Panel unit root tests in the presence of cross-sectional dependence: finite sample performance and an application

This paper examines the finite sample properties of three testing regimes for the null hypothesis of a panel unit root against stationary alternatives in the presence of cross-sectional correlation. The regimes of Bai and Ng (2004), Moon and Perron (2004) and Pesaran (2007) are assessed in the presence of multiple factors and also other non-standard situations. The behaviour of some information criteria used to determine the number of factors in a panel is examined and new information criteria with improved properties in small-N panels proposed. An application to the efficient markets hypothesis is also provided. The null hypothesis of a panel random walk is not rejected by any of the tests, supporting the efficient markets hypothesis in the financial services sector of the Australian Stock Exchange.

Panel Stationarity Test with Structural Breaks

In this paper, we extend the heterogeneous panel data stationarity test of Hadri [Econometrics Journal, Vol. 3 (2000) pp. 148–161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion-i-Silvestre et al.[Econometrics Journal,Vol. 8 (2005) pp. 159–175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions.We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion-i-Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175]showed that the number of breaks and their positions may be allowed to differ acrossindividuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross-sectional dependence are accommodated.

PANEL DATA UNIT ROOT TEST WITH FIXED TIME DIMENSION

The consideration of the limit theory in which T is fixed and N is allowed to go to infinity improves the finite-sample properties of the tests and avoids the imposition of the relative rates at which T and N go to infinity.

TESTING FOR STATIONARITY IN HETEROGENEOUS PANEL DATA IN THE CASE OF MODEL MISSPECIFICATION

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 -> infinity 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 (

ARE OECD MACROECONOMIC VARIABLES TREND STATIONARY? EVIDENCE FROM PANEL STATIONARITY TESTS ALLOWING FOR A STRUCTURAL BREAK AND CROSS-SECTIONAL DEPENDENCE

This article applies the panel stationarity test with a break proposed by Hadri and Rao (2008) to examine whether 14 macroeconomic variables of OECD countries can be best represented as random walk or stationary fluctuations around a deterministic trend. In contrast to previous studies, based essentially on visual inspection of the break type or just applying the most general break model, we use a model selection procedure based on BIC. We do this for each time series so that heterogeneous break models are allowed for in the panel. Our results suggest, overwhelmingly, that if we account for a structural break, cross-sectional dependence and choose the break models to be congruent with the data, then the null of stationarity cannot be rejected for all the 14 macroeconomic variables examined in this article. This is in sharp contrast with the results obtained by Hurlin (2004), using the same data but a different methodology.