IDEAS home Printed from https://ideas.repec.org/a/cuf/journl/y2010v11i1p155-184.html
   My bibliography  Save this article

A More Efficient Best Spatial Three-stage Least Squares Estimator for Spatial Autoregressive Models

Author

Listed:
  • Zhengyu Zhang

    (Research Center of Econometrics, Shanghai Academy of Social Sciences)

  • Pingfang Zhu

    (Research Center of Econometrics, Shanghai Academy of Social Sciences)

Abstract

Lee (2003) proposed for spatial autoregressive (SAR) model the best spatial two-stage least squares estimator (BS2SLSE) as an improvement on Kelejian and Prucha (1998)¡¯s S2SLSE. In this paper, we show that one more step iteration based on BS2SLSE gives a spatial counterpart of the three-stage least squares estimator for a system of J equations. This estimator, named BS3SLSE, is shown to be equivalent to BS2SLSE under normality and more efficient under non-normality. The proposed BS3SLSE can be interpreted as a GMM estimator where the number of moments increases with the sample size n at some slow rate. The asymptotic efficiency of BS3SLSE relative to other previously proposed estimators such as MLE (Lee, 2004) and GMME (Lee, 2007a) is also discussed. As an empirical illustration, we apply these estimation procedures to re-examining the presence of environmental ¡°race-to-the-bottom¡± effect in competition for FDI across China municipal governments.

Suggested Citation

  • Zhengyu Zhang & Pingfang Zhu, 2010. "A More Efficient Best Spatial Three-stage Least Squares Estimator for Spatial Autoregressive Models," Annals of Economics and Finance, Society for AEF, vol. 11(1), pages 155-184, May.
    • Handle: RePEc:cuf:journl:y:2010:v:11:i:1:p:155-184
    as

    Download full text from publisher

    File URL: http://aeconf.com/Articles/May2010/aef110106.pdf
    Download Restriction: no
    File URL: http://down.aefweb.net/AefArticles/aef110106.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. James C. Murdoch & Tod Sandler & Keith Sargent, 1997. "A Tale of Two Collectives: Sulphur versus Nitrogen Oxides Emission Reduction in Europe," Economica, London School of Economics and Political Science, vol. 64(254), pages 281-301, May.
    2. Wheeler, David, 2001. "Racing to the bottom : foreign investment and air pollution in developing countries," Policy Research Working Paper Series 2524, The World Bank.
    3. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    4. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    5. 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.
    6. 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.
    7. 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.
    8. Case, Anne, 1992. "Neighborhood influence and technological change," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 491-508, September.
    9. Fredriksson, Per G. & Millimet, Daniel L., 2002. "Strategic Interaction and the Determination of Environmental Policy across U.S. States," Journal of Urban Economics, Elsevier, vol. 51(1), pages 101-122, January.
    10. Jamuna Agarwal, 1980. "Determinants of foreign direct investment: A survey," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 116(4), pages 739-773, December.
    11. Werner Antweiler & Brian R. Copeland & M. Scott Taylor, 2001. "Is Free Trade Good for the Environment?," American Economic Review, American Economic Association, vol. 91(4), pages 877-908, September.
    12. 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.
    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. Marius C. O. Amba & Taoufiki Mbratana & Julie Gallo, 2023. "Spatial panel simultaneous equations models with error components," Empirical Economics, Springer, vol. 65(3), pages 1149-1196, September.

    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. 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.
    2. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    3. repec:esx:essedp:772 is not listed on IDEAS
    4. Pesaran, M. Hashem & Yang, Cynthia Fan, 2021. "Estimation and inference in spatial models with dominant units," Journal of Econometrics, Elsevier, vol. 221(2), pages 591-615.
    5. 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.
    6. Peter M Robinson, 2009. "Developments in the Analysis of Spatial Data," STICERD - Econometrics Paper Series 531, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. 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.
    8. 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.
    9. Kripfganz, Sebastian, 2014. "Unconditional Transformed Likelihood Estimation of Time-Space Dynamic Panel Data Models," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100604, Verein für Socialpolitik / German Economic Association.
    10. Zhenlin Yang, 2006. "On Joint Modelling and Testing for Local and Global Spatial Externalities," Working Papers 25-2006, Singapore Management University, School of Economics.
    11. Gupta, A, 2015. "Nonparametric specification testing via the trinity of tests," Economics Discussion Papers 15619, University of Essex, Department of Economics.
    12. Yueqin Wu & Yan Sun, 2017. "Shrinkage estimation of the linear model with spatial interaction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 51-68, January.
    13. 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.
    14. Gupta, Abhimanyu & Robinson, Peter M., 2018. "Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension," Journal of Econometrics, Elsevier, vol. 202(1), pages 92-107.
    15. Mynbaev, Kairat T., 2010. "Asymptotic distribution of the OLS estimator for a mixed spatial model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 733-748, March.
    16. 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.
    17. 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.
    18. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
    19. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    20. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    21. Robinson, Peter M., 2007. "Efficient estimation of the semiparametric spatial autoregressive model," LSE Research Online Documents on Economics 4535, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    Spatial autoregressive model; 3SLSE; GMME; Relative asymptotic efficiency;
    All these keywords.

    JEL classification:

    • 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:cuf:journl:y:2010:v:11:i:1:p:155-184. 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: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.html .

    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.