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 NT consistent but the normal asymptotic distribution might not be centred, 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 tests have good performance even in moderately small panels.