Computational Issues in the Estimation of the Spatial Probit Model: A Comparison of Various Estimators

In spatial discrete choice models the spatial dependent structure adds complexity in the estimation of parameters. Appropriate general method of moments (GMM) estimation needs inverses of n-by-n matrices and an optimization complexity of the moment conditions for moderate to large samples makes practical applications more difficult. Recently, Klier and McMillen (2008) have proposed a linearized version of the GMM estimator that avoids the infeasible problem of inverting n-by-n matrices when employing large samples. They show that standard GMM reduces to a nonlinear two-stage least squares problem. On the other hand, when we deal with full maximum likelihood (FML) estimation, a multidimensional integration problem arises and a viable computational solution needs to be found. Although it remains somewhat computationally burdensome, since the inverses of matrices dimensioned by the number of observations have to be computed, the ML estimator yields the potential advantage of efficiency. Therefore, through Monte Carlo experiments we compare GMM-based approaches with ML estimation in terms of their computation times and statistical properties. Furthermore, a comparison in terms of the marginal effects also is included. Finally, we recommend an algorithm based on sparse matrices that enables more efficient use of both ML and GMM estimators.