Thursday, May 21, 2015

Stephen Williamson — Don't get mathy with me, or I'll give you a good shunning

Stephen Williamson gets back to Paul Romer.

Stephen Williamson: New Monetarist Economics
Don't get mathy with me, or I'll give you a good shunning
Stephen D. Williamson | Robert S. Brookings Distinguished Professor in Arts and Sciences, Washington University in St. Louis


John said...

Paul Romer: "...we put more weight on the views of people who have more status in the community and are recognized as having more expertise on the topic."

By that measure, a clerk at the Swiss Patent Office would have been dismissed as a nobody. And in economics, Lucas trumps Minsky and day of the week.

Don't forget, economics is apparently a science.

Brian Romanchuk said...

Williamson's article is good, but his comment about internally-consistent models not necessarily being good models tells us a lot about economist's grasp of mathematics.

A mathematical model is internally consistent, or it is not mathematics. Otherwise, it's just economist pretend mathematics.

John said...


Perhaps Williamson's comment could be read in the following way. There are many theories in science that are internally consistent but untrue or simply not taken seriously despite their internal consistency. Aether-type theories can be conjured up, but aren't believable, though they are not scientifically refutable.

I should imagine with a great deal of hard work Ptolemy's crystal spheres can be made consistent with nearly all astronomical observations, and certainly no less than the current reigning theories which are incapable of accounting for all observations. Indeed, within its own terms Ptolemaic theory is internally consistent to a very high level, but no one believes it.

It's difficult to tell what he meant. Economists aren't known for their verbal fluency. It seems to take away from the profundity of the mathematics they think is sophisticated but isn't.

Tom Hickey said...

Right, and it is very difficult to construct an internally consistent model that is built on the assumptions to model a modern economy realistically enough to produce causal explanation.

This is largely because the subject matter doesn't lend itself to quantification very well, since the subject matter of economics is psychological, cultural and institutional rather than physical and homogenous, as Keynes pointed out.

There is very little that is "natural" in the sense of either physical or invariant in economics. Economies are constructs based on human ingenuity and they all differ among each other as well as internally over time as human factors shift in response to the interaction of changing mindsets and external conditions.

The bottom line as I see it is assuming homo economics instead of homo socialis. This involves assuming methodological individualism rather than systems thinking. In addition, economic rationality and utility maximization are further assumed even though they are not supported by evidence from the sciences that study human behavior.

Furthermore, macro models assume general equilibrium and perfect competition, neither of which are realisitc. This results in a conceptual framework that favors mathematical modeling over realism.

Economics is simply not like natural science. If it were psychology and the social sciences would resemble natural science, too. The reason that they don't is that humans are not like atoms and groups of humans are not like molecules. Assuming they are is for methodological convenience to make the math tractable.

Keynes was fully capable of creating mathematical models and would have done so if he thought it possible. But his criticism of econometrics shows he did not think it possible to do.

Business figured this out and went with the case study approach rather than the grand theory approach of economics. Social scientists other than economists are more circumspect also, as are psychologists.

Not that these sciences don't use math. But they fit the math to what is being modeled instead of what is being modeled to the math, which is just a form of curve fitting and handwaving instead of actual scientific explanation.

John said...


That's very nicely put.

I'm always amazed when you hear modern economists seemingly dismiss Keynes for his lack of mathematical sophistication. Another case of the necessity of the history of economic thought being taught. So in their ignorance and hubris they overlook or are blind to the following:

1. Keynes was a far better mathematician than almost any economist in the history of the subject. He'd wipe the floor with any of today's narcissistic pseudo-mathematicians. As if constrained optimisation and a little calculus is sophisticated mathematics!

2. Keynes simply had a different vision of how to think about economics. You can argue whether he was right or wrong to think that, but it is unbelievably ignorant for them to somehow conclude that they are somehow more sophisticated than he was.

I note that Krugman's written an introduction to the General Theory. Funny that. Keynes thought that money was important and wrote a massive treatise on the subject. Meanwhile, the Keynesian Krugman thinks money is on the whole unimportant. Who better to write an introduction to Keynes? Maybe Krugman found a way to make money neutral using hyper-sophisticated tools like the oh-so-difficult constrained optimisation!

Tom Hickey said...

Assuming money neutrality is the killer. Once the non-neutraltiy of money is discarded, then econometric modeling gets a whole lot more complicated, especially when money is recognized as chiefly a legal institution under the control of the state, whose arrangements are subject to the will of the state.

Krugman only figured out that there is a key difference between the US, UK, Canada, Japan and Australia and the EZ after it was continually pointed out to him by MMTers and Post Keynesians. Most of the them haven't figured it out yet, or least admitted it if they have and they haven't changed their approach to accommodate it.

Marx called attention to the difference between C-M-C' and M-C-M' with the latter being the foundation of capitalism.

On the other hand, Say's followers believed that money was such a hot potato that firms immediately re-invested profits so that money flow is always instantly circular maintaining the circular flow of factors through the production-distribution-consumption cycle at equilibrium. Inflation is no problem for them either since prices and wages are flexible and reset to maintain real relationships constant. This got modified to approximation in the long run, e.g., because stickiness, but it was never abandoned. Hey, you can always address wage stickiness by creating a buffer stock of unemployed aka reserve army of the destitute and desperate.

Conventional economists think they are pros when they aren't even playing in the ballpark. Talk about taking your eye of the ball and "this is a football."

Keynes did his best to give them a way out without having to attribute M-C-M' to Marx, but they didn't pick up on it and are doubling down on C-M-C'.

It doesn't take a Sherlock Holmes here to realize, "It's elementary, my dear Watson."

Brian Romanchuk said...


Whether or not a model corresponds to reality is an open question. I have my doubts whether it can be done in the case of macroeconomics. But a mathematical model has to be internally consistent, or else it cannot be solved and it's meaningless. DSGE macro economists write down equations, wave their hands, and allegedly the solution appears. There's a huge gap between what they say the mathematical model is, and what they say the solution is.

Tom Hickey said...

If a model is not internally consistent, then anything follows from it.

Notice how such models are adjusted ad hoc to account ex post for stuff they missed ex ante, supposedly justifying the model.

Logically, that's just farce.

Tom Hickey said...

Consistency is the deductive constraint that produces logical necessity.

If the input is true and the model is valid deductively, then the conclusions are necessarily true as articulations of true premises. But logical validity-mathematical consistency cannot add semantical truth.

If facts and events are different from what the model represents, then either the observations were deficient or else the model is deficient because of the inputs or the logic.

That's the beauty of logic. It is pretty easy to check validity-consistency in terms of the formation and transformation rules.

Accurate observation and testing can be more problematic. This is an issue in economics which deals with aggregation that is estimated rather than counted and data that doesn't lend itself to rigorous experiment. even history is only a loose guide since context is seldom more than similar and often it's not even possible to determine essential aspects of context in the past.

The purpose of mathematics is to increase clarity by reducing ambiguity, precision by reducing inaccuracy, and economy by eliminating the non-essential and irrelevant.

Math is a powerful instrument when used properly as it logic in dealing with conceptual models. But used improperly they can lead astray inadvertently or be use sophistically to deceive by rhetoric and erudite obfustication.

No one is against logic and math but only their uncritical or improper use, which is either ignorant or unethical.

Calgacus said...

John:Keynes was a far better mathematician than almost any economist in the history of the subject.

Forget if I've posted this here before - but you might like this extract from Jack Schwartz's The Pernicious Influence of Mathematics on Science. Link to the whole essay at top. Schwartz could find no better source than Keynes to quote from; any mathematician can recognize in a couple of minutes that Keynes was one & would likely agree with your 1 & 2. I'm a little less grouchily critical of math than Schwartz, but he is worth reading.

Tom Hickey said...

Dave Marsay: "What seems to be needed is a greater appreciation of the proper role of mathematics in science and similar endeavours, emphasising its role in criticism as well as computation."

Alfred Marshall:

Balliol Croft, Cambridge
27. ii. 06
My dear Bowley,

I have not been able to lay my hands on any notes as to Mathematico-economics that would be of any use to you: and I have very indistinct memories of what I used to think on the subject. I never read mathematics now: in fact I have forgotten even how to integrate a good many things.

But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules — (1) Use mathematics as a short-hand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This last I did often.

I believe in Newton’s Principia Methods, because they carry so much of the ordinary mind with them. Mathematics used in a Fellowship thesis by a man who is not a mathematician by nature — and I have come across a good deal of that — seems to me an unmixed evil. And I think you should do all you can to prevent people from using Mathematics in cases in which the English language is as short as the Mathematical …

Your emptyhandedly,

Alfred Marshall

Tom Hickey said...

The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and, after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves. This is the nature of economic thinking. Any other way of applying our formal principles of thought (without which, however, we shall be lost in the wood) will lead us into error. It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section vi of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish. Too large a proportion of recent 'mathematical' economics are merely concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.

— John Maynard Keynes, The General Theory of Employment, Interest and Money
Chapter 21. The Theory of Prices, III

John said...

Brian, "But a mathematical model has to be internally consistent, or else it cannot be solved and it's meaningless."

That's absolutely right. But I would only add that is a necessary not sufficient condition. It is the very minimum required. It doesn't mean it's right. The experiments at CERN and the Plank satellite are starting to take apart many years of brilliantly constructed internally consistent theories.

In the case of economics, the DSGE models and nearly all other economic models may be internally consistent but they have no correspondence with the real world.

Calgacus, that's absolutely superb. Thank you so much for that. I just may print that out and frame it! Interesting that Keynes took the line of the heretics, like Einstein and Schrodinger, on quantum mechanics.

Tom, another fantastic quote. The history of economic thought can simply be done by quoting the greats! homo economicus will be hunted down and bludgeoned to death by homo philosophicus.

John said...


The more I learn about economics, the more terrible it is that Keynes never fully broke away from neoclassical economics. The revolution he initiated was profound, but imagine how much more profound it could have been had he been able to break away from old ideas. All revolutionaries are conservative to some extent, and Keynes was no different.

The Keynesian revolution continued through Minsky and others, but imagine Keynes ditching all that neoclassical junk.

Sometimes I wonder how much Marx Keynes read. He claims never to have read him or very little because it made his head hurt or something, but that doesn't seem plausible. Some of Keynes's writings seem distinctly Marxist...