Background
Rather than provide a tutorial, I’m going to introduce an interesting topic for this month’s blog.
In difference-in-differences (DID) estimation, one of the key assumptions is this idea of parallel trends. More specifically, the trends between the treatment group and control group should be parallel prior the period when the intervention occurs (“index period”). When the parallel trends assumption holds, then we can make causal claims that any change in the treatment group after the index period is due to the intervention and not to the secular effects of time.
The figure below illustrates the parallel trends between the treatment and control groups prior to the index period.
However, where the parallel trends assumption does not hold, then any changes observed in the treatment group is really difficult to attribute to the intervention that occurred at the index period.
When this occurs does it mean that your DID estimation is wrong?
Maybe.
But how wrong?
That’s what Ashesh Rambachan and Jonathan Roth set out to figure out with their recent paper, “A More Credible Approach to Parallel Trends.”[1]
“Honest” DID
Initially called the “honest” DID, Rambachan and Roth provided a way for us to estimate the magnitude of impact that violation of the parallel trends would have on our DID estimate.[1] As I have interpreted their paper, they wanted to provide a way to show how “honest” the DID estimate is when there is a violation in parallel trends.
Their paper provides an innovative approach to relax the parallel trends assumption and seeing how this impacts the DID estimations. They do this by setting the post-treatment difference based on the pre-treatment differences. The pre-treatment differences are extrapolated into the post-treatment period to see how much the differences would have been observed.
They argue that you can use an interval of differences in trends to see when the pre-treatment violations lead to post-treatment violations of the parallel trends.
Current status
I’m still going through this myself, so I plan to provide a follow-up on this. Right now, this is pretty exciting stuff, and I’m looking forward to seeing how I can apply this to some work that I’m currently doing where we have a violation in the parallel trends prior to the index period.
So stay tuned for more updates.
References
Here is the citation for their paper on “honest” DID:
1. Rambachan A, Roth J. A More Credible Approach to Parallel Trends. Rev Econ Stud. 2023;90(5):2555-2591. doi:10.1093/restud/rdad018
Here is the GitHub site for the “honest” DID packages in R and Stata:
https://github.com/asheshrambachan/HonestDiD
Here is Jonathan Roth’s page with more on DID:
https://www.jonathandroth.com/did-resources/