A colleague writes:
Why do people keep praising matching over regression for being non parametric? Isn’t it f’ing parametric in the matching stage, in effect, given how many types of matching there are… you’re making structural assumptions about how to deal with similarities and differences…. the likelihood two observations are similar based on something quite similar to parametric assumptions… you’re just hiding the parametric part..
My reply: It’s not matching or regression, it’s matching and regression. Matching is a way to discard some data so that the regression model can fit better. Trying to do matching without regression is a fool’s errand or a mug’s game or whatever you want to call it. Jennifer and I discuss this in chapter 10 of our book, also it’s in Don Rubin’s PhD thesis from 1970!