Archive for March, 2010
The Problem of Sample Selection
Posted by Christian in News and Current Events on March 23, 2010
When evaluating a policy program, researchers face a huge problem: sample selection. Consider the following example: suppose we offered kids summer classes to practice and improve their math and reading skills. After the program has ended, we compare the test scores of the kids who took the summer classes to the test scores of kids who didn’t. We find that the program kids’ test scores are significantly higher than the other kids’ test scores. Does this mean our program succeeded in raising test scores?
Not necessarily. We can imagine that the academically strongest, most enthusiastic kids would jump at the opportunity to join this summer program while the less-motivated kids would prefer to stay at home. That is, the program kids are mostly comprised of kids from the “smarter” group. In the absence of the program, the program kids would still have outperformed the other kids. Thus a simple comparison of test scores does not allow us to separate the innate ability of the program kids from the benefit of the summer program, and so we can’t tell how beneficial the program was.
If you take 14.74, examples and arguments like these will become second nature to you. You’ll explore several techniques to get around sample selection, including randomized control trials (used extensively by JPAL, where I currently UROP), difference-in-differences (particularly applicable to the example above), and ATE/TOT/LATE/ITT (average treatment effect, treatment on the treated, local treatment on the treated, and intention to treat, of which ATE is the topic of my 14.36 paper).
Feel free to email me (csperez@mit.edu) if you want to discuss sample selection or the econometrics used to get around it.
What Math classes should I take for an Econ major?
As a second-term senior, I feel the need to leave my experiences at MIT somewhere permanently. Here’s edition 1 of that.
The Economics classes at MIT are very math-heavy in comparison to what I’ve heard about economics elsewhere, and it’s a good idea to take a few math classes concurrent with your economics curriculum, especially if you’re aiming to go to grad school. I’ll list a few here that I’ve taken with econ classes they’re useful in.
You should take these math classes:
18.01/.02: required for 14.01/.02, I think, and it’s a good idea to have basic calculus down pat before you take any economics classes at MIT. Especially get comfortable with Lagrange multipliers; they will be with you for the rest of your economics career.
18.03: You’ll need this in the macro sequence, to solve the Solow model and some other differential equation problems. Other than that, this stuff doesn’t appear until grad-level classes. I took a PhD labor class, and there were a good number of people in it that never took a diffeq class in undergrad.
6.041/18.440/14.30: A statistics/probability class is immensely useful in the higher level economics classes; this comes up over and over and over, in econometrics, in finance, in labor, etc. etc. The ostensible rank in difficulty, hardest to easiest, is 18.440>6.041>14.30, though I think the curve is worse in 6.041 because of the course 6 masters students. Take this and know it well; it’s a requirement anyway. If you like this stuff, I hear 14.381, the PhD econ stats class is pretty good, too.
18.06: A linear algebra class is a needed to understand econometrics past the very basics. I don’t think anyone actually enjoys 18.06, but it’ll teach you what you need to know and more. Take this with Strang if you can.
18.100A/B/C: Real Analysis comes into play if you want to think about theory and proofs. This class is necessary if you want to go do a PhD in economics. Which level of the class you take will depend on your comfort with proofs and reading math. 100B/C is taught out of an incredibly dense book (Rudin) that is written in all math, and at a speed that was too much for me. 100A has more guidance for intuition, and is generally easier. I haven’t had to do any proofs in my undergrad classes; I think this comes in useful if you want to take the PhD intro classes.
Some other math classes that I took that aren’t so related:
18.443: More statistics, somewhat useful as a reference for econometrics, but I haven’t used it
18.310C: CI-M for math majors, discrete math with random topics about compsci, signals, sorting, etc. Makes you do dumb things like fourier transforms in Excel.
18.311: No tests. Ever. Continuous version of .310
If you have taken any interesting math classes that are relevant, leave it in comments.