This paper presents results on the size and power of first generation panel unit root and stationarity tests obtained from a large scale simulation study. The tests developed in the following papers are included: Levin et al. ( 2002 Levin , A. , Lin , C. F. , Chu , C.-S. J. ( 2002 ). Unit root tests in panel data: asymptotic and finite sample properties . Journal of Econometrics 108 : 1 – 22 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar] ), Harris and Tzavalis ( 1999 Harris , R. D. F. , Tzavalis , E. ( 1999 ). Inference for unit roots in dynamic panels where the time dimension is fixed . Journal of Econometrics 90 : 1 – 44 . [CROSSREF] [CSA] [Google Scholar] ), Breitung ( 2000 Breitung , J. ( 2000 ). The local power of some unit root tests for panel data . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam: Elsevier , pp. 161 – 177 . [Crossref] , [Google Scholar] ), Im et al. ( 1997 Im , K. S. , Pesaran , M. H. , Shin , Y. ( 1997 ). Testing for Unit Roots in Heterogeneous Panels . Mimeo : Cambridge University . [Google Scholar] 2003 Im , K. S. , Pesaran , M. H. , Shin , Y. ( 2003 ). Testing for unit roots in heterogeneous panels . Journal of Econometrics 115 : 53 – 74 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar] ), Maddala and Wu ( 1999 Maddala , G. S. , Wu , S. ( 1999 ). A comparative study of unit root rests with panel data and a simple new test . Oxford Bulletin of Economics and Statistics 61 : 631 – 652 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar] ), Hadri ( 2000 Hadri , K. ( 2000 ). Testing for stationarity in heterogeneous panel data . Econometrics Journal 3 : 148 – 161 . [CROSSREF] [CSA] [Crossref] , [Google Scholar] ), and Hadri and Larsson ( 2005 Hadri , K. , Larsson , R. ( 2005 ). Testing for stationarity in heterogeneous panel data where the time dimension is fixed . Econometrics Journal 8 : 55 – 69 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar] ). Our simulation set-up is designed to address inter alia the following issues. First, we assess the performance as a function of the time and the cross-section dimensions. Second, we analyze the impact of serial correlation introduced by positive MA roots, known to have detrimental impact on time series unit root tests, on the performance. Third, we investigate the power of the panel unit root tests (and the size of the stationarity tests) for a variety of first order autoregressive coefficients. Fourth, we consider both of the two usual specifications of deterministic variables in the unit root literature.

This article presents results concerning the performance of both single equation and system panel cointegration tests and estimators. The study considers the tests developed in Pedroni ( 1999 Pedroni , P. ( 1999 ). Critical values for cointegration tests in heterogeneous panels with multiple regressors . Oxford Bulletin of Economics and Statistics 61 : 653 – 670 . [Crossref], [Web of Science ®] [Google Scholar] , 2004 Pedroni , P. ( 2004 ). Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis . Econometric Theory 20 : 597 – 625 . [Crossref], [Web of Science ®] [Google Scholar] ), Westerlund ( 2005 Westerlund , J. ( 2005 ). New simple tests for panel cointegration . Econometric Reviews 24 : 297 – 316 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ), Larsson et al. ( 2001 Larsson , R. , Lyhagen , J. , Löthgren , M. ( 2001 ). Likelihood-based cointegration tests in heterogeneous panels . Econometrics Journal 4 : 109 – 142 . [Crossref] [Google Scholar] ), and Breitung ( 2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) and the estimators developed in Phillips and Moon ( 1999 Phillips , P. C. B. , Moon , H. R. ( 1999 ). Linear regression limit theory for nonstationary panel data . Econometrica 67 : 1057 – 1111 . [Crossref], [Web of Science ®] [Google Scholar] ), Pedroni ( 2000 Pedroni , P. ( 2000 ). Fully modified OLS for heterogeneous cointegrated panels . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 93 – 130 . [Crossref] [Google Scholar] ), Kao and Chiang ( 2000 Kao , C. , Chiang , M.-H. ( 2000 ). On the estimation and inference of a cointegrated regression in panel data . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 179 – 222 . [Crossref] [Google Scholar] ), Mark and Sul ( 2003 Mark , N. C. , Sul , D. ( 2003 ). Cointegration vector estimation by panel dynamic OLS and long-run money demand . Oxford Bulletin of Economics and Statistics 65 : 655 – 680 . [Crossref], [Web of Science ®] [Google Scholar] ), Pedroni ( 2001 Pedroni , P. ( 2001 ). Purchasing power parity tests in cointegrated panels . Review of Economics and Statistics 83 : 1371 – 1375 . [Google Scholar] ), and Breitung ( 2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ). We study the impact of stable autoregressive roots approaching the unit circle, of I(2) components, of short-run cross-sectional correlation and of cross-unit cointegration on the performance of the tests and estimators. The data are simulated from three-dimensional individual specific VAR systems with cointegrating ranks varying from zero to two for fourteen different panel dimensions. The usual specifications of deterministic components are considered.

This paper develops a fully modified OLS (FM-OLS) estimator for cointegrating polynomial regressions, i.e., regressions that include as explanatory variables deterministic variables, integrated processes, and integer powers of integrated processes. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The paper extends the fully modified estimator of Phillips and Hansen (1990) from cointegrating regressions to cointegrating polynomial regressions. The FM-OLS estimator has a zero-mean Gaussian mixture limiting distribution that allows for standard asymptotic inference. Wald and LM specification tests as well as a KPSS-type test for cointegration are derived. The theoretical analysis is complemented by a simulation study which shows that this FM-OLS estimator, as well as tests based upon it, perform well in the sense that the performance advantages over OLS are largely similar to the performance advantages of FM-OLS over OLS in standard cointegrating regressions.