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 (Fleming, 2004). GMM estimation of Pinkse and Slade (1998) needs inverses of n by n matrices and an optimization complexity of the moment conditions for moderate-large samples makes practical application more difficult. Recently, Klier and McMillen (2008) proposed a linearized version of Pinkse and Slade’s GMM to avoid the infeasible problem for large samples of inverting n by n matrices, in which standard GMM reduces to non-linear 2SLS. On the other hand, a multidimensional integration problem arises when we use ML estimation and a computational solution needs to be found (e.g. Beron et al., 2003). Although a problem of computational burdensomeness exists, especially due to the calculation of inverses of n by n matrices, the primary advantage of the ML estimator is the potential for efficiency (e.g. Wang et al., 2013). Therefore, in this paper through Monte Carlo experiments we compare the Linearized GMM with the ML estimation in terms of their computational times and their statistical properties. Furthermore, a comparison with standard GMM will be also included. Finally, we propose a computational solution that allows a more efficient use of both ML and GMM estimators.