Fast Simulated Maximum Likelihood Estimation of the Spatial Probit Model Capable of Handling Large Samples

We show how to quickly estimate spatial probit models for large data sets using maximum likelihood. Like Beron and Vijverberg (2004), we use the GHK (Geweke-Hajivassiliou-Keane) algorithm to perform maximum simulated likelihood estimation. However, using the GHK for large sample sizes has been viewed as extremely difficult (Wang, Iglesias, & Wooldridge, 2013). Nonetheless, for sparse covariance and precision matrices often encountered in spatial settings, the GHK can be applied to very large sample sizes as its operation counts and memory requirements increase almost linearly with n when using sparse matrix techniques.