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

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.