Estimation of Fractionally Integrated Panels with Fixed Effects and Cross-Section Dependence

We consider large N, T panel data models with fixed effects, common factors allowing 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. Generalizing the basic setup to include covariates and heterogeneous parameters, we propose individual and common-correlation estimates for the slope parameters, while error memory parameters are estimated from regression residuals. The two parameter estimates are root-T consistent and asymptotically normal and mutually uncorrelated, irrespective of possible cointegration among idiosyncratic components. A study of small-sample performance and an empirical application to realized volatility persistence are included.