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GM Estimation of Higher-Order Spatial Autoregressive Processes in Cross-Section Models with Heteroskedastic Disturbances

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  • Harald Badinger
  • Peter Egger

Abstract

This paper generalizes the approach to estimating a first-order spatial autoregressive model with spatial autoregressive disturbances (SARAR(1,1)) in a cross-section with heteroskedastic innovations by Kelejian and Prucha (2008) to the case of spatial autoregressive models with spatial autoregressive disturbances of arbitrary (finite) order (SARAR(R,S)). We derive the moment conditions and the optimal weighting matrix for a generalized moments (GM) estimation procedure of the spatial regressive parameters of the disturbance process and define a generalized two-stages least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their (joint) asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2356.

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Date of creation: 2008
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Handle: RePEc:ces:ceswps:_2356

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Related research

Keywords: higher-order spatial dependence; heteroskedasticity; two-stages least squares; generalized moments estimation; asymptotics;

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References

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  1. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
  2. 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.
  3. Jeffrey P. Cohen & Catherine Morrison Paul, 2007. "The Impacts Of Transportation Infrastructure On Property Values: A Higher-Order Spatial Econometrics Approach," Journal of Regional Science, Wiley Blackwell, vol. 47(3), pages 457-478.
  4. Badi Baltagi & Dong Li, 2000. "LM Tests for Functional Form and Spatial Correlation," Econometric Society World Congress 2000 Contributed Papers 0099, Econometric Society.
  5. Shroder, Mark, 1995. "Games the States Don't Play: Welfare Benefits and the Theory of Fiscal Federalism," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 183-91, February.
  6. 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.
  7. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
  8. Peter Egger & Horst Raff, 2011. "Tax Rate and Tax Base Competition for Foreign Direct Investment," CESifo Working Paper Series 3596, CESifo Group Munich.
  9. Harry H. Kelejian & Ingmar R. Prucha, 2008. "Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances," CESifo Working Paper Series 2448, CESifo Group Munich.
  10. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
  11. Besley, Timothy & Case, Anne, 1995. "Incumbent Behavior: Vote-Seeking, Tax-Setting, and Yardstick Competition," American Economic Review, American Economic Association, vol. 85(1), pages 25-45, March.
  12. 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.
  13. Jeffrey P. Cohen & Catherine J. Morrison Paul, 2004. "Public Infrastructure Investment, Interstate Spatial Spillovers, and Manufacturing Costs," The Review of Economics and Statistics, MIT Press, vol. 86(2), pages 551-560, May.
  14. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
  15. Holtz-Eakin, Douglas, 1994. "Public-Sector Capital and the Productivity Puzzle," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 12-21, February.
  16. 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.
  17. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
  18. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
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Cited by:
  1. Harald Badinger & Peter Egger, 2009. "Estimation of Higher-Order Spatial Autoregressive Panel Data Error Component Models," CESifo Working Paper Series 2556, CESifo Group Munich.
  2. Harald Badinger & Peter Egger, 2014. "Fixed Effects and Random Effects Estimation of Higher-Order Spatial Autoregressive Models with Spatial Autoregressive and Heteroskedastic Disturbances," Department of Economics Working Papers wuwp173, Vienna University of Economics, Department of Economics.

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