Working Papers Series

Papers below are in pdf.

Chao Gu

WP 11-14
Unconventional Optimal Repurchase Agreements
Chao Gu and Joe Haslag

We build a model in which verifiability of private debts, timing mismatch in debt settlements and borrowing leverage lead to liquidity crisis in the financial market. Central bank can respond to the liquidity crisis by adopting an unconventional monetary policy that resembles repurchase agreements between the central bank and the lenders. This policy is effective if the timing mismatch is nominal (i.e., a settlement participation risk). It is ineffective if the timing mismatch is driven by a real shock (i.e., preference shock).

JEL Codes: E44, E52, G01
Keywords: liquidity problem, timing mismatch, leveraging, liquidity shock, settlement risk,
repurchase agreement, consumption shock

WP 10-11
Endogenous Credit Cycles
Chao Gu & Randall Wright

We study models of credit with limited commitment, which implies endogenous borrowing constraints. We show that there are multiple stationary equilibria, as well as nonstationary equilibria, including some that display deterministic cyclic and chaotic dynamics. There are also stochastic (sunspot) equilibria, in which credit conditions change randomly over time, even though fundamentals are deterministic and stationary. We show this can occur when the terms of trade are determined by Walrasian pricing or by Nash bargaining. The results illustrate how it is possible to generate equilibria with credit cycles (crunches, freezes, crises) in theory, and as recently observed in actual economies.

JEL Codes: E2
Bank runs, credit, commitment, dynamics, cycles

WP 10-06
Herding and Bank Runs
Chao Gu

Traditional models of bank runs do not allow for herding effects, because in these models withdrawal decisions are assumed to be made simultaneously. I extend the banking model to allow a depositor to choose his withdrawal time. When he withdraws depends on his consumption type (patient or impatient), his private, noisy signal about the quality of the bank's portfolio, and the withdrawal histories of the other depositors. Some of these runs are efficient in that the bank is liquidated before the portfolio worsens. Others are not efficient; these are cases in which the herd is misled

JEL Codes: C73, D82, E59, G21
Bank runs, herding, imperfect information, perfect Bayesian equilibrium, optimal bank contract, sequential-move game, fundamental-based bank runs

WP 10-05
Asymmetric Information and Bank Runs
Chao Gu

In the existing literature, panic-based bank runs are triggered by a commonly acknowledged and observed sunspot signal. There are only two equilibrium realizations resulting from the commonly observed sunspot signal: Everyone runs or no one runs. I consider a more general and more realistic situation in which consumers observe noisy private sunspot signals. If the noise in the signals is sufficiently small, there exists a proper correlated equilibrium for some demand deposit contracts. A full bank run, a partial bank run (in which some consumers panic whereas others do not), or no bank run occurs, depending on the realization of the sunspot signals. If the probabilities of runs are small, the optimal demand deposit contract tolerates full and partial bank runs.

JEL Codes: D82, G21
Keywords: sunspot equilibrium, correlated equilibrium, imperfect coordination, imperfect information.

WP 10-04
Production, Hidden Action, and the Payment System
Chao Gu, Mark Guzman & Joseph H. Haslag

In this paper, we study a model economy that can account for the distribution of payments within a day. In our model, debtors choose when to arrive at the settlement location. Concomitant with choosing their arrival, debtors are making a production decision. We assume there is a cost to arriving early; that is, late-arrival is associated with a technology that dominates early arrival/production. Second, we treat the debtor's choice as hidden from creditors. We derive conditions under which the planner allocates production to each type of agents. In the decentralized setting, there is a nonarbitrage condition that is consistent with a positive intraday rate. The central bank may be able to implement the planner's allocation with a proper intraday interest rate. In some cases, the optimal intraday rate is positive.

JEL Codes: E31, E51, E58
Keywords: Friedman rule; discount window policy; payment system, intraday rate, settlement risk

WP 07-21
Asymmetric Information and Bank Runs
Chao Gu

It is known that sunspots can trigger panic-based bank runs and that the optimal banking contract can tolerate panic-based runs. The existing literature assumes that these sunspots are based on a publicly observed, extrinsic randomizing device. In this paper, I extend the analysis of panic-based runs to include an asymmetric-information, extrinsic randomizing device. Depositors observe different, but correlated, signals on the stability of the bank. I find that if the signals that depositors obtain are highly correlated, there exists a correlated equilibrium for some demand deposit contracts. In this equilibrium, a full bank run, a partial bank run, or non-bank run occurs depending on the realization of the signals. Computed examples indicate that in some economies, a demand-deposit contract that tolerates bank runs and partial bank runs is optimal, whereas in some other economies a run-proof contract is optimal.

JEL Codes: D82, G21, P11
Keywords: Bank runs, randomizing device, sunspot equilibrium, correlated equilibrium, imperfect information.

Substantially revised and updated in WP 10-05

WP 07-16
Herding and Bank Runs
Chao Gu

Traditional models of bank runs do not allow for herding effects, because in these models withdrawal decisions are assumed to be made simultaneously. I extend the banking model to allow a depositor to choose his withdrawal time. When he withdraws depends on his liquidity type (patient or impatient), his private, noisy signal about the quality of the bank's portfolio, and the withdrawal histories of the other depositors. In some cases, the optimal banking contract permits herding runs. Some of these "runs" are efficient in that the bank is liquidated before the portfolio worsens. Others are not efficient; these are cases in which the herd is misled.

JEL Codes: C73, D82, E59, G21
Keywords: Bank runs, herding, imperfect information, perfect Bayesian equilibrium, optimal bank contract, sequential-move game, fundamental-based bank runs.

Significantly updated in WP 10-06