Convergence of prices and rates of ination

We consider how unit root and stationarity tests can be used to study the convergence of prices and rates of ination. We show how the joint use of these tests in levels and \u85rst di¤erences allows the researcher to dis-tinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence oc-curs in relative prices or just in rates of ination. Special attention is paid to the issue of whether a mean should be extracted in carrying out tests in rst di¤erences and whether there is an advantage to adopting a (Dickey-Fuller) unit root test based on deviations from the last observation. The asymptotic distribution of this last test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with relatively largeinitial conditions. The tests are applied to the monthly series of the Consumer Price Index in the Italian regional capitals over the period 1970-2003