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

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  • 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
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    1. Jon Fiva & Jørn Rattsø, 2007. "Local choice of property taxation: evidence from Norway," Public Choice, Springer, vol. 132(3), pages 457-470, September.
    2. 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.
    3. Wollni, Meike & Andersson, Camilla, 2014. "Spatial patterns of organic agriculture adoption: Evidence from Honduras," Ecological Economics, Elsevier, vol. 97(C), pages 120-128.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Anselin, Luc, 2007. "Spatial econometrics in RSUE: Retrospect and prospect," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 450-456, July.
    11. 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.
    12. repec:rre:publsh:v:40:y:2010:i:2:p:197-226 is not listed on IDEAS
    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. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. Berg, Birgitta & Kilvits, Kaarel & Tombak, Mihkel, . "Technology Policyfor Improving Competitiveness of Estonian Industries," ETLA C, The Research Institute of the Finnish Economy, number 73.
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