Endogenous Selection and Moral Hazard in Compensation Contracts

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. Electronic copy available at: http://ssrn.com/abstract=1553004 Electronic copy available at: http://ssrn.com/abstract=1553004 Endogenous Selection and Moral HazardIn Compensation Contracts AbstractThe 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 principalagent 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 stateof-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.JEL Classification: C60, C61, J33, M52

Procurement Contracts in the Presence of Endogenous Disruption Risk

“…Our study focuses on analyzing the sourcing strategies of the manufacturer, whereas they concentrate on a measure of incentives that evaluates the effectiveness of the agent's payoff on his action. Despite the differences, observations from the numerical results of Armstrong et al (2010) prove our finding that MI weakly dominates SI in terms of the manufacturer's profit. Chaturvedi and Martínez-de-Albéniz (2011) study optimal auction design when both production cost and exogenous risk are the suppliers' private information.…”

“…Despite the differences, observations from the numerical results of Armstrong et al. () prove our finding that MI weakly dominates SI in terms of the manufacturer's profit. Chaturvedi and Martínez‐de‐Albéniz () study optimal auction design when both production cost and exogenous risk are the suppliers’ private information.…”

“…In this sense, this article is also related to literature investigating multidimensional asymmetric information. Similar to our research, Armstrong, Larcker, and Su (2010) compare a pure adverse selection model with a combination of adverse selection and moral hazard. Our study focuses on analyzing the sourcing strategies of the manufacturer, whereas they concentrate on a measure of incentives that evaluates the effectiveness of the agent's payoff on his action.…”

A Polynomial Optimization Approach to Principal-Agent Problems

“…For this purpose, we first revisit a counterexample to the classical first-order approach presented by Mirrlees (1999) (originally circulated in 1975) and show that we can solve this example with the polynomial approach. Subsequently, we investigate an economic application of principal-agent models, namely, the executive compensation problem in Armstrong, Larcker, and Su (2010). Both examples have in common that they involve exponential functions and, therefore, do not satisfy the assumptions of Theorem 1.…”

“…At least as early as in Haubrich (1994), principal-agent models have been applied to the study of executive compensation contracts. Armstrong, Larcker, and Su (2010) presented a sophisticated study of optimal compensation contracts that emerge from principal-agent models with pure moral hazard, pure adverse selection, or a combination thereof. They pointed out that "the firstorder approach typically fails when realistic contracting features (e.g., nonlinear compensation contracts and nonnormal probability distributions) are incorporated in the model."…”