Persistence Heterogeneity Testing in Panels with Interactive Fixed Effects

Abstract

We consider large N, T panel data models with fixed e↵ects, 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 di↵erences after factor removal by projection on the cross-section average. The pooled conditional-sum-ofsquares estimate is pNT 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, which 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.