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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