Spatial Differencing: Estimation and Inference

Spatial differencing is a spatial data transformation pioneered by Holmes (1998) increasingly used to estimate causal effects with non-experimental data. Recently, this transformation has been widely used to deal with omitted variable bias generated by local or site-specific unobservables in a "boundary-discontinuity" design setting. However, as well known in this literature, spatial differencing makes inference problematic. Indeed, given a specific distance threshold, a sample unit may be the neighbor of a number of units on the opposite side of a specific boundary inducing correlation between all differenced observations that share a common sample unit. By recognizing that the spatial differencing transformation produces a special form of dyadic data, we show that the dyadic-robust variance matrix estimator proposed by Cameron and Miller (2014) is, in general, a better solution compared to the most commonly used estimators.