How Do Unisex Rating Regulations Affect Gender Differences in Insurance Premiums?

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.

Appendix

Kernel density plots

Figure A1

Figure A2

Figure A3

Poisson and claims regression

Table A1

Table A2

Table A2 Claims regression results for full and omitted model

Simulation

Explanation of variables:

x1, x2, x3, x5::

uniformly distributed on the interval [0, 1) and correlated with each other

x4, x6::

uniformly distributed on the interval [0, 1) and correlated with each other

x7::

uniformly distributed on the interval [0, 1)

x2x3::

interaction term x2∗x3

x3x4::

interaction term x3∗x4

x2x6::

interaction term x2∗x6

y::

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::

represents the insurer’s predicted premium

Explanation of the simulation approach:

• See Table A3 for the outputs of the linear models and Table A4 for the outputs of the non-linear models.

  Table A3 Extended simulation—linear model

  Table A4 Extended simulation—non-linear model

• Column (1): Regression of y on all variables that are generating y.

• 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.

• Column (3): Estimation of the insurers pricing formula including the discriminating variable, this regression resembles the full model.

• Column (4): Estimation of the omitted model on the insurers prices y_hat.

• Column (5): Estimation of the omitted model on the true claims y.

• Columns (6)–(9): Repetition of columns (2)–(5), but the “insurer” additionally includes the interaction term x2x6.

Key findings

• The results of the simple simulation (see Table 3 in the paper) also hold for a more general setting.

• 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.

Table A3

Table A4