Difference-in-differences with a Continuous Treatment

Brantly Callaway, Andrew Goodman-Bacon and Pedro Sant'Anna ()

No 32117, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment effect on the treated-type parameters can be identified under a generalized parallel trends assumption that is similar to the binary treatment setup. However, interpreting differences in these parameters across different values of the treatment can be particularly challenging due to selection bias that is not ruled out by the parallel trends assumption. We discuss alternative, typically stronger, assumptions that alleviate these challenges. We also provide a variety of treatment effect decomposition results, highlighting that parameters associated with popular linear two-way fixed-effect (TWFE) specifications can be hard to interpret, even when there are only two time periods. We introduce alternative estimation procedures that do not suffer from these TWFE drawbacks, and show in an application that they can lead to different conclusions.

JEL-codes: C01 C14 (search for similar items in EconPapers)
Date: 2024-02
Note: LS
References: Add references at CitEc
Citations: View citations in EconPapers (48)

Downloads: (external link)
http://www.nber.org/papers/w32117.pdf (application/pdf)
Access to the full text is generally limited to series subscribers, however if the top level domain of the client browser is in a developing country or transition economy free access is provided. More information about subscriptions and free access is available at http://www.nber.org/wwphelp.html. Free access is also available to older working papers.

Related works:
Working Paper: Difference-in-Differences with a Continuous Treatment (2024)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:32117

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w32117
The price is Paper copy available by mail.

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().