Cross-Sectional Dependence Robust Block Bootstrap Panel Unit Root Tests

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectionaldependence including (but not exclusive to) the popular common factor framework. Weconsider block bootstrap versions of the group-mean Im, Pesaran, and Shin (2003) and thepooled Levin, Lin, and Chu (2002) unit root coefficient DF-tests for panel data, originallyproposed for a setting of no cross-sectional dependence beyond a common time effect. Thetests, suited for testing for unit roots in the observed data, can be easily implemented asno specification or estimation of the dependence structure is required. Asymptotic propertiesof the tests are derived for T going to infinity and N finite. Asymptotic validity of thebootstrap tests is established in very general settings, including the presence of commonfactors and even cointegration across units. Properties under the alternative hypothesisare also considered. In a Monte Carlo simulation, the bootstrap tests are found to haverejection frequencies that are much closer to nominal size than the rejection frequenciesfor the corresponding asymptotic tests. The power properties of the bootstrap tests appearto be similar to those of the asymptotic tests.Economics (Jel: A)

Panel Cointegration Testing in the Presence of Common Factors

Panel unit root and no-cointegration tests that rely on cross-sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has e.g. been shown by Banerjee, Marcellino and Osbat (2004, 2005) via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit root test using a common factor structure to model the cross-sectional dependence, but not much work has been done yet for panel no-cointegration tests. This paper proposes a model for panel no-cointegration using an unobserved common factor structure, following the work on Bai and Ng (2004) for panel unit roots. The model enables us to distinguish two important cases: (i) the case when the non-stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We study the asymptotic behavior of some existing, residual-based panel no-cointegration, as suggested by Kao (1999) and Pedroni (1999, 2004). Under the DGP used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than sqrt(N)T as for independent panels. We then examine the properties of residual-based tests for no-cointegration applied to defactored data from which the common factors and individual components have been extracted.econometrics;

A Sieve Bootstrap Test for Cointegration in a Conditional Error Correction Model

In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid.We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. It also performs at least as well as the alternative bootstrap tests considered in terms of size and power.The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic componentsincluded are insensitive to the true value of the trends in the model, and retain correct size.econometrics;

Bootstrap Unit Root Tests: Comparison and Extensions

In this paper we study and compare the properties of several bootstrap unit root tests recently proposed in the literature. The tests are Dickey-Fuller or Augmented DF-tests, either based on residuals from an autoregression and the use of the block bootstrap (Paparoditis & Politis, 2003) or on first differenced data and the use of the stationary bootstrap (Swensen, 2003a) or sieve bootstrap (Psaradakis, 2001; Chang & Park, 2003). We extend the analysis by interchanging the data transformations (differences versus residuals), the types of bootstrap and the presence or absence of a correction for autocorrelation in the tests. We prove that two sieve bootstrap tests based on residuals remain asymptotically valid, thereby completing the proofs of validity for all the types of DF bootstrap tests. In contrast to the literature which basically focuses on a comparison of the bootstrap tests with an asymptotic test, we compare the bootstrap tests among them using response surfaces for their size and power in a simulation study. We also investigate how the tests behave when accounting for a deterministic trend, even in the absence of such a trend in the data. This study leads to the following conclusions: (i) augmented DF-tests are always preferred to standard DF-tests; (ii) the sieve bootstrap performs slightly better than the block bootstrap; (iii) difference-based and residual-based tests behave similarly in terms of size although the latter appear more powerful. The results for the response surfaces allow us to make statements about the behaviour of the bootstrap tests as sample size increases.Economics ;