When observational data includes a treatment indicator and some possible confounders, it is very tempting to simply regress the outcome on all features (confounders and treatment alike), extract the coefficients associated with the treatment indicator, and proudly proclaim that “we have controlled for confounders and estimated the treatment effect”.

This approach is wrong. Very wrong. At least as wrong as that DIY electrical job you did last week: it looks all good and neat but you’ve made a critical mistake and there’s no way you can find out without killing yourself.

I can’t explain why this is wrong (I’m not sure I understand it myself) but I can show you some examples proving that this approach is wrong. We’ll work through a few examples, where we compare the results with a traditional regression with a couple of legit causal inference libraries. Since we use simulated data, we’ll also be able to compare with the “true” treatment effect.

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