Matt from Western Kentucky U comments on Chapter 3. . .
Question: You state:
“Our view is that regression can be motivated as a particular sort of
weighted matching estimator, and therefore the differences between
regression and matching estimates are unlikely to be of major
empirical importance” (Chapter 3 p. 70)
I take this to mean that in a ‘mostly harmless way’ regular OLS
regression is in fact a method of matching, or is a matching
estimator. Is that an appropriate interpretation? In ‘The Stata
Journal and his blog, Andrew Gelman takes issue with my understanding,
he states:
“A casual reader of the book might be left with the unfortunate
impression that matching is a competitor to regression rather than a
tool for making regression more effective.”
Any guidance?
Well Matt, Andrew Gelman’s intentions are undoubtedly good but I’m afraid he risks doing some harm here. Suppose you’re interested in the effects of treatment, D, and you have a discrete control variable, X, for a selection-on-observables story. Regress on D an a full set of dummies (i.e., saturated) model for X. The resulting estimate of the effect of D is equal to matching on X, and weighting across covariate cells by the variance of treatment conditional on X, as explained in Chapter 3. While you might not always want to saturate, any other regression model for X gives the best linear approx to this version subject to whatever parameterization you’re using.
This means that i can’t imagine a situation where matching makes sense but regression does not (though some my say that I’m known for my lack of imagination when it comes to econometric methods)
JA
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