Posts Tagged ‘mathematics’


Sebastian Mallaby referred to Paul Romer’s scheme of building charter cities as Empire 2.0 (which is much the same connection I made back in 2010).

the largest obstacle Romer faces, by his own admission, still remains: he has to find countries willing to play the role of Britain in Hong Kong. Despite the good arguments that Romer makes for his vision, the responsibilities entailed in Empire 2.0 are not popular. How would a rich government contend with the shantytowns that might spring up around the borders of a charter city? Would it deport the inhabitants, and be accused of human-rights abuses? Or tolerate them and allow its oasis to be overrun with people who don’t respect its city charter? And what would the foreign trustee do if its host tried to nullify the lease? Would it defend its development experiment with an expeditionary army, as Margaret Thatcher defended the Falklands? A top official at one of Europe’s aid agencies told me, “Since we are responsible for our remaining overseas territories, I can tell you there is much grief in running these things. I would be surprised if Romer gets any takers.”

According to an announcement on his own blog, Romer is now headed to the World Bank.

There, Romer will be able to develop his imperial scheme—and, presumably, as I described his work last year, eliminate political “mathiness” and steer the focus of attention to “nonrival ideas” and away from capital and the real problems of growth within capitalist economies.


Harmen de Hoop and Jan Ubøe, “Permanent Education (a mural about the beauty of knowledge)” (Nuart 2015, Stavanger, Norway)

Ubøe, Professor of Mathematics and Statistics at the Norwegian School Of Economics, gives a 30-minute lecture on the streets of Stavanger on the subject of option pricing.

Drawing on Black and Scholes explanation of how to price options, Ubøe will explain how banks can eliminate risk when they issue options. Black and Scholes explained how banks (by trading continuously in the market) can meet their obligations no matter what happens. The option price is the minimum amount of money that a bank needs to carry out such a strategy.

While the core argument is perfectly sound, it has an interesting flaw. If the market suddenly makes a jump, i.e. reacts so fast that the bank does not have sufficient time to reposition their assets, the bank will be exposed to risk. This flaw goes a long way to explain the devastating financial crisis.

This theory, and similar other theories, led banks to believe that risk no longer existed, so why not lend money to whoever is in need of money? In the end the losses peaked at 13,000 billion dollars – more than the total profits from banking since the dawn of time.

My guess is, most of the members of the audience did not understand the mathematics. However, Ubøe assures them it works—both as a form of knowledge (the manipulation of the mathematics) and as a strategy for banks (to eliminate risk)—and they can’t but believe him. It has a kind of beauty.

And then he explains that other effect of the math: it led banks to believe they had found a way of eliminating risk (because, like the audience, they believed the mathematicians), which fell apart when markets made sudden jumps and the traders weren’t able to reposition their assets quickly enough.

In that case, the beauty of the knowledge is undermined by the ugliness of the results.


I’m taking nominations for the best examples of dismal economic scientists.

While I wait for your suggestions, I’m going to offer two of my own nominations: Tyler Cowen and Paul Romer.

I am nominating Cowen because, in his argument that the economy probably needs a “reset,” he only focuses on lowering workers’ wages. First, he makes no mention of resetting corporate profits or the incomes of those at the very top, as if what they manage to capture were completely off limits. All the adjustment in the new, “grimmer future” will be born by those at the bottom. Second, he completely overlooks the mechanisms of his own economic theory: if lower rates of economic growth are the product of lower rates of growth of available workers (a key factor in the theory of secular stagnation), then the relative scarcity of workers should mean higher—not lower—wages. In other words, Cowen is determined to make sure all the costs of the new, slower-growing economy will be born by shifted onto those who can least afford it. For that reason, I nominate Cowen for the title of dismal economist.

I also want to nominate Romer, who continues to double down on his “mathiness” argument, by asserting (against all the work that has taken place in the philosophy of science in recent decades) that (a) there’s a single truth, (b) that truth can only be obtained via science, and (c) mathematical modeling is the singular method for making progress in science to obtain truth. There are so many things wrong with each of those assertions it’s hard to know where to begin. And I won’t, at least right now. Let me just say Romer deserves his nomination as one of the most dismal economists because of the extraordinary arrogance, pretentiousness, and ignorance of the following statements:

About math:. . .I’ve seen clear evidence that math can facilitate scientific progress toward the truth.

If you think that math is worthless or dangerous, I’m sure that there are people who will be happy to discuss this with you. I’m not interested. I’m busy.

About truth and science: My fundamental premise is that there is an objective notion of truth and that science can help us make progress toward truth.

If you do not accept this premise, I’m sure that there are people who would be happy to debate it with you. I’m not interested. I’m busy.

And please do not write to tell me that science is a social process or that the progress it makes toward the truth can be irregular. I know.

Me, I’m not too busy to discuss either the fundamental injustices of contemporary capitalism or the often-worthless and dangerous role mathematics, truth, and science have played and continue to play in the discipline of economics.

I’m also not too busy to post additional nominations for dismal economists.



You remember the dialogue:

Queen: Slave in the magic mirror, come from the farthest space, through wind and darkness I summon thee. Speak! Let me see thy face.

Magic Mirror: What wouldst thou know, my Queen?

Queen: Magic Mirror on the wall, who is the fairest one of all?

Magic Mirror: Famed is thy beauty, Majesty. But hold, a lovely maid I see. Rags cannot hide her gentle grace. Alas, she is more fair than thee.

I was reminded of this particular snippet from Snow White and the Seven Dwarfs while reading the various defenses of contemporary macroeconomic models. Mainstream macroeconomists failed to predict the most recent economic crisis, the worst since the Great Depression of the 1930s, but, according to them everything in macroeconomics is just fine.

There’s David Andolfatto, who argues that the goal of macro models is not really prediction; it is, instead, only conditional forecasts (“IF a set of circumstances hold, THEN a number of events are likely to follow.”). So, in his view, the existing models are mostly fine—as long as they’re supplemented with some “financial market frictions” and a bit of economic history.

Mark Thoma, for his part, mostly agrees with Andolfatto but adds we need to ask the right questions.

we didn’t foresee the need to ask questions (and build models) that would be useful in a financial crisis — we were focused on models that would explain “normal times” (which is connected to the fact that we thought the Great Moderation would continue due to arrogance on behalf of economists leading to the belief that modern policy tools, particularly from the Fed, would prevent major meltdowns, financial or otherwise). That is happening now, so we’ll be much more prepared if history repeats itself, but I have to wonder what other questions we should be asking, but aren’t.

Then, of course, there’s Paul Krugman who (not for the first time) defends hydraulic Keynesianism (aka Hicksian IS/LM models)—”little equilibrium models with some real-world adjustments”—which in his view have been “stunningly successful.”

And, finally, to complete my sample from just the last couple of days, we have Noah Smith, who defends the existing macroeconomic models—because they’re models!—and chides heterodox economists for not having any alternative models to offer.

The issue, as I see it, is not whether there’s a macroeconomic model (e.g., dynamic stochastic general equilibrium, as depicted in the illustration above, or Bastard Keynesian or whatever) that can, with the appropriate external “shock,” generate a boom-and-bust cycle or zero-lower-bound case for government intervention. There’s a whole host of models that can generate such outcomes.

No, there are two real issues that are never even mentioned in these attempts to defend contemporary macroeconomic models. First, what is widely recognized to be the single most important economic problem of our time—the growing inequality in the distribution of income and wealth—doesn’t (and, in models with a single representative agent, simply can’t) play a role in either causing boom-and-bust cycles or as a result of the lopsided recovery that has come from the kinds of fiscal and monetary policies that have been used in recent years.

That’s the specific issue. And then there’s a second, more general issue: the only way you can get an economic crisis from mainstream models (of whatever stripe, using however much math) is via some kind of external shock. The biggest problem with existing models is not that they failed to predict the crisis; it’s that the only possibility of a crisis comes from an exogenous event. The key failure of mainstream macroeconomic models is to exclude from analysis the idea that the “normal” workings of capitalism generate economic crises on a regular basis—some of which are relatively mild recessions, others of which (such as we’ve seen since 2007) are full-scale depressions.  What really should be of interest are theories that generate boom-and-bust cycles based on endogenous events within capitalism itself.

With respect to both these issues, contemporary mainstream macroeconomic models have “stunningly” failed.

I imagine that’s what the slave in the magic mirror, who simply will not lie to the Queen, would say.


Since we’re on the topic of the supposed superiority of economists, I thought I would provide a link to one of my first published articles, “The Merchant of Venice, or Marxism in the Mathematical Mode” [pdf], which appeared in the journal Rethinking Marxism.*

My basic argument is that, while mathematics has been granted the status of a special code in economic discourse (including in Marxian theory)—thus demonstrating the superiority of economists who use that special code—it is actually a set of metaphors that can be useful and harmful in turn. In other words, the use of mathematics “does not guarantee the scientificity of the theory in question; it is merely one discursive strategy among others.”

There are two interesting stories associated with this article. First, it was used against my case for tenure, by a member of the committee who (from what I have been told) was simply incensed that I would attempt to deconstruct the use of mathematics as a special language for doing economics. (Fortunately, it didn’t work and I was in fact granted tenure.)

Second, I disappointed not a few literary scholars who came to one of my seminars on the article expecting a discussion of Shakespeare’s play. The joke is that the title refers to the Treviso Arithmetic, which was written by an anonymous author in 1478 in Treviso, a commercial town annexed to the Venetian Republic in 1339, and is considered to be the first book on mathematics ever published in the West.

The problem that begins in the middle of the left-hand page of the illustration above is the following:

Two merchants, Sebastiano and Jacomo, enter into partnership. Sebastiano put in 350 ducats on the first day of January, 1472; Jacomo put in 500 ducats, 14 grossi on the first day of July, 1472. On the first day of January, 1474 they find that they have gained 622 ducats. Required is the share of each.


*A scholar overseas, without access to the journal, asked me to send him a copy of the article. That’s the reason I now have a pdf file of the article on hand.


The storm unleashed by Chris Giles’s takedown (follow the links) of Thomas Piketty for the Financial Times (with responses now by Piketty himself, Neil Irwin, Simon Wren-Lewis, Steven Pressman, and others) reminds me of two stories.

First, there’s the story of a seminar by Hollis Chenery, one of the pioneers of economy-wide development planning models, at Yale University in the early 1970s. One of the participants in the seminar, who later was one of my professors in graduate school, offered Chenery a large sum of money to put together the appropriate matrix of data—and then an even larger sum of money not to invert the matrix. The point: there are so many mistakes, assumptions, and elements of pure guesswork involved in compiling any set of economic data, it is a fundamental mistake to presume the correct economic policy or strategy can be devised—and then offered as objective and accurate “expert” advice—by simply running the model.

Second, a friend in graduate school, who already had a Ph.D. in mathematics, took it upon himself to work through the mathematics presented in the tenth edition of Paul Samuelson’s famous Foundations of Economic Analysis. He told me he was amazed to find more than one hundred mistakes in the book, even after so many editions. The point of this example: lots of errors are made—and then repeated by authors and overlooked by readers—even in the most famous writings of economists. And the errors committed in Samuelons’ Foundations certainly didn’t stop the mathematization of mainstream economics in the postwar period.

As for Piketty, my view is, first, we need to give him credit for making all of his data, mistakes and all, freely available on-line. Second, even if in one or another country, during one or another period of time, the distribution of wealth has not become more unequal, the fact remains that the distribution of wealth is and remains profoundly and grotesquely unequal. Even Giles can’t dispute that point. And finally, I can only imagine what the reaction would be if Piketty had actually collected data not on wealth, but on capital in the twenty-first century, and had attempted to calculate changes in the rate of exploitation over time.


Every time there’s a controversy in economics, the problem of mathematics seems to be at the center of the discussion. That’s because, in economics, discussing the role of mathematics is inextricably related to issues of science, epistemology, and methodology, which are themselves rarely discussed but are implicit in pretty much all of these discussions.

In short, we’re never very far from physics-envy.

That’s certainly the starting point of Noah Smith, who compares the mathematics of physics (the supposed “language of nature”) with that of macroeconomics (in which it serves to “signal intelligence”). And then, of course, Paul Krugman rides to the rescue, arguing that mathematical models, when “used properly,. . .help you think clearly, in a way that unaided words can’t.”

Uh, OK. “Used properly” is the operative clause there. The real question is, what is the proper use of mathematics in economics? And, what is the proper way of thinking about the proper use of mathematics? That’s where all the issues of science, epistemology, and methodology come to the fore.

As it turns out, one of the first articles I ever published, “The Merchant of Venice, or Marxism in the Mathematical Mode,” was on that very subject. I had mostly ignored mathematics during my undergraduate years but then, in graduate school and especially when I began to conduct the research for my dissertation (on mathematical planning models), I realized I wanted both to learn the econmath and to learn how to think about the econmath. Ironically, I ended up teaching “Mathematics for Economists” to first-year doctoral students for over a decade (it was basically a course in linear algebra and multivariate calculus, in which students also had to write a paper on the history and/or methodology of the mathematization of economics).

The argument I made in my dissertation and later in the “Merchant of Venice” article was that economists (mainstream economists especially, but also not a small number of heterodox economists, including Marxists) treated mathematics as a special language or code. They considered it special either in the sense that it was the language of nature (and therefore overprivileged) or a neutral medium for thinking and expressing ideas (and therefore underprivileged). Either way, it was considered special.

My alternative view was that mathematics was just one language among many, and therefore one set of metaphors among many. And like all metaphors, it served at one and the same time to enable and disable particular kinds of ideas. Therefore, we need to both write mathematical models and to erase them in order to produce new ideas.*

But that’s not how most economists think about mathematical models. And when they do think and write about them, they tend to invoke one or another argument for mathematics as a special code. They also tend to forget about all the other uses of mathematics in economics—not only as a signalling device but as a hammer to bludgeon all other approaches out of existence.

It’s the tool that is often used, in economics, to separate science from non-science—which, of course, if you say it quickly, becomes nonsense.

*That argument, concerning the not-so-special status of mathematics, so incensed one of my colleagues he attempted to derail my tenure case. Fortunately, another of my colleagues forced him to back down and I ended up receiving a unanimous recommendation.