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GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors

CentER Discussion Paper No. 2015-003

67 Pages Posted: 12 Dec 2011 Last revised: 21 Jan 2015

Pavel Cizek

Tilburg University - Department of Econometrics & Operations Research

Jan P. A. M. Jacobs

University of Groningen - Faculty of Economics and Business

Jenny E. Ligthart

Tilburg University - CentER, Department of Economics; University of Groningen - Faculty of Economics and Business; CESifo (Center for Economic Studies and Ifo Institute)

Hendrik Vrijburg

Erasmus University Rotterdam (EUR)

Date Written: November 2014

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.

Keywords: dynamic panel models, spatial lag, spatial error, GMM estimation

JEL Classification: C15, C21, C22, C23

Suggested Citation

Cizek, Pavel and Jacobs, Jan P. A. M. and Ligthart, Jenny E. and Vrijburg, Hendrik, GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (November 2014). CentER Discussion Paper No. 2015-003. Available at SSRN: https://ssrn.com/abstract=1971176 or http://dx.doi.org/10.2139/ssrn.1971176

Pavel Cizek

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Jan P.A.M. Jacobs (Contact Author)

University of Groningen - Faculty of Economics and Business ( email )

Postbus 72
9700 AB Groningen
Netherlands

Jenny E. Ligthart

Tilburg University - CentER, Department of Economics ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 8755 (Phone)
+31 13 466 4032 (Fax)

University of Groningen - Faculty of Economics and Business ( email )

Postbus 72
9700 AB Groningen
Netherlands

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

Hendrik Vrijburg

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

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