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Instrumental Variable Quantile Estimation of Spatial Autoregressive Models

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  • Liangjun Su

    (SMU)

  • Zhenlin Yang

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.

Suggested Citation

  • Liangjun Su & Zhenlin Yang, 2007. "Instrumental Variable Quantile Estimation of Spatial Autoregressive Models," Development Economics Working Papers 22476, East Asian Bureau of Economic Research.
    • Handle: RePEc:eab:develo:22476
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    Cited by:

    1. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    2. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    3. Danqing Chen & Jianbao Chen & Shuangshuang Li, 2021. "Instrumental Variable Quantile Regression of Spatial Dynamic Durbin Panel Data Model with Fixed Effects," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
    4. He Jiang, 2023. "Robust forecasting in spatial autoregressive model with total variation regularization," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 195-211, March.
    5. Philip Kostov & Julie Le Gallo, 2015. "Convergence: A Story of Quantiles and Spillovers," Kyklos, Wiley Blackwell, vol. 68(4), pages 552-576, November.
    6. Philip Kostov, 2009. "A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(1), pages 53-72.
    7. Stephen Matthews & Daniel M. Parker, 2013. "Progress in Spatial Demography," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(10), pages 271-312.
    8. 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.
    9. Coro Chasco & Julie Le Gallo, 2015. "Heterogeneity in Perceptions of Noise and Air Pollution: A Spatial Quantile Approach on the City of Madrid," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(3), pages 317-343, September.
    10. Jiawei Hou & Yunquan Song, 2022. "Interquantile shrinkage in spatial additive autoregressive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1030-1057, December.
    11. Alfredo Cartone & Paolo Postiglione, 2016. "Modelli spaziali di regressione quantilica per l?analisi della convergenza economica regionale," RIVISTA DI ECONOMIA E STATISTICA DEL TERRITORIO, FrancoAngeli Editore, vol. 2016(3), pages 28-48.
    12. Weiguang Wang & Yangyang Wang, 2023. "Regional Differences, Dynamic Evolution and Driving Factors Analysis of PM 2.5 in the Yangtze River Economic Belt," Sustainability, MDPI, vol. 15(4), pages 1-24, February.
    13. Liao, Wen-Chi & Wang, Xizhu, 2012. "Hedonic house prices and spatial quantile regression," Journal of Housing Economics, Elsevier, vol. 21(1), pages 16-27.
    14. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
    15. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    16. Marusca De Castris & Daniele Di Gennaro, 2018. "Does agricultural subsidies foster Italian southern farms? A Spatial Quantile Regression Approach," Papers 1803.05659, arXiv.org.

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    More about this item

    Keywords

    Spatial Autoregressive Model; Quantile Regression; Instrumental Variable; Quasi Maximum Likelihood; GMM; Robustness;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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