IDEAS home Printed from https://ideas.repec.org/a/eee/regeco/v76y2019icp74-102.html
   My bibliography  Save this article

The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation

Author

Listed:
  • Silveira Santos, Luís
  • Proença, Isabel

Abstract

This paper presents a new method to approximate the inverse of the spatial lag operator, used in the estimation of spatial lag models for binary dependent variables. The related matrix operations are approximated as well. Closed formulas for the elements of the approximated matrices are deduced. A GMM estimator is also presented. This estimator is a variant of Klier and McMillen's iterative GMM estimator. The approximated matrices are used in the gradients of the new iterative GMM procedure. Monte Carlo experiments suggest that the proposed approximation is accurate and allows to significantly reduce the computational complexity, and consequently the computational time, associated with the estimation of spatial binary choice models, especially for the case where the spatial weighting matrix is large and dense. Also, the simulation experiments suggest that the proposed iterative GMM estimator performs well in terms of bias and root mean square error and exhibits a minimum trade-off between computational time and unbiasedness within a class of spatial GMM estimators. Finally, the new iterative GMM estimator is applied to the analysis of competitiveness in the U.S. Metropolitan Statistical Areas. A new definition for binary competitiveness is introduced. The estimation of spatial and environmental effects are addressed as central issues.

Suggested Citation

  • Silveira Santos, Luís & Proença, Isabel, 2019. "The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation," Regional Science and Urban Economics, Elsevier, vol. 76(C), pages 74-102.
    • Handle: RePEc:eee:regeco:v:76:y:2019:i:c:p:74-102
    DOI: 10.1016/j.regsciurbeco.2019.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016604621730399X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.regsciurbeco.2019.01.003?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Garth Holloway & Ma. Lucila A. Lapar, 2007. "How Big is Your Neighbourhood? Spatial Implications of Market Participation Among Filipino Smallholders," Journal of Agricultural Economics, Wiley Blackwell, vol. 58(1), pages 37-60, February.
    2. Daniel L. Millimet & John A. List & Thanasis Stengos, 2003. "The Environmental Kuznets Curve: Real Progress or Misspecified Models?," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1038-1047, November.
    3. Kurt J. Beron & James C. Murdoch & Wim P. M. Vijverberg, 2003. "Why Cooperate? Public Goods, Economic Power, and the Montreal Protocol," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 286-297, May.
    4. Grossman, G.M & Krueger, A.B., 1991. "Environmental Impacts of a North American Free Trade Agreement," Papers 158, Princeton, Woodrow Wilson School - Public and International Affairs.
    5. Rice, Patricia & Venables, Anthony J. & Patacchini, Eleonora, 2006. "Spatial determinants of productivity: Analysis for the regions of Great Britain," Regional Science and Urban Economics, Elsevier, vol. 36(6), pages 727-752, November.
    6. Fagerberg, Jan, 1996. "Technology and Competitiveness," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 12(3), pages 39-51, Autumn.
    7. 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.
    8. Wollni, Meike & Andersson, Camilla, 2014. "Spatial patterns of organic agriculture adoption: Evidence from Honduras," Ecological Economics, Elsevier, vol. 97(C), pages 120-128.
    9. 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.
    10. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    11. Anselin, Luc, 2007. "Spatial econometrics in RSUE: Retrospect and prospect," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 450-456, July.
    12. 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.
    13. Martinetti, Davide & Geniaux, Ghislain, 2017. "Approximate likelihood estimation of spatial probit models," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 30-45.
    14. 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.
    15. R. Kelley Pace & James P. LeSage, 2016. "Fast Simulated Maximum Likelihood Estimation of the Spatial Probit Model Capable of Handling Large Samples," Advances in Econometrics, in: Spatial Econometrics: Qualitative and Limited Dependent Variables, volume 37, pages 3-34, Emerald Group Publishing Limited.
    16. Berg, Birgitta & Kilvits, Kaarel & Tombak, Mihkel, . "Technology Policyfor Improving Competitiveness of Estonian Industries," ETLA C, The Research Institute of the Finnish Economy, number 73.
    17. repec:rre:publsh:v:40:y:2010:i:2:p:197-226 is not listed on IDEAS
    18. James P. LeSage & R. Kelley Pace & Nina Lam & Richard Campanella & Xingjian Liu, 2011. "New Orleans business recovery in the aftermath of Hurricane Katrina," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(4), pages 1007-1027, October.
    19. Holloway, Garth & Shankar, Bhavani & Rahman, Sanzidur, 2002. "Bayesian spatial probit estimation: a primer and an application to HYV rice adoption," Agricultural Economics, Blackwell, vol. 27(3), pages 383-402, November.
    20. Klier, Thomas & McMillen, Daniel P, 2008. "Clustering of Auto Supplier Plants in the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 460-471.
    21. Jon Fiva & Jørn Rattsø, 2007. "Local choice of property taxation: evidence from Norway," Public Choice, Springer, vol. 132(3), pages 457-470, September.
    22. Lapar, Ma. Lucila A. & Holloway, Garth J. & Ehui, Simeon K., 2003. "How Big Is Your Neighborhood? Spatial Implications Of Market Participation By Smallholder Livestock Producers," 2003 Annual Meeting, August 16-22, 2003, Durban, South Africa 25860, International Association of Agricultural Economists.
    23. Murdoch, James C. & Sandler, Todd & Vijverberg, Wim P. M., 2003. "The participation decision versus the level of participation in an environmental treaty: a spatial probit analysis," Journal of Public Economics, Elsevier, vol. 87(2), pages 337-362, February.
    24. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
    25. Harry H. Kelejian & Dennis P. Robinson, 1995. "Spatial Correlation: A Suggested Alternative to the Autoregressive Model," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax (ed.), New Directions in Spatial Econometrics, chapter 3, pages 75-95, Springer.
    26. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Isabel Proença & Ludgero Glórias, 2021. "Revisiting the Spatial Autoregressive Exponential Model for Counts and Other Nonnegative Variables, with Application to the Knowledge Production Function," Sustainability, MDPI, vol. 13(5), pages 1-22, March.
    2. 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).

    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. 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.
    2. repec:asg:wpaper:1013 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Gilles Allaire & Eric Cahuzac & Michel Simioni, 2009. "Contractualisation et diffusion spatiale des mesures agro-environnementales herbagères," Review of Agricultural and Environmental Studies - Revue d'Etudes en Agriculture et Environnement, INRA Department of Economics, vol. 90(1), pages 23-50.
    6. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    7. Heijnen, P. & Samarina, A.. & Jacobs, J.P.A.M. & Elhorst, J.P., 2013. "State transfers at different moments in time," Research Report 13006-EEF, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    8. 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.
    9. repec:dgr:rugsom:13006-eef is not listed on IDEAS
    10. Carrión-Flores, Carmen E. & Flores-Lagunes, Alfonso & Guci, Ledia, 2018. "An estimator for discrete-choice models with spatial lag dependence using large samples, with an application to land-use conversions," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 77-93.
    11. repec:asg:wpaper:1048 is not listed on IDEAS
    12. Martinetti, Davide & Geniaux, Ghislain, 2017. "Approximate likelihood estimation of spatial probit models," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 30-45.
    13. Corral, Paul & Radchenko, Natalia, 2017. "What’s So Spatial about Diversification in Nigeria?," World Development, Elsevier, vol. 95(C), pages 231-253.
    14. T. Randall Fortenbery & Steven C. Deller & Lindsay Amiel, 2013. "The Location Decisions of Biodiesel Refineries," Land Economics, University of Wisconsin Press, vol. 89(1), pages 118-136.
    15. 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.
    16. 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.
    17. Wollni, Meike & Andersson, Camilla, 2014. "Spatial patterns of organic agriculture adoption: Evidence from Honduras," Ecological Economics, Elsevier, vol. 97(C), pages 120-128.
    18. Dorian Balvir, 2024. "Fiscal rules: the imitation game," Applied Economics, Taylor & Francis Journals, vol. 56(6), pages 708-727, February.
    19. Lukas Dargel, 2021. "Revisiting estimation methods for spatial econometric interaction models," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-41, December.
    20. Dogan, Osman & Taspinar, Suleyman, 2016. "Bayesian Inference in Spatial Sample Selection Models," MPRA Paper 82829, University Library of Munich, Germany.
    21. 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.
    22. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    23. 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.

    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:eee:regeco:v:76:y:2019:i:c:p:74-102. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/regec .

    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.