Run equilibria in the Green–Lin model of financial intermediation

doi:10.1016/j.jet.2009.05.001

Journal of Economic Theory

Volume 144, Issue 5, September 2009, Pages 1996-2020

https://doi.org/10.1016/j.jet.2009.05.001 Get rights and content

Abstract

We study the Green–Lin model of financial intermediation [E.J. Green, P. Lin, Implementing efficient allocations in a model of financial intermediation, J. Econ. Theory 109 (2003) 1–23] under a more general specification of the distribution of types across agents. We derive the efficient allocation in closed form. We show that, in some cases, the intermediary cannot uniquely implement the efficient allocation using a direct revelation mechanism. In these cases, the mechanism also admits an equilibrium in which some (but not all) agents “run” on the intermediary and withdraw their funds regardless of their true liquidity needs. In other words, self-fulfilling runs can arise in a generalized Green–Lin model and these runs are necessarily partial, with only some agents participating.

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Citation Excerpt :
Relaxing this set of constraints, as in Green and Lin (2003)—so traders have some, imperfect information about their order in the sequence—may allow for a more general proof of uniqueness with i.i.d. types and many traders. However, in the banking context, as shown by Peck and Shell (2003) and Ennis and Keister (2009b), relaxing these further—so traders have no information about their order in the sequence—may imply that uniqueness is unattainable for some parameter values.9 These results suggest the possibility of an interesting tradeoff between the nature of traders’ information, the existence of speculative attack equilibria, and the value of (constrained) efficient exchange rate policy.
To date, cryptocurrency prices are volatile and many cryptocurrency developers have adopted ad hoc approaches to stabilize their cryptocurrency price. When these currencies are not 100% backed by other valued assets, part of their price volatility may arise from self-fulfilling expectations of a speculative attack (as in Obstfeld (1996)). We show that an exchange rate policy, which is less than 100% backed and dynamically adjusts in response to traders’ conversion demand eliminates speculative attacks while, under some conditions, preserving much of the desired exchange rate stability. This dynamic exchange rate policy admits a great deal of discretion to and requires commitment by the party implementing the policy. We demonstrate how to implement this policy using the Ethereum network—a smart contract blockchain environment—and how this implementation yields commitment to the policy.

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Run equilibria in the Green–Lin model of financial intermediation

Abstract

J. Econ. Theory

J. Econ. Theory

J. Monet. Econ.

J. Econ. Theory

Bank runs, deposit insurance, and liquidity

J. Polit. Economy