• Principal–agent model;
  • moral hazard;
  • first-order approach;
  • multiple signals

This paper presents simple new multisignal generalizations of the two classic methods used to justify the first-order approach to moral hazard principal–agent problems, and compares these two approaches with each other. The paper first discusses limitations of previous generalizations. Then a state-space formulation is used to obtain a new multisignal generalization of the Jewitt (1988) conditions. Next, using the Mirrlees formulation, new multisignal generalizations of the convexity of the distribution function condition (CDFC) approach of Rogerson (1985) and Sinclair-Desgagné (1994) are obtained. Vector calculus methods are used to derive easy-to-check local conditions for our generalization of the CDFC. Finally, we argue that the Jewitt conditions may generalize more flexibly than the CDFC to the multisignal case. This is because, with many signals, the principal can become very well informed about the agent's action and, even in the one-signal case, the CDFC must fail when the signal becomes very accurate.