Memory, Multiple Equilibria and Emerging Market Crises

We present a new Generalized Markov Equilibrium (GME) approach to studying sudden stops and financial crises in emerging countries in small open economies with price dependent equilibrium collateral constraints. These models are known to have multiple equilibria. Our approach to characterizing and computing stochastic equilibrium dynamics is global, encompasses recursive equilibrium as a special case, yet allows for a much more flexible approach to modeling memory and multiple equilibrium in models with equilibrium price-dependent collateral constraints. We construct ergodic GME selections from the sequential competitive equilibrium that at the same time can replicate all the observed phases of the macro crises associated with a sudden stop (boom, collapse, spiralized recession, recovery) while still being able to capture the long-run stylized behavior of the data. We also compute stochastic equilibrium dynamics associated with stationary and a non-stationary GME selections, and we find that a) the ergodic GME selectors generate stochastic dynamics which are less financially constrained, b) non-stationary GME selections exhibit a great range of fluctuations in macroeconomic aggregates compared to the stationary selections. Finally, from a theoretical perspective, we prove the existence of both sequential competitive equilibrium and (minimal state space) recursive equilibrium, and provide a complete constructive qualitative theory of recursive equilibrium comparative statics in deep parameters of these economies. Consistent with recent results in the literature, relative to the set of recursive equilibrium, we find 2 stationary equilibrium: one with high/over borrowing, the other with low/under borrowing. These equilibrium are extremal and self-fulfilling under rational expectations.