IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v167y2012i2p543-560.html
   My bibliography  Save this article

Semiparametric GMM estimation of spatial autoregressive models

Author

Listed:
  • Su, Liangjun

Abstract

We propose semiparametric GMM estimation of semiparametric spatial autoregressive (SAR) models under weak moment conditions. In comparison with the quasi-maximum-likelihood-based semiparametric estimator of Su and Jin (2010), we allow for both heteroscedasticity and spatial dependence in the error terms. We derive the limiting distributions of our estimators for both the parametric and nonparametric components in the model and demonstrate the estimator of the parametric component has the usual n-asymptotics. When the error term also follows an SAR process, we propose an estimator for the parameter in the SAR error process and derive the joint asymptotic distribution for both spatial parameters. Consistent estimates for the asymptotic variance-covariance matrices of both the parametric and nonparametric components are provided. Monte Carlo simulations indicate that our estimators perform well in finite samples.

Suggested Citation

  • Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
  • Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:543-560
    DOI: 10.1016/j.jeconom.2011.09.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407611002156
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1321-1342, October.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, April.
    6. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    7. 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.
    8. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    9. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    10. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    11. Yang, Zhenlin & Li, Chenwei & Tse, Y.K., 2006. "Functional form and spatial dependence in dynamic panels," Economics Letters, Elsevier, vol. 91(1), pages 138-145, April.
    12. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    13. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    14. Zhenlin Yang & Liangjun Su, 2007. "Instrumental Variable Quantile Estimation of Spatial Autoregressive Models," Working Papers 05-2007, Singapore Management University, School of Economics.
    15. Xiao Z. & Linton O.B. & Carroll R.J. & Mammen E., 2003. "More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 980-992, January.
    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. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.
    18. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    19. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    20. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    21. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    22. 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.
    23. 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.
    24. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    2. Su, Liangjun & Yang, Zhenlin, 2015. "QML estimation of dynamic panel data models with spatial errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 230-258.
    3. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.
    4. repec:gam:jecnmx:v:4:y:2016:i:1:p:6:d:63356 is not listed on IDEAS
    5. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    6. Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
    7. Mustafa Koroglu & Yiguo Sun, 2016. "Functional-Coefficient Spatial Durbin Models with Nonparametric Spatial Weights: An Application to Economic Growth," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-16, February.
    8. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.
    9. DUo Qin & Yimeng Liu, 2013. "Modelling Scale Effect in Crosssection Data:The Case of Hedonic Price Regression," Working Papers 184, Department of Economics, SOAS, University of London, UK.
    10. Sun, Yiguo & Malikov, Emir, 2017. "Estimation and Inference in Functional-Coefficient Spatial Autoregressive Panel Data Models with Fixed Effects," MPRA Paper 83671, University Library of Munich, Germany.
    11. James Wolter, 2015. "Kernel Estimation Of Hazard Functions When Observations Have Dependent and Common Covariates," Economics Series Working Papers 761, University of Oxford, Department of Economics.
    12. repec:eee:ecmode:v:64:y:2017:i:c:p:553-559 is not listed on IDEAS
    13. Sun, Yiguo, 2016. "Functional-coefficient spatial autoregressive models with nonparametric spatial weights," Journal of Econometrics, Elsevier, vol. 195(1), pages 134-153.
    14. Tiziano Arduini & Eleonora Patacchini & Edoardo Rainone, 2015. "Parametric and Semiparametric IV Estimation of Network Models with Selectivity," EIEF Working Papers Series 1509, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2015.
    15. Zhang, Yuanqing & Sun, Yanqing, 2015. "Estimation of partially specified dynamic spatial panel data models with fixed-effects," Regional Science and Urban Economics, Elsevier, vol. 51(C), pages 37-46.

    More about this item

    Keywords

    Generalized method of moments; Local instruments; Nonlinearity; Semiparametrics; Spatial autoregression;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:167:y:2012:i:2:p:543-560. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.