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 are multiple tests that determine which individual series satisfies the null hypothesis. 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. Simulation studies show that the proposed statistics out-perform the t-statistic, and the results are robust with respect to the miss-specification of prior distributions.

Keywords: Empirical Bayes, Multiple test, Panel time series, Random effect model, Shrinkage estimator, Unit root test

JEL Classification: C12, C32