I have an exam tomorrow morning, so I need to make this quick so I can keep studying. But, of course, it's the exam that this post is about.

I've mentioned on several occasions my dissatisfaction with my econometrics professor, and the course itself. (It's the same professor I spent time whining about in my posts several months ago related to economics and statistics.) We're using weird statistical analysis software, after three weeks we still haven't done multivariable regressions, and there's no matrix algebra to speak of.

The strangest part of the course, though, is my professor's obsession with having us not only derive equations in class, but also memorize how to perform those derivations. I suppose in some sense this might be called "rigorous," but really it's just a pointless exercise in frivolity. The real derivations — the ones that might actually be worth knowing — use matrix algebra, which, of course, we can't use in this econometrics course because the economics department has what I consider an insufficient mathematics prerequisite.

But back to the exam. One of the "proofs" my professor wants me to be able to recite has to do with showing that a particular estimator is unbiased, which, of course, involves showing that the expected value of that estimator is the value it's trying to estimate. I couldn't remember how exactly to do the proof, so I looked in my notes. I don't know whether I was bored to death, just took bad notes, or the professor didn't do a very good job of explaining the derivation. Whatever the case, I couldn't obtain the information I wanted from my notes. So I opened the course textbook — the one my professor chose — to find what I needed.

It was then that I realized how perverse this course and my professor is. Even the authors of my textbook — two MIT professors — don't think these proofs are worth knowing particularly well. As they put it, "The details are relatively straightforward, but since they are somewhat tedious, we have relegated them to Appendix 3.1" (Econometric Models and Economic Forecasts, Pindyck and Rubinfeld, pp. 63).

I feel like my professor really misses the point when it comes to teaching. The details are doubtlessly important, but it's a whole lot more important — especially in a course that's about economics more than rigorous mathematics — to understand the economic principles behind and the application of the formulas.

Update: Because I'm angry and frustrated, I thought I'd vent some of my other dissatisfaction with this professor too.

Often, in the course of doing these banal derivations, he will make an offhanded comment that one particularly bizarre reformulation of a particular formula would be "the one you'd use if you were a writing software for Microsoft." It's clear to me that he does not understand algorithmic analysis.

The unviolated formulas he has spent so much time tinkering with would, as algorithms, all grow in linear time. And so would all of his reformulations. So, from an algorithmic analysis point of view, neither algorithm is preferable! On the other hand, some forms of the formulas would, from my point of view, be better because they would be easier to maintain and support, always big concerns when one is writing software.

Back to my studying.