The Efficiency of Categorical Discrimination in Insurance Markets

ABSTRACT Crocker and Snow (1986) show that banning categorization based on risk-related characteristics such as gender or race in pricing insurance policies is inefficient whenever categorization is costless. Their analysis, by contrast, suggests ambiguous welfare effects of banning costly categorization. I show that this latter conclusion is incorrect: categorical pricing bans are inefficient even when categorization is costly. Whenever the ban-imposing government can instead provide breakeven partial social insurance, it can remove its ban in such a way that the insurance market will choose to employ the categorizing technology only when doing so is Pareto improving. INTRODUCTION Regulations outlawing the use of categorical characteristics such as gender, race, geographic location, and health status in pricing insurance policies are widespread. Such regulations are likely to become more common with the advent of genetic testing and with increasingly sophisticated information technologies. There appears to be a basic economic trade-off involved in employing these sorts of categorical pricing bans. On the one hand, they artificially introduce what amounts to asymmetric information and its associated market inefficiencies (Akerlof, 1970). On the other hand, they may have desirable distributional consequences insofar as they equalize insurance prices or availability across individuals with different characteristics. That is, they may provide implicit insurance against the ex ante risk of being in a risky category (Hirshleifer, 1971). This apparent trade-off is actually illusory in a broad class of settings. For example, Crocker and Snow (1986) show that when firms can costlessly observe categorical characteristics, categorical pricing bans are not merely inefficient at the interim stage after types have been realized but are also a suboptimal way to provide ex ante insurance. Crocker and Snow's analysis suggests, however, that bans on costly categorization have ambiguous welfare effects. I argue in this article that, contrary to their analysis, even bans on costly categorization are inefficient. Crocker and Snow's analysis relies on comparing the utility possibilities frontier in two regimes: one in which categorization is prohibited and one in which it is employed. They show that when categorization is costless, the frontier for the nocategorization regime lies everywhere inside the corresponding frontier for the categorizing regime. When categorization is costly, however, the two frontiers always cross. As such, the two regimes are Pareto incomparable, and the welfare effects of bans on categorical pricing appear to be ambiguous. Crocker and Snow's utility possibilities frontier-based analysis of costly categorization is correct but misleading: it implicitly conflates a regime where categorization is employed with a regime in which it is permitted but in which it may or may not be actually employed in equilibrium. When I carefully disentangle the difference between employing and merely permitting categorization, I show that the apparent ambiguity of the welfare effects of categorical pricing bans disappears. There is a trivial theoretical sense in which "permitting" categorization is more efficient, even if it is costly: the (informationally constrained) utilities possibility frontier in an environment in which categorization can optionally be employed is simply the upper envelope of the "categorize" and "do-not-categorize" frontiers. In practice, however, the decision to employ a costly categorizing technology is a decision made by profit-maximizing firms, and as noted by Crocker and Snow, competitive pressures can lead firms to employ a costly categorizing technology even when doing so does not lead to efficiency gains. To illustrate, consider a market in which categorization is banned. Suppose that there are two categories and that the market equilibrium involves cross-subsidies from individuals in the low-risk category to individuals in the high-risk category. …