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1、 GEORGETOWN LAW The Scholarly Commons 2012 Unlucky or Risky? Unobserved Heterogeneity and Experience Rating in Insurance Markets Levon Barseghyan Cornell University Francesca Molinari Cornell University Darcy Steeg Morris U.S. Census Bureau Joshua C. Teitelbaum Georgetown University Law Center, jct4
2、8law.georgetown.edu Georgetown Business, Economics and Regulatory Law Research Paper No. 12-040 This paper can be downloaded free of charge from: http:/scholarship.law.georgetown.edu/facpub/1127 http:/ This open-access article is brought to you by the Georgetown Law Library. Posted with permission o
3、f the author. Unlucky or Risky? Unobserved Heterogeneity and Experience Rating in Insurance Markets Levon Barseghyan Francesca Molinari Cornell University Cornell University Darcy Steeg Morris Joshua C. Teitelbaum U.S. Census Bureau Georgetown University Draft: November 14, 2012 Abstract We investig
4、ate whether an insureds claims experience contains valuable informa- tion about its latent risk type. Using data on households claims histories in auto and home insurance, we estimate the variance-covariance matrix of unobserved heterogene- ity and utilize the estimates to update a priori prediction
5、s about the households claim risk. The estimates reveal that unobserved heterogeneity is positively correlated across coverages. We then explore how households demand for insurance would respond to experience rating under different theories of risky choice. We conclude that the po- tential for exper
6、ience rating to meliorate adverse selection depends crucially on the sources of insureds aversion to risk. (JEL C58, D12, D82, G22, K23) Corresponding author: Levon Barseghyan, Department of Economics, Cornell University, 456 Uris Hall, Ithaca, NY 14853 (lb247cornell.edu). We acknowledge financial s
7、upport from National Science Foundation grant SES-1031136. Molinari also acknowledges financial support from NSF grant SES-0922330. This paper is released to inform interested parties of research and to encourage discussion. The views expressed are those of the authors and not necessarily those of t
8、he U.S. Census Bureau. 1 1 Introduction Since the seminal work of Akerlof (1970) and Rothchild and Stiglitz (1976), economists have been attuned to the problem of adverse selection in insurance markets. In the standard model, the source of the problem is unobserved heterogeneity in insureds claim ri
9、sk. The general assumption is that there are variables which affect an insureds claim risk that are observable to the insured but not to the insurer.1 In other words, there is asymmetric informationthe insured has more information about its claim risk than does the insurer. Of course, even if there
10、is asymmetric information at the time the insurer underwrites and rates an insureds policy, the insurer subsequently receives signals about the insureds latent risk type. In particular, the insurer observes the insureds claims experience. A key question is whether and to what extent an insureds clai
11、ms experience contains valuable information about its claim risk. Do claims signify that an insured is risky or just unlucky? If the former, then the insurer can update its prior belief about the insureds risk type. In particular, the insurer can update its prior prediction about an insureds claim r
12、isk by conditioning on the insureds claims experience. The insurer can then use its posterior prediction to adjustor experience ratethe insureds premium. An important related question is whether and to what extent an insureds claims expe- rience in one line of insurance contains valuable information
13、 about its claim risk in another line of insurance. For example, do claims in automobile insurance signify that an insured is a risky homeowner (and vice versa)? If so, then the insurer can update its prior prediction about an insureds claim risk in one line of insurance by conditioning on the insur
14、eds claims experience in another line of insurance. The insurer can then experience rate the insureds premiums across lines of insurance. In principle, experience rating within and across line of insurance can meliorate the demand distortions arising from adverse selection, because premiums will mor
15、e accurately reflect insureds true actuarial risk. In this paper, we utilize data on claims in automobile and homeowners insurance to explore the information value of insureds claims experience and the potential for experience rating to mitigate adverse selection. The data comprise an unbalanced pan
16、el of 62, 425 households who held auto and home policies between 1998 and 2006. Among other things, the data record the number of claims filed by each household in three lines of coverage: auto collision, auto comprehensive, and home all perils. In addition, the data contain detailed information abo
17、ut the households and their policies. As a first step, we use the data to estimate the variance-covariance matrix of un- 1 Alternatively, there may be variables that are observable to the insurer but that the insurer is prohibited from using when it underwrites and rates the insureds policy (Salani
18、1997; Avraham et al. 2012). 2 observed heterogeneity in claim risk, as well as the households a priori claim rates based on observables. We model households claim counts using a Poisson mixture model with correlated random effects. To estimate the model, we take a moments-based approach that uses ge
19、neralized estimating equations based on marginal moments (Morris 2012). Unlike the standard approachmaximum likelihood estimation of a parametric mixture of Poisson distributionsour estimation approach is semiparametric and unconstrained with respect to the parameters of the mixing distribution (Pin
20、quet 2012). Among other things, the estimates reveal that unobserved heterogeneity is positively correlated across coverages, suggesting that there is a domain-general component to risk type. We then demonstrate the value of the information contained in b and, by implication, the value of the inform
21、ation contained in the households claims historiesby showing that conditioning on claims experience leads to material refinements of the households predicted claim rates. For instance, we find that (i) among households with downward revisions, their predicted claim rates decrease on average by 7 per
22、cent in auto collision, 13 percent in auto comprehensive, and 19 percent in home and (ii) among households with upward revisions, their predicted claim rates increase on average by 10 percent in auto collision, 23 percent in auto comprehensive, and 28 percent in home. Moreover, we demonstrate the in
23、cremental value of conditioning across lines of coverage (in addition to conditioning within lines of coverage) by showing that it not only leads to material incremental refinements of the households predicted claim rates but also improves their accuracy. Next, we show that experience ratingi.e., ad
24、justing premiums to reflect households a posteriori predicted claim ratesleads to material refinements of the households premi- ums in home insurance.2 For example, we find that (i) among households with downward adjustments, their premiums decrease on average by 11 percent and (ii) among households
25、 with upward adjustments, their premiums increase on average by 25 percent. As before, we demonstrate the incremental value of experience rating across lines of coverage (as op- posed to experience rating only within lines of coverage) by showing that it leads to material incremental refinements of
26、premiums. Lastly, we investigate the extent to which households demand for insuranceas cap- tured by their deductible choicesis responsive to experience rating. To model households deductible choices, we adopt the theoretical framework of Barseghyan et al. (2012) and con- sider two models of risky c
27、hoice featured therein: (i) the standard expected utility model and (ii) a generalization of the expected utility model that allows for generic probability distor- 2 When we turn to experience rating, we restrict attention to home insurance out of necessity. Our rating model requires as an input the
28、 value of the insured property. We observe this value in the home policies but not in the auto policies. 3 tions. After calibrating the models using the parameter estimates reported by Barseghyan et al. (2012), we use both models to generate home deductible choices for the households in our data ass
29、uming first that premiums are not experience rated and then that they are experi- ence rated. We find that (i) under the expected utility model, nearly 7 percent of households would choose a different home deductible if their premiums were experience rated, but that (ii) under the probability distor
30、tion model, only 1 percent of households would choose a different home deductible if their premiums were experience rated. We close the paper by discussing legal restrictions on experience rating and what our findings imply about their economic consequences. In a nutshell, we argue that although our
31、 findings suggest that such restrictions have the potential to induce regulatory adverse selection, they also suggest that the magnitude of the problem depends critically on the sources of insureds aversion to risk.3 More specifically, we argue that our findings suggest that the size of the demand d
32、istortions arising from a failure to experience rate premiums depends on whether and to what extent insureds risk aversion arises from diminishing mar- ginal utility for wealth or from other sources such as probability weighting or loss aversion. On the basis of our findings, and of recent work sugg
33、esting that insureds risk aversion arises in part from sources other than diminishing marginal utility for wealth, we speculate that the selection effects of legal restrictions on experience rating are likely small. The paper operates at the intersection two literatures. The first is the empirical l
34、iter- ature on adverse selection in insurance markets, and in particular the recent strand that moves beyond testing for the presence of adverse selection to quantifying its economic effects and considering the implications for public policy (e.g., Cutler and Reber 1998; Einav et al. 2010a).4 Survey
35、s of this strand are contained in Einav et al. (2010b) and Chetty and Finkel- stein (2012).5 Most closely related are the papers that focus on the selection effects of legal restrictions on risk classification by insurers. For example, Buchmueller and DiNardo (2002), Simon (2005), and Bundorf and Si
36、mon (2006) study the effects of community rating in U.S. health insurance markets. More recently, Finkelstein et al. (2009) study the effects of a ban on gender-based pricing in the U.K. annuity market, and Bundorf et al. (2012) and Geruso (2012) study the effects of uniform contribution requirement
37、s in the U.S. employer-provided health insurance market.6 The second is the literature on experience rating in insurance 3 Coined by Hoy (2006), regulatory adverse selection refers to adverse selection arising from asymmetric information that is created artificially by legal restrictions on risk cla
38、ssification. 4 See also, e.g., Carlin and Town (2010), Brown et al. (2011), Handel (2011), Lustig (2011), Dardanoni and Donni (2012), Spinnewijn (2012), and Starc (2012). 5 For a survey of the strand of the literature that tests for the presence of adverse selection, see Cohen and Siegelman (2010).
39、6 Though it is not their focus, Einav et al. (2010a) also consider the effects of legal restrictions on risk classification in the U.S. employer-provided health insurance market. Other papers focus on the converse 4 markets. For surveys, see Pinquet (2000, 2012) and Antonio and Valdez (2012).7 Most
40、closely related are the handful of papers on multidimensional experience rating, beginning with Jewell (1974). For example, Pinquet (1998) studies experience rating across claims at fault and not at fault. Desjardins et al. (2001) and Angers et al. (2006) study experience rating for fleets of vehicl
41、es. More recently, Englund et al. (2008) and Englund et al. (2009) study experience rating across various types of commercial coverage, Frees et al. (2010) study experience rating across multiple perils within home insurance, and Antonio et al. (2011) study experience rating across multiple auto ins
42、urance policies. To our knowledge, ours is the first paper to study experience rating across auto and home insurance and to assess, under different theories of risky choice, the extent to which experience rating can meliorate adverse selection in insurance markets. 2 Description of the Data The sour
43、ce of the data is a large U.S. property and casualty insurance company. The company offers several lines of insurance, including auto and home. The full data set includes annual information on more than 400, 000 households who held auto or home policies between 1998 and 2006. The data contain all th
44、e information in the companys records regarding the households and their policies (premiums, deductibles, etc.). In addition, the data record the number of claims that each household filed with the company under each of its policies during the period of observation. We focus our attention on three l
45、ines of coverage: auto collision, auto comprehensive, and home all perils. Auto collision coverage pays for damage to the insured vehicle caused by a collision with another vehicle or object, without regard to fault. Auto comprehensive coverage pays for damage to the insured vehicle from all other c
46、auses (e.g., theft, fire, flood, windstorm, glass breakage, vandalism, hitting or being hit by an animal or by falling or flying objects), without regard to fault. Home all perils coverage pays for damage to the insured home from all causes (e.g., fire, windstorm, hail, tornadoes, vandalism, or smok
47、e damage), except those that are specifically excluded (e.g., flood, earthquake, or war).8 In most of the analysis, we consider an unbalanced panel of 62, 425 households who held all three coverages (auto collision, auto comprehensive, and home) in one or more years between 1998 and 2006. In all, th
48、is tricoverage sample comprises 294, 917 household-years. Descriptive statistics are set forth in the Appendix. topic of the potential for regulation to mitigate adverse selection in insurance markets. For example, Einav et al. (2010c) study the welfare consequences of legal mandates in the U.K. annuity market. 7 For textbook treatments, see Lemaire (1995), Bhlmann and Gisler (2005), and Denuit et al. (2007). 8 For simplicity, we often refer to home all perils merely as home. 5 itk 2 h c m Table 1 summarizes the claims, premiums, and
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