GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Revised version of CentER DP 2011-134)

P. Cizek, J. Jacobs, J.E. Ligthart, H. Vrijburg

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Abstract

The three-step generalized methods of moments (GMM) approach of Kapoor, Kelejian and Prucha (2007), which corrects for spatially correlated errors in static panel data models, is extended by introducing fixed effects, a spatial lag, and a one-period lag of the dependent variable as additional explanatory variables. Combining this approach with the dynamic panel-data GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) and specifying moment conditions for various time lags, spatial lags, and sets of exogenous variables yields new spatial dynamic panel data estimators. The proposed spatially corrected GMM estimates are based on a spatial lag and a transformation correcting for the spatial error correlation. We prove their consistency and asymptotic normality for a large number of spatial units and a fixed number of time periods. Feasible spatial correction based on estimated spatial error correlation is shown to lead to estimators that are asymptotically equivalent to the infeasible estimators based on a known spatial error
correlation. Monte Carlo simulations show that the root mean squared error of spatially corrected GMM estimates is generally smaller than that of corresponding spatial GMM estimates in which spatial error correlation is ignored.
Original languageEnglish
PublisherCentER, Center for Economic Research
Number of pages67
Volume2015-003
Publication statusPublished - 20 Jan 2015

Publication series

NameCentER Discussion Paper
Volume2015-003

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panel data
effect
method
simulation

Keywords

  • Dynamic panel models,
  • spatial lag,
  • spatial error,
  • GMM estimation

Cite this

Cizek, P., Jacobs, J., Ligthart, J. E., & Vrijburg, H. (2015). GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Revised version of CentER DP 2011-134). (CentER Discussion Paper; Vol. 2015-003). CentER, Center for Economic Research.
Cizek, P. ; Jacobs, J. ; Ligthart, J.E. ; Vrijburg, H. / GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Revised version of CentER DP 2011-134). CentER, Center for Economic Research, 2015. (CentER Discussion Paper).
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abstract = "The three-step generalized methods of moments (GMM) approach of Kapoor, Kelejian and Prucha (2007), which corrects for spatially correlated errors in static panel data models, is extended by introducing fixed effects, a spatial lag, and a one-period lag of the dependent variable as additional explanatory variables. Combining this approach with the dynamic panel-data GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) and specifying moment conditions for various time lags, spatial lags, and sets of exogenous variables yields new spatial dynamic panel data estimators. The proposed spatially corrected GMM estimates are based on a spatial lag and a transformation correcting for the spatial error correlation. We prove their consistency and asymptotic normality for a large number of spatial units and a fixed number of time periods. Feasible spatial correction based on estimated spatial error correlation is shown to lead to estimators that are asymptotically equivalent to the infeasible estimators based on a known spatial errorcorrelation. Monte Carlo simulations show that the root mean squared error of spatially corrected GMM estimates is generally smaller than that of corresponding spatial GMM estimates in which spatial error correlation is ignored.",
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Cizek, P, Jacobs, J, Ligthart, JE & Vrijburg, H 2015 'GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Revised version of CentER DP 2011-134)' CentER Discussion Paper, vol. 2015-003, CentER, Center for Economic Research.

GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Revised version of CentER DP 2011-134). / Cizek, P.; Jacobs, J.; Ligthart, J.E.; Vrijburg, H.

CentER, Center for Economic Research, 2015. (CentER Discussion Paper; Vol. 2015-003).

Research output: Working paperDiscussion paperOther research output

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N2 - The three-step generalized methods of moments (GMM) approach of Kapoor, Kelejian and Prucha (2007), which corrects for spatially correlated errors in static panel data models, is extended by introducing fixed effects, a spatial lag, and a one-period lag of the dependent variable as additional explanatory variables. Combining this approach with the dynamic panel-data GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) and specifying moment conditions for various time lags, spatial lags, and sets of exogenous variables yields new spatial dynamic panel data estimators. The proposed spatially corrected GMM estimates are based on a spatial lag and a transformation correcting for the spatial error correlation. We prove their consistency and asymptotic normality for a large number of spatial units and a fixed number of time periods. Feasible spatial correction based on estimated spatial error correlation is shown to lead to estimators that are asymptotically equivalent to the infeasible estimators based on a known spatial errorcorrelation. Monte Carlo simulations show that the root mean squared error of spatially corrected GMM estimates is generally smaller than that of corresponding spatial GMM estimates in which spatial error correlation is ignored.

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Cizek P, Jacobs J, Ligthart JE, Vrijburg H. GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Revised version of CentER DP 2011-134). CentER, Center for Economic Research. 2015 Jan 20. (CentER Discussion Paper).