Dynamic Incentive Contracts under Parameter Uncertainty

Dynamic Incentive Contracts under Parameter Uncertainty We analyze a long-term contracting problem involving common uncertainty about a parameter capturing the productivity of the relationship, and featuring a hidden action for the agent. We develop an approach that works for any utility function when the parameter and noise are normally distributed and when the effort and noise affect output additively. We then analytically solve for the optimal contract when the agent has exponential utility. We find that the Pareto frontier shifts out as information about the agent’s quality improves. In the standard spot-market setup, by contrast, when the parameter measures the agent’s “quality”, the Pareto frontier shifts inwards with better information. Commitment is therefore more valuable when quality is known more precisely. Incentives then are easier to provide because the agent has less room to manipulate the beliefs of the principal. Moreover, in contrast to results under one-period commitment, wage volatility declines as experience accumulates. JEL Classification: D82, D83, E24, J41 Keywords: principal-agent model, optimal contract, learning, private information, reputation, career Corresponding author: Julien Prat Institute of Economic Analysis (IAE-CSIC) Campus UAB 08193 Bellaterra, Barcelona Spain E-mail: [email protected] * We thank Heski Bar-Isaac, Pieter Gautier, Robert Kohn, Albert Marcet, Ennio Stacchetti as well as seminar participants at the IMT Institute in Lucca, the Tinbergen Institute, University of CergyPontoise, University of Essex, Stockholm Institute for International Economic Studies (IIES), and the Minnesota Macro Workshop for comments and suggestions. We acknowledge the support of the Kauffman Foundation and of the Barcelona GSE. 1 Introduction Agency relationships often preclude complete monitoring so that a principal cannot observe the agent’s actions. Other features of the environment, such as the manager’s ability, the quality of his match with the …rm, or the pro…tability of the project under management, can also be a source of uncertainty. Many relationships between …rms and workers, as well as between lenders and borrowers, are of this general form. Yet, little is known about how parameter and e¤ort uncertainty interact to shape the optimal design of incentive contracts. Does parameter uncertainty reinforce or alleviate moral hazard concerns? Does it render commitment more or less valuable? This paper provides some answers to these questions by focusing on cases where: (i) the unknown parameter remains constant over time; and (ii) a risk neutral principal and a risk averse agent commit to a long-term contract. Under full-commitment, incentives are designed to reward e¤ort and not ability. Disentangling the two is not always feasible for the principal because they both in‡uence his only source of information, i.e., realized revenues. Signal confusion enables the agent to manipulate the principal’s beliefs. If the agent shirks (i.e., provides less e¤ort than recommended), output will be below expectation and the principal will infer that the match productivity is lower than he had thought. The agent, on the other hand, knows that low output was caused not by low productivity but by low e¤ort and so, after shirking, is more optimistic about the value of the unknown parameter than the principal. Compared to the situation in which all parameters are known, a given indexation of future earnings to performance entails lower punishments for shirkers. By inducing the principal to underestimate the match productivity, a shirker knows that he will bene…t in the future from overestimated inferences about his e¤ort and thus higher rewards. In order to prevent such belief manipulation, a long-term contract under parameter uncertainty must entail a higher indexation to performance. This raises income volatility, which lowers the welfare of the risk-averse agent. Moreover, if the unknown parameter is constant, belief manipulation is more e¤ective early on in the relationship because posteriors put higher weight on new information. This is why the sensitivity of pay to performance declines over time.1 These implications stand in sharp contrast to the ones derived in the literature on career concerns where the unknown parameter measures the agent’s general ability, transferable from job to job. Analyzing this class of problems under spot markets with up-front pay only, Holmström (1999) concludes that incentives are more easily 1Given a level of lifetime utility that the contract promises him, it is in the agent’s interest to bias downward the principal’s belief about his ability. This was also a feature in the ratchet e¤ect model of La¤ont and Tirole (1988). They consider an environment with adverse selection so that the agent knows the actual productivity. By contrast, asymmetric beliefs do not exist from the outset in our model but arise endogenously, and then only o¤ the equilibrium path.