Yao Rao

Testing For Stationarity With a Break in Panels Where the Time Dimension is Finite

In this paper, we consider the case of finite time dimension in the panel stationarity tests with structural breaks. By fixing T; the finite sample properties of the tests for both micro (T small and N large) and macro (both T and N large) panel data are generally greatly improved. More importantly, the derivation of the tests for finite T and N -> infinity, as opposed to joint asymptotic where N and T -> infinity simultaneously, avoids the imposition of the rate condition N/T -> 0; making the test valid for any (T;N) blend. Four models corresponding to the usual combination of breaks are considered. The asymptotic distributions of the test are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically employing two approaches. The first method is based on the Laplace Transform and the second derivation is based on Ghazal’s (1994) corollary. The case with unknown breaks is also considered. The proposed tests have generally empirical sizes that are very close to the nominal size. The Monte-Carlo simulations show that the power of the test statistics increases substantially with N and T.

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 →∞ 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).

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.

KPSS test and model misspecifications

The KPSS test is very popular and used extensively by practitioners. The test considers two models under the null: stationarity around a deterministic level or 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. This article endeavour to fill this gap. We found, using simulation, that choosing a deterministic trend when a deterministic level is true does not affect significantly the properties of the test. But, choosing a deterministic level when a deterministic trend is true leads to extreme over-rejection of the null. These results are obtained for i.i.d. and autocorrelated errors.

The Effect of Regression Design on Optimal Tests for Finding Break Positions

In this paper, we derive an optimal test for determining break positions in Gaussian linear regressions. The procedure is an admissible rule in a multiple decision theory setting and the results are exact and valid in small samples. The analysis indicates that regression design can have a very significant effect on the ability of the optimal test to find the position of the break. Some regression designs make it all but impossible to successfully identify a break location in certain subsections of the sample span. Two graphical devices, the cq and ω-plots are available to identify those subsets of the sample span where locating a break position is difficult or impossible.

Novel panel cointegration tests emending for cross‐section dependence with N fixed

In this paper, we propose new cointegration tests for single equations and panels. In both cases, the asymptotic distributions of the tests, which are derived with N fixed and T going to infinity, are shown to be standard normals. The effects of serial correlation and cross-sectional dependence are mopped out via long-run variances. An effective bias correction is derived which is shown to work well in finite samples; particularly when N is smaller than T. Our panel tests are robust to possible cointegration across units.