Nonstationarity and Level Shifts With an Application to Purchasing Power Parity

This study considers testing for a unit root in a time series characterized by a structural change in its mean. The analysis is in the spirit of Perron (1990a), who showed that the existence of such a shift in a stationary time series biases the usual tests for a unit root toward nonrejection. The approach is, however, different given that we suppose the date of the change to be unknown. The statistic of interest is then the minimal t statistic over all possible breakpoints in regressions similar to those proposed by Perron (1990a). Other related statistics are also discussed. We derive and tabulate the asymptotic distributions of interest. Most of the emphasis, however, is given to the tabulation of finite-sample critical values using simulation experiments. Particular attention is given to the effect, on the finite-sample critical values, of various procedures to select the appropriate order of the estimated autoregressions. We apply the tests to analyze the issue of purchasing power parity between the United States and the United Kingdom and also between the United States and Finland, whose real exchange rates are characterized by apparent shifts in level when using particular price indexes.