Estimation of Nonlinear Models in a Quasi-Maximum Likelihood Framework with Spatial Data

Abstract

In this paper, I study the estimation of nonlinear models of spatial processes. Generalized estimating equations (GEE) are applied to cross section data with spatial correlations. I use a partial quasi-maximum likelihood estimator (PQMLE) in the first step and use a GEE approach in the second step. Given some regularity conditions and assumptions, the asymptotic distribution of the two-step estimator is derived in the framework of M-estimation. I use a probit model and a count data model to demonstrate the GEE procedure. Monte Carlo simulations show the efficiency comparison of different estimation methods for the two nonlinear models. The results show that correct modeling of the structure of the working correlation matrix is very important in nonlinear models, which is quite different from the linear model.

Keywords: partial quasi-maximum likelihood estimation, generalized estimating equations, M-estimation, two-step estimator, spatial data, probit model, count data model

JEL Classification: C13, C21, C35, C51