Broken mean stationarity and the validity of the Dickey-Fuller test: the case of controlled inflation

This article proves the asymptotic efficiency of the Dickey Fuller (DF) test when the data generating process of the variable under consideration is in fact mean stationary with breaks. Monte Carlo simulations show that asymptotic properties remain valid for sample sizes of practical interest. Our results complement those already available in the literature, which can be summarized as follows: DF-type tests (i) over-accept the null hypothesis of unit root when there is a break in the trend-stationary process, and; (ii) over-reject the null hypothesis when there is a level/trend break in the unit root process. We illustrate the performance of the DF-t test by studying inflation rate series, a variable that should be stationary if the monetary authority follows an effective monetary policy: shocks are short-lived, therefore, inflation fluctuates randomly around specific goals