Geographic difference-in-discontinuities

ABSTRACT

A recent econometric literature has critiqued the use of regression discontinuities where administrative borders serve as the ‘cutoff’. Identification in this context is difficult since multiple treatments can change at the cut-off 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. This paper formalizes the identifying assumptions in this context, which will allow for the removal of time-invariant sorting and multiple treatments similar to the difference-in-differences methodology.

KEYWORDS:

• Difference-in-discontinuities
• spatial econometrics
• sorting
• compound treatment
• causal inference

JEL CLASSIFICATION:

• C00
• R15
• R58

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹. Identification through randomization local to the cut-off does not make sense in the geographic context because that would require people to randomly be located on either side of the border.

² See Cattaneo, Idrobo, and Titiunik (2019) and Cattaneo, Idrobo, and Titiunik (2020) for an overview of modern techniques. The formulation using first-differences is practically useful as estimation can be done using the suite of RD packages found at https://rdpackages.github.io/https://rdpackages.github.io/.

³ Keele and Titiunik (2015) discuss the choice of using a single measure of distance versus a two-dimensional running variable. The difference-in-discontinuity method can be extended into the two-dimensional framework easily, but data will usually render the two-dimensional case implausible.

⁴ See Theorem 1 in Hahn, Todd, and Klaauw (2001).

⁵ This is similar to the difference-in-differences methodology that allows for time-invariant differences in levels.