# Meyerson the Magnificently Mistaken

by Don Boudreaux on October 1, 2009

in Economics

Here’s a letter that I sent yesterday to the *Washington Post*:

Using a big floppy roller to paint a fine portrait creates only a mess as unintelligible as it is ugly. And so it is with Harold Meyerson’s attempt to portray modern market-oriented economics (“Economists for an Imaginary World,” Sept. 30).

For example, Mr. Meyerson’s suggestion that free-market economics relies uniquely and especially heavily upon elegant mathematics is flat-out wrong. Perhaps the greatest champion of the mathematical modeling of economic relationships is Paul Samuelson, who is no one’s idea of a free-marketeer. And perhaps the greatest free-market economist of the 20th century, F.A. Hayek, not only used almost no math in his own work, but he also literally wrote a book – *The Counter-Revolution of Science* (1952) – to warn economists of the severe limits of mathematics as a language for learning about, and discussing, a phenomenon as complex as a modern human economy.

Sincerely,

Donald J. Boudreaux

### Comments

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{ 51 comments }

Laying out a theory mathematically more readily permits evaluation of its assumptions. The problem is not the use of mathematics in economics per se, it is the lack of economists challenging ridiculous model assumptions.

One example is the keynesiac aggregates. Where are the economists to point out that government spending to raise demand actually bifurcates demand into one for the productive and another for the government-induced economy? Why are keynesiacs permitted to start with fundamentally flawed ideas and then build an elaborate mathematical edifice upon it?

Is it that only keynesiacs are proficient in mathematics? Are Austrians simply afraid of math?

Complex ideas may make for complex mathematics, but mathematics being nothing more than rational thinking regarding the relationship of quantities, there will always be a useful role for clarifying at least aspects of complex theories. If the assumptions are reasonable, so too will be the model.

So your solution to an oversimplified, unified aggregate is to… bifurcate it???? Dividing it in two doesn’t seem to me to address the fundamental aggregation problem that any reasonable person admits exists.

I hope you realize this is a silly representation anyway. Yes, in an introductory course you may talk in terms of big bolded capital letter aggregates. But in an actual Keynesian model you can have “i” differentiated firms and solve for whatever value of “i” you can dream up. The idea that because many people find it convenient to talk about aggregates like GDP implies that Keynesians don’t think in terms of micro-level variation is a persistent myth that never ceases to amaze me. At least we can agree on your last paragraph.

Daniel,

“Dividing it in two doesn’t seem to me to address the fundamental aggregation problem that any reasonable person admits exists.”

Sorry I need to catch up, what is the fundamental aggregation problem?

The demand caused by gov’t spending so you don’t need to divide demand?

Again I am asking truthfully with no tone in my words.

I’m sure there are lots of ways to explain it, but I just think of it as the fallacy of describing the behavior of an aggregate or collective and ignoring the fact that an aggregate in and of itself is not an active agent. Different agents that make up the aggregate respond to changes differently. So to use a recent example (the fiscal multiplier), someone who commits the aggregation fallacy may just assume that when a dollar of government money is spent, GDP goes up by a dollar. That’s a fallacy because (1.) some of that dollar of government spending may be borrowed – and could displace money that is invested elsewhere, or it could be taxed and in the absence of the tax it would be spent, or (2.) the dollar of government money may be inefficiently used, resulting in a smaller impact on GDP than it could otherwise, or a bunch of other potential reasons. Ignoring the fact that the behavior of aggregates reflects the cumulative behavior of all it’s constituent parts is a fallacy. In reality, these multipliers could be less than one or they could be more than one depending on the extent to which they crowd in or crowd out alternative investment and spending.

What bugs me is that some people won’t even accept an aggregate as a useful pedagogical strategy, or as a useful, if imperfect, summary statistic.

So why not divide demand like vikingvista says. Your explaination to me seems to agree with it. You’re saying in 1&2 that the gov’t maybe destroying wealth and in the long run destroying aggregate demand. Vikingvista (I think) was trying to divide demand in the form of which is productive and non-productive (gov’t spending). Not that the two divided parts make up the aggregate, its that the gov’t spending should not be apart of it.

I am not sure if I make any sense, but this is why I am here.

DK, you are tiring. When I publish my own General Theory, you’ll be the first to know.

Paul Samuelson notes that both Alfred Marshall and John Stuart Mill spoke “of the dangers involved in long chains of logical reasoning;” and he explains:

Marshall treated such chains as if their truth content was subject to radioactive decay and leakage—at the end of n propositions only half the truth was left, at the end of a chain of 2n propositions, only half of half the truth remained, and so forth in a geometric multiplier series converging to zero truth. (Samuelson 1952, 57, emphasis added)

Donald F. Gordon (1955, 160) said: “It is frustrating but nevertheless true that, where mathematics is most likely to be useful, the theory is least likely to be valid, while, where the theory is most likely to be true, complex deduction is generally not needed.” Using an example of a theory relating three distinct variables x, y, and z, Gordon reasoned: “Again, the relationship between x and y may be stable long enough for a shift along that function but not stable long enough for a shift along that function plus a subsequent shift along another [z]” (155).

A co-author and I have tested Gordon’s hypothesis and failed to refute.

“at the end of n propositions only half the truth was left”

That is a problem with complex ideas in general, not just mathematics. On the contrary, if a reasonable mathematical model can be formulated, then tautological mathematical relationships can significantly reduce the possibility of error. But, the model must be well-formulated.

Mathematics clarifies. It allows you to see more precisely what a person is trying to communicate. The subsequent manipulations and conclusions are almost always true, given the assumptions, since even keynesiacs tend to be reasonably good mathematicians.

Whether the keynesiac takes his assumption and writes a nonmathematical treatise, or lays it out symbolically, makes no difference. The concepts are the same.

My fear is that the sophists have made such extensive use of mathematics, that some people are becoming critical of mathematics.

Re: “My fear is that the sophists have made such extensive use of mathematics, that some people are becoming critical of mathematics.”

I have the same fear for science concerning AGW. I think it’s only a matter of time before the data finally throws the whole notion of AGW out the window forever, the problem I see is that when that happens, all those people that have so much time, money and personal reputation on the line for AGW will not just admit that they were duped by the politicians and rent seeking scientists, but they will blame all of science for “letting them down.” I think there might a a significant revolt against science when science doesn’t prove what they think is right.

Yes. That is the danger of politicization of science. It should be a part of a scientists ethic to NEVER advocate a political position regarding his research.

And to be fair, not all climate scientists are political activists. But too many are. They don’t realize the risk that creates for the reputation of science in general.

Another thing I want to point out too is that this and my fear on AGW, is caused by a basic mass ignorance of the scientific method.

People confuse “theory” and “hypothesis” all the time and in doing so seriously confuse the order in the scientific method. It happens all the time, especially from scientists. I’m constantly correcting my peers, when they say they have a “theory.” No I tell them, you have a hypothesis, we have to test it first to see if it is true, only then can you have a “theory” and even then it’s only valid until data comes back that contradicts it.

There is something of a continuum there, but people definitely don’t seem to have a good notion of the strength of evidence.

I have no beef with mathematics. But Gordon’s prediction (extending and refining Marshall) that there is a negative relation between mathematical complexity and resultant operational propositions remains unrefuted in my co-authored investigations into the matter.

“negative relation between mathematical complexity and resultant operational propositions”

There just isn’t enough information in what you said for me to interpret what you mean. Do you have a link to a paper?

I will say this: if the most complex mathematics is being used in the description of the least valid or meaningful economic theories, that cannot be a fault of either mathematics or mathematicians. It is the fault of economists.

Mathematics is not “rational thinking regarding the relationship of quantities,” although that’s included in mathematics. Many maths do not study quantity at all, and indeed were created precisely to avoid quantities.

Mathematics is distinguished by the axiomatic method, and is the study of axiomatic systems. Thus, math is linguistic. Mathematics differs from praxeology in two ways. (1) Math proceeds from undefined terms; praxeology begins with meaningful definitions. The definitions are either (a) a priori (a la Mises) or (b) radically empirical (a la Rothbard). It is one of the startling demosntratiosn of Rothbard that both Kantian and Empiricist epistemologies yield the saem body of economics. IMHO, this makes the theory quite strong. (2) Axiomatic systems, happily, have the property that valid grammatical derivations are guaranteed to be true in an model of the system. This is not true of the informal logical system of praxeology. Thus the need to start with meaningful definitions. In practice, we carve out a piece of an informal system and attempt to model it with a formal system. This allows us to reduce a partial praxeological model to syntax rules in a formal grammar. The limitations are obvious.

In any case, it is a great error to think maths are merely reasoning about quantities.

Nice post. And I didn’t know that about Rothbard.

BUT, the discovery that most of mathematics could be described by a set of axioms in set theory is a relatively recent (but monumental) development. Mathematics long precedes that. And at its core is the abstraction of quantity from observed groupings (2 ducks and 1 duck, 2 sticks and 1 stick, 2 fish and 1 fish ==> 2 and 1 ==> x + y). Even that is apparent in Cantor’s initial naive set theory, which was an introspective recognition of the conceptual apparatus of identification and differentiation for the purpose of grouping quantities of objects of intuition.

It is not a great error, but rather a recognition of math’s etymology. Of course what is derived from that basic origin is very rich and elaborate.

When I saw that article I hoped somehow you’d magically fail to read it… I knew it wasn’t likely

What I was most afraid of is that you’d hold the perpetually confused Meyerson up as an apologist for Keynes (who he spent a lot of time in the article talking about). Thank goodness you didn’t give him that much credit!

I know don’t you hate it when people start questioning Keynesian econ?

If I hated that I wouldn’t show up to Cafe Hayek

What I don’t like is having Meyerson come to the defense of Keynes. With friends like him…

Then you have to ask yourself, what about Keynes, attracts people like Meyerson. It’s like our argument sometimes, you argue that Keynes wanted to expand freedom, even if I concede that point to you, it still doesn’t change the fact that people use his econ to decrease freedoms by an ever expanding government.

RE: “even if I concede that point to you, it still doesn’t change the fact that people use his econ to decrease freedoms by an ever expanding government”

But if you conceded that point to me, you’d also have to concede that the people who use his econ to decrease freedoms aren’t really using his econ at all – they’re using a distortion of his econ. I’m not obligated to apologize for those sorts of mistakes.

“If mainstream economics doesn’t change, however, it may eventually face the worst of all possible fates: market failure. How many students want to spend their lives quantifying a world that doesn’t exist? ”

I’ve never wanted to return to school more! I’m studying for my GRE and saving money. Or maybe I should return to school to become a newspaper journalist.

Might as well take the GRE. It can only expand your options.

What is ironic is it will expand my options if I score well in the math. Looking at the average scores for entrance the verbal is not as important. It could be argued that today economist need to be able to express themselves better, but schools don’t require that.

And I hope you’ve taken a lot of math courses as well. At this point, GRE math scores are just a way to weed out applications that aren’t even worth looking at. Most departments have an average score of 780 or 800 on the math. At that point, you can’t differentiate people based on their GRE score and they rely on your transcript. Good GRE just gets your foot in the door – make sure you don’t stop there.

So you would say the econ grad departments are flooded with applicants and is very competitive and there are plenty who “want to spend their lives quantifying a world that doesn’t exist? ”

Okay, so, we all know that Harold Myerson is a complete idiot, but Don, you need to make a stronger argument than that!

It’s not saying much to give a non-randomized, highly biased sample of two to make your point.

One could, of course, point to free market economists like, say, my non-random sample of one in Milton Friedman (Who, of course, was a superb statistician also, developing the non-parametric Friedman test as well as Sequential Sampling) to validate Mr. Myerson, or, one could point to market hostile economists like Joseph Stiglitz whose mathematical work also warranted a Nobel Prize for demonstrating that the Fundamental Theorems of Welfare Economics are not how the real, information problematic economy works.

Bottom line, there is no relationship between positive mathematical training and normative belief in market economics.

Any economist worth his salt must be thoroughly trained in math to even become considered a real scholar, irrespective of his or her normative preferences for the appropriate role for market and government.

Mathematics has severe limits as a language for discussing a phenomenon as complex as a modern human economy, but Hayek is mistaken if he thinks that another language is less limited. vikingvista is right. Mathematics is as expressive as a language can be, and its precision is no vice. If you want to model the vagaries of a complex system mathematically, you can do that, but it’s still a complex system with vagaries. A proper mathematical formulation can express the vagaries, just as a less formal model can gloss over the complexities.

But you CAN paint a portrait with a roller brush.

(It just has to be a damned big portrait, and viewed from a distance…)

No one who read lewrockwell.com a few years ago can take this article seriously. The Miseans were calling the bubble a “bubble” all along, and frankly, they were much more prescient than the Hayekians at this site. Maybe, Lew Rockwell is always predicting the next depression, but he certainly hit the mark on this one.

You can’t keep our resident mathematical economists down. You can drive a stake through their hearts, and Count Kuehns, LimitedVista, and Indiana Jerk will still come popping up from the grave, mocking the laws of nature and common sense logic.

Ah dear DG. What did math ever do to you? Did it pick on you when you were little?

I have nothing against mathematics. What do you have against logic?

Please Dear DG. Please correct my logic.

I think he’s actually under the impression that Don is agreeing with him in this post. In reality Don is just saying that you shouldn’t make sweeping declarations about whether mathematical economics is always good or bad.

Which is ironic, given how sweeping dg’s declarations always are on this subject!!

Vikingvista wrote,

“Please Dear DG. Please correct my logic.”

It is illogical to lump non-quantitative relations into the same category with quantitative relations, and nullify the distinction between them.

And to those who cannot see the difference, I can only say that I see it, and regret that I cannot give sight to the blind.

“Illogical” or “inexact, and that inexactness should always be kept in mind when interpreting results”?

Sorry, Count old boy, buy you’re not going to drain me dry.

For example?

Vike asked for an example of lumping non-quantitative relations into the same category as quantitative relationships.

Jeff, above, wrote:

“Many maths do not study quantity at all, and indeed were created precisely to avoid quantities.”

And that’s what Daniel’s mathematical economics always came down to, and what mathematical economics must always come down to, counting without numbers and measuring without magnitudes. For the mathematical economists can never give you any actual examples of their alleged mathematical economics, ecconomics with actual numbers. All they can ever give you are symbolic allusions to actual numbers, or some isolated number, such as the number of dollars in circulation at a given point in time. But mathematics implies at least two numbers yielding a third, and that they cannot give you. Hence, “non-quantititative mathematics,” and a new priestcraft, with a new priesthood, in academic rather than ecclesiastical robes, and chanting in mathematics rather than Latin.

By the way, couldn’t get that reply function to accept this reply.

Jeff was taking a very shallow wade through the ambiguities. The abstractions that form mathematics are precisely abstractions from quantities. The relations are abstractions of relationships among quantities. Mathematics is THE discipline for thinking about quantities.The “counting without numbers and measuring without magnitudes” isn’t false. It is merely abstraction–the recognition of similarities and differences between observations. And it is abstraction so close to its concretes that it is prime facie true. How can you deny that a common characteristic of 2 feet, 2 dollars, 2 Euros, 2 fish, and 2 seconds, is accurately embodied in the concept of “2″? Would you deny that the quantitative relationships derived from “2″ are not precisely those observed in the collection of concretes from which it was abstracted?And whether you want to just think through the relationships internally, or describe them in written English, or express them in the well-developed symbolics of mathematics, makes no difference when it is the same concepts being communicated. If your thinking is rational, your conclusions will be the same. However, mathematics is a recommended language, since it is less ambiguous and may by virtue of the symbolic presentation reveal insights into the greater well-developed field of mathematics that you otherwise would not have seen.Mathematics is completely innocent of anything, in every possible context, in the same way that noncontradiction, identity, consciousness, and monitor you are looking at are innocent. They simply are.Now if you think some mathematical model of reality is false or unrealistic, it makes no sense for you to blame “mathematics”. If his model doesn’t work, there must be a REAL reason for it not working. Assuming his mathematical manipulations are correct, then there must be something in his implicit or explicit assumptions. At least the fact that he laid it out mathematically gives you a clearer picture of what he is claiming (provided you have sufficient mathematics proficiency), and therefore an easier task of identifying the mistakes.To complain THAT he laid it out mathematically is as meaningless as claiming that he laid it out in Latvian. You must find the misidentified concepts in his assumptions, or confess that you don’t really know why or if he is wrong.”can never give you any actual examples of their alleged mathematical economics, ecconomics with actual numbers”Maybe that is asking too much. Can your English descriptions come up with actual numbers? If not, then why would you hold a mathematical description to a different standard? Isn’t it useful to understand the abstract relationship between quantities? If not, then what exactly do your English-described concepts tell us that is useful?Errors of thought and sophistry are false thinking–regardless of how those thoughts are expressed.

Viking,

I sure can’t understand you in English, so why didn’t you try explaining all that to me in mathematics, if it’s such a superior language?

And why don’t we dispense with English altogether, and speak mathematics in everything, not just economics?

Vike,

I don’t think you understand how I really feel about you, so tell me how to say I love you in mathematics. And, while you’re at it, can’t stand you.

Vike,

I was in a hurry before, but can answer you with a little more care now.

You start out agreeing that there is no non-quantitative mathematics, that it is all about quantities. So where are the quantities in economics?

You talk about abstractions from them. But that is to presume the quantities to be abstracted from. Where are they?

Next, you say that mathematics is a superior language. Is that just in economics or in everything? Why in economics any more than anything else, or, if in everything, why don’t we drop English altogether, and speak only in mathematics?

You say that mathematics is innocent, and it makes no sense for me to blame it for its misuse.

Mathematics: I find you guilty of short-cuts, and sentence you to five years of hard labor on the rock pile, counting the rocks, one by one.

You said, “To complain THAT he laid it out mathematically is as meaningless as claiming that he laid it out in Latvian.”

And as meaningful.

You said, “You must find the misidentified concepts in his assumptions, or confess that you don’t really know why or if he is wrong.”

He has confused mathematical with logical concepts.

You asked, “Can your English descriptions come up with actual numbers? If not, then why would you hold a mathematical description to a different standard?”

I wouldn’t. I wouldn’t expect any language or method of description to come up with examples of something that didn’t exist.

You asked, “Isn’t it useful to understand the abstract relationship between quantities?”

Yes.

And then you asked, “If not, then what exactly do your English-described concepts tell us that is useful?”

Would you like an example?

You conclude: “Errors of thought and sophistry are false thinking–regardless of how those thoughts are expressed.”

You ought to know.

Yes there are some scientists that don’t politicize their science but that is moot considering where they get their funding from. The very nature of applying for grants makes it impossible to not get politicized sometimes.

You are making great sense – let me clarify what I said. It’s definitely a reasonable impulse for vikingvista to do that. What I found incredible was that he was upset about aggregating into one measure of demand, but he was totally fine with two measures of demand, as if two aggregates somehow avoided the problems associated with aggregation. In reality, a lot of new Keynesian models go much, much farther than even what he suggested and look at demand for an index of differentiated products – potentially infinite differentiated products, if you want.

I noted different ways that the government could destroy wealth. That doesn’t mean I think it always does. I would disagree with vikingvista’s a priori assumption that whatever government spends on is “nonproductive”. That’s ideology, not economics. Obviously anyone looking at issues of government spending needs to understand the efficiency problems associated with the government. But understanding that those problems exist is different from assuming government destroys wealth from the outset.

So new Keynesian models not only divide demand once, but “potentially infinite” times? Is this to look at each sector/product/industry, etc to find where the increase or decrease in demand is happening most?

At this point all I can say is “it depends”. In terms of pure theoretical modeling, it gets even higher resolution than the sectoral level. Models account for “i” different monopolistically competitive firms that can either respond identically (a less realistic assumption) or that can respond differently (a more realistic assumption). Empirically speaking, people who model the US economy definitely model down to the sub-sector level.

Aggregation always presents obstacles – but I think ultimately if you approach something empirically the obstacles are much more surmountable. So let’s say you’re modeling at the sub-sector level. That gets pretty refined: “women’s apparel”, “auto mechanics”, etc. You obviously still have an aggregation problem because even within those subsectors there is heterogeneity. But if you let the data speak for itself and observe how each subsector differentially reacts to something like a change in the interest rate, then you’ve essentially figured out how that heterogeneity impacts your result, even if you can’t actually model all the heterogeneous firms.

Models are never perfect – but they’re not as dumbed down as anti-Keynesians like to imagine they are. And they certainly are more accomodative to the problems associated with aggregation than vikingvista’s proposed solution.

I prefer “imperfectly quantifying a world that does exist”

Here are two links:

http://cms.bsu.edu/Academics/CollegesandDepartments/MCOB/Programs/Depts/Economics/ResearchandCommunityImpact/FacultyResearch/~/media/DepartmentalContent/MillerCollegeofBusiness/Econ/research/FacultyPapers/coelho2005sej.ashx

http://cms.bsu.edu/Academics/CollegesandDepartments/MCOB/Programs/Depts/Economics/ResearchandCommunityImpact/FacultyResearch/~/media/DepartmentalContent/MillerCollegeofBusiness/Econ/research/FacultyPapers/coelho2005sej.ashx

In case the links don’t work, the first is from the Southern Economic Journal, 71(3), 556-565.

The second was published in Econ Journal Watch, 5(1), 78-90.

Well good thing I didn’t concede anything.