The Value of Information About an Agent's Ability in the Presence of Adverse Selection

We derive the expected value of information about an agent's type in the presence of moral hazard and adverse selection. We show that because of the tradeoff inherent in dealing with two types of information problems, the value is decreasing in the variability of output and the agent's risk aversion, two factors that are typically associated with the severity of the moral hazard problem. This tradeoff occurs because the means available to the principal to induce effort -- namely, the pay performance sensitivity -- must also be used to sort the agents, and these two goals conflict. In contrast, while the value of information initially increases in the severity of the adverse selection problem, it eventually peaks and decreases thereafter. This decline in value occurs despite the uniformly increasing importance of the information in determining the principal's expected profits. Further, we show that the peak value of information occurs at a predictable level of adverse selection. Taken together, these results imply that over some range, the importance of the information will be increasing, while the value of the information will be simultaneously decreasing, in the severity of adverse selection. Finally, we show that for a wide variety of common distributions, information about the agent's ability can be linearly aggregated without loss using relative weights that depend only on the characteristics of the information itself, and not on the production environment nor the agents' preferences. Thus, the optimal weights are more likely to be identical across some groups of agencies, in contrast to those on information about the agent's action in a purely moral hazard setting.