by From Lars Syll Many American undergraduates in Economics interested in doing a Ph.D. are surprised to learn that the first year of an Econ Ph.D. feels much more like entering a Ph.D. in solving mathematical models by hand than it does with learning economics. Typically, there is very little reading or writing involved, but loads and loads of fast algebra is required. Why is it like this? The first reason is that mathematical models are useful … A second beneficial reason is signalling. This reason is not to be discounted given the paramount importance of signalling in all walks of life … Smart people do math. Even smarter people do even more complicated-looking math … A third reason to use math is that it is easy to use math to trick people. Often, if you make your assumptions in plain
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from Lars Syll
Many American undergraduates in Economics interested in doing a Ph.D. are surprised to learn that the first year of an Econ Ph.D. feels much more like entering a Ph.D. in solving mathematical models by hand than it does with learning economics. Typically, there is very little reading or writing involved, but loads and loads of fast algebra is required. Why is it like this?
The first reason is that mathematical models are useful …
A second beneficial reason is signalling. This reason is not to be discounted given the paramount importance of signalling in all walks of life … Smart people do math. Even smarter people do even more complicated-looking math …
A third reason to use math is that it is easy to use math to trick people. Often, if you make your assumptions in plain English, they will sound ridiculous. But if you couch them in terms of equations, integrals, and matrices, they will appear more sophisticated, and the unrealism of the assumptions may not be obvious, even to people with Ph.D.’s from places like Harvard and Stanford, or to editors at top theory journals such as Econometrica. A particularly informative example is the Malthusian model proposed by Acemoglu, Johnson, and Robinson in the 2001 version of their “Reversal of Fortune” paper …
What’s interesting about the Acemoglu et al. Malthusian model is that they take the same basic assumptions, assign a particular functional form to how population growth is influenced by income, and arrive at the conclusion that population density (which is proportional to technology) will be proportional to income …
The crucial assumption, unstated in words but there in greek letters for anyone to see, was that income affects the level of population, but not the growth rate in population. Stated differently, this assumption means that a handful of individuals could and would out-reproduce the whole of China and India combined if they had the same level of income … Obviously, this is quite a ridiculous assumption when stated in plain language. A population can grow by, at most, a few percent per year. 100 people can’t have 3 million offspring. What this model does successfully is reveal how cloaking an unrealistic assumption in terms of mathematics can make said assumption very hard to detect, even by tenured economics professors at places like MIT. Math in this case is used as little more than a literary device designed to fool the feebleminded …
Given that this paper then formed part of the basis of Acemoglu’s Clark medal, I think we can safely conclude that people are very susceptible to bullshit when written in equations …
Given the importance of signaling in all walks of life, and given the power of math, not just to illuminate and to signal, but also to trick, confuse, and bewilder, it thus makes perfect sense that roughly 99% of the core training in an economics Ph.D. is in fact in math rather than economics.
Indeed.
No, there is nothing wrong with mathematics per se.
No, there is nothing wrong with applying mathematics to economics.
Mathematics is one valuable tool among other valuable tools for understanding and explaining things in economics.
What is, however, totally wrong, are the utterly simplistic beliefs that
• “math is the only valid tool”
• “math is always and everywhere self-evidently applicable”
• “math is all that really counts”
• “if it’s not in math, it’s not really economics”
• “almost everything can be adequately understood and analyzed with math”
One must, of course, beware of expecting from this method more than it can give. Out of the crucible of calculation comes not an atom more truth than was put in. The assumptions being hypothetical, the results obviously cannot claim more than a vey limited validity. The mathematical expression ought to facilitate the argument, clarify the results, and so guard against possible faults of reasoning — that is all.
It is, by the way, evident that the economic aspects must be the determining ones everywhere: economic truth must never be sacrificed to the desire for mathematical elegance.
Neoclassical mainstream economists have wanted to use their hammer, and so have decided to pretend that the world looks like a nail. Pretending that uncertainty can be reduced to risk and that all activities, relations, processes and events can be adequately converted to pure numbers, have only contributed to making economics irrelevant and powerless when confronting real-world financial crises and economic havoc.
How do we put an end to this intellectual cataclysm? How do we re-establish credence and trust in economics as a science? Five changes are absolutely decisive.
(1) Stop pretending that we have exact and rigorous answers on everything. Because we don’t. We build models and theories and tell people that we can calculate and foresee the future. But we do this based on mathematical and statistical assumptions that often have little or nothing to do with reality. By pretending that there is no really important difference between model and reality we lull people into thinking that we have things under control. We haven’t! This false feeling of security was one of the factors that contributed to the financial crisis of 2008.
(2) Stop the childish and exaggerated belief in mathematics giving answers to important economic questions. Mathematics gives exact answers to exact questions. But the relevant and interesting questions we face in the economic realm are rarely of that kind. Questions like “Is 2 + 2 = 4?” are never posed in real economies. Instead of a fundamentally misplaced reliance on abstract mathematical-deductive-axiomatic models having anything of substance to contribute to our knowledge of real economies, it would be far better if we pursued “thicker” models and relevant empirical studies and observations.
(3) Stop pretending that there are laws in economics. There are no universal laws in economics. Economies are not like planetary systems or physics labs. The most we can aspire to in real economies is establishing possible tendencies with varying degrees of generalizability.
(4) Stop treating other social sciences as poor relations. Economics has long suffered from hubris. A more broad-minded and multifarious science would enrich today’s altogether too autistic economics.
(5) Stop building models and making forecasts of the future based on totally unreal micro-founded macromodels with intertemporally optimizing robot-like representative actors equipped with rational expectations. This is pure nonsense. We have to build our models on assumptions that are not so blatantly in contradiction to reality. Assuming that people are green and come from Mars is not a good – not even as a ‘successive approximation’ – modelling strategy.