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Analysis of discrete dependent variable models with spatial correlation

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  • Liesenfeld, Roman
  • Richard, Jean-François
  • Vogler, Jan

Abstract

In this paper we consider ML estimation for a broad class of parameter-driven models for discrete dependent variables with spatial correlation. Under this class of models, which includes spatial discrete choice models, spatial Tobit models and spatial count data models, the dependent variable is driven by a latent stochastic state variable which is specified as a linear spatial regression model. The likelihood is a high-dimensional integral whose dimension depends on the sample size. For its evaluation we propose to use efficient importance sampling (EIS). The specific spatial EIS implementation we develop exploits the sparsity of the precision (or covariance) matrix of the errors in the reduced-form state equation typically encountered in spatial settings, which keeps numerically accurate EIS likelihood evaluation computationally feasible even for large sample sizes. The proposed ML approach based upon spatial EIS is illustrated with estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

Suggested Citation

  • Liesenfeld, Roman & Richard, Jean-François & Vogler, Jan, 2013. "Analysis of discrete dependent variable models with spatial correlation," Economics Working Papers 2013-01, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:201301
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    References listed on IDEAS

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    1. Denis Bolduc & Bernard Fortin & Stephen Gordon, 1997. "Multinomial Probit Estimation of Spatially Interdependent Choices: An Empirical Comparison of Two New Techniques," International Regional Science Review, , vol. 20(1-2), pages 77-101, April.
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    3. Lambert, Dayton M. & Brown, Jason P. & Florax, Raymond J.G.M., 2010. "A two-step estimator for a spatial lag model of counts: Theory, small sample performance and an application," Regional Science and Urban Economics, Elsevier, vol. 40(4), pages 241-252, July.
    4. James P. LeSage & Manfred M. Fischer & Thomas Scherngell, 2007. "Knowledge spillovers across Europe: Evidence from a Poisson spatial interaction model with spatial effects," Papers in Regional Science, Wiley Blackwell, vol. 86(3), pages 393-421, August.
    5. Rainer Winkelmann & Stefan Boes, 2006. "Analysis of Microdata," Springer Books, Springer, number 978-3-540-29607-2, January.
    6. Kaiser, Mark S. & Cressie, Noel, 1997. "Modeling Poisson variables with positive spatial dependence," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 423-432, November.
    7. repec:tur:wpaper:10 is not listed on IDEAS
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    Cited by:

    1. Bhat, Chandra R. & Astroza, Sebastian & Hamdi, Amin S., 2017. "A spatial generalized ordered-response model with skew normal kernel error terms with an application to bicycling frequency," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 126-148.
    2. J. Paul Elhorst & Pim Heijnen & Anna Samarina & Jan P. A. M. Jacobs, 2017. "Transitions at Different Moments in Time: A Spatial Probit Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 422-439, March.
    3. Sabina Buczkowska & Nicolas Coulombel & Matthieu de Lapparent, 2015. "Euclidean distance versus travel time in business location: A probabilistic mixture of hurdle-Poisson models," ERSA conference papers ersa15p1060, European Regional Science Association.
    4. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.

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    More about this item

    Keywords

    Count data models; Discrete choice models; Firm location choice; Importance sampling; Monte Carlo integration; Spatial econometrics;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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