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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.

Summary This paper provides a characterisation of the degree of cross‐sectional dependence in a two dimensional array, {xit,i = 1,2,...N;t = 1,2,...,T} in terms of the rate at which the variance of the cross‐sectional average of the observed data varies with N. Under certain conditions this is equivalent to the rate at which the largest eigenvalue of the covariance matrix of xt=(x1t,x2t,...,xNt)′ rises with N. We represent the degree of cross‐sectional dependence by α, which we refer to as the ‘exponent of cross‐sectional dependence’, and define it by the standard deviation, Std(truex̄t)=O()Nα−1, where truex̄t is a simple cross‐sectional average of xit. We propose bias corrected estimators, derive their asymptotic properties for α > 1/2 and consider a number of extensions. We include a detailed Monte Carlo simulation study supporting the theoretical results. We also provide a number of empirical applications investigating the degree of inter‐linkages of real and financial variables in the global economy. Copyright © 2015 John Wiley & Sons, Ltd.

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