Estimation of Spatial Sample Selection Models: A Partial Maximum Likelihood Approach

To analyze data obtained by non-random sampling in the presence of cross-sectional dependence, estimation of a sample selection model with a spatial lag of a latent dependent variable or a spatial error in both the selection and outcome equations is considered. Since there is no estimation framework for the spatial lag model and the existing estimators for the spatial error model are either computationally demanding or have poor small sample properties, we suggest to estimate these models by the partial maximum likelihood estimator, following Wang et al. (2013)'s framework for a spatial error probit model. We show that the estimator is consistent and asymptotically normally distributed. To facilitate easy and precise estimation of the variance matrix without requiring the spatial stationarity of errors, we propose the parametric bootstrap method. Monte Carlo simulations demonstrate the advantages of the estimators.