This paper presents a new approach to estimation and inference in panel data models with a multifactor error structure where the unobserved common factors are (possibly) correlated with exogenously given individual-specific regressors, and the factor loadings differ over the cross section units. The basic idea behind the proposed estimation procedure is to filter the individual-specific regressors by means of (weighted) cross-section aggregates 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 OLS applied to an auxiliary regression where the observed regressors are augmented by (weighted) cross sectional averages of the dependent variable and the individual specific regressors. Two different but related problems are addressed: one that concerns the coefficients of the individual-specific regressors, and the other that focusses on the mean of the individual coefficients assumed random. In both cases appropriate estimators, referred to as common correlated effects (CCE) estimators, are proposed and their asymptotic distribution as N →∞, with T (the time-series dimension) fixed or as N and T →∞(jointly) are derived under different regularity conditions. One important feature of the proposed CCE mean group (CCEMG) estimator is its invariance to the (unknown but fixed) number of unobserved common factors as N and T →∞(jointly). The small sample properties of the various pooled estimators are investigated by Monte Carlo experiments that confirm the theoretical derivations and show that the pooled estimators have generally satisfactory small sample properties even for relatively small values of N and T.

This paper introduces the concepts of time-specific weak and strong cross section dependence. A double-indexed process is said to be cross sectionally weakly dependent at a given point in time, t, if its weighted average along the cross section dimension (N) converges to its expectation in quadratic mean, as N is increased without bounds for all weights that satisfy certain ‘granularity’ conditions. Relationship with the notions of weak and strong common factors is investigated and an application to the estimation of panel data models with an infinite number of weak factors and a finite number of strong factors is also considered. The paper concludes with a set of Monte Carlo experiments where the small sample properties of estimators based on principal components and CCE estimators are investigated and compared under various assumptions on the nature of the unobserved common effects.

The 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 cross-sectional 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 and could be cointegrated. The extension of the results of Pesaran (2006) to the I(1) is remarkable on two counts. Firstly, 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. Secondly, 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 cross-sectional 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.

This paper considers large N and large T panel data models with unobservable multiple interactive effects. These models are useful for both micro and macro econometric modelings. In earnings studies, for example, workers ’ motivation, persistence, and diligence combined to influence the earnings in addition to the usual argument of innate ability. In macroeconomics, the interactive effects represent unobservable common shocks and their heterogeneous responses over cross sections. Since the interactive effects are allowed to be correlated with the regressors, they are treated as fixed effects parameters to be estimated along with the common slope coefficients. The model is estimated by the least squares method, which provides the interactive-effects counterpart of the within estimator. We first consider model identification, and then derive the rate of convergence and the limiting distribution of the interactive-effects estimator of the common slope coefficients. The estimator is shown to be √ NT consistent. This rate is valid even in the presence of correlations and heteroskedasticities in both dimensions, a striking contrast with fixed T framework in which serial correlation and heteroskedasticity imply unidentification. The asymptotic distribution is not necessarily centered at zero. Biased corrected estimators are derived. We also derive the constrained estimator and its limiting distribution, imposing additivity coupled with interactive effects. The problem of testing additive versus interactive effects is also studied. We also derive identification conditions for models with grand mean, time-invariant regressors, and common regressors. It is shown that there exists a set of necessary and sufficient identification conditions for those models. Given identification, the rate of convergence and limiting results continue to hold. Key words and phrases: incidental parameters, additive effects, interactive effects, factor

This paper considers the statistical analysis of large panel data sets where even after conditioning on common observed effects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common effects and/or if there are spill over effects due to spatial or other forms of local dependencies. The paper provides an overview of the literature on cross section dependence, introduces the concepts of time-specific weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence. It is then established that the Common Correlated Effects (CCE) estimator of panel data model with a multifactor error structure, recently advanced by Pesaran (2006), continues to provide consistent estimates of the slope coefficient, even in the presence of spatial error processes. Small sample properties of the CCE estimator under various patterns of cross section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross sectionally correlated errors. We also explore the role of certain characteristics of spatial processes in determining the performance of CCE estimators, such as the form and intensity of spatial dependence, and the sparseness of the spatial weight matrix.

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This paper considers estimation of slope coe ¢ cients in large panel data models where even after conditioning on common observed e¤ects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common e¤ects and/or if there are spill over e¤ects due to spatial or other forms of local dependencies. Initially it focuses on a regression model where the idiosyncratic errors are spatially dependent and possibly serially correlated, and derives the asymptotic distributions of the (generalized) …xed e¤ects and the mean group estimators under homogeneous and heterogeneous slope coe ¢ cients. Semiparametric and non-parametric estimation of the variances of these estimators is considered. The paper then focuses on a panel data model with a multifactor error structure and spatial correlation. It is established that, under this framework, the Common Correlated E¤ects (CCE) estimator, recently advanced by Pesaran (2006), continues to provide estimates of the slope coe ¢ cient that are consistent and asymptotically normal. Small sample properties of the CCE estimator under various patterns of cross section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross sectionally correlated errors.

We investigate the intertemporal linkages between foreign direct investment and disaggregated measures of international trade. We outline a model exemplifying these linkages, describe methods for investigating two-way feedbacks between various categories of trade, and apply them to recent data. We find that the strongest feedback between the sub-accounts is between FDI and manufacturing trade. Applying Geweke’s (1982) decomposition method, we find that most of the linear feedback between trade and FDI can be accounted for by Grangercausality from FDI gross flows to trade openness (50%) and from trade to FDI (31%).

This paper introduces the concepts of time-speci…c weak and strong cross section dependence. A double-indexed process is said to be cross sectionally weakly dependent at a given point in time, t, if its weighted average along the cross section dimension (N) converges to its expectation in quadratic mean, as N is increased without bounds for all weights that satisfy certain ‘granularity’ conditions. Relationship with the notions of weak and strong common factors is investigated and an application to the estimation of panel data models with an in…nite number of weak factors and a …nite number of strong factors is also considered. The paper concludes with a set of Monte Carlo experiments where the small sample properties of estimators based on principal components and CCE estimators are investigated and compared under various assumptions on the nature of the unobserved common e¤ects.

This paper presents a new approach to estimation and inference in panel data models with a multifactor error structure where the unobserved common factors are (possibly) correlated with exogenously given individual-specific regressors, and the factor loadings differ over the cross section units. The basic idea behind the proposed estimation procedure is to filter the individual-specific regressors by means of (weighted) cross-section aggregates 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 OLS applied to an auxiliary regression where the observed regressors are augmented by (weighted) cross sectional averages of the dependent variable and the individual specific regressors. Two different but related problems are addressed: one that concerns the coefficients of the individual-specific regressors, and the other that focusses on the mean of the individual coefficients assumed random. In both cases appropriate estimators, referred to as common correlated effects (CCE) estimators, are proposed and their asymptotic distribution as N →∞, with T (the time-series dimension) fixed or as N and T →∞(jointly) are derived under different regularity conditions. One important feature of the proposed CCE mean group (CCEMG) estimator is its invariance to the (unknown but fixed) number of unobserved common factors as N and T →∞(jointly). The small sample properties of the various pooled estimators are investigated by Monte Carlo experiments that confirm the theoretical derivations and show that the pooled estimators have generally satisfactory small sample properties even for relatively small values of N and T.