Saturday, September 15, 2012

Does Economics Really Need Maths?

Economics has an incredible amount of mathematics. In fact, you wouldn't be too far off the mark if you were to rename it as Applied Mathematics (economy). Take the following model below, from my school notes, which describe how firms collude to set high prices.



Because of this, LSE economics students undergo a gruelling one-month math course before the start of their Masters programme. At the end of it, they take mathematics exams. It is hardly any fun, but does it really help with economics?


To test this out, I compared whether students with high "maths for microeconomics" (micro-maths) scored better for their microeconomics exams. The former is plotted on the y-axis, while the later on the x-axis below:


As you can see from the line of best fit, students who do well in micro-maths also tend to do well in microeconomics. More specifically, if you score 10% higher in your maths (i.e. from 50 to 55 marks), you get a 8.7% boost in your exams (i.e. from 50 to about 54 marks).  So it does seem that maths skills are useful, and students should pay attention in maths classes.

But wait - perhaps it is not the maths itself that helps students. Perhaps students who score well for micro-maths also score well for microeconomics because of their inherent ability, or because they are exam-smart. So a third factor - let's call it "ability" - is causing both scores to be correlated. We call this spurious correlation.

To resolve the problem, all you need is to put a variable to control for ability in the calculations. But is there a good measure of ability? 

During the one-month maths course, students take exams not only for micro-maths, but also for "maths for macroeconomics" (macro-maths). Although both are maths-based, their content is completely unrelated. In micro-maths, students learn how to find maximum, minimum, and other equilibrium points, but in macro-maths students learn how to optimise happiness for an individual who lives forever (!?).

In a nutshell, what you learn in macro-maths has no bearing on your microeconomics exams, and any correlation you observe between the two is due to your ability. In fact, when you compare macro-maths against microeconomics exams scores - shown in the chart below - you get a positive relationship.



Using macro-maths to control for ability, I find that the impact of micro-maths dropped more than 4 times! Previously, a 10% improvement in micro-maths raised your exam score by 8.7%. With ability considered, your exam score goes up by only 2.1%. In contrast, scoring 10% higher for macro-maths - remember that this is a proxy for ability - causes your microeconomics marks to go up by a much higher 7.6%.

I think the key lesson here is that your ability matters more than head knowledge. It is not about nature vs nurture. Rather, understanding and appreciating your subject is a better way to study than rote memorisation. 

In other words, don't just go through your studies, let your studies go through you!

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