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.

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 ADF regressions are augmented with the cross section 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 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.

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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

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This paper considers estimation and inference in panel vector autoregressions (PVARs) where (i) the individual effects are either random or fixed, (ii) the time-series properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time dimension of the panel is short and its cross-sectional dimension is large. Generalized Method of Moments (GMM) and Quasi Maximum Likelihood (QML) estimators are obtained andthencomparedintermsoftheirasymptoticandfinite sample properties. It is shown that GMM estimators based only on standard orthogonality conditions break down if the underlying time series contain unit roots. Extended GMM estimators making use of further moment conditions are not subject to this problem. However, their finite sample performance is shown to deteriorate as a ratio of cross-section to time-series variation is increased, while the performance of the fixed effects QML estimator is invariant to this ratio. The QML estimators also tend to outperform the various GMM estimators in finite sample. Overall, our findings favor the use of the fixed effects QML estimator, given that it does not impose any restrictions on the distribution generating the individual effects. The paper also shows how the fixed effects QML

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.

Yu, de Jong and Lee (2006) established asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both the number of individuals n and the number of time periods T are large. This paper covers a nonstationary case where there are unit roots in the data generating process. When not all the roots in the DGP are unit, the estimators’ rates of convergence will be the same as the stationary case, and the estimators can be asymptotically normal. The presence of the nonstationary components however will make the estimators’ asymptotic variance matrix singular. Consequently, a linear combination of the spatial and dynamic effects can converge at a higher rate. We also propose a bias correction for our estimator. When T grows faster than n 1=3, the correction will asymptotically eliminate the bias and yield a centered confidence interval.

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This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the …rst generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might prevail across the di¤erent units in the panel. In the analysis of cointegration the hypothesis testing and estimation problems are further complicated by the possibility of cross section cointegration which could arise if the unit roots in the di¤erent cross section units are due to common random walk components.