One of the first causal methods we ever learn in statistics class is to “control for X”. We can use a regression that controls for X, and if we wonder what that means, we need only review the Frisch-Waugh-Lovell theorem to see what a multivariate regression is equivalent to. As you progress, you may learn that there are a whole range of estimators, though, that use covariates to reconstruct a missing counterfactual when trying to estimate some average treatment effect. There’s matching methods which basically impute missing counterfactuals by finding units in the comparison group that have the same or almost the same covariate values. There’s even fixes for when you can’t find the exact matches, too, such as Abadie and Imbens (2011) bias correction methods for matching discrepancies. There’s propensity scores which can be used, also, to find matches, as well as used as weights in simple comparisons between treatment and control. And then there are things sort of in between like co…

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