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A spatial autoregressive model with a nonlinear transformation of the dependent variable

Author

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  • Xu, Xingbai
  • Lee, Lung-fei

Abstract

This paper develops a nonlinear spatial autoregressive model. Of particular interest is a structural interaction model for share data. We consider possible instrumental variable (IV) and maximum likelihood estimation (MLE) for this model, and analyze asymptotic properties of the IV and MLE based on the notion of spatial near-epoch dependence. We also design a statistical test to compare the nonlinear transformation against alternatives. Monte Carlo experiments are designed to investigate finite sample performance of the proposed estimates and the sizes and powers of the test.

Suggested Citation

  • Xu, Xingbai & Lee, Lung-fei, 2015. "A spatial autoregressive model with a nonlinear transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 186(1), pages 1-18.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:1:p:1-18
    DOI: 10.1016/j.jeconom.2014.12.005
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    References listed on IDEAS

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    1. 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 509-533, May.
    2. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    3. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
    4. Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
    5. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    6. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    7. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    8. Papke, Leslie E. & Wooldridge, Jeffrey M., 2008. "Panel data methods for fractional response variables with an application to test pass rates," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 121-133, July.
    9. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    10. 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.
    11. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    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. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    14. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    15. 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.
    16. Qu, Xi & Lee, Lung-fei, 2013. "Locally most powerful tests for spatial interactions in the simultaneous SAR Tobit model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 307-321.
    17. 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.
    18. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
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    Citations

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    Cited by:

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    4. Liu, Tuo & Xu, Xingbai & Lee, Lung-fei, 2022. "Consistency without compactness of the parameter space in spatial econometrics," Economics Letters, Elsevier, vol. 210(C).
    5. Wu, Changyan & Huang, Xianjin & Chen, Bowen, 2020. "Telecoupling mechanism of urban land expansion based on transportation accessibility: A case study of transitional Yangtze River economic Belt, China," Land Use Policy, Elsevier, vol. 96(C).
    6. Liu, Xiaodong & Prucha, Ingmar R., 2018. "A robust test for network generated dependence," Journal of Econometrics, Elsevier, vol. 207(1), pages 92-113.
    7. Xu, Xingbai & Lee, Lung-fei, 2018. "Sieve maximum likelihood estimation of the spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 203(1), pages 96-112.
    8. Xu, Xingbai & Lee, Lung-fei, 2015. "Maximum likelihood estimation of a spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 188(1), pages 264-280.
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    10. Hoshino, Tadao, 2022. "Sieve IV estimation of cross-sectional interaction models with nonparametric endogenous effect," Journal of Econometrics, Elsevier, vol. 229(2), pages 263-275.
    11. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    12. Bing Su & Fukang Zhu & Ke Zhu, 2023. "Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables," Papers 2301.06658, arXiv.org.
    13. Baltagi, Badi H. & Egger, Peter H. & Kesina, Michaela, 2017. "Determinants of firm-level domestic sales and exports with spillovers: Evidence from China," Journal of Econometrics, Elsevier, vol. 199(2), pages 184-201.
    14. Xiaowen Dai & Shidan Huang & Libin Jin & Maozai Tian, 2023. "Wild Bootstrap-Based Bias Correction for Spatial Quantile Panel Data Models with Varying Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    15. Debarsy, Nicolas & Yang, Zhenlin, 2018. "Editorial for the special issue entitled: New advances in spatial econometrics: Interactions matter," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 1-5.
    16. Fang Lu & Jing Yang & Xuewen Lu, 2022. "One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data," Empirical Economics, Springer, vol. 62(6), pages 2645-2671, June.
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    18. Glass, Anthony J. & Kenjegalieva, Karligash, 2019. "A spatial productivity index in the presence of efficiency spillovers: Evidence for U.S. banks, 1992–2015," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1165-1179.

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    More about this item

    Keywords

    Nonlinear spatial autoregressive model; Near-epoch dependence; Maximum likelihood; Instrumental variables; Asymptotic distribution of estimators;
    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
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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