Abstract
As of 21 December 2012, the use of gender as an insurance rating category is prohibited in the EU. Any remaining pricing disparities between men and women will now be traced back to the reasonable pricing of characteristics that happen to differ between the groups or to the pricing of characteristics that differ between sexes in a way that proxies for gender. Using data from an automobile insurer, we analyse how the standard industry approach of simply omitting gender from the pricing formula, which allows for proxy effects, differs from the benchmark for what prices would look like if direct gender effects were removed and other variables did not adjust as proxies. We find that the standard industry approach will likely be influenced by proxy effects for younger and older drivers. Our method can simply be applied to almost any setting where a regulator is considering a uniform pricing reform.
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Notes
For example, ABI (2008) and Crocker and Snow (2013).
For example, Harrington and Doerpinghaus (1993).
For example, Oxera (2011c).
A comprehensive analysis of asymmetric information in the German car insurance market can be found in Spindler et al. (2014).
SAI (2004) and SAI (2011).
In an earlier draft of this paper, we also made the analysis for comprehensive and collision coverage. The results were qualitatively the same.
We are very grateful to an anonymous reviewer for suggesting the simulation approach.
For a survey article on hedonic price functions, refer to Nesheim (2006).
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Acknowledgements
We thank Frederick Schlagenhaft and two anonymous referees for their comments. Moreover, we are grateful to Andreas Richter for invaluable discussions and advice.
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Appendix
Appendix
Kernel density plots
Poisson and claims regression
Simulation
Explanation of variables:
- x1, x2, x3, x5::
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uniformly distributed on the interval [0, 1) and correlated with each other
- x4, x6::
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uniformly distributed on the interval [0, 1) and correlated with each other
- x7::
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uniformly distributed on the interval [0, 1)
- x2x3::
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interaction term x2∗x3
- x3x4::
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interaction term x3∗x4
- x2x6::
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interaction term x2∗x6
- y::
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is the “claims” variable, which is a function of the variables x1, x2, x3, x4, x5, x3x4, x2x3 and a uniformly distributed error term
- y_hat::
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represents the insurer’s predicted premium
Explanation of the simulation approach:
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See Table A3 for the outputs of the linear models and Table A4 for the outputs of the non-linear models.
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Column (1): Regression of y on all variables that are generating y.
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Column (2): Regression the insurer presumably does; a subset of the true data generating variables (x1, x2, x3) plus the additional variable x6 which is correlated with x4 and the additional uncorrelated variable x7.
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Column (3): Estimation of the insurers pricing formula including the discriminating variable, this regression resembles the full model.
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Column (4): Estimation of the omitted model on the insurers prices y_hat.
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Column (5): Estimation of the omitted model on the true claims y.
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Columns (6)–(9): Repetition of columns (2)–(5), but the “insurer” additionally includes the interaction term x2x6.
Key findings
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The results of the simple simulation (see Table 3 in the paper) also hold for a more general setting.
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From the comparison of columns (4) and (5) as well as columns (8) and (9) one can see that coefficients are identical, only standard errors are tighter for the regression using “premium” as dependent variable.
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Aseervatham, V., Lex, C. & Spindler, M. How Do Unisex Rating Regulations Affect Gender Differences in Insurance Premiums?. Geneva Pap Risk Insur Issues Pract 41, 128–160 (2016). https://doi.org/10.1057/gpp.2015.22
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DOI: https://doi.org/10.1057/gpp.2015.22