IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/84085.html
   My bibliography  Save this paper

Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension

Author

Listed:
  • Gupta, Abhimanyu
  • Robinson, Peter M.

Abstract

Pseudo maximum likelihood estimates are developed for higher-order spatial autoregressive models with increasingly many parameters, including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component, and regression models with spatial autoregressive disturbances. Consistency and asymptotic normality of the estimates are established. Monte Carlo experiments examine finite-sample behaviour

Suggested Citation

  • Gupta, Abhimanyu & Robinson, Peter M., 2017. "Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension," LSE Research Online Documents on Economics 84085, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:84085
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/84085/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    2. 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.
    3. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    4. Robinson, P.M., 2010. "Efficient estimation of the semiparametric spatial autoregressive model," Journal of Econometrics, Elsevier, vol. 157(1), pages 6-17, July.
    5. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    6. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
    7. Harry H. Kelejian & Ingmar R. Prucha, 1997. "Estimation of Spatial Regression Models with Autoregressive Errors by Two-Stage Least Squares Procedures: A Serious Problem," International Regional Science Review, , vol. 20(1-2), pages 103-111, April.
    8. 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.
    9. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    10. Harald Badinger & Peter Egger, 2011. "Estimation of higher‐order spatial autoregressive cross‐section models with heteroscedastic disturbances," Papers in Regional Science, Wiley Blackwell, vol. 90(1), pages 213-235, March.
    11. 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.
    12. LeSage, James P. & Pace, Robert Kelley, 2011. "Pitfalls in Higher Order Model Extensions of Basic Spatial Regression Methodology," The Review of Regional Studies, Southern Regional Science Association, vol. 41(1), pages 13-26, Summer.
    13. 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.
    14. Harry H. Kelejian & Ingmar R. Prucha & Yevgeny Yuzefovich, 2006. "Estimation Problems In Models With Spatial Weighting Matrices Which Have Blocks Of Equal Elements," Journal of Regional Science, Wiley Blackwell, vol. 46(3), pages 507-515, August.
    15. 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.
    16. Blommestein, Hans J., 1983. "Specification and estimation of spatial econometric models : A discussion of alternative strategies for spatial economic modelling," Regional Science and Urban Economics, Elsevier, vol. 13(2), pages 251-270, May.
    17. A S Brandsma & R H Ketellapper, 1979. "A Biparametric Approach to Spatial Autocorrelation," Environment and Planning A, , vol. 11(1), pages 51-58, January.
    18. Blommestein, H. J., 1985. "Elimination of circular routes in spatial dynamic regression equations," Regional Science and Urban Economics, Elsevier, vol. 15(1), pages 121-130, February.
    19. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers CWP44/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Sargan, J D, 1975. "Asymptotic Theory and Large Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(1), pages 75-91, February.
    21. Case, Anne, 1992. "Neighborhood influence and technological change," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 491-508, September.
    22. 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.
    23. repec:umd:umdeco:kelepruc is not listed on IDEAS
    24. Qu, Xi & Lee, Lung-fei, 2015. "Estimating a spatial autoregressive model with an endogenous spatial weight matrix," Journal of Econometrics, Elsevier, vol. 184(2), pages 209-232.
    25. 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.
    26. Harald Badinger & Peter Egger, 2013. "Estimation and testing of higher-order spatial autoregressive panel data error component models," Journal of Geographical Systems, Springer, vol. 15(4), pages 453-489, October.
    27. Kolympiris, Christos & Kalaitzandonakes, Nicholas & Miller, Douglas, 2011. "Spatial collocation and venture capital in the US biotechnology industry," Research Policy, Elsevier, vol. 40(9), pages 1188-1199.
    28. Robinson, P.M., 2003. "Denis Sargan: Some Perspectives," Econometric Theory, Cambridge University Press, vol. 19(3), pages 481-494, June.
    29. Robinson, Peter M., 2003. "Denis Sargan: some perspectives," LSE Research Online Documents on Economics 292, London School of Economics and Political Science, LSE Library.
    30. Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(1), pages 187-230, February.
    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. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    2. Ayden Higgins & Federico Martellosio, 2019. "Shrinkage Estimation of Network Spillovers with Factor Structured Errors," Papers 1909.02823, arXiv.org, revised Nov 2021.
    3. Jakub Olejnik & Alicja Olejnik, 2020. "QML estimation with non-summable weight matrices," Journal of Geographical Systems, Springer, vol. 22(4), pages 469-495, October.
    4. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    5. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    6. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2022.
    7. Michaelides, Alexander & Kokas, Sotirios & Gupta, Abhimanyu, 2017. "Credit Market Spillovers: Evidence from a Syndicated Loan Market Network," CEPR Discussion Papers 12424, C.E.P.R. Discussion Papers.
    8. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    9. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    10. Huijuan Xiao & Sheng Bao & Jingzheng Ren & Zhenci Xu & Song Xue & Jianguo Liu, 2024. "Global transboundary synergies and trade-offs among Sustainable Development Goals from an integrated sustainability perspective," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    11. Higgins, Ayden & Martellosio, Federico, 2023. "Shrinkage estimation of network spillovers with factor structured errors," Journal of Econometrics, Elsevier, vol. 233(1), pages 66-87.
    12. Sylvain Barde & Rowan Cherodian & Guy Tchuente, 2023. "Moran's I Lasso for models with spatially correlated data," Papers 2310.02773, arXiv.org.
    13. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.

    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, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    3. 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.
    4. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    5. repec:esx:essedp:772 is not listed on IDEAS
    6. repec:esx:essedp:735 is not listed on IDEAS
    7. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    8. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    9. repec:esx:essedp:774 is not listed on IDEAS
    10. Gupta, A, 2015. "Nonparametric specification testing via the trinity of tests," Economics Discussion Papers 15619, University of Essex, Department of Economics.
    11. repec:asg:wpaper:1013 is not listed on IDEAS
    12. 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.
    13. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2022.
    14. LE GALLO, Julie, 2000. "Econométrie spatiale 1 -Autocorrélation spatiale," LATEC - Document de travail - Economie (1991-2003) 2000-05, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
    15. Julie Le Gallo, 2000. "Spatial econometrics (1, Spatial autocorrelation) [Econométrie spatiale (1, Autocorrélation spatiale)]," Working Papers hal-01527290, HAL.
    16. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    17. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.
    18. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    19. 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.
    20. 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.
    21. Zhenlin Yang, 2006. "On Joint Modelling and Testing for Local and Global Spatial Externalities," Working Papers 25-2006, Singapore Management University, School of Economics.
    22. 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.
    23. Doğan, Osman & Taşpınar, Süleyman, 2014. "Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach," Regional Science and Urban Economics, Elsevier, vol. 45(C), pages 1-21.
    24. Anselin, Luc, 2002. "Under the hood : Issues in the specification and interpretation of spatial regression models," Agricultural Economics, Blackwell, vol. 27(3), pages 247-267, November.

    More about this item

    Keywords

    Spatial autoregression; Increasingly many parameters; Consistency; Asymptotic normality; Pseudo Gaussian maximum likelihood; Finite sample performance;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

    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:ehl:lserod:84085. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.