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Testing Adverse Selection and Moral Hazard on French Car Insurance Data

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Testing Adverse Selection and Moral Hazard on French Car Insurance Data TESTING ADVERSE SELECTION AND MORAL HAZARD ON FRENCH CAR INSURANCE DATA Guillaume CARLIER1 Université Paris Dauphine Michel GRUN-REHOMME2 Université Paris Panthéon Olga VASYECHKO3 Université Nationale d'Economie de Kyiv This paper is a modest contribution to the stream of research devoted to find empirical evidence of asymmetric information. Building upon Chiappori and Salanié's (2000) work, we propose two specific tests, one for adverse selection and one for moral hazard. We implement these tests on French car insurance data, circumventing the lack of dynamic data in our data base by a proxy of claim history. The first test suggests presence of adverse selection whereas the second one seems to contradict presence of pure moral hazard. Keywords: empirical evidence of moral hazard, adverse selection, car insurance. JEL Classification: C35, D82. 1 Université Paris Dauphine, CEREMADE, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, FRANCE, [email protected] 2 Université Paris Panthéon, ERMES, 12 Pl. du Panthéon, 75005 Paris, FRANCE, [email protected] 3 Université Nationale d'Economie de Kyiv, UKRAINE, [email protected] BULLETIN FRANÇAIS D’ACTUARIAT, Vol. 13, n° 25, janvier – juin 2013, pp. 117- 130 118 G. CARLIER – M. GRUN-REHOMME – O. VASYECHKO 1. INTRODUCTION There has been an intensive line of research in the last decades devoted to find empirical evidence of asymmetric information on insurance data. Under adverse selection, the insured has some private information about his type of risk, which the insurer cannot observe before the subscription of an insurance contract. The adverse selection assumption stipulates that the high-risks tend to choose more coverage than the low-risks (Rothschild and Stiglitz (1976), Wilson (1977), Spence (1978)). Under moral hazard, the policyholder can change his preventive behavior after contracting. For example, a policyholder can reduce his prevention effort after subscribing a contract with high coverage (Shavell (1979), Holmstrom (1979), Arnott and Stiglitz (1988)). Both adverse selection and moral hazard have been intensively studied in an insurance context and they may take several forms. Any situation in which the insurer faces an heterogenous population of insured, characterized by a type that is private information to them, adverse selection is at stake; this covers as many different phenomena as individual unobservable risk known by the insured, heterogenous risk aversion, income.... Ex-ante moral hazard, deals with the case where the agent chooses a level of effort after the contract is signed; in insurance, this is relevant to capture the idea that a contract with a high deductible will induce some prevention effort from the policyholder and therefore will decrease his accident probability. On the insurance company side, a wide range of contracting instruments may be used to provide suitable incentives: premia, deductibles as well as experience rating systems like the French "bonus/malus" system. A typical prediction of, either moral hazard or adverse selection on car insurance is the fact that more coverage implies a higher accident probability. Indeed, under pure adverse selection case, riskier agents choose contracts with high coverage. Under pure moral hazard, it is the fact that agents have a high coverage that induces them to choose a low effort and thus affects positively their accident probability. In both cases, one should observe a positive correlation (conditionally on the variables that are observable by the insurer) between coverage and risk. This in particular led Chiappori and Salanié (2000) to develop a conditional correlation approach between coverage and accidents and they found no evidence of asymmetric information in their data. The robustness of this approach is outlined in Chiappori et al. (2006). For other empirical studies on car insurance data, we refer the reader to Boyer and Dionne (1989), Puelz and Snow (1994), Dionne, Gouriéroux and Vanasse (2001), Cohen (2005), Saito (2006), Vasyechko et al. (2008) and the references therein. TESTING ADVERSE SELECTION AND MORAL HAZARD 119 ON FRENCH CAR INSURANCE DATA Distinguishing between adverse selection and moral hazard is a difficult task since it requires to identify in which direction is the causality between risk and coverage. To specifically test for moral hazard effects, one should use dynamic data. In fact, on one period-contracting data, the type of asymmetric information cannot be identified with the positive correlation approach whereas, dynamic insurance data can distinguish between moral hazard and adverse selection (Dionne et al. (2004), Abbring et al. (2003a, b), Dionne et al. (2013)). In the present work, we are interested in specific tests for adverse selection and moral hazard on French car insurance data. We do not really have panel data, but some dynamic dimension is present in our records thanks to the French experience rating system of "bonus/malus" which is based on past claim history. Taking advantage of this "bonus/malus" coefficient in our data base, we can reconstruct a proxy of past claim history, and crossing this factor with current coverage choice gives a specific test for adverse selection. Under adverse selection, a positive correlation is expected which a priori could be not be explained by pure moral hazard (i.e. by past efforts). As far as moral hazard is concerned, the theory predicts that a premium discount, as in the case of a bonus increase, lowers the incentive for prevention effort, resulting eventually in a higher accident probability. On the contrary, agents with a malus tend to increase their prevention effort. This is why we test the negativity of the correlation (again conditional) between the malus and current risk and argue that this test is specific to moral hazard. The paper is organized as follows. Section 2 presents the data base and explains how to build a relevant proxy of claim history. In section 3, we recall how some implications of theoretical asymmetric information models can be tested on car insurance data. We emphasize the fact that tests based on accident history rather reflect adverse selection whereas crossing experience rating data with accident data is better suited to detect moral hazard. The results of both tests of adverse selection and moral hazard on our French car insurance data base are presented in section 4. Section 5 concludes. The output tables for the parameter estimates of the bivariate probit models upon which our tests are built are gathered in the appendix. 2. PRESENTATION OF THE DATA Our empirical study is based on a data set provided by a French insurance company. This data set is a cross-section one concerning the year 2004, it is a random sample of the 120 G. CARLIER – M. GRUN-REHOMME – O. VASYECHKO whole portfolio and contains 44.696 observations. Each observation corresponds to a couple (car, policyholder). The data set contains the following individual information for each policyholder: 1. the demographic and driving characteristics of the policyholder, 2. the characteristics of policyholder's car, 3. the coverage choice, 4. the characteristics of the accidents recorded by the insurer during the current year. To be more precise, we describe the four previous items. - The demographic and driving characteristics of the policyholder The age and the gender. The driver status. It is a binary variable that indicates if the insured is the principal or secondary driver. It is important to notice that infractions committed by secondary drivers affect the principal driver's premium. The residence area of the policyholder. It is a binary variable that indicates rural or urban areas. The age of driving license. This variable gives the seniority of the driving license. The Bonus-Malus (BM) coefficient. This system is regulated and spelled out by law since 1984 on all French insurance companies. It is a multiplicative coefficient: new policyholders begin with a rate equal to one. The coefficient decreases every year by 5% if no responsible accident occurs during the current year. However, in the case of an accident, the BM coefficient increases by 25%. It cannot be lower than 0.50 and higher than 3.50 (see Grun-Réhomme (2000) for more details). Thirteen accident-free years are required to obtain the maximal bonus. An important characteristic of the BM rate is its transferability from one insurer to another. According to many insurers, the BM system is a source of reliable information on individual risk. - The characteristics of the insured vehicle The effective power of the vehicle. The insurer asks for the Deutsche Industrie Normen (DIN) horsepower of the car. (It is measured at the output shaft of an engine fully equipped with normal accessories). The age of the car. Most insurance companies usually propose decreasing prices with the age of the car. As the car gets older, an insured pays less insurance premium, due to the decreasing value of the car on the second-hand market. TESTING ADVERSE SELECTION AND MORAL HAZARD 121 ON FRENCH CAR INSURANCE DATA - The coverage choice The insurance company offers a menu of contracts after obtaining all the observable information from the policyholders. This menu contains a third-party insurance contract and three comprehensive insurance contracts (full coverage insurance) differentiated by the value of the deductibles which are fixed by the company. When a policyholder declares an accident at fault, the indemnity is equal to the total loss minus the deductible. If the latter exceeds the amount of loss, no reimbursement is due. Potential policyholders have to choose one of the following contracts: The third-party (TP) insurance contract. It is compulsory liability insurance. It covers property damages (following climatic events, attacks, natural disasters) and bodily injuries of a third party when the driver is at fault (totally or in part). It includes also a guarantee covering travel assistance and domestic assistance in case of physical injury and a guarantee of legal advice.
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