This paper proposes a bias-adjusted version of Breusch and Pagan (1980) Lagrange multiplier (LM) test statistic of error cross-section independence, in the case of panel models with strictly exogenous regressors and normal errors. The exact mean and variance of the test indicator of the LM test statistic are provided for the purpose of the bias-adjustments. It is shown that the centring of the LM statistic is correct for fixed T and N. Importantly, the proposed bias-adjusted LM test is consistent even when the Pesaran's (2004) CD test is inconsistent. Also an alternative bias-adjusted LM test, which is consistent under local error cross-section dependence of any fixed order p, is proposed. The finite sample behaviour of the proposed tests is investigated and compared to that of the LM and CD tests. It is shown that the bias-adjusted LM tests successfully control the size, maintaining satisfactory power in panel with exogenous regressors and normal errors. However, it is also shown that the bias-adjusted LM test is not as robust as the CD test to non-normal errors and/or in the presence of weakly exogenous regressors. Copyright Royal Economic Society 2007

a b s t r a c tThe presence of cross-sectionally correlated error terms invalidates much inferential theory of panel data models. Recently, work by Pesaran (2006) has suggested a method which makes use of crosssectional averages to provide valid inference in the case of stationary panel regressions with a multifactor error structure. This paper extends this work and examines the important case where the unobservable common factors follow unit root processes. The extension to I(1) processes is remarkable on two counts. First, it is of great interest to note that while intermediate results needed for deriving the asymptotic distribution of the panel estimators differ between the I(1) and I(0) cases, the final results are surprisingly similar. This is in direct contrast to the standard distributional results for I(1) processes that radically differ from those for I(0) processes. Second, it is worth noting the significant extra technical demands required to prove the new results. The theoretical findings are further supported for small samples via an extensive Monte Carlo study. In particular, the results of the Monte Carlo study suggest that the crosssectional-average-based method is robust to a wide variety of data generation processes and has lower biases than the alternative estimation methods considered in the paper.

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This paper extends the cross sectionally augmented panel unit root test proposed by Pesaran (2007) to the case of a multifactor error structure. The basic idea is to exploit information regarding the unobserved factors that are shared by other time series in addition to the variable under consideration. Importantly, our test procedure only requires speci…cation of the maximum number of factors, in contrast to other panel unit root tests based on principal components that require in addition the estimation of the number of factors as well as the factors themselves. Small sample properties of the proposed test are investigated by Monte Carlo experiments, which suggest that it controls well for size in almost all cases, especially in the presence of serial correlation in the error term, contrary to alternative test statistics. Empirical applications to Fisher's in ‡ation parity and real equity prices across di¤erent markets illustrate how the proposed test works in practice.