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BANK RUNS: THE PREDEPOSIT GAME

Published online by Cambridge University Press:  07 June 2018

Karl Shell  and
Yu Zhang
Karl Shell
Affiliation:
Cornell University
Yu Zhang*
Affiliation:
Xiamen University
*
Address correspondence to: Yu Zhang, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, Xiamen361005, Fujian Province, China; e-mail: yuzhang2012@xmu.edu.cn.
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Abstract

We analyze in some detail the full predeposit game in a simple, tractable, yet very rich, banking environment. How does run-risk affect the optimal deposit contract? If there is a run equilibrium in the postdeposit game, then the optimal contract in the predeposit game tolerates small-probability runs. However, this does not mean that small changes in run-risk are ignored. In some cases, the optimal contract becomes—as one would expect—strictly more conservative as the run-probability increases (until it switches to the best run-proof contract), and the equilibrium allocation is not a mere randomization over the equilibrium allocations from the postdeposit game. In other cases, the allocation is a mere randomization over the equilibria from the postdeposit game. In the first cases (the more intuitive cases), the incentive constraint does not bind. In the second cases, the incentive constraint does bind.

Keywords

Bank RunsPredeposit GameRun ProbabilitySunspots
Type
Articles
Information
Macroeconomic Dynamics , Volume 24 , Issue 2 , March 2020 , pp. 403 - 420
Copyright
© Cambridge University Press 2018

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Footnotes

We thank Huberto Ennis, Chao Gu, Todd Keister, Jim Peck, the referee, and the associate editor for their helpful comments.

References

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