HIDDEN REGRET IN INSURANCE MARKETS

• Date: 01 January 2016
• Author: Rachel J. Huang,Alexander Muermann,Larry Y. Tzeng
• Published date: 01 January 2016
• DOI: http://doi.org/10.1111/jori.12096

©2015 The Journal of Risk and Insurance. Vol.83, No. 1, 181–216 (2016).

DOI: 10.1111/jori.12096

Hidden Regret in Insurance Markets

Rachel J. Huang

Alexander Muermann

Larry Y. Tzeng

Abstract

We examine insurance markets with two-dimensional asymmetric informa-

tion on risk type and on preferencesrelated to regret. In contrast to Rothschild

and Stiglitz (1976), the equilibrium can be efficient; that is, it can coincide with

the equilibrium under full information. Furthermore, we show that pool-

ing, semipooling, and separating equilibria can exist. Specifically,there exist

separating equilibria that predict a positive correlation between the level

of insurance coverage and risk type, as in the standard economic models of

adverse selection, but there also exist separating equilibria that predict a neg-

ative correlation between the level of insurance coverage and risk type. Since

optimal choice of regretful customers depends on foregone alternatives, the

equilibrium includes a contract that is offered but not purchased.

Introduction

Regret theory was initially developed by Bell (1982) and Loomes and Sugden (1982)

and has been shown in both the theoretical and experimental literature to be an impor-

tant factor in explaining individual behavior.The impact of regret on decision making

has been examined in different economic settings. Braun and Muermann (2004) and

Wethank two anonymous reviewers, as well as Roland Eisen, WandaMimra, Harris Schlesinger,

and seminar participants at the Wharton School Applied Economics workshop, the Goethe Uni-

versity Frankfurt, the Munich Behavioral Insurance Workshop, the Risk Theory Society meet-

ing, the EGRIE meeting, the Symposium on Finance, Banking and Insurance, and the ARIA

meeting for their valuable comments. Muermann gratefully acknowledges financial support of

the National Institutes of Health—National Institute on Aging, Grant number P30 AG12836,

the Boettner Center for Pensions and Retirement Security at the University of Pennsylvania,

and National Institutes of Health—National Institute of Child Health and Development Popu-

lation Research Infrastructure Program R24 HD-044964, all at the University of Pennsylvania.

Rachel J. Huang is at the Department of Finance, National Central University, and Research

Fellow, Risk and Insurance Research Center, College of Commerce, NCCU, 300, Jhongda Rd.,

Jhongli City, Taoyuan County 32001, Taiwan. Alexander Muermann is at the Department of

Finance, Accounting and Statistics, WU (Vienna University of Economics and Business) and

Vienna Graduate School of Finance, Welthandelsplatz 1, A-1020 Wien, Austria, e-mail: alexan-

der.muermann@wu.ac.at. Larry Y. Tzeng is at the Finance Department, National Taiwan Uni-

versity,and Research fellow,Risk and Insurance Research Center, College of Commerce, NCCU,

No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan

181

182 The Journal of Risk and Insurance

Muermann et al. (2006) show that anticipatory regret moves individuals away from

extreme decisions. Compared to preferences that satisfy the axioms of von Neumann

and Morgenstern, regret leads individuals to purchase more (less) insurance cover-

age if insurance is relatively expensive (cheap), and analogously, anticipatory regret

implies that financial investors invest more (less) in risky stocks if the equity risk pre-

mium is relatively high (low). In a dynamic setting, Muermann and Volkman (2006)

show that anticipatory regret and pride can cause investors to sell winning stocks and

hold on to losing stocks; that is, it might help explain behavior that is consistent with

the disposition effect. Regret preferences have also been applied to asset pricing and

portfolio choice in an Arrow–Debreu economy (Gollier and Salani´

e, 2006), to first-

price auctions (Filiz-Ozbay and Ozbay, 2007), and to currency hedging (Michenaud

and Solnik, 2008).1

This article contributes to the literature by examining the equilibrium effects of an-

ticipatory regret under asymmetric information. We consider a perfectly competitive

insurance market with policyholders that are heterogeneous with respect to both risk

type and regret preferences. In particular, there are individuals who account for an-

ticipated regret in their decision making, and there are individuals whose decision

making is not influenced by anticipatory regret.

Rothschild and Stiglitz (1976) show in their classical adverse selection model in insur-

ance markets that in equilibrium—if it exists—lower risk individuals self-select into

contracts that offer lower insurance coverage. Recently, the insurance literature has

extended the model of Rothschild and Stiglitz (1976) in two directions, inspired by the

mixed empirical evidence regarding the residual correlation between risk type and

insurance coverage. 2The first strand of literature examines one-dimensional hetero-

geneity of customers who engage in potentially different, unobservable actions that

1There is much empirical evidence of both individuals experiencing regret and the anticipation

of regret influencing individual decision-making (see, e.g., Loomes, 1988; Loomes et al., 1992;

Simonson, 1992; Larrick and Boles, 1995; Ritov, 1996). We refer to Zeelenberg (1999) who re-

views the evidence fromthese and other studies in which regret is made salient to individuals at

the time of choice and from studies in which the uncertainty resolution of alternative choices is

manipulated. More recently, Zeelenberg and Pieters (2004) compare two lotteries in the Nether-

lands, a regular state lottery and a postcode lottery in which the postcode is the ticket number.

In the latter lottery, individuals who decided not to play the lottery, thus, receive feedback

about whether they would have won had they played the lottery. They conducted different

studies that all confirm that this feedback causes regret and changes the decision whether

to play the lottery. Filiz-Ozbay and Ozbay (2007) conduct first-price auction experiments

and show that individuals experience loser regret—the regret a losing bidder experiences

if the winning bid is revealed—that leads them to overbid. Finally, Camille et al. (2004) and

Coricelli et al. (2005) find that the medial orbitofrontal cortex plays a central role in mediat-

ing the feeling of regret. In the experimental study of Camille et al. (2004) normal subjects

reacted to the experience of regret and chose to minimize it in the future while patients with

orbitofrontal cortex lesions did not report regret or anticipated negative consequences from

their choices. Using functional magnetic resonance imaging (fMRI), Coricelli et al. (2005) find

enhanced activity in the medial orbitofrontal cortex in response to an increase in regret.

2In markets for acute health care insurance and annuities, the empirical evidence is consis-

tent with the prediction of adverse selection and moral hazard models (see e.g., Cutler and

Hidden Regret in Insurance Markets 183

imply heterogeneity in risk type. They show that there could exist equilibria in which

individuals with certain characteristics both purchase more insurance coverage and

invest more in risk-mitigating measures—thereby becoming lower risk types—than

other individuals. This negative relationship between insurance coverage and risk

type is called advantageous selection.3

The second strand of literature considers two-dimensional heterogeneity of cus-

tomers with respect to risk type and risk aversion (see Smart, 2000; Wambach, 2000;

Villeneuve, 2003). Those models predict, as Rothschild and Stiglitz (1976), a positive

correlation between insurance coverage and risk type. Netzer and Scheuer (2010),

however, show that by endogenizing heterogeneity in wealth levels and thereby risk

aversion, a negative correlation between insurance coverage and risk type can be

obtained. Sandroni and Squintani (2007) argue that individuals might be heteroge-

neous in risk perception. Some high-risk policyholders might be overconfident and

mistakenly believe that they are low-risk types. They find that compulsory insurance

might not improve all agents’ welfare.4

In this article, we adopt a two-dimensional approach and analyze the existence and

properties of equilibria. The first dimension is, as in Rothschild and Stiglitz (1976),

risk type. Policyholders are either high risk or low risk. The second dimension relates

to regret preferences. There arepolicyholders who regret not having chosen foregone

better alternatives and policyholders who do not regret.

Regret is interpreted as the anticipated disutility incurred from an ex ante choice that

turns out to be ex post suboptimal. Individuals make their decision by trading off

the maximization of expected utility of wealth against the minimization of expected

Zeckhauser, 2000; Mitchell et al., 1999; Finkelstein and Porteba, 2004). In contrast, a negative

relationship between insurance coverage and claim frequency exists in markets for term-life

insurance and Medigap insurance (see, e.g., Cawley and Philipson, 1999; Fang et al., 2008).

Last, in automobile insurance and long-term care insurance (see, e.g., Chiappori and Salani´

e,

2000; Finkelstein and McGarry, 2006), the correlation between insurance coverage and claim

frequency is not significantly different from zero.

3For example, de Meza and Webb(2001) analyze the effect of hidden information on individuals’

degree of risk aversion combined with hidden action. Similarly, Jullien et al. (2007) study a

principal–agent model in which the agent has private information about his degree of risk

aversion. Sonnenholzner and Wambach(2009) examine insurance markets in which customers

have private information about their time preferences. They show that a negative correlation

between insurance coverage and risk type can emerge in equilibria, since impatient customers

might both spend less on insurance coverage and risk mitigation, thereby becoming higher

risk types. Huang et al. (2010) analyze a setting in which the degree of overconfidence is

hidden information and show that, in equilibrium, overconfidenttypes spend less on insurance

coverage and risk mitigation.

4The empirical evidence, however, on the sign of the negative relationship between degree of

risk aversion and risk type is mixed. Finkelstein and McGarry (2006) find evidence in the long-

term care insurance market that is consistent with advantageous selection; that is, more risk

averse individuals are more likely to purchaselong-term care insurance and less likely to enter

a nursing home. In contrast, Cohen and Einav (2007) and Fang et al. (2008) find the opposite

in automobile and Medigap insurance: risk type is positively correlated with risk aversion.