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Partial maximum likelihood estimation of spatial probit models


  • Wang, Honglin
  • Iglesias, Emma M.
  • Wooldridge, Jeffrey M.


This paper analyzes spatial Probit models for cross sectional dependent data in a binary choice context. Observations are divided by pairwise groups and bivariate normal distributions are specified within each group. Partial maximum likelihood estimators are introduced and they are shown to be consistent and asymptotically normal under some regularity conditions. Consistent covariance matrix estimators are also provided. Estimates of average partial effects can also be obtained once we characterize the conditional distribution of the latent error. Finally, a simulation study shows the advantages of our new estimation procedure in this setting. Our proposed partial maximum likelihood estimators are shown to be more efficient than the generalized method of moments counterparts.

Suggested Citation

  • Wang, Honglin & Iglesias, Emma M. & Wooldridge, Jeffrey M., 2013. "Partial maximum likelihood estimation of spatial probit models," Journal of Econometrics, Elsevier, vol. 172(1), pages 77-89.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:77-89 DOI: 10.1016/j.jeconom.2012.08.005

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    References listed on IDEAS

    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. Robinson, Peter M, 1982. "On the Asymptotic Properties of Estimators of Models Containing Limited Dependent Variables," Econometrica, Econometric Society, vol. 50(1), pages 27-41, January.
    3. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    4. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
    5. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
    6. Dale J. Poirier & Paul A. Ruud, 1988. "Probit with Dependent Observations," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 593-614.
    7. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588.
    8. Joris Pinkse & Margaret Slade & Lihong Shen, 2006. "Dynamic Spatial Discrete Choice Using One-step GMM: An Application to Mine Operating Decisions," Spatial Economic Analysis, Taylor & Francis Journals, vol. 1(1), pages 53-99.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, pages 817-858.
    10. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 125-132.
    11. 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.
    12. 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.
    13. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
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    Cited by:

    1. Luís Silveira Santos & Isabel Proença, 2017. "The Inversion of the Spatial Lag Operator in Binary Choice Models: Fast Computation and a Closed Formula Approximation," Working Papers REM 2017/11, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    2. Jean-François Richard, 2015. "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables," Working Paper 5778, Department of Economics, University of Pittsburgh.
    3. Federico Belotti & Giuseppe Ilardi, 2012. "Consistent Estimation of the “True” Fixed-effects Stochastic Frontier Model," CEIS Research Paper 231, Tor Vergata University, CEIS, revised 18 Apr 2012.
    4. T. Arduini, 2016. "Distribution Free Estimation of Spatial Autoregressive Binary Choice Panel Data Models," Working Papers wp1052, Dipartimento Scienze Economiche, Universita' di Bologna.
    5. Federico Belotti & Giuseppe Ilardi, 2017. "Consistent inference in fixed-effects stochastic frontier models," Temi di discussione (Economic working papers) 1147, Bank of Italy, Economic Research and International Relations Area.
    6. Arbia, Giuseppe, 2016. "Spatial Econometrics: A Broad View," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(3-4), pages 145-265, November.
    7. Anna Gloria Billé, 2013. "Computational Issues in the Estimation of the Spatial Probit Model: A Comparison of Various Estimators," The Review of Regional Studies, Southern Regional Science Association, vol. 43(2,3), pages 131-154, Winter.
    8. Baltagi, Badi H. & Egger, Peter H. & Kesina, Michaela, 2017. "Determinants of firm-level domestic sales and exports with spillovers: Evidence from China," Journal of Econometrics, Elsevier, vol. 199(2), pages 184-201.
    9. Mozharovskyi, Pavlo & Vogler, Jan, 2016. "Composite marginal likelihood estimation of spatial autoregressive probit models feasible in very large samples," Economics Letters, Elsevier, vol. 148(C), pages 87-90.
    10. Dogan, Osman & Taspinar, Suleyman, 2016. "Bayesian Inference in Spatial Sample Selection Models," MPRA Paper 82829, University Library of Munich, Germany.
    11. Yang, Chao & Lee, Lung-fei, 2017. "Social interactions under incomplete information with heterogeneous expectations," Journal of Econometrics, Elsevier, vol. 198(1), pages 65-83.
    12. repec:eee:regeco:v:64:y:2017:i:c:p:30-45 is not listed on IDEAS
    13. Bhat, Chandra R. & Pinjari, Abdul R. & Dubey, Subodh K. & Hamdi, Amin S., 2016. "On accommodating spatial interactions in a Generalized Heterogeneous Data Model (GHDM) of mixed types of dependent variables," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 240-263.
    14. Chandan Singha, 2017. "Analyzing Adoption of soil Conservation Measures by Farmers in Darjeeling District, India," Working Papers id:12204, eSocialSciences.
    15. Chandra Bhat, 2015. "A new spatial (social) interaction discrete choice model accommodating for unobserved effects due to endogenous network formation," Transportation, Springer, vol. 42(5), pages 879-914, September.
    16. Lei, J., 2014. "Essays on nonlinear panel data models," Other publications TiSEM 302d1ae7-0310-43b0-b253-6, Tilburg University, School of Economics and Management.

    More about this item


    Spatial statistics; Maximum likelihood; Probit model;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities


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