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The objective of the paper is to investigate whether price indices of different European stock markets display a common long-run trending behaviour. Using cointegration analysis, we provide empirical evidence of common stochastic trends among five important European stock markets over the period 1975-1991.

JEL classification: C15 C23Keywords: Block bootstrap Panel unit root test Cross-sectional dependence a b s t r a c t 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-sectional dependence including (but not exclusive to) the popular common factor framework. We consider block bootstrap versions of the groupmean (Im et al., 2003) and the pooled (Levin et al., 2002) unit root coefficient DF tests for panel data, originally proposed for a setting of no cross-sectional dependence beyond a common time effect. The tests, suited for testing for unit roots in the observed data, can be easily implemented as no specification or estimation of the dependence structure is required. Asymptotic properties of the tests are derived for T going to infinity and N finite. Asymptotic validity of the bootstrap tests is established in very general settings, including the presence of common factors and cointegration across units. Properties under the alternative hypothesis are also considered. In a Monte Carlo simulation, the bootstrap tests are found to have rejection frequencies that are much closer to nominal size than the rejection frequencies for the corresponding asymptotic tests. The power properties of the bootstrap tests appear to be similar to those of the asymptotic tests.

As has been pointed out in the previous chapter, the choice between a full system approach and a sub-system approach is not clear cut in the case of cointegrated systems. Both have advantages and defects. Conditional sub-systems, in particular, necessitate exogeneity assumptions which, if not fulfilled, may induce loss of efficiency and consistency -as in the usual stationary framework-but in the case .of cointegrated systems also imply a loss of the mixed normal limiting distribution of the cointegrating vector estimators necessitating therefore semi-parametric corrections, model augmentation or two-step approaches (see Phillips and Hansen, 1990, Phillips, 1991, Phillips and Loretan, 1991, Saikkonen, 1991, Stock and Watson, 1991, Boswijk, 1992a.The concept of exogeneity is thus here too of crucial importance for conducting valid inference in (conditional) cointegrated sub-systems. In the recent applied econometric literature, the error correction model (ECM) has become a very popular dynamic specification; both in a multivariate framework and in a single equation framework as pointed out in Chapter 2. In the latter case, exogeneity assumptions are implicitly made on the right hand side variables and the analysis is conducted in limited information. J.-P. Urbain, Exogeneity in Error Correction Models © Springer-Verlag Berlin Heidelberg 1993 T D(Xb.··, xTIXoi 6) = II D(xtIXt-1i 6) t=l Let focus attention on the conditional density function and suppose that there exists a one-to-one transformation f such that f : 0 -+ Ai 6 ~ A = f( 6)Partition A as (At, A2) and A as (AI X A2). We shall say that Al and A2 are variation free (or variation independent in the terminology of Barndorff-Nielsen, 1978, p.26) if (At, A2) E (AI X A2), the product space of their 46 CHAPTER 3. WEAK EXOGENEITY IN ECM respective parameter spaces; i.e. if and only if ,xl and ,x2 are not subject to cross restrictions so that for any specific admissible value in Al for ,xl, ,x2 can take any value in A2. Let ,xl be a one-to-one function of our parameters of interest 1/J and ,x2 be the so-called nuisance parameters.Definition 1 : Weak Exogeneity (Engle et at, 1983) Let focus attention on the conditional density function D(xtIXt-l; 0) and let Xt = (Yh Zt). Zt will be said to be weakly exogenous over the sample period, for the parameter of interest 1/J, if and only if there exists a reparametrisation ,x of 0, with ,x = (,xl, ,x2), such that 1. 1/J depends on ,xl only, Note that conditions 2 and 3 correspond to the notion of "classical sequential cut" (see Engle et al., 1983). Weak exogeneity thus implies that the parameters of interest can be recovered from the conditional model only.

Several panel unit root tests that account for cross-section dependence using a common factor structure have been proposed in the literature recently. Pesaran's (2007) cross-sectionally augmented unit root tests are designed for cases where cross-sectional dependence is due to a single factor. The Moon and Perron (2004) tests which use defactored data are similar in spirit but can account for multiple common factors. The Bai and Ng (2004a) tests allow to determine the source of nonstationarity by testing for unit roots in the common factors and the idiosyncratic factors separately. Breitung and Das (2008) and Sul (2007) propose panel unit root tests when cross-section dependence is present possibly due to common factors, but the common factor structure is not fully exploited. This article makes four contributions: (1) it compares the testing procedures in terms of similarities and differences in the data generation process, tests, null, and alternative hypotheses considered, (2) using Monte Carlo results it compares the small sample properties of the tests in models with up to two common factors, (3) it provides an application which illustrates the use of the tests, and (4) finally, it discusses the use of the tests in modelling in general.Cross-section dependence, Factor models, Non-stationary panel data, Unit root tests, C32, C33,