Characterizing the degree of stability of non-linear dynamic models∗

The purpose of this paper is to show how the stability properties of non-linear dynamic models may be characterized, where the degree of stability is deÞned by the effects of exogenous shocks on the evolution of the observed stochastic system. Smoothed Lyapunov exponents are a generalization of Lyapunov exponents for deterministic systems. We argue that smoothed Lyapunov exponents can be used to measure the degree of stability of a stochastic dynamic model. When such a model is Þtted to observed data, an estimator of the largest smooth Lyapunov exponent is presented which is consistent and asymptotically normal. This is further examined in a Monte Carlo study. Finally, we illustrate how the presented framework can be used to study the degree of stability of exchange rates.