Median-unbiased estimation of structural change models: an application to real exchange rate persistence

Measuring deviations from purchasing power parity has been the subject of extensive investigation. The most common practice in empirical research for measuring real exchange rate persistence is to estimate univariate autoregressive (AR) time series models and calculate the half-life, defined as the number of periods for a unit shock to a time series to decay by 50%. In the presence of structural change, there are two potential biases in the parameter estimates of AR models: (1) a downward small sample median-bias and (2) an upward bias, which occurs when structural change is present and ignored. We conduct a variety of Monte Carlo simulations and demonstrate that the existence of structural change causes a substantial increase in the small sample bias documented in Andrews (1993). We then propose an extension of median-unbiased estimation, which explicitly accounts for structural change, and apply these methods to estimate half-lives of several long-horizon real exchange rates analysed by Lothian and Taylor (1996) and Taylor (2002). The upward bias from neglecting structural change dominates the downward median-bias for these real exchange rates. When structural change is present and accounted for, the median-unbiased half-lives towards a changing mean decrease and the confidence intervals tighten.