EMPIRICAL ANALYSIS OF ASYMMETRIC INFORMATION PROBLEMS IN SWEDISH VEHICLE INSURANCE

Transcription

1 EMPIRICAL ANALYSIS OF ASYMMETRIC INFORMATION PROBLEMS IN SWEDISH VEHICLE INSURANCE SHERZOD YARMUKHAMEDOV The Swedish National Road and Transport Research Institute (VTI), Örebro University Draft, Address: VTI, Box 55685, SE-10215, Stockholm, Sweden Phone: +46 (0)

2 Abstract Vehicle insurance is one of the buttresses of a modern welfare system, where individuals are provided financial protection against unexpected and unforeseen personal injuries and property losses in case of a traffic accident. However, theoretical literature predicts negative incentive effects of insurance provision where the problems of asymmetric information such as moral hazard and adverse selection may arise. Information asymmetries originate from unobservability of driver behavior that hampers an efficient risk classification and leads to inaccurate contract pricing. While theoretical studies are agreed on the presence of asymmetric information problem in insurance markets, empirical studies still provide mixed evidence. Therefore, the purpose of this study is to empirically test the presence of asymmetric information problems in the vehicle insurance market. Moreover, we propose an alternative approach to distinguishing moral hazard from asymmetric learning by modeling the dynamics in coverage choice; we use a large panel dataset from a major Swedish insurance company for the period The results indicate the presence of residual asymmetric information in the choice of a full insurance with a low deductible, where the source of information asymmetry is a moral hazard. No evidence of a residual asymmetric information problem is found in the choice of a full insurance with a high deductible and partial insurance. Policy implications are discussed at the end of the paper. Keywords: asymmetric information, moral hazard, adverse selection, vehicle insurance 2

3 CONTENTS 1. INTRODUCTION 5 2. THEORETICAL AND METHODOLOGICAL FRAMEWORK Literature review Data Methodology Models Stage I: Testing for residual asymmetric information Stage II: Disentangling moral hazard from adverse selection Models estimation EMPIRICAL FRAMEWORK Descriptive statistics Results Regression results stage I: Test for residual asymmetric information a Full insurance vs. Basic insurance b Partial insurance vs. Basic insurance Regression results stage II: Disentangling moral hazard from asymmetric learning Result discussion CONCLUSIONS 23 REFERENCES 24 3

4 LIST OF TABLES AND APPENDICES Table Descriptive statistics 17 Table 3.2.1a Outline of estimation results: Full insurance vs. Basic insurance 19 Table 3.2.1b Outline of estimation results: Partial insurance vs. Basic insurance 20 Table Outline of estimation results: Testing for moral hazard and asymmetric learning 21 APPENDIX Table A.1 Variable definitions 28 Table A.2 Expected number of accidents 29 Table A.3 Wald test for testing the assumption of random effects method 30 Table A.4 Likelihood-ratio test for overdispersion in hybrid model 30 Table A.5 Full insurance vs. Basic insurance 31 Table A.6 Partial insurance vs. Basic insurance 34 Table A.7 Testing for moral hazard and asymmetric learning 36 4

5 1. INTRODUCTION One of the imprescriptible parts of welfare system is insurance. It provides financial protection against fortuitous losses that are unforeseen, and facilitates security and efficiency 1. Despite the benefits of insurance, insurance literature predicts pernicious incentives which give rise to asymmetric information problems such as moral hazard and adverse selection. In vehicle insurance, moral hazard characterizes a situation where possessing insurance may lead to less careful driving behavior, while under adverse selection risky drivers tend to choose high coverage insurance. The underlying reason for these asymmetries is that driver behavior is private information and unobservable by insurance companies. In practice, difficulties of observing driver behavior lead to inefficient risk classification by insurers and to inaccurate contract pricing. Faulty risk classification may also lead to crosssubsidization where risky drivers are subsidized by safe drivers. Basically, insurers may apply strictly discriminative price-setting mechanisms based on sex, age and other parameters which would inflate insurance prices and thus make it expensive for certain groups of individuals, for instance young males. However, a government intervention in the form of rate regulation precludes such practices 2. In order to mitigate the problem of asymmetric information, insurance companies use different instruments such as deductibles, coinsurance and experience rating schemes 3. The choice of a deductible might be indicative of a driver s risk level, which is reflected in contract pricing by the insurer. Besides, deductibles prevent filing small claims, while coinsurance is better against larger claims. Experience rating is considered to be one of the most effective instruments to improve driver incentives, as it allows sequential observability of driver behavior. Theoretically, an asymmetric information problem is present in all insurance markets, because a transfer of responsibility for individual losses to another agent, like an insurance company, may lead to an increase in the probability of those losses. However, empirically, the existence of an information problem is not unambiguously established. Furthermore, identifying the type of information problem creates an additional problem due to the restricted availability of panel data. Therefore, the purpose of this paper is to empirically contribute to the literature on asymmetric information by using unique individual-level data from vehicle insurance. In addition, we use 1 A sense of security comes from possessing insurance against possible losses (e.g. fire, accident), and, being insured, a company may take a reasonable risk to improve the efficiency of sales, e.g. export the product to the whole world. 2 For instance, equal treatment between men and women is required in setting premiums in the EU. 3 In the deductible scheme, a driver pays a fixed amount of losses predetermined in the contract, while, in the coinsurance scheme, the losses are shared between insurer and insured according to certain percentage portions stated in the contract, so that in monetary terms the costs a driver should pay is not fixed. In the experience rating scheme, a driver s claims records are observed by the insurer and taken into account in setting the premium. 5

6 dynamics in coverage choice to develop a model for separating moral hazard from asymmetric learning, which is another contribution of this paper. Empirical analysis is performed with a large panel dataset from a major Swedish insurance company for the period The dataset contains individual, vehicle and contract specific information in detail, which allows us to achieve the purpose of this analysis. The analysis is performed in two stages: the first stage examines the presence of residual asymmetric information with a parametric test, and if residual asymmetric information is found in the first stage, the second stage identifies the source of the information problem by means of a dynamic panel data test for moral hazard and asymmetric learning. We find evidence of residual asymmetric information in the choice of full insurance with a low deductible, while no information asymmetries are found in the choice of full insurance with a high deductible and partial insurance. Further, it is found that the source of this information problem in the choice of full insurance with a low deductible is moral hazard. This implies that a driver possessing full insurance with a low deductible might have private information which is unobservable for the insurer. Possible private information might be past accident records, which do not follow a driver if s(he) changes insurance provider, i.e. insurance companies in Sweden do not have a system of sharing common information on claims. Therefore, in the absence of such a system, an at-fault driver, after causing an accident, may switch to another insurance company to avoid premium increases. A new insurance company would lack access to the past accident records of a new customer. Hence, creating a common system for registering claims would contribute to the efficiency of the insurance companies, and to traffic safety as a whole. The paper is organized as follows. Section 2 presents the literature review, data, methodology and models for testing the presence of residual asymmetric information. It also includes models for separating moral hazard from asymmetric learning. Section 3 contains the estimation results. We draw conclusions in the last section. 6

7 2. THEORETICAL AND METHODOLOGICAL FRAMEWORK 2.1 Literature review Insurance is a fundamental component of a modern welfare system. It provides benefits in the form of health insurance, unemployment insurance, life insurance, property insurance etc. Despite the benefits of insurance there are some welfare losses 4 due to information problems in insurance. For instance, in health insurance, the welfare loss arises when a sick individual purchases health insurance after becoming ill in order to reduce his/her medical expenditures, so that an individual takes a certain actuarially fair loss in the form of a premium in exchange for a larger uncertain loss (Nyman, 1999). Economic theory predicts that shifting the responsibility for the consequences of an event onto another agent increases the probability of that event, or, in other words, purchasing insurance against some loss may lead to an increase in occurrence of that loss (Baker, 1996). For instance, Dave and Kaestner (2009) argue that obtaining health insurance reduces preventive activities and encourages unhealthy behaviors. Cohen and Dehejia(2004) also find that possessing vehicle insurance is associated with an increased number of traffic fatalities. The negative incentive effects of insurance on individual behavior are moral hazard 5 and adverse selection, which are well-known phenomena in insurance literature. Dionne et al.(2012) introduce a concept of asymmetric learning as an initial stage of adverse selection, where the insured learns about his/her risk quicker than the insurer, which may convert into adverse selection over time. The source of the asymmetric information problem is that driver behavior is private information and is difficult for insurance companies to observe. Private information has significant impacts on contract choice and risk preferences, and thus is of high interest for insurers (Muermann and Straka, 2012). Any attempts to completely observe driver behavior, however, require substantial resources which may outweigh the gains from insurance provision. Therefore, insurance companies make use of different instruments, such as deductibles, coinsurance and experience rating (also called bonusmalus) schemes, to reduce the informational advantage of driver over insurer by observing claims and to provide incentives to prevent accidents so that the effects of moral hazard and adverse selection are diminished. 4 Einav et al.(2010) find that welfare losses due to asymmetric information problems are about 2 percent of annual premiums in the UK annuity market. 5 Insurance literature splits moral hazard into ex-ante moral hazard and ex-post moral hazard, where the former characterizes an individual s behavior after obtaining insurance, while the latter describes an individual s actions after incurring losses (e.g., insurance fraud by claim padding). Our paper focuses only on ex-ante moral hazard and, for simplicity, we henceforth use the term moral hazard to refer to ex-ante moral hazard. 7

8 Deductibles are seen as a screening device for predicting adverse selection and as a tool for reducing the negative moral hazard effects on accident frequency and cost distributions. On average, an individual selecting a low deductible is expected to have more accidents than one who chooses a higher deductible (Dionne et al., 1998). The deductible provision also improves incautious driving because financial responsibilities for accident losses are partly shared by the driver, which leads to a decrease in moral hazard (Schmidt, 1961; Li et al., 2007; Wang et al., 2008). Another type of risk sharing provision is a coinsurance scheme, where the size of loss is proportionally shared according to the terms of contract. Some insurers offer contracts with either a deductible or a coinsurance option, while others offer a combination of both. Ligon et al. (2008) find that individuals with low frequency risk and high severity risk prefer contracts with a deductible option, while individuals with low frequency risk and low severity risk choose a combination of coinsurance and deductibles. Generally, deductibles are more advantageous in cases of small claims, whereas coinsurance is more effective with larger claims. Experience rating schemes 6 are based on a claims history, and may either reward or punish a driver in terms of insurance premium, for instance, each filed claim leads to an increase in premium in the next period 7. Therefore, under experience rating drivers are incentivized to undertake preventive activities to avoid accidents; as such it is one of the most efficient tools against moral hazard. However, in order to avoid a penalty in the form of an increased premium, drivers may prefer not to report an accident, which may lead to the undervaluation of accident risks and overvaluation of accident costs (Dionne et al.,1998; Dimitriyadis and Tektas,1998). For instance, Robinson and Zheng (2010) find that an observed decline in the number of accidents in Ontario and Alberta was due to an underreporting problem. Moreover, drivers may also switch to another insurance company after receiving indemnification for accident losses 8 (Pitrebois et al., 2005). Insurance literature justifies the wide adoption of deductibles, coinsurance and experience rating schemes on the basis of a theoretical prediction of asymmetric information problems in the insurance market. While many theoretical studies unanimously support this prediction, empirical studies provide mixed evidence of the presence of asymmetric information. Empirical studies on the presence of asymmetric information are based on testing for a positive correlation between coverage and risk. Some studies (Clement, 2009; Israel, 2004; Kim et al., 2009; Dionne et al., 2012; Dave and Kaestner, 2009; Dunham, 2003; Muermann and Straka, 6 See Frangos and Vrontos (2001) and Mert and Saykan (2005) on the design of experience rating. 7 Some insurance companies may refrain from increasing a premium in case of an accident if the driver had a long claim-free period before this actual claim (Neuhaus, 1988). 8 If there is a common claims database for all insurers within a country, then switching to another company will not conceal accident history. 8

9 2012; Cohen and Dehejia, 2004; Weisburd, 2010; Dionne and Gagne, 2002) find evidence of asymmetric information, while others (Chiappori and Salanie, 2000; Abbring et al., 2003; Saito, 2006; Abbring et al., 2002; Dahchour and Dionne, 2002; Dionne et al., 2004) are unable to discover a predicted positive correlation between coverage and risk. The absence of a positive correlation 9 can be explained by heterogeneity in risk attitudes 10 ; for instance, a risk-averse driver may have higher willingness to pay for insurance and select a comprehensive coverage and still take precautions to avoid accidents 11 (Hemenway, 1992). An efficient risk classification by an insurance company may also eliminate the correlation (Dionne et al., 2001). Moreover, Cohen and Siegelman(2010) argue that the existence of a correlation may depend on the type of insurance market (e.g., vehicle insurance, annuities, life insurance etc.) under consideration, so that a correlation between risk and coverage found in one insurance market is not necessarily present in another. One of the challenges for empirical research on asymmetric information is related to the problem of distinguishing moral hazard from adverse selection, as both yield a positive correlation between coverage and risk, though with reverse causality. For instance, in moral hazard, obtaining more comprehensive coverage results in more risky driving, while in adverse selection there is a reverse causality, i.e. high risk drivers purchase more comprehensive coverage. Using crosssectional data has been insufficient for separating these two effects; panel data is thus considered adequate since it allows modeling dynamic features of insurance contracts. For instance, Dionne et al.(2012) use French panel data on vehicle insurance to model a dynamic process between insurance claim and coverage choice, and succeed in distinguishing moral hazard from adverse selection. However, limited access to individual-level panel data over several periods makes this method challenging. 2.2 Data A micro-level data panel on privately insured passenger vehicles over the period has been obtained from the largest insurance company in Sweden. The database contains all information observed by the insurer on individual, contract and vehicle-specific characteristics such as age, sex, household composition, coverage type, premium, deductible choice, claim type and 9 In contrast, Bolin et al.(2010) find a negative correlation between risk and insurance in a health insurance context, which is explained by a better screening ability of the insurer to distinguish customer riskiness levels. Moreover, Sonnenholzner and Wambach (2009) show that the opposite of adverse selection might be observed if different time preferences among individuals are considered where patience prompts low risk individuals to purchase insurance. 10 Chiappori and Salanie (2012) argue that, in a monopoly context, a failure to completely control for risk aversion may lead to a correlation of both signs between coverage and risk. Cutler et al.(2008) also show that preference heterogeneity may explain mixed results in correlation tests. 11 In this case, correlation between coverage and risk might be negative. 9

10 frequency, age of vehicle, mileage class and a group of variables for owner s residence area and vehicle-make defined by the insurer (Appendix, Table A.1). The data from the largest Swedish insurance company with a market share of about 30 percent contains 1.7 million individuals and 2.5 million vehicles generating 14.2 million observations over the period Applying a sample selection procedure, described in the next section, results in a subsample containing 3.3 million observations on 1.1 million individuals and 1.2 million vehicles. 2.3 Methodology The empirical test for the presence of asymmetric information problems is a two-stage procedure. The first stage tests for the existence of residual asymmetric information problems, i.e. checking for a positive correlation between coverage and risk 12. If the null hypothesis of no correlation is rejected, then one may proceed to the second stage. This stage should identify which information problem it is, i.e. moral hazard or adverse selection (Dionne et al., 2012). The subsample comprises individuals with contract duration longer than six months, because short-term insurance contracts are usually purchased for temporary occasions such as summer trips and do not represent a typical driver. Moreover, only individuals with a maximum of one vehicle are included, because if an individual possesses several vehicles, it will be difficult to verify who is actually driving the vehicle 13. The Swedish vehicle insurance offers three types of coverage: basic, partial and full insurances coverage 14. Basic (a third-party) insurance is compulsory according to the Motor Traffic Damage Act and compensates for the material damages caused to another party by an at-fault policyholder, while personal injuries are indemnified by own insurers irrespective of culpability. Partial insurance consists of basic insurance and covers losses due to fire, glass damage, theft, salvage, and engine impairment. Full insurance includes partial insurance and also compensates for damages inflicted on one s own vehicle regardless of culpability. In testing for a correlation between coverage and risk, a choice between the highest and the lowest possible coverage is modeled, i.e. a choice between full insurance and basic insurance. Moreover, there is also an inbetween coverage, partial insurance, so that we also model a choice between partial insurance and basic insurance in testing for a coverage-risk correlation. 12 Alternatively, testing for residual asymmetric information is based on a conditional independence test between risk and coverage. 13 This procedure does not completely remove a bias associated with the actual driver identification issue, but at least diminishes this bias to some extent. 14 There is also out-of-operation coverage, which insures not-in-use vehicles against damages that occurs when vehicle is not under operation. 10

11 The size of deductibles, which is determined by the insurance company, varies depending on the coverage type. In the case of full insurance, the driver has a choice between two deductibles, i.e. SEK 3000 and SEK The choice of different deductible levels might be indicative of different accident probabilities, where a low deductible is associated with less safe traffic behavior than a higher deductible. In our case, there are two significantly different levels of deductibles (in full insurance), that are treated separately in the analysis of full insurance vis-à-vis the lowest coverage. It is essential to make a distinction between accidents and claims, where insurers observe claims but not the accidents 15, because not all accidents lead to submission of claims (Cohen and Siegelman, 2010). Besides, a claim-underreporting problem arises if loss size is lower than the deductible, which may lead to undervaluation of accident probabilities. However, overvaluation of accident probability with respect to different types of coverage may happen if a researcher counts all the submitted claims. Compared to basic insurance, full insurance has comprehensive features which indemnify many types of damages such as fire damage, glass damage etc. Obviously, full insurance holders have the possibility of submitting more claims although not all damages are caused by traffic accidents. Therefore, disregarding this aspect of claim reporting and comparing accident probabilities among coverage types may lead to measurement issues and spurious regression results. To overcome this problem, we count only those claims that have a traffic moment 16 (basic insurance moment) in full and partial insurance coverage where the driver is partially or completely responsible 17. One of the specific features of panel data models is the presence of unobserved individual effects which cause endogeneity of explanatory variable(s). We use the Allison(2009) hybrid method, which incorporates some features of both fixed and random effects methods, to control for unobserved individual effects. The idea is to decompose time-varying explanatory variables into within-person and between-person parts and estimate them with a random effects method. This method, with transformed time-varying and time-invariant variables, is estimated by a conditional maximum likelihood, where coefficient estimates for deviation variables 18 are equivalent to fixed effects coefficient estimates, because these coefficients depend on the variation within individuals over time. 15 This may lead to spurious correlation between coverage and risk, while neither adverse selection nor moral hazard exists (Chiappori and Salanie, 2000). 16 Traffic moment is an actuarial notion used to denote a right to indemnification pertaining to basic insurance. As full and partial insurances are built on basic insurance, we condition only on traffic moment, which reduces coverage comparison to a common denominator, so that claims related to the traffic moment are considered across coverage types. 17 In the case of an accident, the underreporting problem is of less concern because negotiation between drivers to privately solve consequences of an accident is unlikely, especially if the accident causes personal injuries. 18 Deviations from person-specific means for each time-varying explanatory variable. 11

12 2.4 Models As described in the previous subsection, empirical analysis of asymmetric information problems is a two-stage procedure, where testing for the presence of residual asymmetric information is a first stage, and if this is found, the second stage determines the type of this information problem, i.e. either moral hazard or adverse selection Stage I: Testing for residual asymmetric information A test for the presence of residual asymmetric information is performed by employing a parametric test proposed by Dionne et al.(2001) to examine a correlation between coverage and risk. We extend the Dionne at al.(2001) cross-sectional framework to the panel data case, and unfold deductible preferences in the choice of full insurance so that the choice of a low or a high deductible is treated separately 20. Besides, in contrast to Dionne et al.(2001), we use the choice of coverage instead of deductible choice as a dependent variable in testing the coverage-risk relationship 21. Assume that individual i in period t faces contract C with coverage choice set J and runs into an accident K which is expressed with the following model: = >0 Eq a where j=1,2,3 corresponds to basic, partial and full insurance coverage 22, respectively; I(.) is an indicator function equal to 1 if the expression in brackets holds, otherwise 0; X contains all individual-specific, contract-specific and vehicle-specific characteristics; K is the actual number of accidents, and is the expected number of accidents; is an unobserved heterogeneity and is an error term. The expected number of accidents is used to account for possible problems of model misspecification due to omitted variables or nonlinearities peculiar to risk classification parameters (Dionne et al., 2001). The expected number of accidents in Equation 2.4.1a is obtained in a post-estimation procedure of the accident distribution model (Eq.2.4.1b), i.e. modeling the 19 It might also be the case that both informational problems are present simultaneously, and exploiting the features of panel data may allow separating moral hazard from adverse selection. 20 Different deductible levels may reflect different risk levels, and are treated separately. 21 In testing for coverage-risk correlation, we opt for contract choice as a direct indicator of coverage, for instance as in Chiappori and Salanie(2000). 22 Basic insurance is a reference category, so that three choice models are built with respect to different deductible levels in full insurance, i.e. full insurance (low deductible) vs. basic insurance, full insurance (high deductible) vs. basic insurance, and partial insurance vs. basic insurance. The model estimation section provides more discussion on this. 12

13 conditional distribution of accidents based on all risk classification variables and obtaining predicted values after estimation provides. We assume that the number of accidents follows a Poisson distribution for individual i in period t with probability: Pr = =! Eq b where m is the number of accidents, X is individual-vehicle-contract specific characteristics, and φ is an unobserved individual effect. Due to a restrictive assumption of the Poisson model, in some instances, it is feasible to make an alternative distributional assumption; namely, a negative binomial distribution which is expressed as: Pr = = Eq c where Γ(.) is the gamma function and is the overdispersion parameter. We estimate both Poisson and Negative Binomial models and then test for overdispersion in order to facilitate the model choice. In the presence of residual asymmetric information, a significant positive sign for coefficient estimate is expected (in Eq a), which implies that comprehensive coverage is associated with higher accident occurrences Stage II: Disentangling moral hazard from adverse selection If the presence of residual asymmetric information is established, then the next stage is to uncover the source of this information problem, i.e. either moral hazard or adverse selection. Two approaches (Model A and Model B) are used to disentangle moral hazard from asymmetric learning, which may lead to adverse selection over time. Model A. Dionne et al.(2012) exploit the dynamics in accidents and coverage choice, and propose empirical tests to separate moral hazard from asymmetric learning. 13

14 An equation for testing a moral hazard 23 for individual i at time t is: = >0 and a dynamic test for asymmetric learning is: Eq a = >0 Eq b where and are the number of accidents and coverage choice in previous period, respectively. A conjecture behind the test for moral hazard in Eq a is that the choice of comprehensive coverage in the previous period is associated with more accidents in the present period, i.e. we test the following hypothesis: : 0 : >0 A test for asymmetric learning in Eq b predicts that experiencing an accident in the past period leads to learning about risk type and choosing a higher coverage in this period which is tested in the following hypothesis: : 0 : >0 Therefore, in the presence of moral hazard >0 is expected, while in the presence of asymmetric learning, which over time may lead to adverse selection, >0 is predicted. Model B. We propose an alternative approach to separating moral hazard from asymmetric learning, which is inspired by Dionne et al.(2012). Assume that individual i at time t faces contract C with a coverage choice set J and has an accident K which is expressed as: = >0 Eq c where and denote downgrade and upgrade in the coverage choice compared to the choice of coverage in the previous period. 23 Compared to the presented discrete choice model, in our case, we estimate accident probabilities with count data models (e.g., Poisson and/or Negative Binomial regression models). 14

15 Moral hazard Consider a driver who has invested effort in avoiding accidents in the previous periods, and decides to downgrade his/her coverage in this period. This driver may also choose to downgrade his/her coverage due to financial reasons. The driver may, for instance, have had an accident in the previous period, which implies an increased premium in the present period, so that, in order to avoid a sharp premium increase, s(he) decides to downgrade his/her insurance coverage and put more effort into avoiding accidents in this period. Thus, we expect that downgrading coverage is associated with the low accident frequency, which is an indication of reduced moral hazard effect ( <0). Asymmetric learning Suppose that a driver, based on his/her driving experience from the last period, learns that s(he) is a risky driver (driver does not necessarily need to have an accident in the previous period) and decides to upgrade his/her insurance coverage in this period. This learning is private information which is not observed by an insurance company, so that a driver learns faster than the insurer, leading to the asymmetric learning which may convert to adverse selection over time. Therefore, in the presence of asymmetric learning, we expect a positive relationship between the number of accidents and an upgrade in coverage ( >0) Models estimation The first stage estimation, testing for the presence of residual asymmetric information, is based on estimating the choice of full and partial insurance versus (vs.) basic insurance, meaning that the choice between full insurance and basic insurance, as well as between partial insurance and basic insurance, is estimated. Moreover, the possibility of choosing different deductible levels in full insurance is accounted for by subdividing full insurance into the low and high deductibles options 24, so that two more pairs of regressions are estimated. As a result, three choice models are estimated: full insurance (LD) vs. basic insurance, full insurance (HD) vs. basic insurance, and partial insurance vs. basic insurance. Three model specifications are used in testing for residual asymmetric information for each choice model. The first is a base model 25 (Model 1), then the base model is extended by including the expected number of accidents to take into account the possible nonlinear effects (Model 2), followed by a further extension in a third model in which interaction terms are introduced (Model 24 Hereafter, a low deductible and a high deductible are abbreviated to LD and HD, respectively. 25 Modified Puelz and Snow(1994) model, where the choice of a deductible is substituted with the choice of a coverage. 15

16 3). A comparison of models is performed, based on Akaike s Information Criterion (AIC), where a model with the lowest AIC value should be preferred. The presence of unobserved individual effects in the equations (Eq a, Eq b, Eq c, Eq a, Eq b and Eq.2.4.2c) requires a relevant treatment where available options are random effects and/or fixed effects methods. We estimate the models with the hybrid method, 26 which reflects the features of both random and fixed effects methods. Testing the assumption of the random effects method in the hybrid method with the Wald test facilitates the choice of either the random effects method or fixed effects method. Estimating accident distributions (Eq b, Eq c, Eq a, Eq c) is accomplished by Poisson and/or Negative Binomial Regression models depending on the results of the likelihood-ratio test for overdispersion, which determines the choice of model. The second stage estimation, disentangling moral hazard from asymmetric learning, is based on modeling dynamics in accidents and contract choice. By construction, the lagged dependent variables in equations (Eq a, Eq b) are correlated with the unobserved individual effects. As above, we follow Allison (2009) and apply a hybrid method to control for unobserved individual effects. Equations Eq a and Eq c are presented in a discrete choice form to retain an original equation, though estimated by the count data models due to the variation in accident distribution. 26 The coefficient estimates from the hybrid method are equivalent to the fixed effects coefficient estimates. However, the hybrid method allows estimating time-invariant parameters, which is otherwise impossible with the fixed effects approach. 16

17 3. EMPIRICAL FRAMEWORK 3.1 Descriptive statistics Table Descriptive statistics Obs. Mean SD Min Max Age of driver Age Age Age Age Age Age 65 and older Male No of household members Coverage types Full insurance Partial insurance Basic insurance Deductible choice Low deductible High deductible Premium, SEK Number of accidents Mileage class M1: km/year M2: km/year M3: km/year M4: km/year M5: and over km/year Vehicle age The average age of drivers in the sample is about 53, with drivers aged 35 and over constituting about 88 percent of policyholders. The proportion of male drivers, 57 percent, is 17

18 slightly higher than that of female drivers. The size of household ranges from a single to 10 person household, where the average household consists of 2 people. Figures for coverage type show that full insurance is the most popular coverage of 77 percent of the drivers, while only 5 percent prefer basic insurance. Individuals with full insurance coverage mostly choose the lowest deductible (75%) which is SEK3000 compared to the highest (SEK5000). Premiums range from SEK121 to 43936, the average premium being SEK3551. The number of accidents stretches from no accidents to 4 accidents, where the mean value is 0.02, indicating a low frequency of accidents. Almost half of the policyholders drive up to km/year, while the fraction for long mileage drivers is only 2 percent. The dispersion of vehicle age shows that the sample consists of both new and veteran vehicles (95 year old), with a mean age of about 10 years. 3.2 Results Regression results stage I: Testing for residual asymmetric information In testing for the presence of residual asymmetric information, we make a distinction between different types of insurance coverage, i.e. the analysis is split into two parts where the first part analyzes full insurance and basic insurance, while the second part focuses on partial insurance and basic insurance. In order to obtain the expected number of accidents, we estimate Eq b with both Poisson and Negative Binomial regression models 27, and opt for the latter according to the outcome of the overdispersion test (Appendix, Table A.4, rows 1-3). The results for the Negative Binomial regression model are presented in appendix (Appendix, Table A.2) a Full insurance vs. Basic insurance The two pairs of regressions, i.e. full insurance (LD) vs. basic insurance, and full insurance(hd) vs. basic insurance, are estimated according to the three model specifications; namely, a base model (Model 1), a base model plus expected number of accidents (Model 2), and Model 2 extended by including interaction terms (Model 3). All three model specifications are estimated by both random effects and hybrid methods, and the test results suggest choosing the hybrid method (Appendix, Table A.3, rows 5-7, 12-14). The estimates for the variables of interest 28 for the three model specifications are extracted from Table A.5 (Appendix) and presented in Table 3.2.1a. 27 In turn, Poisson and Negative Binomial regression models are estimated with random effects and hybrid methods, where the results of a Wald test suggests the hybrid method (Appendix, Table A.3, rows 2-3, 9-10, 16-17). 28 Note: Coefficient estimates for deviation variables are reported. 18

19 Table 3.2.1a Outline of estimation results: Full insurance vs. Basic insurance Model 1 (base model) Low deductible Number of accidents 0.077*** (0.027) Model 2 (with expected number of accidents) Model 3 (with expected number of accidents and interaction terms) 0.084*** (0.021) 0.081*** (0.021) Expected number of accidents *** (0.273) *** (0.274) AIC High deductible Number of accidents (0.029) (0.029) Expected number of accidents *** (0.029) *** (0.232) (0.231) AIC ***, **, * Significant at 1%, 5% and 10%, respectively. Standard errors are in parentheses. Model specifications are compared by AIC values, which suggest that Model 2 (in the case of full insurance with a low deductible) and Model 3 (in the case of full insurance with a high deductible) should be preferred. In the choice of full insurance with a low deductible, a statistically significant coefficient estimate for the number of accidents suggests that there is a residual asymmetric information problem. In contrast, no residual asymmetric information is revealed in the choice of full insurance with a high deductible b Partial insurance vs. Basic insurance The choice of partial insurance is also estimated according to the three model specifications, where each model is estimated with random effects and hybrid methods. Results indicate that hybrid method should be chosen (Appendix, Table A.3, rows 19-21). The estimation results of the three model specifications are presented in Table 3.2.1b. AIC value suggests the choice of the model specification with the expected number of accidents and interaction terms (Model 3). The results indicate that no residual asymmetric information is found in the choice of partial insurance. 19

20 Table 3.2.1b Outline of estimation results: Partial insurance vs. Basic insurance Model 1 (base model) Model 2 (with expected number of accidents) (0.036) Model 3 (with expected number of accidents and interaction terms) Number of accidents (0.035) (0.036) Expected number of accidents 0.459*** 0.451*** (0.182) (0.183) AIC ***, **, * Significant at 1%, 5% and 10%, respectively. Standard errors are in parentheses Regression results stage II: Disentangling moral hazard from asymmetric learning According to the results from section 3.2.1a, evidence of residual asymmetric information is found in the choice between full insurance (LD) and basic insurance. Therefore, we proceed to verify the source of the asymmetric information problem by testing for moral hazard and asymmetric learning. The equation for testing the presence of moral hazard (Model A) is estimated by Poisson and Negative Binomial regression models; a test for overdispersion indicates that the Poisson Regression model is more suitable (Appendix, Table A.4, row 5). In the case of Model B, the Negative Binomial regression model is preferred according to the overdispersion test results (Appendix, Table A.4, row 7). Equations for testing the presence of moral hazard and asymmetric learning (Model A and Model B) are estimated with random effects and hybrid methods, where the hybrid method is chosen according to the test results (Appendix, Table A.3, rows 23-24, 26, 29-30). Estimation results for testing moral hazard and asymmetric learning are presented in Table In the case of Model A, the null hypothesis of no moral hazard is rejected at 1% significance level, which implies that the presence of a moral hazard effect is established. The results for the asymmetric learning test suggest that the null of no asymmetric learning is not rejected at 5% significance level; thus, we conclude that there is an absence of asymmetric learning effects. The results for Model B reveal the same findings as for Model A: downgrading a coverage leads to fewer accidents, which implies a reduction of moral hazard effect (significant at 5%). An insignificant coefficient estimate for the coverage upgrade indicator suggests the absence of asymmetric learning effects, which is also in line with our results in Model A. 20

21 Table Outline of estimation results: Testing for moral hazard and asymmetric learning Model A Model B Moral hazard test Asymmetric learning test The choice of full insurance with *** low deductible (0.0862) Number of accidents(t-1) ** (0.3666) Coverage downgrade ** (0.0937) Coverage upgrade (0.1857) ***, **, * Significant at 1%, 5% and 10%, respectively. Standard errors are in parentheses Result discussion The first stage launches the estimation of the expected number of accidents for all three choice models, i.e. full insurance (LD) vs. basic insurance, full insurance (HD) vs. basic insurance and partial insurance vs. basic insurance. Each choice model is estimated with the hybrid method and the assumption of the random effects method is tested with the Wald test. The results suggest the choice of a hybrid method 29. The likelihood-ratio test results for the count data model estimations show that in the first stage estimation models a Negative Binomial regression model is found appropriate, while in the second stage estimation models, the extent of overdispersion is subtle, and thus the Poisson regression model is preferred (Appendix, Table A.4). The analysis of the choice between full insurance (LD) and basic insurance in Model 1(Table 3.2.1a) indicates the presence of residual asymmetric information (0.077, significant at 5%). Including the expected number of accidents in the base model specification (Model 2) to account for nonlinearities of risk classification variables does not change the results (0.084, significant at 1%). Moreover, including interaction terms (Model 3) to account for further possible nonlinearities does not affect our findings. AIC values for the three models advocate the choice of a model specification with the expected number of accidents (Model 2). The results for the choice analysis of full insurance (HD) vs. basic insurance by a base model specification (Model 1) shows no evidence of residual asymmetric information (Table 3.2.1a). Alternative model specifications with the expected number of accidents (Model 2) and interaction terms (Model 3) provide the same results. A model with interaction terms (Model 3) is preferred according to the AIC value. 29 The choice of a hybrid method for all models in the paper is evidenced in Table A.3 (Appendix). To refrain from repetition, we will not declare test results henceforth. 21

22 The choice between partial insurance and basic insurance with a base model (Model 1) indicates the absence of residual asymmetric information. Adding the expected number of accidents (Model 2) and introducing interaction terms (Model 3) still suggests no evidence of a residual asymmetric information problem. Finding residual asymmetric information between the choice of full insurance (LD) and basic insurance initiates a further investigation of the source of information problems in the second stage estimation. In model A, we reject the null hypothesis of no moral hazard in a dynamic test for moral hazard, and therefore establish the evidence of moral hazard in the choice of full insurance with a low deductible vs. basic insurance. In a dynamic test for asymmetric learning, we cannot reject the null of no asymmetric learning, which implies that there is no effect of asymmetric learning in the studied subsample. The results for Model B support the findings in Model A. 22

23 4. CONCLUSIONS An essential element of a welfare system is insurance, which contributes to the sustainable development of a modern society. While a redistribution of different social benefits such as health insurance, unemployment insurance, property insurance etc. is seen as a merit, distortive incentive effects are considered as shortcomings of insurance provision. For instance, obtaining insurance against a certain loss inevitably leads to an increase in the occurrence of that loss. This is explained by a shift of responsibility for the consequences of an event onto an insurance company, which impairs incentives for preventive activities and triggers careless behavior. In a vehicle insurance context, providing insurance may lead to asymmetric information problems, known as moral hazard and adverse selection. The former occurs when possessing vehicle insurance leads to incautious driving behavior, while the latter is the case when high risk individuals purchase comprehensive coverage. The presence of information problems is predicted by the theoretical literature, while the empirical literature provides mixed evidence. Therefore, the purpose of this study is to use the example of the Swedish vehicle insurance to contribute to the empirical literature on asymmetric information. Moreover, we design an alternative model to separate moral hazard from asymmetric learning by exploring the dynamics in coverage choice. The dataset contains a large sample of policyholders from the largest Swedish insurance company for the period of The analysis is performed in two stages: the first stage tests for the presence of residual asymmetric information, and, if found, the second stage makes use of dynamics in accidents and coverage choice to identify the source of asymmetric information, i.e. moral hazard or asymmetric learning which over time may lead to adverse selection. The first stage estimation results indicate the presence of residual asymmetric information in the choice of full insurance with a low deductible, while the same evidence is not found in the choices of full insurance with a high deductible and partial insurance. Having found the presence of residual asymmetric information in the first stage, we proceed to the second stage estimation where results suggest that the source of residual asymmetric information in the choice of full insurance with a low deductible is moral hazard. This implies that a driver possessing full insurance with a low deductible may have private information which is unobservable for the insurer. A possible explanation for the informational advantage of drivers over insurance companies might be the absence of a common system for registering claims among insurers, where at-fault drivers may switch to another insurance company to avoid premium increases. Therefore, creating a joint system for claim registrations might be sufficient to correct information asymmetries between drivers and insurance companies. 23

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