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

Abstract

This paper presents a new method to approximate the inverse of the spatial lag operator matrix, used in the estimation of a spatial lag model with a binary dependent variable. The method is based on an approximation of the high order terms of the inverse series expansion. The proposed method is also applied to approximate other complex matrix operations and closed formulas for the elements of the approximated matrices are deduced. The approximated matrices are used in the gradients of a variant of Klier and McMillen's full GMM estimator, allowing to reduce the overall computational complexity of the estimation procedure. Monte Carlo experiments show that the new estimator performs well in terms of bias and root mean square error and exhibits a minimum trade-off between time and unbiasedness within a class of spatial GMM estimators. The new estimator is also applied to the analysis of competitiveness in the Metropolitan Statistical Areas of the United States of America. A new de_nition of binary competitiveness is proposed. Estimation of the spatial dependence parameter and the environmental effects are addressed as central issues.