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Optimal Dynamic Relative Performance Evaluation

The theoretical prediction of a negative coe¢ cient on positively correlated peer performance that underlies much of the empirical literature on relative performance evaluation, is commonly obtained from the special case where variance-covariance matrix of the performance measures is exogenously restricted to be independent of the evaluee’s action. Using the dynamic approach of Holmstrom and Milgrom (1987), I study the properties of contracts that optimally condition an agent’s compensation both on his own performance and on how well he fares relative to a peer (group) when this restriction is not imposed. I show that if the covariance is non-zero, the optimal contract is linear in own and peer performance as well as the correlation between own and peer performance while, in line with the preponderance of the empirical evidence, in it’s simplest and perhaps most reasonable form the model predicts that the expected coe¢ cient on peer performance is exactly zero.