IDEAS home Printed from https://ideas.repec.org/a/spr/jospat/v3y2022i1d10.1007_s43071-022-00022-x.html
   My bibliography  Save this article

Consistent EM algorithm for a spatial autoregressive probit model

Author

Listed:
  • Wei Cheng

    (East China University of Science and Technology)

Abstract

This paper is concerned with the estimation of spatial autoregressive probit models, which are increasingly used in many empirical settings. Among existing estimators, the EM algorithm for spatial probit models introduced by McMillen (J Reg Sci 32(3):335–348, 1992) is a widely used method, but it lacks proof of consistency. In this paper, we formally show that it is inconsistent by applying the law of large numbers for dependent and non-identically distributed near-epoch dependence (NED) random fields. We provide a modification of the EM algorithm to yield a consistent estimator. Monte Carlo experiments show that in finite samples, our new EM algorithm outperforms McMillen’s EM algorithm, especially for medium to high levels of spatial dependence.

Suggested Citation

  • Wei Cheng, 2022. "Consistent EM algorithm for a spatial autoregressive probit model," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-23, December.
    • Handle: RePEc:spr:jospat:v:3:y:2022:i:1:d:10.1007_s43071-022-00022-x
    DOI: 10.1007/s43071-022-00022-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43071-022-00022-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s43071-022-00022-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lee, Lung-Fei, 1992. "On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models," Econometric Theory, Cambridge University Press, vol. 8(4), pages 518-552, December.
    2. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
    3. 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.
    4. 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.
    5. Lee, Lung-Fei, 1995. "Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 437-483, June.
    6. Cheng, Wei & Lee, Lung-fei, 2017. "Testing endogeneity of spatial and social networks," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 81-97.
    7. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    8. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
    9. 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.
    10. Anping Chen & Marlon Boarnet & Mark Partridge & Raffaella Calabrese & Johan A. Elkink, 2014. "Estimators Of Binary Spatial Autoregressive Models: A Monte Carlo Study," Journal of Regional Science, Wiley Blackwell, vol. 54(4), pages 664-687, September.
    11. 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.
    12. Xu, Xingbai & Lee, Lung-fei, 2015. "Maximum likelihood estimation of a spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 188(1), pages 264-280.
    13. 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.
    14. Qu, Xi & Lee, Lung-fei, 2013. "Locally most powerful tests for spatial interactions in the simultaneous SAR Tobit model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 307-321.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    2. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2018. "Generalized spatial autocorrelation in a panel-probit model with an application to exporting in China," Empirical Economics, Springer, vol. 55(1), pages 193-211, August.
    3. Corral, Paul & Radchenko, Natalia, 2017. "What’s So Spatial about Diversification in Nigeria?," World Development, Elsevier, vol. 95(C), pages 231-253.
    4. Rabovič, Renata & Čížek, Pavel, 2023. "Estimation of spatial sample selection models: A partial maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 232(1), pages 214-243.
    5. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    6. Raffaella Calabrese & Johan A. Elkink & Paolo S. Giudici, 2017. "Measuring bank contagion in Europe using binary spatial regression models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1503-1511, December.
    7. Xu, Xingbai & Lee, Lung-fei, 2018. "Sieve maximum likelihood estimation of the spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 203(1), pages 96-112.
    8. T. Arduini, 2016. "Distribution Free Estimation of Spatial Autoregressive Binary Choice Panel Data Models," Working Papers wp1052, Dipartimento Scienze Economiche, Universita' di Bologna.
    9. Piras, Gianfranco & Sarrias, Mauricio, 2023. "One or two-step? Evaluating GMM efficiency for spatial binary probit models," Journal of choice modelling, Elsevier, vol. 48(C).
    10. Anna Gloria Billé & Samantha Leorato, 2017. "Quasi-ML estimation, Marginal Effects and Asymptotics for Spatial Autoregressive Nonlinear Models," BEMPS - Bozen Economics & Management Paper Series BEMPS44, Faculty of Economics and Management at the Free University of Bozen.
    11. 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.
    12. Haoying Wang & Guohui Wu, 2022. "Modeling discrete choices with large fine-scale spatial data: opportunities and challenges," Journal of Geographical Systems, Springer, vol. 24(3), pages 325-351, July.
    13. repec:asg:wpaper:1048 is not listed on IDEAS
    14. 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.
    15. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    16. Cuicui Lu & Weining Wang & Jeffrey M. Wooldridge, 2018. "Using generalized estimating equations to estimate nonlinear models with spatial data," Papers 1810.05855, arXiv.org.
    17. Bhat, Chandra R. & Sener, Ipek N. & Eluru, Naveen, 2010. "A flexible spatially dependent discrete choice model: Formulation and application to teenagers' weekday recreational activity participation," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 903-921, September.
    18. Martinetti, Davide & Geniaux, Ghislain, 2017. "Approximate likelihood estimation of spatial probit models," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 30-45.
    19. Gustavo Ahumada & Victor Iturra & Mauricio Sarrias, 2020. "We Do Not Have the Same Tastes! Evaluating Individual Heterogeneity in the Preferences for Amenities," Journal of Happiness Studies, Springer, vol. 21(1), pages 53-74, January.
    20. Lee, Lung-Fei, 1997. "Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 82(1), pages 1-35.
    21. Adriana Nikolic & Christoph Weiss, 2014. "Spatial interactions in location decisions: Empirical evidence from a Bayesian spatial probit model," Department of Economics Working Papers wuwp177, Vienna University of Economics and Business, Department of Economics.

    More about this item

    Keywords

    Spatial probit model; EM algorithm; Near-epoch dependence; Consistent estimator;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jospat:v:3:y:2022:i:1:d:10.1007_s43071-022-00022-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.