A New Approach for Analyzing Panel AR(1) Series with Application to the Unit Root Test

Abstract

This paper derives several novel statistics to improve on the t-statistic for testing AR(1) coefficients of panel time series under the scenario of “small n large p”, where n is the sample size and p is the dimension of panel series. These tests aim at maximizing the average power of individual tests while controlling the average type one error. Unlike some approaches in the literature, these tests can determine the acceptance or the rejection of each hypothesis individually while controlling the average type one error. This paper adopts the empirical Bayes approach or equivalently random effect model approach to develop a general theory which leads to several powerful tests. Strikingly, they basically take a simple form similar to a t-statistic; the only difference is that the means and the variances are estimated by shrinkage estimators. Simulations demonstrate that the proposed tests (shrinkage t-tests) have higher average power than the t-test in all settings we examine including those when the priors are miss-specified and the series are dependent. Note that our approach of deriving shrinkage tests can be generalized to other panel models under the scenario of “small n large p”. (This is a joint work with J. T. Gene Hwang.) keywords: Empirical Bayes; Multiple tests; Panel time series; Random effect model; Shrinkage estimator.