Bayesian analysis of nonlinear exchange rate dynamics and the purchasing power parity persistence puzzle

• Algorithm developed for Bayesian estimation of nonlinear threshold models.
• Bayesian model comparison supports nonlinearity in G7 exchange rates.
• Model-averaged estimates of half-lives smaller than for linear models.

We investigate the persistence of real exchange rates using Bayesian methods. First, an algorithm for Bayesian estimation of nonlinear threshold models is developed. Unlike standard grid-based estimation, the Bayesian approach fully captures joint parameter uncertainty and uncertainty about complicated functions of the parameters, such as the half-life measure of persistence based on generalized impulse response functions. Second, model comparison is conducted via marginal likelihoods, which reflect the relative abilities of models to predict the data given prior beliefs about model parameters. This comparison is conducted for a range of linear and nonlinear models and provides a direct evaluation of the importance of nonlinear dynamics in modeling exchange rates. The marginal likelihoods also imply weights for a model-averaged measure of persistence. The empirical results for real exchange rate data from the G7 countries suggest general support for nonlinearity, with the strength of the evidence depending on which country pair is being considered. However, the model-averaged estimates of half-lives are almost always as small or smaller than for the linear models alone, suggesting that the purchasing power parity persistence puzzle is less of a puzzle than previously thought.