Caitlin Myers and myself have been studying the effect of House Bill 2 in Texas, which closed half the state's abortion clinics, on marriage rates using "continuous difference-in-differences" estimation for 14 episodes straight.

But behind every good diff-in-diff estimate lurks a parallel trends assumption, and so we asked Hannah to look into one confounder -- oil! fracking! energy! Perhaps things related to technologies that enhanced the extraction of oil from the ground, like fracking technology, could have alone shifted marriage rates by bringing men into communities but only for work, temporary residence, not permanence.

We talk about a literature where men in transit can alone reshape the marriage markets, which if those events happened disproportionately in our treatment counties, but also our control counties, then parallel trends mechanically *might* be violated. Because remember -- parallel trends is a) about things differentially impacting the treatment and control units on *outcome trends* and b) therefore can impact the treatment group *or* the control group. Hannah comes back with research she did for us on it.

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This week is a hoot! Caitlin and I finally get some estimates of the different target parameters using continuous treatment diff-in-diff! We discuss in detail how the estimator works and then go through our analysis. Watch to the end to see our reaction when we finally see some output in a beautiful deck!

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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!

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