Endogenous Selection and Moral Hazard in Compensation Contracts

TLDR: The authors formulate two complementary generalized principal-agent models that incorporate features observed in real world contracting environments (e.g., agents with power utility and limited liability, lognormal stock price distributions, and stock options) as mathematical programs with equilibrium constraints (MPEC).

Abstract: The two major paradigms in the theoretical agency literature are moral hazard (i.e., hidden action) and adverse selection (i.e., hidden information). Prior research typically solves these problems in isolation, as opposed to simultaneously incorporating both adverse selection and moral hazard features. We formulate two complementary generalized principal-agent models that incorporate features observed in real world contracting environments (e.g., agents with power utility and limited liability, lognormal stock price distributions, and stock options) as mathematical programs with equilibrium constraints (MPEC). We use state- of-the-art numerical algorithms to solve the resulting models. We find that many of the standard results no longer obtain when wealth effects are present. We also develop a new measure of incentives calculated as the change in the agent's certainty equivalent under the optimal contract for a change in action evaluated at the optimal action. This measure facilitates interpretation of the resulting contracts and allows us to compare contracts across different contracting environments.