Caplan on Card
Caplan notes that these results are hard to reconcile: The former suggests that labor demand is highly inelastic, whereas the latter suggests it is highly elastic. That is a very good point. While I was well aware of Card's famous research on these topics, I had not put them together and recognized the tension between them.
To me, this brought to mind an econometrics class I took from Frank Fisher many years ago. Frank used to say that the "iron law of econometrics" is that coefficients are biased toward zero. He meant that various problems, such as measurement error and misspecification, tend to make it hard for researchers to find an effect even when one really exists. Fisher's "law" overstates things, which was Frank's style, but his basic point is often right.