Purchasing Power Parity and the Taylor Rule

It is well known that there is a large degree of uncertainty around Rogoff's consensus half-life of the real exchange rate. To obtain a more efficient estimator, we develop a system method that combines the Taylor rule and a standard exchange rate model to estimate half-lives. Further, we propose a median unbiased estimator for the system method based on the generalized method of moments with non-parametric grid bootstrap confidence intervals. Applying the method to real exchange rates of 18 developed countries against the US dollar, we find that most half-life estimates from the single equation method fall in the range of 3-5 years, with wide confidence intervals that extend to positive infinity. In contrast, the system method yields median-unbiased estimates that are typically shorter than 1 year, with much sharper 95% confidence intervals. Our Monte Carlo simulation results are consistent with an interpretation of these results that the true half-lives are short but long half-life estimates from single-equation methods are caused by the high degree of uncertainty of these methods.