart
ers
forw
ard
from
tim
et,
com
pute
dasln
[EBITA
t−EBITA
t−
1]
as
inShum
way
(2001).σ
(Pro
fita
bil
ity)
isth
evola
tility
of
pro
fita
bilit
y,
whic
hfo
llow
sth
ecom
puta
tion
inH
ob
erg
and
Phillips
(2010)
by
regre
ssin
gR
OE
on
lagged
RO
Efo
rall
firm
sin
each
indust
ryand
findin
gth
est
andard
devia
tion
of
the
resi
duals
.σ
(Sto
ckR
et)
isfo
ur
quart
ers
ahead
avera
ged
standard
devia
tion
of
month
lyst
ock
retu
rn.σ
(RO
A)
isst
andard
devia
tion
of
RO
Aw
ith
afo
ur
quart
ers
ahead
rollin
gw
indow
.σ
(Sale
sGr4q)
isth
est
andard
devia
tion
of
net
sale
sgro
wth
rate
sfo
ra
4-q
uart
er
forw
ard
rollin
gw
indow
as
inR
am
ey
and
Ram
ey
(1995),
andσ
(Sale
sGr8q)
isth
e8-q
uart
er
vers
ion.
Market-
to-B
ook
ism
ark
et
valu
eof
ass
ets
tob
ook
valu
eof
ass
ets
.C
ash
Flo
wis
the
sum
of
earn
ings
befo
reextr
aord
inary
item
sand
depre
cia
tion
and
am
ort
izati
on,
scale
dby
last
peri
od’s
pro
pert
y,
pla
nt,
and
equip
ment.
RO
Eis
com
pute
dby
earn
ings
over
last
peri
od’s
book
equit
y.
Fir
mS
ize
isln
(TotalAssets
).L
evera
ge
islo
ng
term
debt
over
last
peri
od’s
tota
lass
ets
.
Inth
eta
ble
,“*”
denote
ssi
gnifi
cance
at
the
10%
level;
“**”
denote
ssi
gnifi
cance
at
the
5%
level;
“***”
denote
ssi
gnifi
cance
at
the
1%
level.
Quart
erl
yti
me
fixed
eff
ects
and
firm
fixed
eff
ects
are
inclu
ded.
The
bra
ckets
beneath
coeffi
cie
nt
est
imate
sconta
int-
stati
stic
scom
pute
dfr
om
hete
rosk
edast
icit
y-r
obust
standard
err
ors
clu
stere
dby
firm
.
Pefo
rmance
Fir
mR
isk
Gro
ssM
arg
inR
OA
Ass
et
Turn
over
Sale
sG
row
thσ
(Cash
)σ
(Pro
fita
bilit
y)
σ(S
tock
Ret)
σ(R
OA
)σ
(Sale
sGr4
q)
σ(S
ale
sGr8
q)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
CA
PX
’sShare
-0.0
012
0.0
050***
0.0
134***
-0.0
759***
-0.0
218
-0.0
231***
-0.0
373
-0.1
400***
-0.0
162***
-0.0
136***
(-0.0
5)
(7.2
8)
(3.1
0)
(-20.3
7)
(-0.6
4)
(-3.0
9)
(-1.3
4)
(-4.1
7)
(-4.2
7)
(-3.6
2)
R&
D’s
Share
-0.4
888***
-0.0
211***
-0.1
100***
-0.1
048***
0.3
532***
0.0
748**
0.0
642*
0.1
523***
0.0
444***
0.0
477***
(-6.1
1)
(-13.4
7)
(-16.7
8)
(-18.9
6)
(7.0
4)
(2.4
2)
(1.8
8)
(3.1
6)
(5.6
3)
(5.9
6)
Mark
et-
to-B
ook
-0.0
134
0.0
043***
0.0
035***
0.0
113***
0.0
449***
-0.0
183*
-0.0
255***
0.0
440***
-0.0
006
0.0
007
(-0.6
9)
(10.4
1)
(3.7
7)
(14.3
8)
(7.2
2)
(-1.7
8)
(-6.0
4)
(7.9
6)
(-0.6
3)
(0.6
5)
Cash
Flo
w0.0
932***
0.0
025***
0.0
021***
-0.0
009
0.0
025
-0.0
065***
-0.0
023
-0.0
187**
-0.0
041***
-0.0
032**
(2.8
1)
(3.1
7)
(3.3
3)
(-0.8
4)
(0.7
2)
(-3.2
4)
(-0.4
2)
(-2.3
5)
(-3.2
4)
(-2.2
0)
RO
E0.1
884
0.0
709***
0.0
102
-0.0
221
-3.8
416***
1.4
325***
-0.3
074***
-0.0
630
-0.0
616***
-0.0
385***
(1.1
3)
(6.1
2)
(1.0
7)
(-1.1
4)
(-10.1
2)
(8.6
0)
(-4.3
1)
(-0.7
4)
(-4.5
5)
(-2.6
0)
Siz
e0.0
706***
0.0
026***
-0.0
192***
0.0
038***
0.8
872***
-0.0
215***
-0.1
064***
-0.1
576***
-0.0
176***
-0.0
177***
(6.0
6)
(8.9
8)
(-12.3
9)
(4.5
4)
(98.6
7)
(-2.8
6)
(-25.1
5)
(-18.7
3)
(-11.3
1)
(-11.1
4)
Levera
ge
-0.0
768
-0.0
089***
-0.1
757***
0.0
097
-0.4
294***
0.2
334
0.2
167***
-0.5
050***
-0.0
133
-0.0
111
(-0.9
3)
(-4.7
0)
(-12.7
0)
(1.5
1)
(-5.5
0)
(1.2
9)
(5.0
8)
(-6.8
4)
(-0.8
7)
(-0.7
2)
Const
ant
0.0
230
0.0
043
0.3
222***
0.0
681***
-3.6
388***
0.2
357***
-1.9
994***
-3.0
979***
0.9
871***
0.9
540***
(0.2
0)
(0.4
1)
(15.9
5)
(3.1
0)
(-14.6
6)
(2.5
9)
(-14.5
0)
(-8.5
4)
(3.7
4)
(3.7
2)
Tim
eF
EY
es
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Indust
ryF
EY
es
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
R2
0.0
626
0.2
915
0.4
615
0.0
416
0.5
993
0.1
056
0.1
427
0.1
292
0.1
655
0.1
879
Num
.O
bs
82103
82103
82103
71655
52916
53133
47758
47494
74484
61459
Num
.F
irm
s4254
4254
4254
4103
3592
3601
3373
3469
4103
3254
49