Insurance markets and unisex tariffs: is the European Court of Justice improving or destroying welfare?

Abstract

We analyze the effects of mandatory unisex tariffs in insurance contracts, such as those required by a recent ruling of the European Court of Justice, on equilibrium insurance premia and equilibrium welfare. In a unified framework, we provide a quantitative analysis of the associated insurance market equilibria in both monopolistic and competitive insurance markets. We investigate the welfare loss caused by regulatory adverse selection and show that unisex tariffs may cause market distortions that significantly reduce overall social welfare.

Keywords:

• insurance
• regulation
• equilibrium
• unisex tariff

Acknowledgements

The authors wish to thank two anonymous referees for valuable and helpful comments. Jörn Sass gratefully acknowledges financial support by Deutsche Forschungsgemeinschaft.

Notes

¹That is, an increasing, concave function of class .

²For CRRA utility with ρ=1, we have u(x)=ln(x).

³There are some mathematical technicalities related to this assumption; see, for instance, Feldman and Gilles (1985) and Judd (1985).

⁴If but it is not clear which is the more favorable risk profile.

⁵For a rigorous formulation of this argument, we refer to Feldman and Gilles (1985).

⁶For instance, a growing literature has highlighted the impact of systematic risk in longevity insurance; see, e.g., Olivieri and Pitacco (2008).

⁷If overinsurance is prohibited, we obtain similar results with the high-risk insurance demand capped at .

⁸See also Wilson (1977). In contrast to Rothschild and Stiglitz (1976) and Wilson (1977), for our analysis we do not require that all agents encounter the same loss given damage.

⁹Hoy (2006) also clarifies that E2 equilibria are relevant if the poportion of high-risk types is small. This appears unlikely in the context of this article, where ; see also Section 7.

¹⁰The corresponding graphs for price-quantity-competition are omitted since they are constant in the range where the equilibrium exists.

¹¹The precise threshold depends on the parameter specification; for the parameters given in Equation (4) the critical value is slightly below 20%.

¹²This conclusion may not apply to Wilson E2 pooling equilibria, where the fraction of high-risk individuals in the population is small. Such a situation would, for instance, be expected in the context of genetic testing results. In this case, Hoy and Polborn (2000) have shown that welfare may be enhanced by banning risk classification.

¹³Non-feasible uniform contract are irrelevant here since they are not selected by ⊕-agents.