Pitfalls in the implementation of non-discriminatory premiums the case of unisex tariffs in the German automobile insurance market

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1 Pitfalls in the implementation of non-discriminatory premiums the case of unisex tariffs in the German automobile insurance market Vijay Aseervatham Institute for Risk Management and Insurance, University of Munich, Germany Christoph Lex Institute for Risk Management and Insurance, University of Munich, Germany Martin Spindler Max Planck Institute for Social Law and Social Policy, Munich, Germany July, 2013 Abstract As of December 21, 2012, the use of gender as an insurance rating category was prohibited in the European Union. We investigate how this affects the pricing of insurance using data from a German car insurer. We find that the exclusion of gender does not eliminate price differences between male and female drivers because many non-excluded risk factors are correlated with gender. This arguably runs counter to the legislatures intention. We document how this bias can be eliminated, but in order to do so the information on gender must be known. Keywords: Automobile Insurance, Risk Classification, Unisex Premium. JEL classification codes: G22, K20, C20.

2 1 Introduction Unisex premiums are mandatory in the European private insurance market from 21 December 2012 on (Curia Europa o.v. 2011). According to the Court of Justice of the European Union the use of gender information in pricing is discriminatory. The discussion about risk classification in general and with respect to gender specifically is not a new one in the insurance business. Thiery and van Schoubroeck (2006) argue that while insurance companies prefer a group approach for their pricing, so that in this specific case men and women represent two groups, the legislature prefers an individualistic approach, where such group effects are forbidden in the premium calculation. According to the individualistic approach no one should pay more or less because of belonging to a specific group. It is expected that the effects of the gender ban will be different for different types of insurance. While the nondiscrimination rule favors women, e.g., in the annuity and health insurance, it is supposed that they will be disadvantaged in the automobile insurance. Especially, young men are often classified as high risks and thus women will be subsidizing men in their car insurance. Nevertheless, there is only limited knowledge about the size of these effects since the regulator did not specify a methodology for implementing unisex tariffs. Pope and Sydnor (2011) argue that the common method of simply excluding the socially unacceptable variable would yield unintended results if the omitted variable is correlated with other independent variables. This classic omitted variable bias is especially true for the automobile insurance market where several other variables are used for the premium calculation. The premium determinants that are still left in the model and that are correlated with gender would then serve as a proxy for gender. This seems to be the reason why Moennich (2011, 2012) expects that unisex tariffs will not yield big changes in the automobile insurance market. In this paper, we quantify how gender impacts the current premium calculation in the German automobile insurance market before the implementation of unisex tariffs. The ban on gender in private insurance contracts took place in the US already in the 1980s. The effects have been analyzed by Puelz and Kemmsies (1993) using hedonic price (premium) regressions. We apply the same methodology to a data set from a German insurance company. We then anticipate the ban of gender as a pricing variable by simply omitting the gender variable. We assume that insurance companies will use this method because it provides the second best predictive accuracy. Finally, we also provide estimates for what the legislature intended by applying the method proposed by Pope and Sydnor (2011). This method includes two steps: in a first step, a full model with all the independent variables, including gender, is estimated. 2

3 Then, in the second stage, the predicted values are generated from the estimated coefficients of the socially acceptable variables and the average of the banned variable. This ensures that the socially acceptable variables that are correlated with gender remain their predictive power from the full estimation and will not proxy for gender in the unisex estimation. In this paper, we address three research questions: How big are the differences in what male and female drivers pay right now? What would premiums look like when the gender variable is simply omitted? We compare these premiums to differently calculated unisex tariffs and ask the question what the legislature intended? This paper is structured as follows: In Section 2 we give an introduction to the theory of risk classification. In Section 3, the institutional framework of automobile insurance in Germany is presented. Then we describe the data set (Section 4) and present the results (Section 5). Finally, we conclude. 2 Risk Classification and Asymmetric Information Insurance offers protection against adverse events in exchange for a premium and therefore has welfare enhancing effects for risk adverse individuals. This is the fundamental principle of insurance and has been well established in the insurance economics literature. The core task of an insurance company is risk classification for the sake of pricing. Comprehensive surveys have been given in ABI (2008) and in Crocker and Snow (2000). In an economic sense, risk classification can also be regarded as its technology, the channel through which insurance companies compete to reduce the cost of providing insurance contracts. Risk classification refers to the use of observable variables or behavior such as, e.g., gender, age, and smoking, to price or to structure insurance policies. Risk classification is guided by two principles: actuarial equivalence and solidarity. The first one states that the insurance premium should reflect the individual s risk, i.e., the severity and probability of a loss, so that the premium is proportional to their expected future losses (from the point of view of the insurance company). The second one means that the risk is shared between the participants of a risk pool. Therefore insurance, respectively, risk classification is in the area of conflict between efficiency and equity or social fairness, and this trade-off is also in the center of vivid public discussions. On the one hand, each insuree is supposed to pay premiums according to his risk; on the other hand it is perceived as unjust if the pricing of insurance premiums is based on characteristics such as gender or race, which are uncontrollable by the individual. 1 An 1 For a detailed discussion, we refer to Harrington and Doerpinghaus (1993). 3

4 example of this is the late court decision of the European Court of Justice to forbid gender as a variable for risk classification in insurance contracts. But such legal restrictions may lead to a situation in which lower-risk individuals pay higher premiums than those corresponding to their true risk and cross-subsidize high-risk insurees, who pay lower premiums than justified by the actuarial equivalence principle. As a consequence, low-risk individuals might leave the risk-pool and, when the proportion of high-risk individuals is sufficiently high, premiums will rise considerably and this might start a so called death spiral. In the end, both high-risk individuals and the low-risk individuals are worse off. The former pay higher premiums than before and the latter have no insurance protection any more. Therefore, a careful consideration of these two goals is very important for society. Another justification for risk classification is that risk classification might mitigate the (negative) effects of asymmetric information. Asymmetric information potentially leads to adverse selection and moral harzard. Adverse selection in insurance markets was introduced by Rothschild and Stiglitz (1976) and concerns hidden information. This means that the (potential) insured know their individual riskiness better than the insurance company. Moral hazard deals with hidden action and occurs when the expected loss (accident probability or level of damage) is not exogenous, as assumed in the adverse selection case, but depends on some decision or action made by the insured (e.g., effort spent to prevent a damage) which is neither observable nor contractable. Further information on both phenomena can be found in Dionne et al. (2000) and Winter (2000), respectively. By collecting information and classifying the riskiness of the applicants, insurance companies try to reduce informational asymmetries. E.g., in automobile insurance, it is a well known fact that the accident probability changes with age, and using age as a variable for risk classification enables the insurance company to charge risk-adjusted premia. 3 Automobile Insurance in Germany In Germany, as in many other countries, the automobile insurance has three pillars: 1. A third party liability insurance which is mandatory for all cars and covers damage inflicted on other drivers and their cars in the case of an accident. 2. A first party, fire, theft, also called comprehensive coverage, which is non-compulsory and covers own damages and losses caused by theft, natural disasters (storm, hail, lightning strike, flood), collision with furred game animals, and so on. 3. A fully comprehensive or collision coverage, which covers accidental damage on the own 4

5 car, even if caused by oneself, and damages caused by the vandalism of strangers; it is non-compulsory. For both types of comprehensive insurance, a deductible can be chosen. In German car insurance, there is also a uniform experience rating system ( Schadenfreiheitsrabatt ) which, however, applies only to the compulsory liability insurance and to collision coverage but not to the comprehensive coverage. The number of years without an accident is counted separately for the two types (liability and collision) and in accordance with these numbers, every insured is divided into a class ( Schadensfreiheitsklasse ), which is associated with a bonus coefficient b t. For any year t, the premium is defined as the product of a base amount and this coefficient. The base amount can be set freely by the insurance companies according to their risk classification, conditional on the characteristics of the insured (such as age, sex, profession, and location) but it cannot be related to past experience. In 2011, the compulsory liability insurance covered million cars, this is thus the total number of registered cars in Germany. In total, premium income was 20, 887 million Euro and expenditures for claims were 20, 444 million Euro. A detailed overview by the three main types of automobile insurance is given in Table 1. Table 1: Overview of the German car insurance market in 2011 liability comprehensive collision number of insured cars in million number of claims in million claims expenditure in billion Euro average claim in Euro 3, , 545 source: GDV (2012) 4 The Data Set For our analysis, we had access to the database of the insurance contracts of a German insurance company. We analyzed liability, comprehensive, and collision insurance separately, due to the different scopes of the indemnities and liability rules described in the previous section. In fact, these institutional differences are important for the interpretation of the results. We restrict our analysis to a subsample of individual contract owners. By considering contracts which are held by only one person, we make sure that the policy holder s characteristics (and especially their gender) are actually the characteristics (gender) of the driver. I.e. we exclude 5

6 contracts were more than one person is allowed to drive the car to make sure we capture the gender of the person actually driving the car. We use data for the year The data set contains information about each contract for a full contract year. The sample size in the liability insurance is n = 40, 147, n = 12, 574 in the comprehensive insurance, and n = 14, 390 in the collision insurance. There are no deductibles in liability insurance. The level of deductibles in comprehensive insurance are 0, 150, 300, 500 and 1000 Euro; and 0, 150, 300, 500, 1, 000 and 2, 500 Euro in the collision insurance. The collision insurance can be combined with a comprehensive insurance with a deductible of either 0, 150 or the deductible of the collision insurance. Our data set stems from a regional insurance company which has a significant market share in its area. It can be assumed that the data is fairly representative for the German automobile insurance market. 5 Empirical Model and Results 5.1 Pricing in the Automobile Insurance Industry Hedonic Pricing Model Risk classification and the pricing of insurance contracts is the core of actuarial science. 2 To analyze how the characteristic gender enters into the pricing formula and to assess the implicit price of the individual specific characteristics and contract characteristics such as coverage, we apply a hedonic price / premium function approach. A hedonic price function describes the equilibrium relationship between the characteristics of a product and its price. They are used to predict the prices of new goods, to adjust for quality change in price indexes, and to measure consumer and producer valuations of differentiated products. 3 pricing approach was applied to insurance by Puelz and Kemmsies (1993). The hedonic To estimate the implicit prices of gender and other underwriting attributes in the premium functions for the three types of insurance coverage, viz., liability, comprehensive and collision coverage, we apply the following hedonic function for each individual i 2 A comparison of different pricing methods is given in Weisberg et al. (1984). 3 For a survey article on hedonic price functions, we refer to Nesheim (2006). 6

7 k l m P i = β 0 + β 1j Q ij + β 2j T C ij + β 3j RC ij + β KT KT i + + n β 4j AGE ij + β GEN GEN i + 2n β j AGE ij GEN i + +β GAR GAR i + β EP EP i + β P O P O i + β P RO P RO i + l +β AGE CAR AGE CAR i + β 5j BMC ij (5.1) Q ij : choice of deductible (not for third party liability) T C ij : type of car RC ij : regional class KT i : kilometers traveled AGE ij : ageclass of driver GEN i : gender GAR i : garage available EP i : engine power P O i : period of ownership P RO i : proprietary AGE CAR i : age of car (continuous) BMC ij : bonus malus coefficient (not for comprehensive coverage) For categorical variables, e.g., choice of deductible Q ij, type of vehicle T C ij, one category is omitted when estimating the regression equation in order to prevent multicollinearity. This category serves as a reference category when interpreting the results. Only for age of the driver did we use a deviant classification. We defined one age group for people between 17 and 20 years but created the other intervals in steps of 5 years. 7

8 5.1.2 Regression Results The results of our hedonic premium regression are given in Table 2. In this table we only included the variables we discuss. 4 Our main findings can be summarized as follows: young men, respectively, old women, pay higher premiums than young women, respectively, old men. While the pricing difference for young adults is common knowledge among actuaries, the results for old adults is quite surprising as it is also important for the evaluation of the effects of the gender ban in car insurance contracts. In liability insurance, young men (21 25 years) pay about 131 Euro more than middle aged men (41 45), which are used as the reference category. Young females, however, pay ( = -2) 2 Euro less than the group of middle aged men in the age category from 21 to 25. This in turn means that young men pay about 133 Euro more than young females when the age group from 21 to 25 is regarded. A pretty similar picture can be derived by analyzing both collision and comprehensive insurance. In collision insurance, a man aged pays about 94 Euro more than a comparable female driver; in comprehensive insurance, a man aged pays about 26 Euro more than a comparable female driver. However, this relationship turns around when the older population is regarded. In the age groups 66 70, 71 75, and female drivers pay significantly more than comparable male drivers. For instance, women between 71 and 75 pay 34 Euro more than comparable men in the liability insurance, 30 Euro more in the collision insurance and 7 Euro more in the comprehensive insurance. We now derive what unisex tariffs might look like by applying two different methods: one that is more likely to be implemented by the insurance company, and one that is more likely to implement the intentions of the legislature. Table 2: Regression results with gender (liability) (collision) (comprehensive) VARIABLES premium in euro premium in euro premium in euro age *** * *** (29.924) (23.208) (10.907) age *** *** *** (5.942) (13.042) (3.781) age *** *** *** (2.964) (7.479) (1.947) age *** *** *** (2.651) (6.892) (1.475) age *** *** 3.565** (2.725) (7.527) (1.499) age4145 Left out group age *** (2.908) (7.677) (1.375) age *** ** (2.995) (7.676) (1.332) age *** *** 4 The full table can be reviewed in the appendix, which is available upon request from the authors. 8

9 Table 2: Regression results with gender (liability) (collision) (comprehensive) VARIABLES premium in euro premium in euro premium in euro (3.046) (7.410) (1.414) age *** *** *** (3.089) (7.961) (1.426) age *** *** *** (3.423) (7.323) (1.523) age *** *** *** (3.987) (7.855) (1.707) age *** *** *** (6.079) (10.323) (2.068) age *** *** *** (10.155) (14.261) (3.194) age *** *** *** (29.488) (45.036) (4.735) age1720 female *** (33.860) (14.638) age2125 female *** *** *** (7.134) (13.913) (4.142) age2630 female *** *** *** (4.256) (9.058) (2.521) age3135 female *** * (3.898) (8.570) (2.030) age3640 female *** (4.014) (9.297) (2.068) age4145 female Left out group age4650 female (4.380) (9.342) (1.954) age5155 female (4.451) (9.384) (1.888) age5660 female *** (4.509) (9.272) (2.053) age6165 female *** (4.553) (9.838) (2.352) age6670 female ** *** 5.255** (5.179) (9.552) (2.416) age7175 female *** *** 6.726*** (5.901) (10.267) (2.527) age7680 female ** *** 9.791*** (10.516) (13.836) (3.318) age8185 female * (21.749) (38.585) (5.340) age8690 female * (47.778) ( ) (9.596) female 7.996*** *** (3.074) (6.571) (1.426) kilometers per year in *** *** 1.841*** (0.273) (0.435) (0.117) engine power 0.297*** 0.459*** 0.314*** (0.025) (0.072) (0.024) age of car 5.033*** *** 0.601*** (0.180) (0.665) (0.091) period of ownership *** *** *** (0.186) (0.395) (0.091) Observations 32,044 11,891 13,599 Adjusted R-squared Robust standard errors in parentheses *** p < 0.01, ** p < 0.05, * p < 0.1 9

10 5.2 What Unisex Tariffs might look like Overview of different procedures In order to realize a ban of classification variables, gender in our case, there are different possibilities for how to implement the guidelines. Pope and Sydnor (2011) propose several approaches and compare them in the context of regression analysis. The common approach is to exclude the banned variable from the variables used for risk classification. This implies that the other variables which are correlated with the banned variable might take over some of this effect. This might thwart the intended idea of the legislative body to prohibit discrimination, as proxy variables restore discrimination. E.g., in automobile insurance, gender might be correlated with engine power and in the case of a ban on gender as a pricing variable, engine power will serve as a proxy for gender. Pope and Sydnor (2011) propose a method for eliminating such side effects. Their idea is to use all, i.e., even the banned variables, for risk classification and pricing in a first step. Now, in order to make predictions they take, in a second step, the estimated coefficients of the allowed variables and average over the banned variable. In our case, one would use all variables and then set up the pricing formula. The premium of an insuree is then the average of the premium of a male and a female using the pricing formula of the first step, all other variables being equal. There are two comments worth making: The approach of Pope and Sydnor (2011) has a lower predictive power than the common one. Pope and Sydnor (2011) provide both theoretical and empirical support for this ranking. Inasmuch as only the direct use of a certain variable has been forbidden, insurance companies would choose the common approach, as it gives a better risk classification. We assume at this stage that the legislature, however, favor the Pope Sydnor method. This method ensures that gender is fully disregarded in the model. The proposed procedure is not directly applicable to insurance pricing. Under the assumption of actuarially fair premium calculation and that the composition of the risk pool does not change, simple averaging is not sufficient and must be replaced by a weighted average according to the distribution in the data set. E.g., in our application, the premium of male and female must be weighted according to their proportion in the data set. Otherwise the side condition, that the premium income is equal to the payments for claims, is not fulfilled. In order to calculate the gender-adjusted premium according to Pope and Sydnor (2011), the variable gender has to be collected. This might be counterproductive as on the 10

11 one hand discrimination should be prevented, but on the other hand this information must be known by the insurance company What the insurance company implements: the common method In this section, we respond to the question whether the implementation of unisex tariffs will lead to significant changes in what male and female drivers have to pay if the insurance company were to simply drop gender from the equation. This, however, would allow other factors to capture the original gender effects, so that parts of the gender effect might still be in the model even if gender is taken out as a risk factor itself. We apply the following hedonic function, which differs from equation (5.1) only in the fact that gender and the gender interaction terms are left out: k l m P i = β 0 + β 1j Q ij + β 2j T C ij + β 3j RC ij + β KT KT i + + n β 4j AGE ij + β GAR GAR i + β EP EP i + β P O P O i + l +β P RO P RO i + β AGE CAR AGE CAR i + β 5j BMC ij. (5.2) In Table 3 we see the pricing regression results when gender is disregarded as an independent variable. To have an indicator for the loss in predictive power due to omitting gender as a pricing variable, we analyze the decrease in the adjusted R 2. The results are presented in Table 4. The adjusted R 2 decreases by less than 1% in each case. It seems to be the case that still a very high predictive power is present even after omitting the gender variable. So, the gender information seems to be captured quite well in the other independent variables. Engine power, for example has a strong negative correlation to gender (-0.226). If gender is omitted, of course, men and women approaching the insurance company with the exact same driver and car characteristics would pay the same. However, driver and car characteristics are unequally distributed between male and female drivers. Table 7 presents the mean of the variables engine power, kilometers per year, age of car, and period of ownership. On average male drivers are associated with a higher engine power, more kilometers per year, an older car and a shorter period of ownership than female drivers. All of these values lead to a positive price mark-up. It can be easily imagined, how the respective coefficients for the variables 11

12 Table 3: Regression results without gender (liability) (collision) (comprehensive) VARIABLES premium in euro premium in euro premium in euro age *** *** (17.439) (23.156) (7.350) age *** *** *** (3.910) (6.923) (1.813) age *** *** *** (2.306) (5.211) (1.338) age *** *** *** (2.084) (4.821) (1.088) age *** *** 2.825*** (2.087) (5.029) (1.091) age4145 Left out group age *** (2.225) (5.059) (1.007) age *** *** (2.292) (5.110) (0.986) age ** *** *** (2.342) (5.070) (1.062) age *** *** *** (2.397) (5.499) (1.133) age *** *** (2.722) (5.256) (1.201) age *** *** *** (3.194) (5.844) (1.314) age *** *** *** (5.125) (8.096) (1.670) age *** *** *** (9.070) (13.480) (2.635) age *** *** *** (23.582) (62.134) (4.241) kilometers per year in *** *** 1.839*** (0.269) (0.433) (0.116) engine power kw 0.307*** 0.473*** 0.322*** (0.025) (0.072) (0.024) age of car 5.147*** *** 0.638*** (0.180) (0.667) (0.091) period of ownership *** *** *** (0.187) (0.395) (0.091) Observations 32,044 11,891 13,599 Adjusted R-squared Robust standard errors in parentheses *** p < 0.01, ** p < 0.05, * p <

13 Table 4: Adjusted R 2 with gender without gender decrease of adj. R 2 liability % collision % comprehensive % engine power, kilometers per year, age of car, and period of ownership can be adjusted so that they would also capture the gender information. Table 5: Mean Variables by Gender age mean-male mean-female p-value engine power in hp kilometers per year in age of car in years period ownership in years We also analyzed the correlation between predicted premiums and actual premiums when gender is disregarded as a pricing variable. In liability insurance, this correlation is if gender is used as a risk factor and it decreases only marginally when gender is disregarded, to This can be seen as further evidence that most of the gender effect can be captured very easily by other variables. So, even after the implementation of unisex tariffs, insurance firms will be able to establish the same premium differences between male and female drivers. To better understand these results, we also investigat the claims data. We analyzed the effect of gender on the number of claims for different age groups without controlling for other variables, and found evidence that young male drivers indeed seem to have a higher accident probability than young females. To control for the influence of other variables, we also conducted the following Poisson regression with gender as an independent variable and without gender as an independent variable. The number of claims is Poisson distributed P(λ i ) with 13

14 Table 6: Correlation between predicted probabilities and claim frequency including gender excluding gender liability p-value 0 0 collision p-value 0 0 comprehensive p-value 0 0 k l m λ i = β 0 + β 1j Q ij + β 2j T C ij + β 3j RC ij + β KT KT i + + n β 4j AGE ij + 2n β j AGE ij GEN i + β GEN GEN i + +β GAR GAR i + β EP EP i + β P O P O i + β P RO P RO i + l +β AGE CAR AGE CAR i + β 5j BMC ij (5.3) We assume that the number of accidents in which an individual is involved during a period is Poisson distributed (cf. Dionne and Vanasse, 1992). In doing so, we make the assumptions that the accidents of an individual are independent over time, the length of a time period influences the probability that an individual has a certain number of accidents in that period, and the probability that an individual has more than one accident during a period is small (Dionne and Vanasse, 1992). The Poisson regression results reveal that, controlling for all other variables, gender has only a weak influence on the loss probabilities. This means that if we keep all other variables fixed, there is only little difference in the loss probabilities due to gender. We also calculated the correlation between the predicted probabilities from both types of estimations (with gender and without gender) and the actual losses. The correlations summarized in Table 6 support our suggestion that other variables seem to be good enough for an appropriate risk assessment. The results together seem to suggest that gender provides information about loss probabilites however, this information can indeed be captured by other pricing variables. Our 14

15 main finding in this paragraph is that insurance firms could respond to the unisex requirement by simply omitting the gender variable because this methodolgy provides almost an identical predictive accuracy. Due to the high correlations between other pricing variables and gender, omitting the socially unacceptable variable yields an omitted variable bias. Thus, the gender information is partially captured by the other variables as soon as it is disregarded. Therefore, we observe only a slight decrease in the predicitve power of our pricing model when gender is dropped from the premium formula. This in turn shows that even after the implementation of unisex tariffs, insurance firms can establish nearly the exact same premium differences between male and female drivers. Of course, this is not what the legislature intends. In the following subsection we present unisex tariffs for different age groups calculated according to the method of Pope and Sydnor (2011) The Pope and Sydnor (2011) method - a two step procedure For our calculation, we applied the method proposed by Sydnor and Pope (2011). Our weighting is based on the actual proportion of male and female drivers in a specific age group. The figures in the Table 7 are still related to the reference group, males aged In liability insurance, young men (17 20) have to pay about 234 Euro more than middle aged males (the reference group) in the prevalent pricing scheme including gender. Young females, however, have to pay just 154 Euro (154 = ) more than the female reference group. These estimates are derived from Table 2. We then calculate nondiscriminatory tariffs by weighting these estimates with the corresponding gender fraction (i.e., =0.475* *233.85). We make the tacit assumption that the decomposition of gender proportion does not change due to changed premiums. For this exercise, we can conclude that if unisex tariffs are implemented for different age groups, young males will have to pay about 40 Euro less and young females about 40 Euro more than before. We also see how these subsidizing effects turn around for old age women and men: women between 66 and 70 pay about 80 Euro more than the reference group of middle aged men, whereas comparable men pay about 60 Euro more. Our unisex tariff calculation suggests that after the implementation of unisex tariffs, women will pay about 15 Euro less in this age group while male drivers will pay about 5 Euro more. In these calculations, we neglected the fact that the insurance company might add some mark-ups to the premiums because they do not know how the risk pool might change because of the implementation of unisex tariffs. 15

16 Table 7: Tariffs according to the two step procedure Liability insurance Comprehensive insurance Collision insurance delta unisex delta female delta male delta unisex delta female delta male delta unisex delta female delta male age age age age age age age age age age age age age age age Discussion and Policy Implications In this paper, we first analyze the influence of gender as a pricing variable in premium calculations before the implementation of unisex tariffs. Our results revealed that gender is used as a risk factor in the automobile insurance industry and that the differences in prices due to gender differences can be quite high. A 21 year old man would pay 130 Euro more than middle aged men, while comparable female drivers pay even 2 Euro less than the group of middle aged men in liability insurance. The difference in prices due to gender seems to be very high compared to the study of Puelz and Kemmsies (1993) analyzing the gender ban in the U.S. which took place in the 1980s. While it is a commonly known fact that young male drivers pay more than young female drivers, our data reveals that this relation turns around for the old age groups. This means that the introduction of unisex tariffs might not only favor male drivers but also female drivers, something which has been overwhelmingly ignored in this discussion. Although non-discriminatory tariffs are mandatory since December 2012, no methodology was specified. Pope and Sydnor (2011) suggest that two models might fit here: the common method of simply omitting the gender variable and the Pope Sydnor method, which is based on the full information predictive power of the other independent variables and the average of the banned variable. Pope and Sydnor (2011) show theoretically and empirically that the common method is the second best method in terms of predictive accuracy. Since this is the basis of risk classification, we assume that insurance firms will use the common method after the implementation of unisex tariffs. The common method has nearly the exact same predictive power as the full method using all the independent variables, even the 16

17 banned one, for the premium calculation. We showed this by comparing the adjusted R 2 and the correlation between predicted loss probabilities and actual damages. However, we also wanted to see what the regulator intended. We assume that the legislators intended that gender be fully disregarded in the premium calculation, and thus we applied the Pope Sydnor method to derive unisex tariffs. Our results show that a unisex tariff would add a general price mark-up of about 45 Euro for the 21 old drivers over the middle aged group (41 45) years. So, male drivers would pay about 85 Euro less than before, while female drivers would pay 47 Euro more than before. We are aware of the problem that firms might use more sophisticated models to calculate unisex tariffs than in our method of weighting the premium loads with the respective gender proportion however, we think that these results can be used as first estimates. This means that although the legislators intended quite large changes in what male and female drivers have to pay, insurance firms using the common method will be able to establish nearly the exact same pricing differences between male and female drivers even when they have to omit the gender variable. The question arises of how the legislators could make sure that what was intended is actually implemented: one idea might be to specify a methodology for implementing unisex tariffs. If the legislators had required the application of the Pope Sydnor method, this problem would not exist. A second in our opinion less elegant solution would be to also forbid the use of pricing variables that are correlated to gender. Pope and Sydnor (2011) report that in California in 1988 variables such as credit scores that were correlated to banned variables such as income were also forbidden. This would mean that in our case the legislators would have to ban for example the use of engine power as a pricing variable since it is correlated to gender. However, banning all the variables that are correlated to gender will lead to a very restricted model, in the terminology of Pope and Sydnor (2011), with low predictive accuracy. This in turn might induce insurance companies to increase overall premiums because of the increase in estimation uncertainty. This is why we suggest that requiring specific models might be the best way for the legislators to see their intentions implemented. 7 Conclusion In this article, we examined the role of gender in risk classification in the automobile insurance industry. We used a German insurer s risk pool for 2011 to estimate the differences in premiums that exist due to the use of gender as a risk factor. Our estimations revealed that young men pay more than young female drivers, however this relationship turns around for older people. So, one of our first findings was that gender as a tariff calculation component is 17

18 important in interaction with age. We then showed how unisex tariffs could be implemented: first by using the common method of simply dropping the gender variable, and then by using the Pope and Sydnor (2011) method. We find that insurance firms can easily rebuild virtually the exact same differences in prices between male and female drivers when gender is excluded from the calculation of the premium. We then estimated whether the differences in premiums are based on loss data. As it turns out, gender has only weak explanatory power for our loss data when we controlled for all other risk variables. However, our data suggests that gender can be used for an appropriate risk assessment since this variable seems to be correlated with other risk variables. Our Pope and Sydnor (2011) estimates for unisex tariffs suggest that young males would have to pay about 40 Euro less than before whereas young females will have to pay about 40 Euro more for liability insurance. After the implementation of unisex tariffs, women in the age group will pay about 15 Euro less than before, while comparable male drivers will pay about 5 Euro more. 5 As argued above, the Pope and Sydnor (2011) method has less predictive power than the common method. So, we would suggest that insurance firms will simply drop gender out of the equation although the legislators intended the Pope Sydnor method. Thus, our findings have two major implications for the consequences of unisex tariffs in the automobile insurance: first, it might be the case that even after the implementation of unisex tariffs, there might be significant differences in what male and female drivers pay and second, at least in automobile insurance, it seems to be exaggerated that the average premium level has to increase because of the introduction of unisex tariffs and the connected fear of adverse selection. To make sure that insurance firms implement unisex tariffs in the desired way, the legislation would have to make sure that the Pope Sydnor method is applied however, this requirement does not exist. This paper has emphasized that determining what is socially fair and legal is only the first step for the legislators in a second step, the legislators have to specify how their intention is to be put into practice in order to make sure that insurance firms do not exploit methodolocial arbitrage. Ironically, the application of the Pope Sydnor method requires the gender information. So, the legislation would have to make sure that insurance firms still elicit the gender information to guarantee unisex tariffs that really do not incorporate any gender effects. 5 This calculation was carried out under the tacit assumption that the gender decomposition does not change, which might be a first approximation. 18

19 References Association of British Insurers (ABI), The role of risk classification in insurance. ABI Research Paper No. 11, Cohen, A., Siegelman, P., Testing for adverse selection in insurance markets. Journal of Risk and Insurance 77, Crocker, K.-J., Snow, A., The theory of risk classification. In: G. Dionne, editor, Handbook of Insurance, Chapter 8, pp Kluwer Academic Publishers. Curia Europa, Taking the gender of the insured individual into account as a risk factor in insurance contracts constitutes discrimination. Court of Justice of the European Union, 12, pp Dionne, G., Doherty, N., Fombaron, N., Adverse selection in insurance markets. In: G. Dionne, editor, Handbook of Insurance, Chapter 7, pp Kluwer Academic Publishers. Dionne, G., Vanasse, C., Automobile insurance ratemaking in the presence of asymmetrical information. Journal of Applied Econometrics 7(2), Gesamtverband der Deutschen Versicherungswirtschaft (GDV), Statistisches Taschenbuch der Versicherungswirtschaft Harrington, S., Doerpinghaus, H., The economics and politics of automobile insurance rate classification. The Journal of Risk and Insurance 60, Moennich, U., Unisex: Die EuGH-Entscheidung vom und die möglichen Folgen. Versicherungsrecht, 62, Moennich, U., Unisex-Tarife fr Versicherungen: Die EuGH-Entscheidung vom 1. März ein Jahr später. Versicherungsrundschau, 03/12, Nesheim, L., Hedonic price functions. CENMMAP working paper CWP18/06. Pope, D.G., Sydnor, J.R., Implementing anti-discriminating policies in statistical profiling models. American Economic Journal: Economic Policy 3, Puelz, R., Snow, A., Evidence on adverse selection: Equilibrium signaling and crosssubsidization in the insurance market. Journal of Political Economy 102,

20 Puelz, R., Kemmsies, W., Implications for unisex statutes and risk-pooling: The costs of gender and underwriting attributes in the automobile insurance market. Journal of Regulatory Economics 5, Rothschild, M., Stiglitz, J.E., Equilibrium in competitive insurance markets: An essay on the economics of imperfect information. Quarterly Journal of Economics 90, Thiery, Y., Van Schoubroeck, C., Fairness and Equality in Insurance Classification. The Geneva Papers on Risk and Insurance-Issues and Practice, 31, Weisberg, H., Tomberlin, T., Chatterjee, S., Predicting insurance losses under crossclassification: A comparison of alternative approaches. Journal of Business and Economic Statistics 2, Winter, R., Optimal insurance under moral hazard. In: G. Dionne, editor, Handbook of Insurance, Chapter 6, pp Kluwer Academic Publishers. 20

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