Testing for Group-Wise Convergence with an Application to Euro Area Inflation

While panel unit root tests have been used to investigate a wide range of macroeconomic issues, the tests suffer from low power to reject the unit root null in panels of stationary series if the panels consist of highly persistent series, contain a small number of series, and/or have series with a limited length. We propose a new procedure to increase the power of panel unit root tests when used to study convergence by testing for stationarity between a group of series and their cross-sectional means. Although each differential has non-zero mean, the group of differentials has a cross-sectional average of zero for each time period by construction, and we incorporate this constraint for estimation and when generating finite sample critical values. This procedure leads to significant power gains for the panel unit root test. We apply our new approach to study inflation convergence within the Euro Area countries for the post 1979 period. The results show strong evidence of convergence soon after the implementation of the Maastricht treaty. Furthermore, median unbiased estimates of the half life for the period before and after the Euro show a dramatic decrease in the persistence of the differential after the occurrence of the single currency.