IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v196y2017i1p196-214.html
   My bibliography  Save this article

Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models

Author

Listed:
  • Yang, Kai
  • Lee, Lung-fei

Abstract

This paper investigates a simultaneous equations spatial autoregressive model which incorporates simultaneity effects, own-variable spatial lags and cross-variable spatial lags as explanatory variables, and allows for correlation between disturbances across equations. In exposition, we also discuss a multivariate spatial autoregressive model that can be treated as a reduced form of the simultaneous equations model. We study parameter spaces, parameter identification, asymptotic properties of the quasi-maximum likelihood estimation, and computational issues. Monte Carlo experiments illustrate the advantages of the QML, broader applicability and efficiency, compared to instrumental variables based estimation methods in the existing literature.

Suggested Citation

  • Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
    • Handle: RePEc:eee:econom:v:196:y:2017:i:1:p:196-214
    DOI: 10.1016/j.jeconom.2016.04.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407616301683
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2016.04.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Badi H. Baltagi, 2015. "Seemingly Unrelated Regressions," Springer Texts in Business and Economics, in: Solutions Manual for Econometrics, edition 3, chapter 0, pages 233-257, Springer.
    3. Thomas de Graaff & Frank G. van Oort & Raymond J.G.M. Florax, 2012. "Regional Population–Employment Dynamics Across Different Sectors Of The Economy," Journal of Regional Science, Wiley Blackwell, vol. 52(1), pages 60-84, February.
    4. Qu, Xi & Lee, Lung-fei, 2012. "LM tests for spatial correlation in spatial models with limited dependent variables," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 430-445.
    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. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    7. Lung-Fei Lee & Jihai Yu, 2013. "Near Unit Root in the Spatial Autoregressive Model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 314-351, September.
    8. Xiaodong Liu, 2014. "Identification and Efficient Estimation of Simultaneous Equations Network Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 516-536, October.
    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. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    11. Hauptmeier, Sebastian & Mittermaier, Ferdinand & Rincke, Johannes, 2012. "Fiscal competition over taxes and public inputs," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 407-419.
    12. Maarten A. Allers & J. Paul Elhorst, 2011. "A Simultaneous Equations Model Of Fiscal Policy Interactions," Journal of Regional Science, Wiley Blackwell, vol. 51(2), pages 271-291, May.
    13. 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.
    14. Badi H. Baltagi & Chihwa Kao & Long Liu, 2013. "The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 241-270, September.
    15. Badi H. Baltagi & Ying Deng, 2015. "EC3SLS Estimator for a Simultaneous System of Spatial Autoregressive Equations with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 659-694, December.
    16. Gebremeskel H. Gebremariam & Tesfa G. Gebremedhin & Peter V. Schaeffer, 2011. "Employment, Income, And Migration In Appalachia: A Spatial Simultaneous Equations Approach," Journal of Regional Science, Wiley Blackwell, vol. 51(1), pages 102-120, February.
    17. Baltagi, Badi H. & Bresson, Georges, 2011. "Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris," Journal of Urban Economics, Elsevier, vol. 69(1), pages 24-42, January.
    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. 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.
    20. Jeanty, P. Wilner & Partridge, Mark & Irwin, Elena, 2010. "Estimation of a spatial simultaneous equation model of population migration and housing price dynamics," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 343-352, September.
    21. 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.
    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. AMBA OYON, Claude Marius & Mbratana, Taoufiki, 2017. "Simultaneous equation models with spatially autocorrelated error components," MPRA Paper 82395, University Library of Munich, Germany.
    2. William C. Horrace & Hyunseok Jung & Shane Sanders, 2022. "Network Competition and Team Chemistry in the NBA," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 35-49, January.
    3. Yang, Kai & Lee, Lung-fei, 2021. "Estimation of dynamic panel spatial vector autoregression: Stability and spatial multivariate cointegration," Journal of Econometrics, Elsevier, vol. 221(2), pages 337-367.
    4. 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.
    5. Lina Lu, 2017. "Simultaneous Spatial Panel Data Models with Common Shocks," Supervisory Research and Analysis Working Papers RPA 17-3, Federal Reserve Bank of Boston.
    6. 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.
    7. Wang, Wei & Lee, Lung-Fei & Bao, Yan, 2018. "GMM estimation of the spatial autoregressive model in a system of interrelated networks," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 167-198.
    8. Fei Jin & Lung‐fei Lee & Kai Yang, 2024. "Best linear and quadratic moments for spatial econometric models with an application to spatial interdependence patterns of employment growth in US counties," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(4), pages 640-658, June.
    9. Heather D Gibson & Stephen G Hall & Deborah GeFang & Pavlos Petroulas & George S Tavlas, 2021. "Cross-country spillovers of national financial markets and the effectiveness of ECB policies during the euro-area crisis," Oxford Economic Papers, Oxford University Press, vol. 73(4), pages 1454-1470.
    10. Fernando A. López & Román Mínguez & Jesús Mur, 2020. "ML versus IV estimates of spatial SUR models: evidence from the case of Airbnb in Madrid urban area," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 313-347, April.
    11. Heather D. Gibson & Stephen G. Hall & Deborah Gefang & Pavlos Petroulas & George S. Tavlas, 2020. "Did the absence of a central bank backstop in the sovereign bond markets exacerbate spillovers during the euro-area crisis?," Working Papers 281, Bank of Greece.
    12. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    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. Zhu, Xuening & Huang, Danyang & Pan, Rui & Wang, Hansheng, 2020. "Multivariate spatial autoregressive model for large scale social networks," Journal of Econometrics, Elsevier, vol. 215(2), pages 591-606.
    15. Elhorst, J. Paul & Emili, Silvia, 2022. "A spatial econometric multivariate model of Okun's law," Regional Science and Urban Economics, Elsevier, vol. 93(C).
    16. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, vol. 3(2), pages 1-36, May.
    17. 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.
    18. repec:asg:wpaper:1013 is not listed on IDEAS
    19. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    20. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    21. 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.

    More about this item

    Keywords

    Spatial simultaneous equations; Multivariate spatial autoregression; Identification; Quasi-maximum likelihood estimation; Full information maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction 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:196:y:2017:i:1:p:196-214. 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.