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

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 cross-sectional 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-specific 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, R., Bond, S., 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115-143] 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 firm data and the results show little evidence of heterogeneous error cross section dependence.

[1]  Peter Schmidt,et al.  GMM estimation of linear panel data models with time-varying individual effects , 2001 .

[2]  M. Pesaran.  General diagnostic tests for cross-sectional dependence in panels , 2004, Empirical Economics.

[3]  Clive G. Bowsher.  On testing overidentifying restrictions in dynamic panel data models , 2002 .

[4]  J. Stock,et al.  Macroeconomic Forecasting Using Diffusion Indexes , 2002 .

[5]  Hyungsik Roger Moon,et al.  Testing For A Unit Root In Panels With Dynamic Factors , 2002 .

[6]  Lung-fei Lee,et al.  Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models , 2004 .

[7]  Vasilis Sarafidis,et al.  On the Impact of Error Cross-Sectional Dependence in Short Dynamic Panel Estimation , 2009 .

[8]  A. Ullah,et al.  A Bias-Adjusted LM Test of Error Cross-Section Independence , 2008 .

[9]  Peter Schmidt,et al.  Estimation of a Panel Data Model with Parametric Temporal Variation in Individual Effects , 2004 .

[10]  Adrian Pagan,et al.  The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics , 1980 .

[11]  Stephen Bond,et al.  Criterion-Based Inference for GMM in Autoregressive Panel Data Models , 2001 .

[12]  Donald Robertson,et al.  Factor residuals in SUR regressions: estimating panels allowing for cross sectional correlation , 2000 .

[13]  R. Blundell,et al.  Initial Conditions and Moment Restrictions in Dynamic Panel Data Models , 1998 .

[14]  Donggyu Sul,et al.  Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence , 2002 .

[15]  Stan Hurn.  Panel Data Econometrics , 2010 .

[16]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[17]  Badi H. Baltagi,et al.  A companion to theoretical econometrics , 2003 .

[18]  J. Hausman.  Specification tests in econometrics , 1978 .

[19]  Timothy G. Conley.  GMM estimation with cross sectional dependence , 1999 .

[20]  Lung-fei Lee,et al.  GMM and 2SLS estimation of mixed regressive, spatial autoregressive models , 2007 .

[21]  Jan F. Kiviet,et al.  On bias, inconsistency and efficiency of various estimators in dynamic panel data models , 1995 .

[22]  J. Sargan.  THE ESTIMATION OF ECONOMIC RELATIONSHIPS USING INSTRUMENTAL VARIABLES , 1958 .

[23]  M. Friedman.  The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .

[24]  Mudit Kapoor,et al.  Panel data models with spatially correlated error components , 2007 .

[25]  Stephen Bond,et al.  GMM Estimation with persistent panel data: an application to production functions , 1999 .

[26]  W. Newey,et al.  Estimating vector autoregressions with panel data , 1988 .

[27]  J. Bai,et al.  A Panic Attack on Unit Roots and Cointegration , 2001 .

[28]  M. Pesaran,et al.  Estimating Long-Run Relationships From Dynamic Heterogeneous Panels , 1995 .

[29]  Serena Ng,et al.  Testing Cross-Section Correlation in Panel Data Using Spacings , 2006 .

[30]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

[31]  W. Newey,et al.  Generalized method of moments specification testing , 1985 .

[32]  E. Frees.  Assessing cross-sectional correlation in panel data , 1995 .

[33]  M. Arellano,et al.  Another look at the instrumental variable estimation of error-components models , 1995 .

[34]  Lucrezia Reichlin,et al.  Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics , 1998 .

[35]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[36]  J. Kiviet,et al.  The Effects of Dynamic Feedbacks on Ls and Mm Estimator Accuracy in Panel Data Models , 2002 .

[37]  J. Hahn,et al.  Long difference instrumental variables estimation for dynamic panel models with fixed effects , 2007 .

[38]  Peter Schmidt,et al.  Efficient estimation of models for dynamic panel data , 1995 .