Ya, I should probably watch that again soon.
In addition to the normal seminar discussion leadership, we had a lecture by Aman Ullah of UC Riverside on non-parametric econometrics. I thought his criticism of parametric models was a little too harsh, but asked a question that he thought was a good one that was framed a little nicer. One of the things he raised was the specification of the earnings equation by Heckman and his students as a quadratic function of experience. He talked about how he re-estimated it non-parametrically and found a quartic relation - and that this was later confirmed by a more exhaustive parametric analysis which tested a quartic relation against quadratic and other options.
That's all fine, and a nice exercise. But I noted that they didn't use a quadratic relation because they were too lazy to do non-parametrics. They used it for theoretical reasons based in Becker's human capital theory. Then I asked whether any theoretical framework for explaining the quartic relation (he had come up with this in the late 80s) had been developed, because if this is really robust it ought to tell us something about our labor theory. Not that he was aware of, he said.
This is an important point, though. The explanation offered at the time of his paper was the impact of World War II (I believe... maybe Vietnam): a cohort effect. That's fine, but that doesn't suggest there's anything wrong with the quadratic specification - that suggests that there's something wrong with an omitted variable that you ought to have conditioned on.
That's a huge difference! It's the difference between revising human capital theory and not revising human capital theory.
My concern with non-parametrics is that it gives the illusion of being agnostic when actually you are making some very consequential assumptions about whether its OK to be indifferent between a conditioned and unconditioned binary relationship. Now that's not necessarily true of newer advances in non-parametrics, which he talked about as well. Non-parametric methods can be used to estimate "functional coefficient" models that do condition on other variables and in that sense offer the opportunity to get more meaningful stories back into the analysis (albeit not by assuming a parametric specification). He's used these functional coefficient models to look at some of Card's work on the returns to schooling.
One question I didn't ask because time was running over was about the role of non-parametrics in non-experimental techniques that rely on a particular functional form. It's one thing to be agnostic about theory in an empirical question, but if you're using a particular non-experimental technique you cannot be agnostic about the assumptions required for that technique if you're implementing it. The specific example I have in mind is the popularity of using non-parametric methods like local linear regressions to estimate regression discontinuity models. It's always seemed to me that these pose serious risks around violating the local continuity assumptions of RDD, which is critical for identifying the model. I'm going to email this question to him today - because it has implications for one of my dissertation chapters.