The First-Order Approach to Principal-Agent Problems

The first-order approach to principal-agent problems involves relaxing the constraint that the agent choose an action which is utility maximizing to require instead only that the agent choose an action at which his utility is at a stationary point. Although more mathematically tractable, this approach is generally invalid. This paper identifies sufficient conditions-the monotone likelihood ratio condition and convexity of the distribution function condition-for the first-order approach to be valid. The Pareto-optimal wage contract is shown to be nondecreasing in output under these same conditions. MIRRLEES 5 WAS THE FIRST to point out that the standard method for analyzing the principal-agent problem is not generally correct. This method, the so-called first-order approach, involves weakening the constraint that the agent choose a utility-maximizing action to require instead only that the agent choose an action at which his utility is at a stationary point. The resulting problem is more mathematically tractable. However, as Mirrlees 5 has shown, necessary conditions for a contract to solve the first-order program are not generally even necessary conditions for the valid program. Therefore qualitative propositions about the nature of the Pareto-optimal contract derived from the first-order approach are not in general valid. This has motivated researchers to try to identify classes of cases where the first-order approach is valid.