Multiple Signals, Statistical Sufficiency, and Pareto Orderings of Best Agency Contracts

In this study we identify necessary and sufficient conditions for sufficient statistics to strictly (Pareto) dominate all nonsufficient statistics as information for contracting in agencies with moral hazard. We first observe that strict dominance requires that an optimal compensation scheme itself be a sufficient statistic. Since this can occur only in settings where the family of distributions parameterized by the agent's hidden effort admits one-dimensional sufficient statistics, strict dominance is the exceptional case. Nevertheless, we are able to show that there exists a substantial class of distributions, containing many well-known families, for which strict dominance does obtain.