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 in nonstationary panel time series. The estimators are based on the long-run average variance estimate using bandwidth equal to T. The new estimators include the pooled least squares estimator and the fixed effects estimator as special cases. It is shown that the new estimators are consistent and asymptotically normal under both the sequential limit, wherein T → ∞ followed by n → ∞, and the joint limit where T,n → ∞ simultaneously. The rate condition for the joint limit to hold is relaxed to , which is less restrictive than the rate condition n/T → 0, as imposed by Phillips and Moon (1999, Econometrica 67, 1057–1111). By exponentiating existing kernels, this paper introduces a new approach to generating kernels and shows that these exponentiated kernels can deliver more efficient estimates of the long-run average coefficient.I am grateful to Bruce Hansen, Peter Phillips, Zhijie Xiao, and three anonymous referees for constructive comments and suggestions. All errors are mine alone.