On page 209 of Gelman and Hill book, the authors suggest that

Having created and checked appropriateness of the matches by examining balance, we fit a regression model just on the matched data including all the predictors considered so far, along with an indicator to estimate the treatment effect

Why do I still need to include predictors? After matching, all of these predictors are balanced across the control and treatment group, and thus uncorrelated with the treatment variable. Therefore, the coefficient estimate should be no different with and without the predictors.


1 Answer 1


Firstly notice that propensity matching does not perfectly balance the data; this is usually not even possible. It matches the closest control; the closest control can still be quite a bit off.

Consider the case that you have less female controls than females in the treated group.

Secondly, even if you have a perfectly matching group it still makes sense to correct for other factors. They will not bias your estimate, but they will increase the standard error as they are an additional source of variability. Accounting for variability when possible increases your statistical power.

  • $\begingroup$ Re first point: does it mean for other matching methods that claim perfect balance (e.g. coarsened exact matching, genetic matching), I don't need to include controls? What to make of the fact that, despite confirming perfect balance of my co-variates, regression with and without predictors give different estimates? (Re 2nd point: I agree.) $\endgroup$
    – Heisenberg
    Oct 30, 2015 at 15:28
  • 1
    $\begingroup$ @Heisenberg Unfortunately exact does not always mean what we would like it to. Also see Fisher's exact test (it is exact, but conditional on an usually wrong assumption). I am not that familiar with CEM. In this context, I suspect exact means that it optimal in some mathematical sense. But it certainly can't work miracles. As for genetic matching, the claim is that it "reduces bias" and improves covariate balance, not that it is able to achieve perfect balance. $\endgroup$
    – Erik
    Oct 30, 2015 at 15:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.