Josh found a confusing argument on page 67 (how did Steve let this slip in ?!)
The bottom of page 67 discusses proxy control and suggests that if you regress the proxy on the variable of interest (schooling) and find a zero effect, you should be less inclined to worry about the bias from proxy control. This doesn’t make much sense because what we care about when assessing the bias from proxy control is equation 3.2.14, the regression of the proxy on both schooling and the correct control. But of course we can’t run that regression because we don’t have the correct control. The regression of the proxy control on schooling isn’t informative about 3.2.14 unless the correct control is uncorrelated with schooling. In that case, however, we wouldn’t have needed to control for it in the long regression (3.2.13) in the first place.
We’ll clear all this up in the next edition as well!
Josh found a confusing argument on page 67 (how did Steve let this slip in ?!)
The bottom of page 67 discusses proxy control and suggests that if you regress the proxy on the variable of interest (schooling) and find a zero effect, you should be less inclined to worry about the bias from proxy control. This doesn’t make much sense because what we care about when assessing the bias from proxy control is equation 3.2.14, the regression of the proxy on both schooling and the correct control. But of course we can’t run that regression because we don’t have the correct control. The regression of the proxy control on schooling isn’t informative about 3.2.14 unless the correct control is uncorrelated with schooling. In that case, however, we wouldn’t have needed to control for it in the long regression (3.2.13) in the first place.
We’ll clear all this up in the next edition as well!