Linear regression limit theory for nonstationary panel data

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section (n) and time series (T) observations. T he limit theory allows for both sequential limits, wherein T --> infinity f ollowed by n --> infinity, and joint limits where T, n --> infinity simulta neously; and the relationship between these multidimensional limits is expl ored. The panel structures considered allow for no time series cointegratio n, heterogeneous cointegration, homogeneous cointegration, and near-homogen eous cointegration. The paper explores the existence of long-run average re lations between integrated panel vectors when there is no individual time s eries cointegration and when there is heterogeneous cointegration. These re lations are parameterized in terms of the matrix regression coefficient of the long-run average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estima tor is developed and studied. The limit theory enables us to test hypothese s about the long run average parameters both within and between subgroups o f the full population.