Stochastic temporary stabilization: Undiversifiable devaluation and income risks

This paper presents a stochastic model of exchange-rate-based inflation stabilization that explicitly recognizes the role of uncertainty in the dynamics of both the exchange rate and labor income. In our setting, we assume that the exchange rate is driven by a mixed diffusion-jump process, and the consumer's labor income follows a geometric Brownian motion. We suppose that contingent-claims markets for hedging against inflation and future income are not available, so financial markets are incomplete. We examine consumption and portfolio shares dynamics when a stabilization plan is implemented and labor income is uncertain. We also assess the effects on welfare of exogenous shocks in expectations of both devaluation and income. Finally, we use the proposed model to carry out a Monte Carlo simulation experiment that explains the observed orders of magnitude of consumption booms, under uncertain labor income, for the Mexican case between 1989 and 1994.