Quasi-ML estimation, Marginal Effects and Asymptotics for Spatial Autoregressive Nonlinear Models

In this paper we propose a Partial-MLE 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 the SAE(1)-probit model, considered by Wang et al. (2013), and the more interesting SAR(1)-probit model. We perform a complete asymptotic analysis, and account for the possible finite sum approximation of the covariance matrix (Quasi-MLE) to speed the computation. 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. Finally, we provide appropriate definitions of marginal effects for this setting. Finite sample properties of the estimator are studied through a simulation exercise and a real data application. In our simulations, we also consider both sparse and dense matrices for the specification of the true spatial models, and cases of model misspecifications due to different assumed weighting matrices.