Persistence Heterogeneity Testing in Panels with Interactive Fixed Effects

We consider large N,T panel data models with fixed effects, a common factor allowing for cross-section dependence, and persistent data and shocks, which are assumed fractionally integrated. In a basic setup, the main interest is on the fractional parameter of the idiosyncratic component, which is estimated in first differences after factor removal by projection on the cross-section average. The pooled conditional-sum-of-squares estimate is root-NT consistent but the normal asymptotic distribution might not be centered, requiring the time series dimension to grow faster than the cross-section size for correction. We develop tests of homogeneity of dynamics, including the degree of integration, that have no trivial power under local departures from the null hypothesis of a non-negligible fraction of cross-section units. A simulation study shows that our estimates and test have good performance even in moderately small panels.