id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-193947-vcm3v0ix	Pollmann, Michael	Causal Inference for Spatial Treatments	2020-10-31		.txt	text/plain	27979	1791	50	Even when the differences in levels between inner and outer ring are differenced out with individual fixed effects in panel data, the parallel trends assumption is particularly strong in spatial treatment settings. With individuals and treatment locations distributed across space, a large number of covariates, such as population density or average income at different distances, are predictive of both outcomes and treatment assignment probabilities. In the ideal spatial experiment considered in this section, treatment is randomized similar to a completely randomized experiment across regions with outcomes aggregated within regions (and distance bins).�( ) ( ) is the variance of aggregated treated potential outcomes,�( 0) ( ) is the variance of aggregated control potential outcomes, and ( ) ( ) resembles a variance of treatment effects, such that�( ) ( ) +�( 0) ( ) � ( ) ( ) resembles the variance of the difference in means under repeated sampling of fixed individuals but varying treatment assignment, the framework of this paper.	./cache/cord-193947-vcm3v0ix.txt	./txt/cord-193947-vcm3v0ix.txt