Confidence intervals for half-life deviations from Purchasing Power Parity

According to Rogoff (1995), Purchasing Power Parity (PPP) fits well one empirical feature of the data, namely the high short-run volatility of real exchange rates, but also implies that shocks should die away in one to two years (the time interval compatible with price and wage stickiness). However, existing point estimates of half-life deviations from PPP are in the order of 3 to 5 years. This paper assesses how much uncertainty there is around these point estimates by using local to unity asymptotic theory to construct confidence intervals that are robust to high persistence in the presence of small sample sizes. The empirical evidence suggests that the lower bound of the confidence interval is around 4 to 8 quarters for most currencies, which is not inconsistent with PPP. However, the upper bounds are infinity for all currencies so we cannot provide conclusive evidence in favor of PPP either.