On the optimal use of correlated information in contractual design under limited liability

Riordan and Sappington (JET, 1988) show that in an agency relationship in which the type of the agent is correlated with a signal that is observed publicly ex post, the principal may attain first best (full surplus extraction and efficient output levels) if she offers the agent a lottery such that each type is rewarded for one signal realization and punished equally for all the others. Gary-Bobo and Spiegel (RAND, 2006) show that this kind of lottery is most likely to be locally incentive-compatible when the agent is protected by limited liability. In this paper we investigate how the principal should construct the lottery to attain not only local but also global incentive-compatibility. We first assess that the main issue with global incentive-compatibility rests with intermediate types being potentially attractive reports to both lower- and higher-order types. We then show that a lottery including three (rather than two) levels of profit is most likely to be globally incentive-compatible under limited liability, if local incentive constraints are strictly satisfied. We identify conditions under which first best is implemented and pin down the optimal distortions when those conditions are violated. In particular, when the first-best allocation is locally but not globally incentive-compatible, output distortions are induced but no information rent is conceded to the agent.