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Wednesday, August 2, 2017


I have for several days wanted to return to writing about Paris in response to the thunderous demand [well, actually one comment and two emails, but I have very acute hearing].  However, before I do, let me say just a word about mathematics and economics, which has been the subject of several very interesting lengthy comments.

I think it is a mistake to ask whether economists should use mathematics.  That is like asking whether an electrician should use a Philips screwdriver.  The obvious reply is, For what?  The really interesting foundational questions in economics can never be answered by introducing more sophisticated mathematical techniques, fun though they are.  Before all else, one must decide what questions economics should be trying to answer.

The watershed transformation in economic theory is usually identified as the so-called Triple Revolution, or Marginalist Revolution, of the 1870’s, which is to say the work done independently and more or less simultaneously by Jevons in England, Walras in France, and Menger in Austria.  This complete transformation in academic economics was characterized by the introduction of the Differential Calculus, which made it possible to prove all manner of nifty theorems about consumer choice and price determination in a capitalist market.

It is easy and natural to suppose that the marginalist revolution was all about using more sophisticated mathematics, but that is, in my opinion, a complete mistake.  What actually happened in the 1870’s is that economists by and large stopped asking one set of questions and started asking a different set of questions.

There are two possible explanations for the decision of academic economists to change the questions they asked.  The first is that the new mathematical tools were so powerful, so flashy, such sheer fun that any really smart person interested in economics would naturally gravitate to them.  The second is that the old questions were rather uncomfortable, inasmuch as the answers clearly indicated that there was something seriously rotten about the state of things in nineteenth century capitalist Europe.

What were the old questions that economists asked before the 1870’s, and what were the new questions they started to ask afterward?  There were two questions that the old economists asked.  They were asked by Adam Smith, they were asked by David Ricardo, and they were asked by Karl Marx.  They were also asked by all the lesser lights who, together with the leading lights, defined the field known as Political Economy.  The first question was: How is the annual output of a nation divided among the three great classes of society, the Landowners, the Entrepreneurs, and the Workers?  The second question was: What are the conditions of economic growth, and what are the obstacles to growth?  The answers changed over time, of course, and in the work of Marx were profoundly complicated by the introduction of the notions of mystification, false consciousness, and ideological rationalization, but the questions remained the same.

The new economists asked completely different questions, and when they even tried to answer the old questions, their answers, tricked out in fancy math, were transparently ideological rationalizations.  The best summary statement of the new questions can be found in a classic 1932 work by Lord Lionel Robbins, An Essay on the Nature and Significance of Economic Science [notice the term “science.”]  “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.”

Compare this question with the first question of the classical Political Economists.  The classical question presupposes that society is divided economically into classes and thus virtually compels us to recognize that the interests of the classes are antagonistic to one another, inasmuch as what is appropriated each year by one class is thereby unavailable to be appropriated by the other classes.  The new question of “Economic Science” presents the subject as a purely technical study of alternative inputs into production, the goal being to maximize efficiency.

For a variety of historical reasons, it appeared for quite some time that the old Political Economy was just a gentlemanly reflection on the human condition while the new Economics was SCIENCE complete with differential equations and such like.  But in the 1960’s. ‘70’s, and ‘80’s a number of clued up lefty mathematical economists recast the old story in nice, shiny equations, so that it became clear what the real difference between the two traditions was.

There is nothing wrong with mathematics in economics.  As I said, what matters is For What?


Ian J. Seda Irizarry said...

Hi Professor,

Given the previous mentions of Bowles and Gintis within this general topic of math and econ, I thought readers of the blog would be interested in reading an article that will be published in the Cambridge Journal of Economics "History matters: on the mystifying appeal of Bowles and Gintis". I'm hoping for a response from B&G

You can read the abstract here:

If anybody is interested in the pdf file of the article, send me an email to It would be interesting to see peoples' opinions on this appraisal of their work.

JKH said...

More fundamental than "for what" is the question of what kind of mathematics.

To the degree that Keynes invented macroeconomics, it was because he understood the role of accounting logic in relevant fallacies of composition. That's a kind of algebra.

The profession remains mired in approaching this question through the somewhat useless frivolity of differential equations.

Ed Barreras said...

Pssst. (From the APA style guide.) Apostrophes are generally used in contractions and to indicate the possessive case, but they are not used to form plurals of numbers and abbreviations in APA Style. For instance, writing “the 1960's” when referring to that entire decade is incorrect; instead, one should write “the 1960s."

Jerry Brown said...

If it was my comment about the French making you eat the snails (even if they were your neighbors) is making you want to write about your ordeal, I truly apologize. But I am sure whatever you write will be interesting, so I hope you do. But I do request that at some point you might return to your very interesting post about morality and international affairs at

Today, Brian Romanchuk wrote in a comment on his blog post "Decision makers need some wise men to come up with a justification for a policy decision with a lot of mumbo-jumbo to stop the rank and file from questioning the decision. Economists step into that social role admirably."
which makes me think of your post as economists using math often as a ways to come up with the mumbo -jumbo. If you want to read the context of this it is here

If it is any comfort, I don't mind where you use apostrophe's or not even if others do :)

Jerry Brown said...

One of those rare times I disagree with JKH- 'what are you trying to do' is more fundamental in my understanding although 'what kind of tool works best' comes right after when you are talking about using any tool. At least from this carpenter's perspective.

F Lengyel said...

Perhaps economics is still early enough in its development that "[t]he really interesting foundational questions in economics can never be answered by introducing more sophisticated mathematical techniques, fun though they are." At least in some disciplines, there are questions that cannot be expressed without some sophisticated mathematics. One would be loathe to foreclose this possibility--but I suppose the foundational questions are definitionally the ones for which this isn't true.

It is true that much of contemporary mathematical economics has been careful to leave questions of ownership unanalyzed. One would like to know the cost of defending property rights, and the extent to which corporate tax avoidance shifts this burden onto the consumer. My guess is that the externality imposed on the public approaches 100% (for some well-connected firms anyway, with the average not being that far off). The business of deriving the ought of just desert from the is of economic theory seems to be an industry--this is partly the reason why I found Gintis's remarks on the The Fundamental Theorem of Welfare Economics from the first edition of Game Theory Evolving interesting. Around 2008 I asked an Israeli game theorist (the author of a standard in the subject) about his take on the economic crisis. He said that political economics concerned the control of resources, and suggested that it wouldn't be productive for a game theorist to say anything about them. I suspect he meant that such investigations would be career limiting.

I look forward to reading the critical article on Bowles and Gintis. I'm no fan of methodological individualism myself.

JKH said...

thanks Jerry

you are right

I should have qualified it

something like this -

Considering the problem of conceptualizing macroeconomics, what kind of mathematics is fundamental to that task

And I would say that the GT of Keynes is replete with the power of accounting logic as the required fundamental framing

He invented macroeconomic accounting in effect - as the required tool for macroeconomic thinking - the critical thing being consistent algebraic closure in aggregation

His discussion of the difference between saving and finance is an example of this

So is the paradox of thrift

And so on

Interestingly, Keynes was a mathematician before (in effect) he was an economist

That has a lot to do with it

The use of differential equations is secondary to this framing

AXEC / E.K-H said...

Economics, philosophy, and mathematics
Comment on Robert Paul Wolff on ‘Mathematics in economics’

The ancient Greeks started science with the distinction between doxa (= opinion) and episteme (= knowledge). Scientific knowledge is well-defined by material and formal consistency.

Economics is a failed science, that is, there is NO knowledge that satisfies scientific criteria. The four main approaches ― Walrasianism, Keynesianism, Marxianism, Austrianism ― are mutually contradictory, axiomatically false, materially/formally inconsistent, and all got profit wrong.

In the beginning, there was Political Economy. J. S. Mill defined it clearly as a social science: “The fundamental problem, therefore, of the social science, is to find the laws according to which any state of society produces the state which succeeds it and takes it place.” Or, a bit more specific with regard to economics: “The science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object.”

Economics started as a hodgepodge of sociology, history, folk psychology, and folk philosophy, which came under the heading of utilitarianism.

Classical Political Economy was carried one step further with methodological individualism: “It is a touchstone of accepted economics that all explanations must run in terms of the actions and reactions of individuals. Our behavior in judging economic research, in peer review of papers and research, and in promotions, includes the criterion that in principle the behavior we explain and the policies we propose are explicable in terms of individuals, not of other social categories.” (Arrow)

Orthodox economics is built upon the Walrasian axioms which are verbally given as follows: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub)

These axioms and the analytical superstructure have been given a mathematical form by Debreu, Arrow, McKenzie.

The representative economist has not realized it but methodologically, the Walrasian premises are forever unacceptable. It should be pretty obvious that the axiomatic core contains THREE NONENTITIES: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5). Every model that contains a nonentity is A PRIORI false. The lethal methodological blunder of economics is NOT mathiness but the NONENTITIES in the premises.

What is missing among economists is a proper understanding of what science is all about. Aristotle gave a working definition 2000+ years ago: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” When the premises are NONENTITIES this is cargo cult science and produces nothing but pathetic blather.

The mathiness problem of economists does not consist in the application of advanced mathematics but in the incapacity to apply the straightforward arithmetic of accounting. Fact is that economists are since Adam Smith too stupid to put 2 and 2 together.#1

Fact is also that the subject matter of economics is ill-defined since the founding fathers. Economics is NOT a social science but a system science.#2

Egmont Kakarot-Handtke

#1 Economists: just too stupid for counting

#2 For more details see ‘The myth of economics knowledge

Écrasez L'infâme said...

Here's my slight extension of Prof W's argument. Marx had already developed Ricardo and Smith in ways that the establishment of the time found threatening, yet found difficult to argue against. Everyone before the Triple Revolution thought in "political economy" terms, and of course they accepted the Labour Theory of Value, and by those lights Marx's arguments seemed reasonable; indeed, Smith himself would have agreed with Marx more than he would with modern neo-liberals like "the Adam Smith Institute". What to do? The establishment needed economics as a foundation for capitalism, but they didn't want to endorse revolution. Luckily, Providence - or the dialectic, perhaps! - often gives us solution and problem at the same time, and Jevons etc found they could replace the labour theory with subjective utility and selfishness and, remarkably, save the results the establishment wanted while discarding the revolutionary stuff. (Incidentally, I once read one of Jevon's books on logic. Let's just say it was... uninspiring.)

Now, obviously mathematics only answers mathematical questions, and so it sidelines non-mathematical ones. Questions that can't be answered soon stop being asked, and eventually stop being thought about at all. The class struggle Prof W talks about becomes "marginalised" as the politics is taken out of economics. Without politics, the normative and positive branches can not be separated, and economies start to have to conform to rules whose purpose was to show the rules economies have to conform to: economics becomes the study of itself. Eventually the whole field becomes a branch of magic, where the wrong person talking about a crash can cause a crash, even though the underlying fundamentals can be healthy (or, conversely, a speculator like Warren Buffet can make money in whatever he invests in, because so many other speculators follow him and it pushes the stockprice up).

All this is tied with my aesthetic sense that the mathematics in micro-economics is ugly, bolted on, assumes what it tries to prove, has no explanatory power, and generally feels like the homework assignment of a precocious 14-year old. As Prof W says, economists are very proud of the "difficulty" of their mathematics - look, calculus! - but would run a mile if faced with genuinely advanced maths; the whole project just feels childish to me. Even Black-Scholes - probably the hardest maths around in micro at the moment - is only about as hard with Maxwell in physics (mid- to late-C19th). That's one reason I call myself a Marxist - Marxism puts the politics back into economics and therefore is much more adult.

(BTW, I don't feel the same about modern macro-economics; the maths there isn't much more difficult, but feels necessary and comes naturally out of the subject. Yup, I know it's typically micro-founded.)

Écrasez L'infâme said...

To poster Ed Barreras: I use the apostrophe in things like the 1960's or mind your p's and q's or do's and don'ts. It's true I no longer have to get grades, but the principle of the freedom of the fluent speaker of any language to use it how they damn well please trumps any mere style guide. If you're writing for publication, either whoever you're writing for cares enough to pay for a sub-editor and it'll be subbed anyway, or they don't in which case do what you want. (Maybe this attitude was why my grades were never much good).

AXEC / E.K-H said...

Écrasez L'infâme

You say: “Marx had already developed Ricardo and Smith in ways that the establishment of the time found threatening, yet found difficult to argue against.”

Marx was a philosopher, sociologist, soap box economist, and agenda pusher but NOT a scientist. He never understood what profit is. See ‘Profit for Marxists’

The four main approaches ― Walrasianism, Keynesianism, Marxianism, Austrianism ― are at the SAME proto-scientific level, i.e. axiomatically false, materially/formally inconsistent, and all got profit wrong.

Egmont Kakarot-Handtke

AXEC / E.K-H said...


You say: “And I would say that the GT of Keynes is replete with the power of accounting logic as the required fundamental framing.”

Fact is that Keynes got the accounting logic wrong. The formal core of the General Theory is given with: “Income = value of output = consumption + investment. Saving = income - consumption. Therefore saving = investment.” (p. 63)

This two-liner is conceptually and logically defective because Keynes did not come to grips with profit: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson et al.)

Because profit is ill-defined the whole theoretical superstructure of Keynesianism is false, in particular all I=S and IS-LM models.

Let this sink in: Keynes had NO idea of the fundamental concepts of economics, viz. profit and income.#1 After-Keynesians did not spot the foundational blunder until this day.#2

You say: “Interestingly, Keynes was a mathematician before (in effect) he was an economist.”

I doubt this. Keynes was a lifelong agenda pusher and not of the stuff mathematicians are made of: “I consider that Keynes had no real grasp of formal economic theorizing (and also disliked it), and that he consequently left many gaping holes in his theory.” (Hahn)

As a soap box economist, Keynes never rose above common sense: “In the early thirties he [Keynes] confessed to Roy Harrod that he was ‘returning to an age-long tradition of common sense’.” (Coates) No one who has tasted mathematics ever returns to common sense.

Keynes was a fake scientist. In a fake science this is not a disadvantage.

Egmont Kakarot-Handtke

#1 How Keynes got macro wrong and Allais got it right

#2 Economists: just too stupid for counting