Short-memory and the PPP hypothesis

The purchasing power parity (PPP)-puzzle has been framed in recent years in terms of half-lives of real-exchange rate shocks that exceed 3 years. Recent studies have attempted to solve that puzzle by adopting nonlinear stochastic models of real exchange rates. The notion of half-life is fundamentally linear, and therefore is inappropriate for those nonlinear models. We provide operational algorithms for estimating more general measures of persistence that are appropriate for nonlinear as well as linear models: memory-in-mean and memory-in-distribution. We study three parametric models: autoregression, threshold autoregression and exponential smooth threshold autoregression. Our Monte Carlo simulations suggest that all three models can produce biased estimates of persistence measures, depending on the true data generating process. In addition, the sample size is found to be too small for reliable nonparametric estimation, suggesting that we need to impose parametric structure. In the empirical application, all three parametric models provided general support for the long-term PPP-hypothesis, suggesting that there is no puzzle, and questioning the need for recently introduced nonlinear models.