Optimal Banking Contracts and Financial Fragility

Abstract

We study a finite-depositor version of the Diamond-Dybvig model of financial intermediation in which the bank and all depositors observe withdrawals as they occur. We derive the (constrained) efficient allocation of resources in closed-form and show that this allocation provides liquidity insurance to depositors. The contractual arrangement that decentralizes this allocation has debt-like features and resembles the type of demand deposits commonly offered by banking institutions. We provide examples where this arrangement admits another equilibrium in which some depositors run on the bank, withdrawing funds regardless of their liquidity needs. A bank run in our setting is always partial, with only those depositors who can withdraw sufficiently early participating. Depositors who are late to withdraw during a run suffer significant discounts from the face value of their deposits. The run, while partial, may involve a large number of depositors and result in significant inefficiencies. JEL Classification Numbers: G21,G01, D82 We thank seminar participants at the University of Iowa, the Federal Reserve Bank of Richmond, and 2010 Winter Meetings of the Econometric Society for useful comments.

On Freezing Depositor Funds at Financially Distressed Banks: An Experimental Analysis

“…9 Over the last 30 years an extensive theoretical literature analyzing and developing the basic Diamond-Dybvig framework has evolved. 10 In particular, banking economists have devoted considerable effort to identifying contract conditions that eliminate the degenerate "run" outcome as a Nash equilibrium under various information conditions (see, e.g., Green and Lin 2003, Peck and Shell 2003, Ennis and Keister, 2016 A corresponding experimental literature on financial fragility has also developed in the last several years. See, for example, Madiés (2006), Garratt and Keister (2009), Schotter and Yorulmazer (2009), Arifovic, Jaing and Xu (2013, 2015, Klos and Sträter (2008), Trautmann and Vlahu (2013), Kiss, Rodriguez-Lara, and Rosa-Garcia (2012, 2014a, 2014b, Brown, Trautmann, and Vlahu (2016), and Chakravarty, Fonseca, and Kaplan (2014).…”

“…Under a different information scheme Peck and Shell (2003) show that the inefficient "run" solution cannot be ruled out-specifically in the case that depositors do not know their order in the queue of depositors and that only those depositors wishing to withdraw actually approach the bank. More recently Ennis and Keister (2016) examine a hybrid of these two models in which depositors know something about their order in sequence (as in Green and Lin), but only those depositors making withdrawals actually go to the bank (as in Peck and Shell). Ennis and Keister establish the appealing result that in such a situation the inefficient "run" equilibrium cannot be ruled out, but the fragile outcome will necessarily involve only a partial run, with a subset of depositors approaching the bank first choosing to withdraw.…”