Fractionally Integrated Panel Data Systems

Abstract

We consider large n, T panel data models with fixed effects, persistent common factors allowing for cross-section dependence, and possibly correlated persistent innovations that are assumed fractionally integrated. In the model, a) persistence in the innovations and the common factor allows for cointegrating relationships in the unobserved idiosyncratic components; b) the vector of innovations, whose elements can be contemporaneously correlated, can also exhibit short-memory dynamics in the form of a finite-order vector autoregressive process; c) deterministic linear and nonlinear trends can be nested. We perform estimations on the defactored observed series where the projections are based on the sample averages of fractionally differenced data. In the estimation, we use a computationally convenient equation-by-equation conditional-sum-of-squares (CSS) criterion, leading to GLS-type estimates for slope parameters. The CSS estimates of individual slope and long-range dependence parameters are root-T consistent while the mean-group slope estimate is root-n consistent, all with centered asymptotic normal distributions, irrespective of cointegration. A study of small-sample performance is carried out showing desirable properties for our estimation method. Finally, an empirical application to the long-run relationship between real GDP and debt is included.