Median-Unbiased Estimation in DF-GLS Regressions and the PPP Puzzle

Using median-unbiased estimation, recent research has questioned the validity of Rogoff’s “remarkable consensus” of 3-5 year half-lives of deviations from PPP. These half-life estimates, however, are based on estimates from regressions where the resulting unit root test has low power. We extend median-unbiased estimation to the DF-GLS regression of Elliott, Rothenberg, and Stock (1996). We find that median-unbiased estimation based on this regression has the potential to tighten confidence intervals for 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 under 3 years. Thus, while previous confidence intervals for half-lives are consistent with virtually anything, our tighter confidence intervals now rule out economic models with nominal rigidities as candidates for explaining the observed behavior of real exchange rates. Therefore, while we obtain more information using efficient unit root tests on longer term data, this information moves us away from solving the PPP puzzle.