We consider how unit root and stationarity tests can be used to study the convergence properties of prices and rates of inflation. Special attention is paid to the issue of whether a mean should be extracted in carrying out unit root and stationarity tests and whether there is an advantage to adopting a new (Dickey-Fuller) unit root test based on deviations from the last observation. The asymptotic distribution of the new test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with relatively large initial conditions, the case of primary interest for analysing convergence. We argue that the joint use of unit root and stationarity tests in levels and first differences allows the researcher to distinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence occurs in relative prices or just in rates of inflation. The tests are applied to the monthly series of the Consumer Price Index in the Italian regional capitals over the period 1970-2003. It is found that all pairwise contrasts of inflation rates have converged or are in the process of converging. Only 24% of price level contrasts appear to be converging, but a multivariate test provides strong evidence of overall convergence.
