*Lynne Kiesling*

Steven Postrel is guest-blogging at Organizations and Markets. Steve teaches at the Cox School of Business at Southern Methodist University (and also happens to be Mr. Virginia Postrel). I look forward to his contributions to O&M!

Steve’s first guest post tackles the question of “physics envy” in economics and the use of mathematical tools in economics. His opening statement captures some things that I myself have said at various points:

We often hear (sometimes on this blog) that mainstream economics suffers from an excess of mathematical modeling. Supposedly, math is distracting, or misleading, or limits the questions one can study. Occasionally it is asserted that math serves the purpose of disguising the triviality of one’s thoughts, or that it serves as a guild’s protectionist barrier against the worthy but unschooled.

He (and the commenters on the post) then proceed to discuss what I think is an important part of the question: what tools provide clarity and usefulness in understanding the ideas we are exploring? Like any other specialized tool, mathematical models can provide clarity and be useful (although as the statistician George Box said, all models are wrong, but some are useful). For me the skepticism I have about formal, mathematical economic theory is more about whether or not the tail wags the dog. In other words, have we become so enamoured of our tools that we innovate them and focus on them, and then try to drum up economic questions and problems of human action to which to apply them?

I fear that when we let our techniques and our tools drive the types of questions that it is considered acceptable to answer, because only certain methodologies are acceptable (by which I mean publishable in the major journals), that we lose the ability to understand problems for which mathematical tools do not provide as much clarity as other tools (remember, people, we’re economists, so even when it comes to choosing tools we want to bear in mind opportunity cost!).

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I think the problem with modeling is multifold:

What is your data? Where did you get it from? How was it collected? How have you modified it before analysis (got rid of outliers, etc.).

Then you get into the data analysis itself. What statistical tools did you use? Once you get beyond simple linear regression, the tools can start influencing the model. Yeah, you got a great fit when you used a polynomial model instead of linear regression, for example, but does it make any sense whatsoever to fit the data that way? Can you extrapolate from such a model?

This is not just an issue with economics. Any field that uses modeling has this issue. What boundary conditions did you apply? Do they make sense?

I think that, a lot of times, KISS is a good philosophy. Guys like Steve Levitt violate it with regularity. I’ve downloaded some of his papers and couldn’t make heads or tails of what he was doing.

I think that he gets away with this because he writes a great story about what the data is saying, and few people can look at the data and come up with any story at all.

“(although as the statistician George Box said, all models are wrong, but some are useful).”

Perhaps Box and the AGW “affirmers” should have a conversation about his work.

Ed,

What’s AGW?

Buzzcut,

I was talking about theory models, not statistical models and their associated data and specification issues.

Lynne,

Abiogenic Global Warming – as in, we are responsible. AGW “affirmers” are the opposite of AGW “deniers” (who are held in great contempt by the “climatological consensus”).

My point was that Box’ assessment applies to climate change models as well.

Lynne,

Yeah, I realized that after I read the referenced blog.

Theory models are the most unscientific aspect of economics. Yeah, physicists use math models to describe physical processes (F=ma, for example). But every single math model has been verified by experimental data (except perhaps for some real advanced stuff in particle physics).

Is that the case in economics? Maybe to a certain extent, but you can’t say that every single math model has been verified by experimental data. Not even close.

Economics is not a hard science like physics. It’s not an applied science like engineering. It is a social science, like sociology or anthropology. If that’s the case, why do economics professors haze their grad students with all the math? Why is graduate economics taught any differently than graduate political science, for example?

Why would mathematical statements need experimental support while non-mathematical statements wouldn’t? I don’t see what the linkage is. If I make the same statement in non-mathemenatical language, the conditions of proof should not change.

And why would you need an experimental test of the formula for compound interest? That would be dopey.

The easiest non-econ example of a good mathematical theory that applies to the real world and where experimental testing misses the point is Shannon’s communication theory. The whole thing is derived from first principles and applies to the real world. Of course, that is pretty much a best-case scenario. The reason why it works so well without a need for experimentation is because the mapping between the assumptions of the theory and the real world are sharp, clear, and one-to-one. We rarely can do that in economics nearly so well. Some of the arbitrage stuff in finance, maybe.

Why would mathematical statements need experimental support while non-mathematical statements wouldn’t? I don’t see what the linkage is. If I make the same statement in non-mathemenatical language, the conditions of proof should not change.

And why would you need an experimental test of the formula for compound interest? That would be dopey.

The easiest non-econ example of a good mathematical theory that applies to the real world and where experimental testing misses the point is Shannon’s communication theory. The whole thing is derived from first principles and applies to the real world. Of course, that is pretty much a best-case scenario. The reason why it works so well without a need for experimentation is because the mapping between the assumptions of the theory and the real world are sharp, clear, and one-to-one. We rarely can do that in economics nearly so well. Some of the arbitrage stuff in finance, maybe.

>>Why would mathematical statements need experimental support while non-mathematical statements wouldn’t?

I never said that they wouldn’t. But math seems more rigorous.

Isn’t “freakonomics” nothing more than making “non-mathematical statements” and backing it up with statistical analysis of datasets?

>>And why would you need an experimental test of the formula for compound interest?

What do you mean? Compound interest can easily be verified by experiment. In fact, you verify it every time you make a mortgage payment or a savings deposit.

Too much maths spoil the spirit of economics, for example, Prof.Debreu’s “Theory of Value”.

Too much maths spoil the spirit of economics, for example, Prof.Debreu’s “Theory of Value”.

Buzzcut writes: “Yeah, physicists use math models to describe physical processes (F=ma, for example). But every single math model has been verified by experimental data (except perhaps for some real advanced stuff in particle physics).”

Um, no.

Consider http://en.wikipedia.org/wiki/Density_functional_theory, a model I learned a bit about when I was studying chemistry. More or less DFT removes some hard-to-compute terms out of the more fundamentally correct calculation, and approximates them with some other mathematical expressions whose virtues are that they have some similar properties and are much easier to calculate. The model often does give usefully accurate results, so if by “verified” you mean “it turned out to be a very good model for cases I, II, III, VII, and VIII, then it’s “verified”; but then you also happen to be speaking your own private language. We only imperfectly understand in which cases the model will give usefully accurate results instead of totally misleading ones: if that level of “verified” is all that you require of a model, then haven’t you set the bar so low that a very large proportion of economics models (or, stretching a bit, astrological models:-) meet your requirements?

I’m not trying to say DFT is bad, either: people do lots of good chemistry and solid state physics with it. But it’s a sufficiently fiddly model that you need to be quite careful about when it applies, which reminds me more of economics than it reminds me of your idealized vision of a physics where every model is rigorously verified.

I would criticize with economists not so much for too much math as for sometimes falling in love with mathmodel-able stuff so much that they look for their keys only under the lightpost. Things like corruption and lawlessness and insecurity are hard to model, but http://en.wikipedia.org/wiki/Hernando_de_Soto_(economist) has built a career hammering on how huge they are in the real world. People who model a country’s economy in terms of nice smooth numerical statistics like money supply and exports and interest rates without including harder-to-measure stuff don’t seem mathematically sophisticated to me, they seem like doctors building theories of human health based solely on temperature and blood pressure. E.g., any model of the Great Depression which doesn’t have any term which corresponds to far (2%? 11%?) along the USA1920-to-Zimbabwe2006 axis the New Deal pushed the US, and how that affected performance, seems suspect to me. Brad DeLong is a smart guy with a Berkeley professorship, but that doesn’t make his 0% the right answer, just (granting that his politics don’t color his favorable economic analysis of FDR) the answer of an economist who likes to exclude hard-to-model terms not because they’re negligible but because they’re hard to model.

Physicists often seem to be better about that, but I think that’s largely because they can work with clean systems where they can arrange for only a few nice modelable terms to be nonnegligible. Given a fixed messy real-world physical problem which can only be analyzed by approximation and whose results are politically charged, even physics throws up things like Sagan’s analysis of nuclear winter (and, I’m guessing about what lies behind top-secrecy, Teller’s analysis of xray lasers too).

Buzzcut writes: “Yeah, physicists use math models to describe physical processes (F=ma, for example). But every single math model has been verified by experimental data (except perhaps for some real advanced stuff in particle physics).”

Um, no.

Consider http://en.wikipedia.org/wiki/Density_functional_theory, a model I learned a bit about when I was studying chemistry. More or less DFT removes some hard-to-compute terms out of the more fundamentally correct calculation, and approximates them with some other mathematical expressions whose virtues are that they have some similar properties and are much easier to calculate. The model often does give usefully accurate results, so if by “verified” you mean “it turned out to be a very good model for cases I, II, III, VII, and VIII, then it’s “verified”; but then you also happen to be speaking your own private language. We only imperfectly understand in which cases the model will give usefully accurate results instead of totally misleading ones: if that level of “verified” is all that you require of a model, then haven’t you set the bar so low that a very large proportion of economics models (or, stretching a bit, astrological models:-) meet your requirements?

I’m not trying to say DFT is bad, either: people do lots of good chemistry and solid state physics with it. But it’s a sufficiently fiddly model that you need to be quite careful about when it applies, which reminds me more of economics than it reminds me of your idealized vision of a physics where every model is rigorously verified.

I would criticize with economists not so much for too much math as for sometimes falling in love with mathmodel-able stuff so much that they look for their keys only under the lightpost. Things like corruption and lawlessness and insecurity are hard to model, but http://en.wikipedia.org/wiki/Hernando_de_Soto_(economist) has built a career hammering on how huge they are in the real world. People who model a country’s economy in terms of nice smooth numerical statistics like money supply and exports and interest rates without including harder-to-measure stuff don’t seem mathematically sophisticated to me, they seem like doctors building theories of human health based solely on temperature and blood pressure. E.g., any model of the Great Depression which doesn’t have any term which corresponds to far (2%? 11%?) along the USA1920-to-Zimbabwe2006 axis the New Deal pushed the US, and how that affected performance, seems suspect to me. Brad DeLong is a smart guy with a Berkeley professorship, but that doesn’t make his 0% the right answer, just (granting that his politics don’t color his favorable economic analysis of FDR) the answer of an economist who likes to exclude hard-to-model terms not because they’re negligible but because they’re hard to model.

Physicists often seem to be better about that, but I think that’s largely because they can work with clean systems where they can arrange for only a few nice modelable terms to be nonnegligible. Given a fixed messy real-world physical problem which can only be analyzed by approximation and whose results are politically charged, even physics throws up things like Sagan’s analysis of nuclear winter (and, I’m guessing about what lies behind top-secrecy, Teller’s analysis of xray lasers too).

I’ll say it again:

“But every single math model has been verified by experimental data (except perhaps for some real advanced stuff in particle physics).”

I think DFT would fit into the disclaimer at the end of my statement. And at least chemistry does have an equation that better describes reality, even if it is much more difficult to calculate.

Anyway, that still doesn’t address my question as to why economics is any different than the other social sciences. The top school for anthropology doesn’t require 800 on the Math GRE to get in. Why does economics?

I’ll say it again:

“But every single math model has been verified by experimental data (except perhaps for some real advanced stuff in particle physics).”

I think DFT would fit into the disclaimer at the end of my statement. And at least chemistry does have an equation that better describes reality, even if it is much more difficult to calculate.

Anyway, that still doesn’t address my question as to why economics is any different than the other social sciences. The top school for anthropology doesn’t require 800 on the Math GRE to get in. Why does economics?

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