Math and Econ

Dani Rodrik has a comment
today about why we have to use mathematics in economics. First of all, I'd like to mention that the resistance he's getting from his students makes me glad I didn't go into the MPA/ID program there. But second of all, it's worth mentioning the implied difference between mathematics in the physical sciences and in economics. In mechanics, the mathematical laws that we work with are simple, nearly universal, and exhaustively verified by controlled experiment. In this sense, they are proscriptive -- if you can derive a result mathematically that follows from the basic laws of mechanics, it's pretty likely to be true. In this sense, you can explore using only pencil and paper and still produce interesting results.

By contrast, in economics mathematics is only descriptive. We use it to force ourselves to express our ideas clearly, both to communicate our ideas to others and to check our own understanding for inconsistency. (George Akerlof's famous Lemons paper is a good example of deep economic meaning expressed with trivial mathematics, in which algebra is simply an efficient way of communicating an economic idea with the greatest clarity.) The "axioms" of economics are not universally applicable nor unambiguously true. Consequently, in economics, mathematical proofs without intuitive interpretations are worthless.

But econometrics is a different story! A further benefit of describing your economic model in mathematical terms is that by doing so, you subject it to statistical testing. The role of the econometricist is take a model and find its parameters, extrapolate what would be observed if it were true, what would be observed if it were false, and draw meaningful conclusions from what we actually see. This is essentially a mathematical question -- how do you connect a model to observable data? The process of understanding then goes (1) economic insight leads to (2) a mathematical model which leads to (3) a probabilistic framework which admits (3) statistical testing which can be compared with (4) empirical data which qualifies or informs (1) economic insight. (A very cool example of this is a series of papers I'm reading (but only partly understanding) that performs empirical testing on the introductory economic theory that consumers make consumption choices that maximize lifetime expected utility.)

In other words: no matter how much I may care about development, I think econometrics, as opposed to public policy, was the right choice for me.