If Econ Poked, Would Math Poke Back?
I was walking back from class with Dylan when we decided that if political science had a facebook profile (assuming political science could be personified), that it would list its relationship with math (also personified) as “it’s complicated.” Political science does not really know how to handle math; While the sub-discipline of comparative politics is witnessing an influx of math-oriented talent, ushered in by quantitative political scientists like Robert Axelrod at the University of Michigan, the sub-disciplines of international relations, political theory, and american politics seem to ignore math entirely. At best they flirt by using summations and unnecessarily complicated graphs to express intuitive ideas; seldom does the incorporation of math do much to expand the logic of insights and observations. Upon thinking later, I began to question whether it is good or bad that political science’s fling with math seems to never progress beyond linear regression and standard deviations; Should we be concerned that political science continues to reject math’s relationship requests?
If economics is any indication of how political science would fare if too involved with math, we should be very happy to keep the two at a distance; we should probably make sure math’s marriages to physics and engineering stay strong and passionate. After 3 weeks of econometrics (the metrics of economics; the bastion of the bastardization of theoretical empiricism) I have experienced withdrawal from those old intuitive graphs that still dominate the high end of political science, so much so that when my friends are studying for econ 101 I beg them to let me help them, as doing so gives me a chance to relive the glory days of supply and demand curves. In the politics of development I hear “Solow Model” and instantly begin trying to draw the equilibrium of capital steady states. But then sifting through 12 pages of econometrics notes – 12 pages of 15+ variable calculations, no pictures, no economic concepts (not even a dollar sign), and certainly no practical application – I conclude: This shit has gone too far. Maybe political science’s cursory involvement of math is limiting, but at least it resembles the world. I ask my metrics professor: “Why do we list special cases for the Gauss-Markov theorem when those special cases are true within the confines of the theorem; they aren’t exceptions at all.” Response: “We wouldn’t want the variable ‘k’ to be a fraction, now would we?” Me: “You haven’t told us what the fuck k is, who the fuck k helps, or what k even affects, so I wouldn’t have a fucking clue what k should be.” Fuck k.
The problem with math’s relationship with economics is not that it frustrates students like me (I can and will get over it). There is, to be sure, nothing intrinsically wrong with using theoretical math in a social science discipline; after all, where would the hard sciences be without theoretical math? Why would we not expect the social sciences to have the same luck? The problem is with the normative choice to use a methodology that cannot be objectively applied to the social sciences. Whereas theoretical math works extremely well with sciences that rely on testable observations and static realities, when applied to the social sciences theoretical math forces unreliable results. In fact, the methodology determines the results in many cases. Rational choice theory is a good example: there is no metaphysical reason (a priori) that we should agree with rational choice theory, but since we are constrained by a mathematical methodology, we need to assume rational choice; otherwise we simply could not use theoretical math to garner results. Economists choose the theory because it fits the methodology, not because it has its own merits. Here is a list of more esoteric but equally damning assumptions that are forced on econ in order to use theoretical math: Rational saving (money not spent on consumption by an individual will be invested in the option with highest expected returns), phi (the government scalar) must be strictly less than 1 (resulting in government spending being less efficient than government spending), Nonstochasticity (that variables will not be random), identification (that observable x values will vary), the expected value of epsilon (residual or the arbitrarily small value) is equal to zero, Homoskedasticity (distance of variables from the best fit line are uniform), no serial correlation (that output values cannot be related), normal distribution of errors (this one is just ridiculous), etc.
These assumptions must be made because there is uncertainty in human decision making and because theoretical math requires certainty in its functions. If we cannot be sure of the principles of human behavior – if humanity is not actually comprised of predictable individuals – then the methodology used in economics demands unfair assumptions. Not only does the methodology force predictability, it forces a determination of the type of predictability of human behavior. In doing so, economic theories do not offer information about how the world would be if certain actions were taken, rather they only give information about how an arbitrarily defined world would respond to theoretical actions. I have no interest in how a population of rational, homeskedastic, and nonstochastic individuals would respond to a tax change of epsilon units; I want to know the way things are in our world.
Until we have magical formulae for solving the uncertainty of humanity, the social sciences should be no more than friends with theoretical math. And in the midst of economics’ continued facebook pokes of math, math should probably do all the social sciences a favor by messaging back: “Get the fuck away, I was never meant for you.”
