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Instrumental Variable Quantile Estimation of Spatial Autoregressive Models

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  • Zhenlin Yang

    ()
    (School of Economics, Singapore Management University)

  • Liangjun Su

    ()
    (School of Economics, Singapore Management University)

Abstract

We propose an instrumental variable quantile regression (IVQR) estimator for spatial autoregressive (SAR) models. Like the GMM estimators of Lin and Lee (2006) and Kelejian and Prucha (2006), the IVQR estimator is robust against heteroscedasticity. Unlike the GMM estimators, the IVQR estimator is also robust against outliers and requires weaker moment conditions. More importantly, it allows us to characterize the heterogeneous impact of variables on different points (quantiles) of a response distribution. We derive the limiting distribution of the new estimator. Simulation results show that the new estimator performs well in finite samples at various quantile points. In the special case of median restriction, it outperforms the conventional QML estimator without taking into account of heteroscedasticity in the errors; it also outperforms the GMM estimators with or without considering the heteroscedasticity.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 05-2007.

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Length: 35 pages
Date of creation: Aug 2007
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:05-2007

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Keywords: Spatial Autoregressive Model; Quantile Regression; Instrumental Variable; Quasi Maximum Likelihood; GMM; Robustness.;

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References

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  1. 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.
  2. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September.
  3. Honore, Bo E & Hu, Luojia, 2004. "On the Performance of Some Robust Instrumental Variables Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 30-39, January.
  4. 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.
  5. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
  6. 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.
  7. Elie Tamer, 2000. "Inference in Censored Models with Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1815, Econometric Society.
  8. Joris Pinkse & Margaret Slade & Lihong Shen, 2006. "Dynamic Spatial Discrete Choice Using One-step GMM: An Application to Mine Operating Decisions," Spatial Economic Analysis, Taylor & Francis Journals, vol. 1(1), pages 53-99.
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  12. Pinkse, Joris & Shen, Lihong & Slade, Margaret, 2007. "A central limit theorem for endogenous locations and complex spatial interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 215-225, September.
  13. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-33, May.
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  15. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
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  17. 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.
  18. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  19. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
  20. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  21. Sakata, Shinichi, 2007. "Instrumental variable estimation based on conditional median restriction," Journal of Econometrics, Elsevier, vol. 141(2), pages 350-382, December.
  22. 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. Bernardo Furtado & Frank van Oort, 2011. "Neighborhood weight matrix in a spatial-quantile real estate modeling environment: Evidence from Brazil," ERSA conference papers ersa10p424, European Regional Science Association.

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