Decentralizing Incentive E¢cient Allocations of Economies with Adverse Selection

We study competitive economies with adverse selection and fully exclusive contractual relationships. We consider economies where agents are privately informed over the probability distribution of their endowments, and trade to insure against this uncertainty. As in Prescott-Townsend (1984), we model exclusivity by imposing the incentive compatibility constraints directly on the agents’ consumption possibility set. In this set-up, we identify the externality associated with the presence of adverse selection as a special form of consumption externality. We consider a structure of markets which allows to internalize such externality, for which we show that competitive equilibria exist and are incentive e¢cient. On the other hand, when this ’expanded’ set of markets required to internalize such externality does not exist, competitive equilibria are shown to be, typically, not incentive e¢cient, but to satisfy an appropriately de...ned notion of third best e¢ciency. Appropriate versions of the second welfare theorem for these two market structures are also established. ¤We are grateful to Douglas Gale, Danilo Guaitoli, Atsushi Kajii, Ramon Marimon, Ilya Segal, Paolo Siconol..., Rajiv Vohra, and seminar audiences at the Venice Workshop in Economic Theory, the Minneapolis Fed, the Universities of Harvard-MIT, EUI, Illinois at Urbana-Champaign, Chicago, Hitotsubashi, Tsukuba and Keio for very helpful comments and discussions. The Appendix has been written with Giuseppe Lopomo (NYU-Stern). Part of the work for this paper was carried out when the ...rst author was visiting the Minnenapolis Fed and when the second author was visiting Brown and NYU; we wish to thank the three institutions for their very kind hospitality. We bene...ted from the technical and ...nancial support of the C.V. Starr Center for Applied Economics, the ...nancial support from a NSF Grant to the ...rst author and from a grant from MURST to the second author.