Spatial differencing for sample selection models with ‘site-specific’ unobserved local effects

This paper proposes an estimator which combines spatial differencing with a two-step sample selection estimator. We derive identification, estimation, and inference results from ‘site-specific’ unobserved effects. These effects operate at a spatial scale that cannot be captured by administrative borders. Therefore, we use spatial differencing. We show that under justifiable assumptions, the estimator is consistent and asymptotically normal. A Monte Carlo experiment illustrates the small sample properties of our estimator. We apply our procedure to the estimation of a female wage offer equation in the United States and the results show the relevance of spatial differencing to account for ‘site-specific’ unobserved effects.