On the Non-Optimality of a Diamond-Dybvig Contract in the Goldstein-Pauzner Environment

Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded offi cial Federal Reserve Bank of Cleveland publications. The views stated herein are those of the authors and are not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System. I show, under intuitive conditions on the risk-averse utility function, the non-optimality of the Diamond and Dybvig (1983) contract in the Goldstein and Pauzner (2005) environment. If marginal utility at zero is low enough, then Goldstein and Pauzner (2005)'s claim about the optimality of the Diamond and Dybvig (1983) contract is true. When it is not, the optimal contract insures the patient depositor against a project default. The contract may exhibit risk-sharing with the impatient depositor. Unlike when Goldstein and Pauzner (2005)'s claim is correct, relative risk aversion greater than 1 does not necessarily make the optimal bank contract run-prone. I present a condition under which it is. Mahmoud Elamin is at the Federal Reserve Bank of Cleveland and can be reached at [email protected]. He thanks Joe Haubrich, James Thomson, and Filippo Occhino for helpful conversations and the Cleveland Fed's game theory reading group and seminar participants at the Cleveland Fed for comments.