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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


  • Baltagi, Badi H.
  • Bresson, Georges


This paper proposes maximum likelihood estimators for panel seemingly unrelated regressions with both spatial lag and spatial error components. We study the general case where spatial effects are incorporated via spatial errors terms and via a spatial lag dependent variable and where the heterogeneity in the panel is incorporated via an error component specification. We generalize the approach of Wang and Kockelman (2007) and propose joint and conditional Lagrange multiplier tests for spatial autocorrelation and random effects for this spatial SUR panel model. The small sample performance of the proposed estimators and tests are examined using Monte Carlo experiments. An empirical application to hedonic housing prices in Paris illustrate these methods. The proposed specification uses a system of three SUR equations corresponding to three types of flats within 80 districts of Paris over the period 1990-2003. We test for spatial effects and heterogeneity and find reasonable estimates of the shadow prices for housing characteristics.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:juecon:v:69:y:2011:i:1:p:24-42

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    References listed on IDEAS

    1. Ingrid Nappi-Choulet Pr. & Tristan-Pierre Maury, 2009. "A Spatiotemporal Autoregressive Price Index for the Paris Office Property Market," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 37(2), pages 305-340.
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    3. Fack, Gabrielle & Grenet, Julien, 2010. "When do better schools raise housing prices? Evidence from Paris public and private schools," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 59-77, February.
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    6. Arguea, Nestor M. & Hsiao, Cheng, 1993. "Econometric issues of estimating hedonic price functions : With an application to the U.S. market for automobiles," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 243-267, March.
    7. Can, Ayse, 1992. "Specification and estimation of hedonic housing price models," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 453-474, September.
    8. Baltagi, Badi H. & Heun Song, Seuck & Cheol Jung, Byoung & Koh, Won, 2007. "Testing for serial correlation, spatial autocorrelation and random effects using panel data," Journal of Econometrics, Elsevier, vol. 140(1), pages 5-51, September.
    9. Dubin, Robin A., 1992. "Spatial autocorrelation and neighborhood quality," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 433-452, September.
    10. Xiaokun Wang & Kara Kockelman, 2007. "Specification and estimation of a spatially and temporally autocorrelated seemingly unrelated regression model: application to crash rates in China," Transportation, Springer, vol. 34(3), pages 281-300, May.
    11. 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.
    12. Halvorsen, Robert & Pollakowski, Henry O., 1981. "Choice of functional form for hedonic price equations," Journal of Urban Economics, Elsevier, vol. 10(1), pages 37-49, July.
    13. Magnus, Jan R., 1982. "Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 239-285, August.
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    Cited by:

    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. Mark J. Holmes & Jesús Otero & Theodore Panagiotidis, 2016. "Climbing the property ladder: An analysis of market integration in London property prices," Working Paper series 16-30, Rimini Centre for Economic Analysis.
    3. Cizek, P. & Jacobs, J.P.A.M. & Ligthart, J.E. & Vrijburg, H., 2011. "GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors (Replaced by CentER DP 2015-003)," Discussion Paper 2011-134, Tilburg University, Center for Economic Research.
    4. Hailong Qian & Heather L. Bednarek, 2015. "Partial efficient estimation of SUR models," Economics Bulletin, AccessEcon, vol. 35(1), pages 338-348.
    5. 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.
    6. Fernando López & Jesús Mur & Ana Angulo, 2014. "Spatial model selection strategies in a SUR framework. The case of regional productivity in EU," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 197-220, August.
    7. Badi H. Baltagi & Georges Bresson & Jean‐Michel Etienne, 2015. "Hedonic Housing Prices in Paris: An Unbalanced Spatial Lag Pseudo‐Panel Model with Nested Random Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(3), pages 509-528, April.
    8. Georges Bresson & Cheng Hsiao, 2011. "A functional connectivity approach for modeling cross-sectional dependence with an application to the estimation of hedonic housing prices in Paris," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(4), pages 501-529, December.
    9. Marko Kryvobokov & Louafi Bouzouina, 2014. "Willingness to pay for accessibility under the conditions of residential segregation," Post-Print halshs-01082820, HAL.
    10. Hernán Enríquez Sierra & Carlos Barreto Nieto & Carolina Correa Caro & Jacobo Campo Robledo, 2013. "Precio del suelo y regalías en Colombia: un análisis espacial para los municipios productores de petróleo," REVISTA DESARROLLO Y SOCIEDAD, UNIVERSIDAD DE LOS ANDES-CEDE, June.
    11. Wang, Luya & Li, Kunpeng & Wang, Zhengwei, 2014. "Quasi maximum likelihood estimation for simultaneous spatial autoregressive models," MPRA Paper 59901, University Library of Munich, Germany.
    12. Benjamin Verhelst & Dirk Van den Poel, 2014. "Deep habits in consumption: a spatial panel analysis using scanner data," Empirical Economics, Springer, vol. 47(3), pages 959-976, November.
    13. Celbis M.G. & Crombrugghe D.P.I. de, 2014. "Can internet infrastructure help reduce regional disparities? : evidence from Turkey," MERIT Working Papers 078, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    14. Lu, Lina, 2017. "Simultaneous Spatial Panel Data Models with Common Shocks," Risk and Policy Analysis Unit Working Paper RPA 17-3, Federal Reserve Bank of Boston.
    15. Gauvin, Laetitia & Vignes, Annick & Nadal, Jean-Pierre, 2013. "Modeling urban housing market dynamics: Can the socio-spatial segregation preserve some social diversity?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1300-1321.
    16. repec:wyi:journl:002130 is not listed on IDEAS

    More about this item


    Hedonic housing prices Lagrange multiplier tests Maximum likelihood Panel spatial dependence Spatial lag Spatial error SUR;

    JEL classification:

    • 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
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • R21 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Housing Demand


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