This paper overviews some recent developments in panel data asymptotics, concentrating on the nonstationary panel case and gives a new result for models with individual effects. Underlying recent theory are asymptotics for multi-indexed processes in which both indexes may pass to infinity. We review some of the new limit theory that has been developed, show how it can be applied and give a new interpretation of individual effects in nonstationary panel data. Fundamental to the interpretation of much of the asymptotics is the concept of a panel regression coefficient which measures the long run average relation across a section of the panel. This concept is analogous to the statistical interpretation of the coefficient in a classical regression relation. A variety of nonstationary panel data models are discussed and the paper reviews the asymptotic properties of estimators in these various models. Some recent developments in panel unit root tests and stationary dynamic panel regression models are also reviewed.
This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section (n) and time series (T) observations. The limit theory allows for both sequential limits, wherein T → ∞ followed by n → ∞, and joint limits where T,n → ∞ simultaneously; and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence of long-run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parametrized 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 estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.
A new model of near integration is formulated in which the local to unity parameter is identifiable and consistently estimable with time series data. The properties of the model are investigated, new functional laws for near integrated time series are obtained, and consistent estimators of the localizing parameter are constructed. The model provides a more complete interface between I(0) and I(1) models than the traditional local to unity model and leads to autoregressive coefficient estimates with rates of convergence that vary continuously between the O(/n) rate of stationary autoregression, the O(n) rate of unit root regression and the power rate of explosive autoregression. Models with deterministic trends are also considered, least squares trend regression is shown to be efficient, and consistent estimates of the localising parameter are obtained for this case as well. Conventional unit root tests are shown to be consistent against local alternatives in the new class.