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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

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  • Baltagi, Badi H.

    () (Syracuse University)

  • Bresson, Georges

    () (University of Paris 2)

Abstract

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 illustrates 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, 2010. "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," IZA Discussion Papers 5227, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp5227
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    References listed on IDEAS

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    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, June.
    2. Bernard Fingleton, 2008. "A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(1), pages 27-44.
    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.
    4. Baltagi, Badi H, 1980. "On Seemingly Unrelated Regressions with Error Components," Econometrica, Econometric Society, vol. 48(6), pages 1547-1551, September.
    5. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
    6. Can, Ayse, 1992. "Specification and estimation of hedonic housing price models," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 453-474, September.
    7. 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.
    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. 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.
    13. 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.
    14. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
    15. 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.
    16. Glaeser, Edward L., 2008. "Cities, Agglomeration, and Spatial Equilibrium," OUP Catalogue, Oxford University Press, number 9780199290444.
    17. Avery, Robert B, 1977. "Error Components and Seemingly Unrelated Regressions," Econometrica, Econometric Society, vol. 45(1), pages 199-209, January.
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    More about this item

    Keywords

    spatial lag; panel spatial dependence; maximum likelihood; Lagrange multiplier tests; hedonic housing prices; 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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