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Large sample properties of the matrix exponential spatial specification with an application to FDI

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  • Nicolas Debarsy

    ()
    (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR7322 - Université d'Orléans, CERPE - Centre de recherche en Economie Régionale et Politique Economique - Facultés Universitaires Notre Dame de la Paix (FUNDP) - Namur)

  • Fei Jin

    ()
    (SUFE - School of Economics - Shanghai University of Finance and Economics)

  • Lung-Fei Lee

    ()
    (Department of Economics - Ohio State University - Ohio State University)

Abstract

This paper considers the large sample properties of the matrix exponential spatial specification (MESS) and compares its properties with those of the spatial autoregressive (SAR) model. We find that the quasi-maximum likelihood estimator (QMLE) for the MESS is consistent under heteroskedasticity, a property not shared by the QMLE of the SAR model. For the MESS in both homoskedastic and heteroskedastic cases, consistency is proved and asymptotic distributions are derived. We also consider properties of the generalized method of moments estimator (GMME). In the homoskedastic case, we derive a best GMME that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the QMLE under non-normality. In the heteroskedastic case, an optimal GMME can be more efficient than the QMLE asymptotically and the possible best GMME is also discussed. For the general model that has MESS in both the dependent variable and disturbances, labeled MESS(1,1), the QMLE can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two MESS processes are commutative. Also, properties of the QMLE and GMME for the general model are considered. The QML approach for the MESS model has the computational advantage over that of a SAR model. The computational simplicity carries over to MESS models with any finite order of spatial matrices. No parameter range needs to be imposed in order for the model to be stable. Furthermore, the Delta method is used to derive test statistics for the impacts of exogenous variables on the dependent variable. Results of Monte Carlo experiments for finite sample properties of the estimators are reported. Finally, the MESS(1,1) is applied to Belgium's outward FDI data and we observe that the dominant motivation of Belgium's outward FDI lies in finding cheaper factor inputs.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00858174.

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Date of creation: 04 Sep 2013
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Handle: RePEc:hal:wpaper:hal-00858174

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00858174
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Related research

Keywords: Spatial autocorrelation ; MESS ; QML ; GMM ; Heteroskedasticity ; Delta method ; FDI;

This paper has been announced in the following NEP Reports:

References

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  1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  2. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
  3. Blonigen, Bruce A. & Davies, Ronald B. & Waddell, Glen R. & Naughton, Helen T., 2007. "FDI in space: Spatial autoregressive relationships in foreign direct investment," European Economic Review, Elsevier, vol. 51(5), pages 1303-1325, July.
  4. G�ran Therborn & K.C. Ho, 2009. "Introduction," City, Taylor & Francis Journals, vol. 13(1), pages 53-62, March.
  5. Ronald B. Davies, 2003. "Fragmentation of Headquarter Services and FDI," University of Oregon Economics Department Working Papers 2003-25, University of Oregon Economics Department, revised 01 Sep 2003.
  6. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2007. "Estimating Regional Trade Agreement Effects on FDI in an Interdependent World," Center for Policy Research Working Papers 100, Center for Policy Research, Maxwell School, Syracuse University.
  7. Cletus C. Coughlin & Eran Segev, 1999. "Foreign direct investment in China: a spatial econometric study," Working Papers 1999-001, Federal Reserve Bank of St. Louis.
  8. Jin, Fei & Lee, Lung-fei, 2012. "Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 446-458.
  9. Baltagi, Badi H. & Egger, Peter & Pfaffermayr, Michael, 2007. "Estimating models of complex FDI: Are there third-country effects?," Journal of Econometrics, Elsevier, vol. 140(1), pages 260-281, September.
  10. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
  11. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
  12. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
  13. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
  14. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
  15. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
  16. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
  17. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
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