Spatial Differencing for Sample Selection Models with Unobserved Heterogeneity

TL;DR

This paper introduces a spatial differencing approach for sample selection models with unobserved heterogeneity, enabling identification and consistent estimation by leveraging smooth spatial variations.

Contribution

It develops a novel method using spatial differencing to identify and estimate sample selection models with unobserved heterogeneity, including asymptotic properties and standard error formulas.

Findings

Estimator is consistent and asymptotically normal with increasing clusters.

Monte Carlo simulations demonstrate small sample performance.

Application shows the importance of accounting for unobserved heterogeneity.

Abstract

This paper derives identification, estimation, and inference results using spatial differencing in sample selection models with unobserved heterogeneity. We show that under the assumption of smooth changes across space of the unobserved sub-location specific heterogeneities and inverse Mills ratio, key parameters of a sample selection model are identified. The smoothness of the sub-location specific heterogeneities implies a correlation in the outcomes. We assume that the correlation is restricted within a location or cluster and derive asymptotic results showing that as the number of independent clusters increases, the estimators are consistent and asymptotically normal. We also propose a formula for standard error estimation. A Monte-Carlo experiment illustrates the small sample properties of our estimator. The application of our procedure to estimate the determinants of the municipality tax rate in Finland shows the importance of accounting for unobserved heterogeneity.