Partially Linear Spatial Probit Models

TL;DR

This paper introduces a new partially linear spatial probit model that accounts for complex spatial dependencies and heteroscedasticity, providing consistent estimators with proven asymptotic properties.

Contribution

It develops a novel estimation procedure combining weighted likelihood and GMM for spatial probit models with heteroscedasticity and dependence.

Findings

Establishes consistency and asymptotic normality of estimators.

Demonstrates finite sample performance through simulations.

Abstract

A partially linear probit model for spatially dependent data is considered. A triangular array setting is used to cover various patterns of spatial data. Conditional spatial heteroscedasticity and non-identically distributed observations and a linear process for disturbances are assumed, allowing various spatial dependencies. The estimation procedure is a combination of a weighted likelihood and a generalized method of moments. The procedure first fixes the parametric components of the model and then estimates the non-parametric part using weighted likelihood; the obtained estimate is then used to construct a GMM parametric component estimate. The consistency and asymptotic distribution of the estimators are established under sufficient conditions. Some simulation experiments are provided to investigate the finite sample performance of the estimators.