Estimation of the Long-run Average Relationship in Nonstationary Panel Time Series

This paper proposes a new class of estimators of the long-run average relationship when there is no individual time series cointegration. Using panel data with large cross section (n) and time series dimensions (T), the estimators are based on the long-run average variance estimate using bandwidth equal to T. The new estimators include the panel pooled least squares estimators and the limiting cross sectional least squares estimator as special cases. It is shown that the new estimators are consistent and asymptotically normal under both the sequential limit, wherein T goes to infinity followed by n going to infinity, and the joint limit where T and n go to infinite simultaneously. The rate condition for the joint limit to hold is relaxed to the condition that sqrt(n)/T goes to infinity, which is less restrictive than the rate condition that n/T goes to infinity, as imposed by Phillips and Moon (1999). By taking powers of the Bartlett and Parzen kernels, this paper introduces two new classes of kernels, the sharp kernels and steep kernels, and shows that these new kernels deliver new estimators of the long-run average relationship that are more efficient than the existing ones. A simulation study supports the asymptotic results.