Math and Economics

Perhaps because I went to Minnesota, and dynamic general equilibrium and modeling in general were emphasized, I still feel this is the right approach. Creating computable general equilibrium models has been a challenge because they are so difficult to compute. For that reason, one could argue that nothing much has come from that research. But eventually, these computational hurdles will become less steep and economists will be do some really interesting modeling.

If you look at some of the most important results of the optimal tax literature, none of that would be understandable without a strong math background. For example, the Diamond-Mirrles Theorem that says we should not tax intermediate goods or the Chamley Theorem which says we should not tax investment, have both had an impact on the tax code. Better modeling might allow us to experiement more with the tax code to see the impact of taxes and avoid the bad ones.

I have a BS in economics, and I have to admit that I do have a heavy bias toward mathematical models: I like math, I’m decent at it, and I think it’s generally pretty useful. However, I’m interested primarily in areas of economics where you mention that mathematical models do very well, namely international trade and financial markets. I think everyone should be required to understand calculus and theory at some basic level just for the sake of general knowledge, but I don’t see any reason why those interested in Economic History, Law and Economics, or other areas of the discipline should be subjected to that sort of hazing.

I’m hoping to persue a doctorate in a few years, and I think I’m much more likely to succeed in a program that has mathematical requirements but not to an insane extent. In all likelihood, I’ll persue something in the field of Law and Econ because I’m interested in those issues as well and I think there are enough trade theorists out there already.

I’m finding myself increasingly drawn to looking at programs like the one at GMU, for instance, that don’t seem to place as heavy an emphasis on high-level mathematics. I like math, but I don’t really want to be tortured with it.

Hayek’s mid 50s book The Counter Revolution of Science said much the same thing. He was concerned that the seeming precision of math in economics would lead to the wrong focus.

At a lunch recently I sat with three owners of business economics shops and it seems each had a very similiar pattern of employees although their firms sold very different products. They had a bimodal distribution of very senior — old, in one case a 72 year old woman — that really knew the nuts and bolts of the industries they covered.
The other group of employees were young hotshots that really knew the math. The combination of these two types working together seemed to generate very good results.

The preference for math over “Learning” economics may have something to do with personality. Some personalities prefer the abstract, others the practical. I earned an MA in Managerial Econ, which dodged heavy math requirements, such as advanced calculus, but introduced applied econometrics. Since I have a practical bent, I ate up the applied econometrics. The mathermatical approach has adequately demonstrated its failures. Real economists need sociology, history, phychology, etc., a whole range of tools, in order to derive economic models that correspond with the real world. We can test those models with applied econometrics. A good example might be the use of structural equation modeling by sociologists. It’s a fantastic statistical tool for understanding the structure of relationships and causality. As far as I know, no one in economics uses it. But it would be great for validating such econ theories as the Austrian business cycle.

I am currently in my first year in the PhD program at GMU and I am constantly amazed/dismayed at how many highly esteemed economists spend their entire careers creating incredibly elegant mathematical models that are neither applicable to reality nor truly add to mankind’s understanding of human action.

I was fortunate enough to acquire an MS in Operations Research a few years ago and my full time job requires the extensive use of these skills, so I have been able to achieve a certain amount of mathematical competence. I have also gained an immense understanding of the limitations of mathematical models. The extended order of our society is an amazingly complex system of billions of interactions between thinking, feeling heterogeneous individuals that do not always act as predicted. A model that could accurately forecast what willful human beings would actually do would be prohibitively complex, at least until economists achieve omniscience (mainly because the economist would need to be privy to the particular knowlege of each market participant, in order to “guess” what he would do). But simple models, with less predictive power, do not/cannot tell us anything we do not already know (because the theory is already built into the assumptions, in other words, the outcome can be deduced from the assumptions – why do you need the model?).

I am a firm believer that all models are wrong, but some are useful. I try to create useful mathematical models every day at work. However, when the assumptions that economists make are geared towards making the math more tractible, as opposed to making the economic theory more credible (read: representative agent, ge, etc) I wonder if many economic models are useful at all.

A Soldier does not go to War without his rifle. Math is important to Economics, but Samuelson may have given it too much impetus. An Economist needs the final Readouts, and need to be determine whether a Model is constructed properly; but Analysis of the Data is in itself a Voodoo craft. lgl

I came to this post from the Carnival of the Capitalists, over at blogcritics.org. So, yes, I’m a bit late.

Economics has been called the ‘dismal science’, but if there is a trend for allowing PhDs in Economics without mathematics, then the word ‘science’ has to be scrapped.

I have a Master’s degree in mechanical engineering. A stack of my courses in different branches of maths is taller than me. The point of the mathematics and the formulas is to describe and calculate what is possible and what not. There are newer branches of engineering where the description and calculation methods are still sketchy. So we still have software projects that go hopelessly wrong even when everybody thinks it’s a routine project and while all available means are used. But when a routine structural or mechanical engineering project fails, you will not expect it to be because the mathematics cannot accurately describe the physical part of the project. Let’s not talk about computer software, but do you expect the building you’re sitting in to collapse?

However, I cannot survive on calculations alone. To see how critical the non-math parts of my work are, read ‘The Design of Everyday Things’ by Donald Norman (about usability) or ‘To Engineer is Human’ by Henry Petrosky (about engineering error and safety). No math required.

I can expect to exchange numbers and drawings with the technical people at a customer’s factory. There might be discussions about which technical standards are applicable. My calculations might be looked over very carefully.

But for the man in the street? The most engineered items ordinary people come into contact with are cars and airplanes. Have you ever questioned the calculations for a car? Will you step on an aircraft built by “engineers” who consider mathematics irrelevant to what they do?

And what about economics? My oldest economics book with ‘real’ formulas is ‘The Theory of Political Economy’ by Williams Stanley Jevons, dating back to 1888. There’s nothing similar in Smith’s ‘Wealth of Nations’ or Ricardo’s ‘On the Principles of Political Economy and Taxation’. So the economists have only been using maths for about 120 years. Maths for engineers stretches back 2000 years. And a lot of maths that is now available was developed to describe the physics that form the core of structural and mechanical engineering.

When you question the use of maths for economics, you’re telling me that either the maths are insufficient to describe or solve the problem, or that you don’t like the implications of the calculation results.

If the available maths are insufficient, who will develop better maths specifically tuned to the problem? It can only be people highly skilled in maths who know the problem inside out – so you need Economics PhDs with lots of mathematical knowledge. Meanwhile for some economics problems the description and the solution is still very incomplete. Can’t be helped yet.

If you don’t like the implications of the calculation results, you have to call this by its real name : politics.

And what of those who can’t handle the math? Too bad. They’ll have to call themselves politicians, pundits, opinion makers, … – anything but economists.

Engineers face this problem too. We can build nuclear powerplants, or road cars that reach 300 miles per hour. Do we want to? Are we permitted to? People come to us with answers to these questions, and while we can accept their answers, we will not call those people engineers. Why should economists have a different attitude?