Information Cycles and Depression in a Stochastic Money-in-Utility Model

Abstract

This paper presents a simple model in which the learning behavior of agents generates fluctuations in money demand and possibly causes a prolonged depression. We consider a stochastic Money-in-Utility model, where agents receive utility from holding money only when a liquidity shock (e.g., a bank run) occurs. Households update the subjective probability of the shock based on the observation and change their money demand accordingly. In this setting, we first derive a stationary cycles under perfect price adjustment, which is characterized by periods of gradual inflation and sudden sporadic falls of the price level. When the nominal stickiness is introduced, the liquidity shock is followed by a period of low output. We show that the adverse effects of the shocks are largest when they occur in succession in an economy which has enjoyed a long period of stability.Bayesian Learning; Money Demand; Hamilton-Jacobi-Bellman Equations; Markov Modulated Poisson Processes; Partial Delay Differential Equations