A key bone of contention for PCES is that the maths in economics is rarely linked to the real world. The charge that many of us don’t understand why there’s maths in economics is therefore true on one level: we do not understand because nobody tells us! Mathematical models are often learned by rote instead of being introduced to solve an economic problem. As one student put it, ‘you learn to solve models before you even know what a model is and its purpose.’ Economics students typically come from very different backgrounds and so expecting them to automatically understand the purpose of maths is unfair – in fact, we believe that grounding the teaching of maths in real world problems would help many students to understand it better.There's nothing wrong with modelling exercises that act as if something is observable when it is not, treated as modelling exercises. The Welfare Economics Paradigm is rife with fully-informed super-agents (masquerading as Government Officials, or Philosopher Kings) who are capable of identifying the exernality-causing activity and optimally taxing it, and perhaps uber-managers capable of measuring effort can optimally reward it.
Should economics use maths? Since large parts of economics deal with mathematical quantities and dynamic processes, the subject can clearly benefit from quantitative analysis and mathematical modelling. The question is whether it is appropriate to use maths in a particular case, and what is gained by doing so. For example, looking at financial flows and balance sheets surely invites the use of mathematics, as do macroeconomic quantities such as GDP, unemployment and inflation. At a micro level, it seems absurd to study the impact of (say) sugar taxes on sugar prices and consumption without using mathematical quantities.
On the other hand, modern economics is rife with mathematics used to represent things which are simply unquantifiable in the real world. One example is ‘effort’, a key variable in the kind of contract models for which the 2016 Nobel Prize was awarded to Oliver Hart and Bengt Holmström, and which are the bane of all Manchester Micro III students.
Implementing such models might be more difficult, although the idea of tinkering with the incentives by imposing taxes on polluting activities with the hope of rolling them back isn't exactly the same. At the same time, who among us hasn't heard a gym teacher or athletics coach suggesting a laggard is "dogging it." Relying on a proxy for effort, maybe?
More to the point, the message is about treating the mathematics as the servant.
We embrace maths and statistics as invaluable tools in the study of economics, but believe that students should learn a variety of these tools so that they can know which types of maths to use and when. Perhaps most importantly, students should be made aware of times where maths is not appropriate so that they have a critical grasp of how to use it most effectively in economics.It's better to understand the stories first. Good mathematics or statistics adds precision to the parables. If you understand how the incentives align, or fail to, you can even pose econometric questions without using "heteroskedasticity" or "autocorrelation."
2 comments:
Agreed. CSS has previously linked to Cochrane's piece on the corporate tax incidence. He has a lovely quote about the math:
This is also a lovely little example for people who decry math in economics. At a verbal level, who knows? It seems plausible that a $1 tax cut could never raise wages by more than $1. Your head swims. A few lines of algebra later, and the argument is clear. You could never do this verbally.
There should be quotes around that second paragraph. My bad.
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