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Testing for spatial error dependence in probit models

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  • Pedro Amaral
  • Luc Anselin
  • Daniel Arribas-Bel

Abstract

In this note, we compare three test statistics that have been suggested to assess the presence of spatial error autocorrelation in probit models. We highlight the differences between the tests proposed by Pinkse and Slade (J Econom 85(1):125–254, 1998 ), Pinkse (Asymptotics of the Moran test and a test for spatial correlation in Probit models, 1999 ; Advances in Spatial Econometrics, 2004 ) and Kelejian and Prucha (J Econom 104(2):219–257, 2001 ), and compare their properties in a extensive set of Monte Carlo simulation experiments both under the null and under the alternative. We also assess the conjecture by Pinkse (Asymptotics of the Moran test and a test for spatial correlation in Probit models, 1999 ) that the usefulness of these test statistics is limited when the explanatory variables are spatially correlated. The Kelejian and Prucha (J Econom 104(2):219–257, 2001 ) generalized Moran’s I statistic turns out to perform best, even in medium sized samples of several hundreds of observations. The other two tests are acceptable in very large samples. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Pedro Amaral & Luc Anselin & Daniel Arribas-Bel, 2013. "Testing for spatial error dependence in probit models," Letters in Spatial and Resource Sciences, Springer, vol. 6(2), pages 91-101, July.
    • Handle: RePEc:spr:lsprsc:v:6:y:2013:i:2:p:91-101
    DOI: 10.1007/s12076-012-0089-9
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    References listed on IDEAS

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    1. Hendry, David F., 2006. "A comment on "Specification searches in spatial econometrics: The relevance of Hendry's methodology"," Regional Science and Urban Economics, Elsevier, vol. 36(2), pages 309-312, March.
    2. 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.
    3. repec:rre:publsh:v:37:y:2007:i:1:p:5-27 is not listed on IDEAS
    4. 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.
    5. Mark M. Fleming, 2004. "Techniques for Estimating Spatially Dependent Discrete Choice Models," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax & Sergio J. Rey (ed.), Advances in Spatial Econometrics, chapter 7, pages 145-168, Springer.
    6. Pedro V. Amaral & Luc Anselin, 2014. "Finite sample properties of Moran's I test for spatial autocorrelation in tobit models," Papers in Regional Science, Wiley Blackwell, vol. 93(4), pages 773-781, November.
    7. Kurt J. Beron & Wim P. M. Vijverberg, 2004. "Probit in a Spatial Context: A Monte Carlo Analysis," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax & Sergio J. Rey (ed.), Advances in Spatial Econometrics, chapter 8, pages 169-195, Springer.
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    Cited by:

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    3. Andrea Amaral & Margarida Abreu & Victor Mendes, 2014. "The Spatial Probit Model – An Application to the Study of Banking Crises at the End of the 90’s," CEFAGE-UE Working Papers 2014_05, University of Evora, CEFAGE-UE (Portugal).
    4. Wrenn, Douglas H. & Sam, Abdoul G., 2014. "Geographically and temporally weighted likelihood regression: Exploring the spatiotemporal determinants of land use change," Regional Science and Urban Economics, Elsevier, vol. 44(C), pages 60-74.
    5. Amaral, Andrea & Abreu, Margarida & Mendes, Victor, 2014. "The spatial Probit model—An application to the study of banking crises at the end of the 1990’s," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 251-260.
    6. López-Valcárcel, Beatriz G. & Jiménez, Juan Luis & Perdiguero, Jordi, 2017. "Danger: Local corruption is contagious!," Journal of Policy Modeling, Elsevier, vol. 39(5), pages 790-808.

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    More about this item

    Keywords

    Spatial econometrics; Spatial probit; Moran’s I; C21; C25;
    All these keywords.

    JEL classification:

    • 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

    Statistics

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