Estimating Risk Preferences from Deductible Choice - MIT

1 harvard Law SchoolHarvard Law School John M. Olin Center forLaw, Economics and Business DiscussionPaper SeriesNELLCOYear2007 Estimating Risk Preferences fromDeductible ChoiceAlma CohenLiran EinavThis paper is posted at NELLCO Legal Scholarship 1045- 6333 harvard JOHN M. OLIN CENTER FOR LAW, ECONOMICS, AND BUSINESS Estimating RISK Preferences FROM Deductible Choice Alma Cohen and Liran Einav Discussion Paper No. 582 03/2007 harvard Law School Cambridge, MA 02138 This paper can be downloaded without charge from: The harvard John M. Olin Discussion Paper Series: The Social Science Research Network Electronic Paper Collection: Forthcoming, American Economic ReviewEstimating Risk Preferences from Deductible Choice By Alma Cohen and Liran Einav Abstract:We estimate the distribution of risk Preferences using a large data set of deductiblechoices in auto insurance contracts.

2 To do so, we develop a structural econometric model of adverseselection that allows for unobserved heterogeneity in both risk (claim rate) and risk aversion. Weuse data on realized claims to estimate the distribution of claim rates and data on Deductible andpremium choices to estimate the distribution of risk aversion and how it correlates with risk. We nd large heterogeneity in risk attitudes: while the majority of individuals are almost risk neutralwith respect to lotteries of 100 dollar magnitude, animportantfractionoftheindividualsexhib itsigni cant risk aversion even with respect to such relatively small bets. The estimates imply thatwomen are more risk averse than men, that risk aversion exhibits a U-shape with respect to age,and that most proxies for income and wealth are positively associated with absolute risk , unobserved heterogeneity in risk aversionismoreimportantthanthatofrisk,an driskandrisk aversion are positively of Economic Literature classi cation numbers:D82, :risk aversion, adverse selection, structural estimation, mixture thank two anonymous referees and Judy Chevalier, the editor, for many helpful comments, which greatly im-proved the paper.

3 We are also grateful to Susan Athey, Lucian Bebchuk, Lanier Benkard, Tim Bresnahan, Raj Chetty,Ignacio Esponda, Amy Finkelstein, Igal Hendel, Mark Israel, Felix Kubler, Jon Levin, Aviv Nevo, Harry Paarsch,Daniele Paserman, Peter Rossi, Esteban Rossi-Hansberg,Morten Sorensen, Manuel Trajtenberg, Frank Wolak, andseminar participants at UC Berkeley, CEMFI, Chicago GSB,Duke,Haas, harvard ,Hoover,theInterdis ciplinaryCenter in Herzliya, Minnesota, Northwestern, Penn State,Stanford,TelAviv,UWMadison,Wharton ,SITE2004,the Econometric Society 2005 and 2006 winter meetings, and the NBER IO 2005 winter meeting for many usefuldiscussions and suggestions. All remaining errors are, of course, ours. Einav acknowledeges nancial support from theNational Science Foundation (Grant No. SES-0452555) and from Stanford s O!ce of Technology Licensing, and thehospitality of the Hoover Institution.

4 Address correspondence to Liran Einav, Department of Economics, StanfordUniversity, Stanford, CA 94305-6072; Tel: (650) 723-3704; E-mail: Department of Economics, Tel-Aviv University, NationalBureauofEconomicResearch,andHarv ardLawSchoolJohn M. Olin Research Center for Law, Economics, and Business. E-mail: Department of Economics, Stanford University, and National Bureau of Economic Research. 2006. Alma Cohen and Liran Einav1 IntroductionThe analysis of decisions under uncertainty is central to many elds in economics, such as macro-economics, nance, and insurance. In many of these applications it is important to know the degreeof risk aversion, how heterogeneous individuals areintheirattitudestowardsrisk,andhowthe seattitudes vary with individuals characteristics. Somewhat surprisingly, these questions have re-ceived only little attention in empirical microeconomics, so answering them using direct evidencefrom risky decisions made by actual market participants is this study, we address these questions by Estimating risk Preferences from the Choice ofdeductible in insurance contracts.

5 We use a richdata set of more than 100,000 individuals choosingfrom an individual-speci cmenuofdeductibleandpremiumcombinationso ered by an Israeli autoinsurance company. An individual who a chooses low Deductible is exposed to less risk, but is facedwith a higher level of expected expenditure. Thus,anindividual sdecisiontochoosealow(high) Deductible provides a lower (upper) bound for his coe!cient of absolute risk risk Preferences from insurance data is particularly appealing, as risk aversion is theprimary reason for the existence of insurance markets. To the extent that extrapolating utilityparameters from one market context to another necessitates additional assumptions, there is anadvantage to obtaining such parameters from the same markets to which they are subsequentlyapplied. The Deductible Choice is (almost) an ideal setting for Estimating risk aversion in thiscontext.

6 Other insurance decisions, such as thechoiceamonghealthplans,annuities,orju stwhether to insure or not, may involve additional preference -based explanations that are unrelatedto nancial risk and make inference about risk aversion di! contrast, the Choice amongdi erent alternatives that vary only in their nancial parameters (the levels of deductibles andpremiums) is a case in which the e ect of risk aversion can be more plausibly isolated and average Deductible menu in our data o ers an individual to pay an additional dollars in order to save182dollars in Deductible payments in the event of a individual should choose a low Deductible if and only if his claim propensity is greaterthan the ratio between the premium (55)andthepotentialsaving(182), which is0= is actuarially unfair with respect to the average claim rate of0=245,18percent of the samplechoose to purchase it.

7 Are these individuals exposed to greater risk than the average individual,are they more risk averse, or a combination ofboth? We answer this question by developing astructural econometric model and Estimating benchmark speci cation uses expected utility theory to model individuals deductiblechoices as a function of two utility parameters, the coe!cient of absolute risk aversion and a claim1 For example, Matthew Rabin and Richard H. Thaler (2001, footnote 2) point out that one of their colleaguesbuys the insurance analyzed by Charles J. Cicchetti and Je rey A. Dubin (1994) in order to improve the service hewill get in the event of a claim. We think that our Deductible Choice analysis is immune to such ease of comparison, we convert many of the reported gures from New Israeli Shekels to dollars. It isimportant to keep in mind, however, that GDP per capita in Israel was0=5230=56of that in the (0=6730=70>when adjusted for PPP) during the observation We allow both utility parameters to dependonindividuals observableandunobservablecharacteristics , and assume that there is no moral hazard.

8 Two key assumptions that claims aregenerated by a Poisson process at the individual level, and that individuals have perfect informationabout their Poisson claim rates allow us to use data on (ex post) realized claims to estimate thedistribution of (ex ante) claim rates. Variation inthe Deductible menus across individuals and theirchoices from these menus are then used to estimate the distribution of risk aversion in the sampleand the correlation between risk aversion and claim risk. Thus, we can estimate heterogeneous riskpreferences from Deductible choices, accounting for adverse selection (unobserved heterogeneity inclaim risk), which is an important confounding results suggest that heterogeneity in risk Preferences is rather large. While the majorityof the individuals are estimated to be close to risk neutral with respect to lotteries of100dollarmagnitude, a signi cant fraction of the individuals in our sample exhibit signi cant levels of riskaversion even with respect to such relatively small bets.

9 Overall, an individual with the averagerisk aversion parameter in our sample is indi erent about participating in a fty- fty lottery inwhich he gains100dollars or loses56dollars. We nd that women are more risk averse than men,that risk Preferences exhibit a U-shape with respect to age, and, interestingly, that most proxiesfor income and wealth are positively associated with absolute risk perform an array of tests to verify that these qualitative results are robust to deviationfrom the modeling assumptions. In particular, we explore alternative distributional assumptions,alternative restrictions on the von Neumann-Morgenstern (vNM) utility function, and a case inwhich individuals are allowed to make mistakes in their coverage choices due to incompleteinformation about their own risk types. We also show that the risk Preferences we estimate arestable over time and help predict other (but closely related) insurance decisions.

10 Finally, we justifyour assumption to abstract from moral hazard, and we discuss the way this and other featuresof the setup (sample selection and additional costs associated with an accident) may a ect theinterpretation of the we mostly focus on absolute (rather than relative) risk allowsus to take a neutral position with respect to the recent debate over the empirical relevance ofexpected utility theory (Matthew Rabin, 2000; Matthew Rabin and Richard H. Thaler, 2001; ArielRubinstein, 2001; Richard Watt, 2002; Nicholas Barberis et al., 2006; Ignacio Palacios-Huerta etal., 2006). While the debate focuses on how the curvature of the vNM utility function varies withwealth or across di erent settings, we only measure this curvature at a particular wealth level,whatever this wealth level may be. By allowing unobserved heterogeneity in this curvature acrossindividuals, we place no conceptual restrictions onthe relationship between wealth and risk estimated distribution of risk Preferences can bethoughtofasaconvolutionofthedistributi onof (relevant) wealth and risk attitudes.