Median-unbiased estimation in DF-GLS regressions and the PPP puzzle

Abstract

Using median-unbiased estimation based on Augmented Dickey–Fuller (ADF) regressions, recent research has questioned the validity of Rogoff's ‘remarkable consensus’ of 3–5 year half-lives of deviations from Purchasing Power Parity (PPP). The confidence intervals of these half-life estimates, however, are extremely wide, with lower bounds of about 1 year and upper bounds of infinity. We extend median-unbiased estimation to the Dickey–Fuller Generalized Least Square (DF-GLS) regression of Elliott et al. (1996). We find that combining median-unbiased estimation with this regression has the potential to tighten confidence intervals for the half-lives. Using long-horizon real exchange rate data, we find that the typical lower bound of the confidence intervals for median-unbiased half-lives is just below 3 years. Thus, while previous confidence intervals for median-unbiased half-lives are consistent with virtually anything, our tighter confidence intervals are inconsistent with economic models with nominal rigidities as candidates for explaining the observed behaviour of real exchange rates and move us away from solving the PPP puzzle.