On sunspots, bank runs, and Glass–Steagall

• Date: 01 March 2019
• Author: Yu Zhang,Karl Shell
• Published date: 01 March 2019
• DOI: http://doi.org/10.1111/ijet.12208

doi: 10.1111/ijet.12208

On sunspots, bank runs, and Glass–Steagall

Karl Shell∗and Yu Zhang†

We analyze the pre-deposit game in a two-depositor banking model. The Glass–Steagall bank

is assumed to be restricted to holding only liquid assets. Depositors tolerate a panic-based run

if its probability of occurrence sis small. How saffects the allocation of assets depends on the

incentive compatibility constraint (ICC). When the ICC is not binding, the sunspot allocation

is not a mere randomization over the run and non-run outcomes under the so-called “optimal

contract.” We offer this paper as a contribution to both the literature on banking and financial

fragility and also the broader literature on sunspot equilibrium.

Key wor ds bank run, deposit contract, Glass–Steagall banking, illiquid asset, liquid asset,

merchant banking, pre-deposit game, post-deposit game, run probability, sunspot

JEL classification G21, E44

Accepted 26 June2018

1 Introduction

We analyze a banking model based on Peck and Shell (2010). As in Wallace (1996), there are two

investment assets: one liquid and the other illiquid. Two financial systems are compared. In the

separated financial system there are two separate institutions. One holds only the liquid asset. This

might be thought of as a Glass–Steagall bank (GSB), or a narrow bank. The other financial institution

holds only the illiquid asset. It is like a stock brokerageor mutual fund. In the unified financ ial system,

or consolidated system, one institution holds the two assets. This might be thought of as a merchant

bank, or merely a post-Glass–Steagall, pre-Dodd–Frank, modern bank.

As in Peck and Shell (2010), we introduce intrinsic aggregate uncertainty by assuming that the

realized fraction of impatient consumers is itself stochastic. Peck and Shell (2010) assume that there

is a continuum of consumers. We assume that there are only a finite number of consumers.

In the post-deposit game, the unified financial system is immune from sunspot-driven runs, but

for some parameters the unified system runs out of cash when the realized fraction of impatient

consumers is high. The GSB is always susceptible to a sunspot-drivenr un. The run probability sis an

exogenous parameter summarizing the “mood” of the financial sector.If the contract permits a run,

then the probability of the run is s. Of course, if the contract does not permit a run, the probability of

a run is 0. How does the run probability saffect the optimal contract? For small s, runs are tolerated.

In some cases, the contract becomes (as one would expect) strictly more conservative as sincreases.

∗Cornell University,Ithaca, New York, USA. Email: karl.shell@cornell.edu

†Xiamen University,Siming District, Xiamen, Fujian Province, China.

We dedicate this paper to Jess Benhabib and Roger Farmer, the fathers of empirical sunspot modeling of the macro-

economy.

International Journal of Economic Theory 15 (2019) 13–25 © IAET 13

International Journal of Economic Theory