Stephen Gordon reflects on some esoteric math - asymptotic theory - he's had to teach his econometrics students.
Why do we force our students to learn these things?
Although from an empirical perspective it probably doesn't make sense in the slightest to worry about the distinction between the two types of convergence, I am quite certain it makes a difference in theory papers. Unlike most economists, I tend to use 'theory paper' in a pejorative sense, because too many theory papers:
- Make assumptions that cannot possibly be true and are not reasonable simplifications of the 'real world'.
- Are non-falsifiable, do not make predictions, or have so many free parameters they can be used to predict anything.
You need to know this math in order to be able to publish 'theory papers'. The larger question should be, "why does the economics profession put any value on this work?"
Of course a lot of it goes to the recently-late Paul Samuelson who mathematized so much of the discipline. Part of it, I think, has a practical use. By developing a rigorous mathematical model, the theorist can make sure that a theory is tight and makes logical sense throughout. In fact, by working through mathematical theories, the researcher might see a testable hypothesis that was otherwise obscured. The trick is to put it back into conversational language.
But on the other side of the coin, some mathematical models seems to be there for mathematical masturbatory pleasure.
And don't forget opportunity costs: time spent learning math - like I did the year before I went to Mizzou for grad school - is time not spent learning qualitative economics. Dan Marburger commented on Facebook (reproduced with his permission):
I'll do you one better. My (lawyer) brother and I have been doing some interdisciplinary work over the past year. In reading relevant literature in scholarly journals, I've noticed that legal scholars do a far better job of explaining economic concepts than academic economists. Deirdre McCloskey's criticism of how economists write is spot on!
One of the problem with academic economists is that we write for each other in the professional journals. Up until the blogosphere came around, there weren't too many professional trained economists writing for a general audience. Hopefully we're effectively filling in the gaps.