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

Abstract

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.

Forecasting regional GDPs: a comparison with spatial dynamic panel data models

“…Anyway, correlation can change if we generally used dense matrices instead of sparse matrices, please see for example Billé and Leorato (2020), and references therein. 6 Before considering the forecasting procedure, we define the structural model (1) in time first-differencing.…”

GMM Estimators for Binary Spatial Models in R

“…Based onVijverberg (1997),Beron and Vijverberg (2004) introduce the so-called recursive importance sampling (RIS) estimator and show how this estimator can be used to evaluate an n-dimensional normal probability. More recently,Billé and Leorato (2020), put forth a partial maximum likelihood estimator for a general spatial non-linear probit model, and perform a complete asymptotic analysis of their estimator.…”

Fitting spatial autoregressive logit and probit models using Stata: The spatbinary command

“… 3 For a thorough analytic formulation of g i , see Beron and Vijverberg (2004) and Billé and Leorato (2020). …”