Difference-in-Differences with a Continuous Treatment

By Brantly Callaway, Andrew Goodman-Bacon, Pedro H. C. Sant’Anna. Social Science Research Network, 2021

361 citations recorded by the source corpus.

This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment-on-the-treated-type parameters are identified under a parallel trends assumption analogous to the binary treatment case. However, comparing these parameters across treatments is challenging because parallel trends does not rule out selection bias. We discuss alternative, typically stronger, assumptions that eliminate selection bias. We further show that popular two-way fixed effects estimands admit multiple interpretations, depending on the underlying causal building block, all having important limitations as meaningful summaries of treatment effects. Finally, we introduce alternative estimation procedures that avoid these drawbacks and demonstrate them in an empirical application.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/785ac1d24d3fcd25b16bcd889f44712d8a171aaa

Citations in the corpus

• What’s trending in difference-in-differences? A synthesis of the recent econometrics literature (2022, neutral): “For example, Callaway and Sant’Anna (2021) consider a relaxation of Assumption 4 that imposes (4) only for years after some units are treated: Assumption 4.a ( Parallel Trends for Staggered Setting — Post-Treatment Only ) . for all t , t ′ ≥ g min − 1, where g min = min G is the first period where…”