IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v157y2010i1p18-33.html
   My bibliography  Save this article

Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models

Author

Listed:
  • Su, Liangjun
  • Jin, Sainan

Abstract

We propose profile quasi-maximum likelihood estimation of spatial autoregressive models that are partially linear. The rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model. The estimators of other finite-dimensional parameters in the model have the regular -rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth parameter associated with different natures of the spatial weights. Monte Carlo simulations verify our theory and indicate that our estimators perform reasonably well in finite samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:1:p:18-33
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(09)00286-3
    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. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. 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.
    4. 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.
    5. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, November.
    6. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
    7. Reinaud A. J. J. Gastel & Jean H. P. Paelinck, 1995. "Computation of Box-Cox Transform Parameters: A New Method and its Application to Spatial Econometrics," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax (ed.), New Directions in Spatial Econometrics, chapter 6, pages 136-155, Springer.
    8. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    9. 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.
    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. 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.
    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. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 252-277, April.
    14. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    15. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    16. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    17. 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.
    18. 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.
    19. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
    20. Gao, Jiti, 1995. "The laws of the iterated logarithm of some estimates in partly linear models," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 153-162, November.
    21. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    2. Zhang Yuanqing, 2014. "Estimation of Partially Specified Spatial Autoregressive Model," Journal of Systems Science and Information, De Gruyter, vol. 2(3), pages 226-235, June.
    3. Zhengyu Zhang, 2013. "A Pairwise Difference Estimator for Partially Linear Spatial Autoregressive Models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(2), pages 176-194, June.
    4. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    5. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    6. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    7. Jin, Fei & Lee, Lung-fei, 2012. "Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 446-458.
    8. 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.
    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. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    11. 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.
    12. Yong Bao & Xiaotian Liu & Lihong Yang, 2020. "Indirect Inference Estimation of Spatial Autoregressions," Econometrics, MDPI, vol. 8(3), pages 1-26, September.
    13. Gupta, Abhimanyu & Robinson, Peter M., 2015. "Inference on higher-order spatial autoregressive models with increasingly many parameters," Journal of Econometrics, Elsevier, vol. 186(1), pages 19-31.
    14. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    15. 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.
    16. 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.
    17. repec:esx:essedp:772 is not listed on IDEAS
    18. Zhenlin Yang, 2006. "On Joint Modelling and Testing for Local and Global Spatial Externalities," Working Papers 25-2006, Singapore Management University, School of Economics.
    19. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    20. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
    21. 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.

    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:157:y:2010:i:1:p:18-33. See general information about how to correct material in RePEc.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.