SUMMARYThis paper develops a new approach to the problem of testing the existence of a level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend-or first-difference stationary. The proposed tests are based on standard F-and t-statistics used to test the significance of the lagged levels of the variables in a univariate equilibrium correction mechanism. The asymptotic distributions of these statistics are non-standard under the null hypothesis that there exists no level relationship, irrespective of whether the regressors are I 0 or I 1 . Two sets of asymptotic critical values are provided: one when all regressors are purely I 1 and the other if they are all purely I 0 . These two sets of critical values provide a band covering all possible classifications of the regressors into purely I 0 , purely I 1 or mutually cointegrated. Accordingly, various bounds testing procedures are proposed. It is shown that the proposed tests are consistent, and their asymptotic distribution under the null and suitably defined local alternatives are derived. The empirical relevance of the bounds procedures is demonstrated by a re-examination of the earnings equation included in the UK Treasury macroeconometric model.

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A number of panel unit root tests that allow for cross-section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross-dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard augmented Dickey-Fuller (ADF) regressions are augmented with the crosssection averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual cross-sectionally augmented ADF (CADF) statistics and for their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data.T (the time series dimension) and N (the cross-section dimension) are large. However, as shown by Im KS and Pesaran MH (unpublished 2003), her test is valid only if N is fixed as T ! 1. Using Monte Carlo techniques, Im and Pesaran show that Chang's test is grossly oversized for moderate degrees of cross-section dependence, even for relatively small values of N. 1 Choi (2002) models the cross-dependence using a two-way error-component model which imposes the same pair-wise error covariances across the different cross-section units. This provides a generalization of the cross-section de-meaning procedure proposed in Im et al. (1995) but it can still be restrictive in the context of heterogeneous panels. Smith et al. (2004) use bootstrap techniques, andChue (2007) employ subsampling techniques to deal with cross-section dependence. Breitung and Das (2005) adopt least-squares and feasible generalized least-squares estimates that are applicable in cases where T ½ N. Harris et al. (2004) propose a test of joint stationarity (as opposed to unit roots) in panels under cross-section dependence using the sum of lag-k sample autocovariances where k is taken to be an increasing function of T. make use of residual factor models to take account of the cross-section dependence. In the case of a residual onefactor model Phillips and Sul (2003) propose an orthogonalization procedure that asymptotically eliminates the common factors. Similar procedures are used by Bai and Ng (2004) and Moon and Perron (2004) in a more general set-up. Moon and Perron (2004) propose a pooled panel unit root test based on 'de-factored' observations and suggest estimating the factor loadings by the principal component method. They derive asymptotic properties of their test under the unit root null and local alternatives, assuming in particular that N/T ! 0, as N and T ! 1. They show that their proposed test has good asymptotic power properties if the model does n...

This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual-specific errors are allowed to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual-specific regressors by means of cross-section averages such that asymptotically as the cross-section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross-sectional averages of the dependent variable and the individual-specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T. Copyright The Econometric Society 2006.

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