Panel data limit theory and asymptotic analysis of a panel regression with near integrated regressors

This chapter develops a new limit theory for panel data with large numbers of cross section, n, and time series, T, observations. The results apply when n and T tend to infinity simultaneously and provide useful tools for obtaining convergencies in probability and in distribution in cases where the panel data may be cross sectionally heterogenous in a fairly general way. We demonstrate how the new theory can be applied to derive asymptotics for a panel regression where regressors are generated by a local to unit root process with heterogenous localizing coefficients across cross section.