A test of cross section dependence for a linear dynamic panel model with regressors

Abstract

Please cite this article as: Sarafidis, V., Yamagata, T., Robertson, D., A test of cross section dependence for a linear dynamic panel model with regressors. Journal of Econometrics (2008Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Abstract This paper proposes a new testing procedure for detecting error cross section dependence after estimating a linear dynamic panel data model with regressors using the generalised method of moments (GMM). The test is valid when the crosssectional dimension of the panel is large relative to the time series dimension. Importantly, our approach allows one to examine whether any error cross section dependence remains after including time dummies (or after transforming the data in terms of deviations from time-speci…c averages), which will be the case under heterogeneous error cross section dependence. Finite sample simulation-based results suggest that our tests perform well, particularly the version based on the Blundell and Bond (1998) system GMM estimator. In addition, it is shown that the system GMM estimator, based only on partial instruments consisting of the regressors, can be a reliable alternative to the standard GMM estimators under heterogeneous error cross section dependence. The proposed tests are applied to employment equations using UK …rm data and the results show little evidence of heterogeneous error cross section dependence. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

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“…Cross-sectional dependence among errors can be eliminated by including time dummies or by cross-sectionally demeaning the data. We created year-dummy control variables to prevent cross-individual correlation [84,85], thereby improving the robustness of our results [86]. It calls for a first-order dynamic panel-data approach to exploring the relationships between the variable in question.…”

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“…Another concern related to the specification of panel data models has been raised by Sarafidis et al (2009), who claim that panel data are likely to suffer from crosssectional dependence, which may arise due to spatial dependence, economic distance and common shocks. In order to tackle this problem, we have followed the conventional method of including year dummies in the model.…”

“…In order to tackle this problem, we have followed the conventional method of including year dummies in the model. However, Sarafidis et al (2009) claim that the inclusion of time dummies may not be sufficient to tackle the problem of cross-sectional dependence. These authors suggest that the above tests of instrument validity may be indicative for the presence of a cross-sectional dependence problem.…”

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“…For instance, where a multifactor error structure is employed for the purpose of dimension reduction, or simply when explanatory variables may not be observable. In such cases, it could be relevant to know whether there is indeed a factor structure in (1), or whether common effects can be adequately represented by more parsimonious models such as a model with cross-sectional or time dummies, as also studied by Sarafidis, Yamagata andRobertson (2009), and in the context of model (1) with homogeneous slopes. In this case, the asymptotics of the estimated common factors and loadings is obviously a first, fundamental step in order to construct tests for the presence of a multifactor error structure.…”

“…γ i = γ), equation (1) is tantamount to a panel regression with a time effect -therefore there is no real common factor structure. This fact is used by Sarafidis, Yamagata and Robertson (2009) to test for cross dependence in a dynamic panel context. Similarly, in the case of homogeneous factors (i.e.…”