Diff-in-Diff: a small sample size of the control group

[Carl Lin]

Dear all,
I have two questions about diff-in-diff that I recently encountered:
(1) In a diff-in-diff model, if the number of observations in the treatment group is much larger than the control group, for example, 2400 vs. 125, does this make the estimated result invalid, or just less precise? Could you recommend any readings (such as books or articles)?
I do obtain statistically significant estimated coefficients of the interaction terms

(2) Can I implement matching techniques (nearest neighbor, kernel, radius matchings) to get a more comparable treatment and control sample and then do diff-in-diff in such a case? What are the caveats?

Thank you.

[Carlo Lazzaro]

Carl:
welcome to this forum.
The 2nd volume of this outstanding textbook (Stata Bookstore: Microeconometrics Using Stata, Second Edition) covers all these issues in Chapters 24 and 25.

[Carl Lin]

Carlo: Thank you so much!

[Jared Greathouse]

Another option would be to use the synthetic control method. You'd generate 2400 synthetic controls from the 125 untreated units. SCM is better than DID, abs you can even use penalized variants of it in Stata.

[Carl Lin]

Jared: Thank you for the suggestion!

[Jeff Wooldridge]

Carl: How many time periods do you have? Is this common timing case? And I would push back a bit on "SCM is better than DiD." SCM requires large T, for one. It is easy to do matching combined with DiD methods. I can point you to my recent paper with Soo Jeong Lee to show how to use matching methods after a simple transformation.