Testing for Stationarity in Heterogeneous Panel Data in the Case of Model Misspecification

Abstract

This paper investigates the performance of the tests proposed by Hadri and by Hadri and Larsson for testing for stationarity in heterogeneous panel data under model misspecification. The panel tests are based on the well known KPSS test (cf. Kwiatkowski et al.) which considers two models: stationarity around a deterministic level and stationarity around a deterministic trend. There is no study, as far as we know, on the statistical properties of the test when the wrong model is used. We also consider the case of the simultaneous presence of the two types of models in a panel. We employ two asymptotics: joint asymptotic, T, N →∞  simultaneously, and T fixed and N allowed to grow indefinitely. We use Monte Carlo experiments to investigate the effects of misspecification in sample sizes usually used in practice. The results indicate that the assumption that T is fixed rather than asymptotic leads to tests that have less size distortions, particularly for relatively small T with large N panels (micro-panels) than the tests derived under the joint asymptotics. We also find that choosing a deterministic trend when a deterministic level is true does not significantly affect the properties of the test. But, choosing a deterministic level when a deterministic trend is true leads to extreme over-rejections. Therefore, when unsure about which model has generated the data, it is suggested to use the model with a trend. We also propose a new statistic for testing for stationarity in mixed panel data where the mixture is known. The performance of this new test is very good for both cases of T asymptotic and T fixed. The statistic for T asymptotic is slightly undersized when T is very small (≤10).