Caitlin and I are back after a one week hiatus as we each ran around traveling in our respective parts of the world. Probably for the best, as it allowed two weeks of twoway fixed effects decompositions to marinate. But now it’s time — can we finally see what a continuous treatment difference-in-differences estimator actually is for goodness sake? And the answer is sort of!

In this episode, me and Caitlin wrap up a walk through of what parameters we are identifying with our abortion-marriage paper. I was really puzzled to be honest in the last episode as to what a “dose” even meant in our context. As you may recall, we are studying the effect of House Bill 2 which caused half of Texas’s abortion clinics to close, and in turn made the distance to the nearest abortion clinic to rise. But that led us to wonder:

1. Are we studying the effect of distance to the nearest clinic after House Bill 2, or

2. Are we studying the effect of the change in distance to the nearest clinic after House Bill 2?

So, have fun as you listen to us talk through it out and finally realize at the end that it would appear our dose must be one of those and cannot be the other due to the nature of the design and diff-in-diff itself. Hint: no anticipation places some rails on us. See if you can figure out why.

But then we also dive into the continuous treatment diff-in-diff estimator. You’ll learn about splines! You’ll learn about kernels! You’ll learn about polynomials! You’ll learn about b-splines and wavelets and a bunch of other things that draw curvy lines! And you’ll learn about the one situation when you have the permission to interpret that line as a causal effect too!

Thanks again for all your support! We hope you enjoy this episode!

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In one sense, causal inference has two approaches. You can run a regression and then backwards engineer what it means. Think of Imbens and Angrist's 1994 classic Econometrica on the local average treatment effect (LATE) where they show that the Wald estimator (binary treatment, binary instrument) is the average effect for the complier subpopulation.

But the other way that causal inference often runs is you start with the parameter of interest, not the regression, and then build the regressions to identify them under minimal but acceptable assumptions. In this episode of the Odd Couple, we switch from estimation to description of the causal parameters introduced in Callaway, Goodman-Bacon and Sant'Anna (2026, AER). These are the well known ATT parameter, but not the ACRT, which is the slope of the dose response curve. We also puzzle over whether our treatment is, in fact, distance measured in levels or is it distance measured as changes. Which is probably one of the values of starting with parameters: it forces you to figure out what your question is!

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Welcome to the 11th episode of The Mixtape with Scott, season 5, “The Odd Couple” featuring Caitlin Myers! This week we continue the riveting material from last week where we walked through a decomposition of the twoway fixed effects estimator when it’s 2 period, diff-in-diff with a continuous treatment! Yes, you heard me right — be still my beating heart.

Scott's Mixtape Substack is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber.

Me and Caitlin continue to go through this deck that Claude made for us explaining the new Callaway, Goodman-Bacon and Sant’Anna paper, forthcoming at AER, about continuous treatment diff-in-diff. Mainly, though, we are just working our way painstakingly slow through this Frisch-Waugh-Lovell decomposition of the OLS regression to better understand just what OLS is doing.

I thought this episode was pretty interesting though your mileage may vary. I mean, if you don’t find two economists trying to help each other understand an econometrics paper, then probably the floor on this episode could be a little low. But that said, I did enjoy it. We both really seemed to help one another better understand the decomposition formula, plus we got to see it with our own eyes. And Claude made some really intuitive graphics that helped both of us.

So check it out! As always thanks for tuning in!

Scott's Mixtape Substack is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber.