Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In this paper, I introduce a potential outcomes framework to model spillover effects and decompose the estimate's bias in two parts: (1) the control group no longer identifies the counterfactual trend because their outcomes are affected by treatment and (2) changes in treated units' outcomes reflect the effect of their own treatment status and the effect from the treatment status of "close" units. I propose estimation strategies that can remove both sources of bias and semi-parametrically estimate the spillover effects themselves. I extend Callaway and Sant'Anna (2020) to allow for event-study estimates that control for spillovers. To highlight the importance of spillover effects, I revisit analyses of three place-based interventions.
This paper formalizes a common approach for estimating effects of treatment at a specific location using geocoded microdata. This estimator compares units immediately next to treatment (an inner-ring) to units just slightly further away (an outer-ring). This paper formalizes the necessary assumptions to identify the average treatment effect among the effected units and illustrates potential pitfalls when these assumptions fail. Since one of these assumptions requires knowledge of exactly how far treatment effects are experienced, I propose a new method that relaxes this assumption and allows for non-parametric estimation using partitioning-based least squares developed in Cattaneo et. al. (2020). Since treatment effects typically decay/change over distance, this estimator improves analysis by estimating a treatment effect curve as a function of distance from treatment. This is contrast to the traditional method which, at best, identifies the average effect of treatment. To illustrate the advantages of this method, I show that Linden and Rockoff (2008) under estimate the effects of increased crime risk on home values closest to the treatment and overestimate how far the effects extend by selecting a treatment ring that is too wide.
A recent econometric literature has critiqued the use of regression discontinuities where administrative borders serves as the `cutoff'. Identification in this context is difficult since multiple treatments can change at the cutoff and individuals can easily sort on either side of the border. This note extends the difference-in-discontinuities framework discussed in Grembi et. al. (2016). to a geographic setting. The paper formalizes the identifying assumptions in this context which will allow for the removal of time-invariant sorting and compound-treatments similar to the difference-in-differences methodology.
The goal of
did2s is to estimate two-way fixed effects models without running into the problem of staggered treatment adoption. This package, available in both
Stata, implement the method by Gardner (2021). This method entails the following two-step estimation procedure: