Partial ML estimation for spatial autoregressive nonlinear probit models with autoregressive disturbances

In this paper, we propose a Partial MLE (PMLE) for a general spatial nonlinear probit model, i.e., SARAR(1,1) probit, defined through a SARAR(1,1) latent linear model. This model encompasses both the SAE(1) probit and the more interesting SAR(1) probit models, already considered in the literature. We provide a complete asymptotic analysis of our PMLE as well as appropriate definitions of the marginal effects. Moreover, we address the issue of the choice of the groups (couples, in our case) by proposing an algorithm based on a minimum KL divergence problem. Finite sample properties of the PMLE are studied through extensive Monte Carlo simulations. In particular, we consider both sparse and dense matrices for the true spatial model specifications, and cases of model misspecification given wrong assumed weighting matrices. In a real data example, we finally also compare our estimator with different MLE-based estimators and with the Bayesian approach.