Category Archives: economics

“Mathiness” vs. the Logic of Action

Mathematical economics is fraying at both ends. Critics of the over-mathematization of economics keep chipping away at the spurious correlations and the theoretical equations that are either too simple or too complicated. At the other end, notable mainstream economists like Paul Romer see fundamental problems in the way economics is done today.

His paper on “Mathiness” was picked up by the Wall Street Journal. “Mathiness” is “the use of mathematics to persuade or mislead rather than to clarify,” and is ubiquitous in the economics profession these days.

Unfortunately, Romer’s conclusion in his paper offers a non-solution:

[back in the good ol’ days] Not universally, but much more so than today, when economic theorists used math to explore abstractions, it was a point of pride to do so with clarity, precision, and rigor. Then too, a faction like Robinson’s [politically motivated] that risked losing a battle might resort to mathiness as a last-ditch defense, but doing so carried a risk. Reputations suffered.

So all the profession needs to do to get over this destructive love affair with mathiness is a fresh injection of “clarity, precision, and rigor.” This is like telling a group of criminal graffiti artists to use stencils when they’re defacing buildings.

The real problem is much deeper than Romer realizes. Economics is the science of human action. It deals with motivated human choice. As such, there are no strict quantitative relationships like the ones in the hard sciences. Objects don’t choose to fall at a certain speed, or choose to react to other objects in certain ways. Humans choose. Our choices are based on preferences which change unpredictably in an infinite number of ways over equally unpredictable and infinite varieties of circumstances.

The details of human action are unpredictable and not conducive to strict quantitative rules, but the logic of action provides a rich framework for doing economics.

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The N.S.P.H.H.B.O.P., the market, and the “Beepocalypse”

The number of honey-producing bee colonies is higher than it has been in 20 years, according to the newest USDA data. After consistent decline from the late 1980s to the early 2000s, there has been a recent rise in the number of colonies due to federal regulations promoting bee health—scratch that—beekeepers responding to changing prices of honey, bees, and beekeeping equipment.

The first-of-its-kind “National Strategy to Promote the Health of Honey Bees and Other Pollinators” was only introduced by the Executive Branch this year, after the recent bee population increase, and will probably try to steal credit from the market naturally working toward an increased bee population in the years to come.

The Washington Post article reports that the price of honey has just about doubled over the course of 2006-2014, and so have the fees beekeepers charge to farmers for bringing their colonies to pollinate fruit, nut, and veggie crops.

These increasing prices for beekeeping outputs make the purchase of beekeeping inputs a more profitable investment. Beekeeping inputs include bees, which mean more colonies are created and maintained by beekeepers.

Consumer demand drives the price of honey, which makes honey production profitable, which increases the demand for the factors of production specific to honey production. Voilà, more bees.

Also, consumer demand drives the price of food, including fruits, nuts, and veggies, which makes farming profitable, which increases the demand for pollinating services, which increases the profitability of beekeeping, which increases the demand for the factors of production specific to beekeeping, like bees.

Contrast these natural, fine-tuned, and self-regulating market mechanisms (profit/loss, imputation, supply and demand) to a few of the proposed actions from the N.S.P.H.H.B.O.P., below:

Screen Shot 2015-08-07 at 3.25.30 PM

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Broken website code? Or just Paul Samuelson?

{d/dA} FL[L, T; A] =FLA[L/T; 1; A] < 0 (A12)
{d/dA} FT[L, T; A] = FTA[L, T; A] > – (L/T) FLA[L, T; A] > 0, from (A11)
FLA[L, T; A] > 0, FTA(L, T; A] < 0 (A13)
FLA[L, T; A] > 0, FTA(L, T; A] > 0 (A14)
FLA[L, T; A] < 0, FTA(L, T; A] < 0: not viable. (A15)
Your browser is probably fine, even though this looks like malfunctioning HTML code or something.
It’s just Paul Samuelson “disproving” Bastiat and Mises.
He continues:
That (A12) is manifestly possible makes it laughable that Ricardo or McCullough should ever have thought differently. Only ignoramuses or zealots like Bastiat or von Mises, could believe that laissez faire always makes each of us better off.
A12 shows that a new production technique can lower wages for laborers in that line of production. Some assumptions made to get there include:
  1. no money (just an output numeraire),
  2. no heterogeneity of labor,
  3. no heterogeneity of land,
  4. no substitution into producing other goods (one-sector model),
  5. no competition for laborers among different lines of production (since there’s only one sector),
  6. no time,
  7. no production time (no competition for laborers among stages of production),
  8. no interest,
  9. no produced factors of production (because that would be another sector, and because then increases in K could increase MPL, and we can’t have that), and
  10. laborers only ever get a subsistence wage (later added to show how such a new production technique like this results in people dying–we all remember the genocide that resulted from the invention of the washing machine).

Source: Paul Samuelson (1989), “Ricardo was Right!” Scandinavian Journal of Economics 91(1), pages 58-59. (emphasis mine)

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Eduard Braun on Opportunity Cost

From Finance Behind the Veil of Money, page 32:

The opportunity-cost concept does not allow for the inclusion of time. Opportunity costs, in other words, are not a matter of action but of choice. James Buchanan is not the only one who stresses the close relationship between choice and opportunity cost. G. F. Thirlby, who published a lot on the cost problem, also writes: “By deciding to take the preferred course, he [any person] incurs the cost—he displaces the alternative opportunity.” According to this opinion, costs appear at the point of time when the decision is made and then lose all of their “significance . . . because the decision displaces the alternative course of action.” However, it seems to be problematical to link cost to choice. Decisions are not bound up with costs. To illustrate this hazardous statement, let’s have a look at an example.

Let us suppose friends X and Y are on a trip in the mountains. X has two apples in his bag. Y loves apples, but has forgotten to pack one. During the first break, X permits Y to take one of the apples. Well, one could say this is a great deal for Y! However, things look differently if one takes into account opportunity cost. As soon as Y takes one of the two apples, he abstains from taking the other one. If we assume, for simplicity, that the two apples are alike, then the disadvantage in this decision is just as great as the advantage. According to opportunity-cost theory, Y is not better off at all although he has received an apple for free. His preference for one of them cost him the other one.

It is interesting to see that the story would run totally differently if X had not offered that Y take one of the apples, but if X had given one to Y. In this case, Y does not have any opportunity costs. Those only appear when he has to choose like he had to in the first example. From this point of view, as George Reisman also notes, the possibility of choosing between several alternatives—a possibility that one would think to be beneficial from the point of view of the person choosing—appears to be something bad, even destructive. The best that could happen to anyone would be to have no freedom of choice. No opportunity cost means—from the point of view of most economists—no cost at all.

My response to this is that if X says Y can have one apple, the other apple is not the opportunity cost. The forgone alternative is not having an apple. This solution is the same as Rothbard’s solution to the Buridan’s Ass problem–the ass does not just face the choice between two equal bales of hay, but the choice to eat or not to eat.* Therefore indifference is never, ever a problem in economics, because there is always a third “option” of not having the satisfaction at all.

Just because X was not specific about which apple was the gift doesn’t mean that the choice is between one apple or the other. It means that the choice is between taking an apple or not taking one, just like the donkey facing the choice between eating from one of the bales of hay and going hungry.

This may actually help explain time preference (which is what Braun was on his way to redefining). If action is undertaken to remove some “uneasiness” (Mises, Human Action), then there is an universal reason for preferring the satisfaction of an end sooner rather than later: the longer it takes to have the satisfaction, the more time is spent feeling the “uneasiness”. Indeed, with each passing moment in which the choice in question is not made, the actor incurs the opportunity cost of not having the end satisfied.


*Rothbard on Buridan’s Ass:

Buridan postulated a perfectly rational ass who found himself equidistant between two equally attractive bundles of hay. Indifferent between the two choices and therefore unable to choose, the perfectly rational ass could choose neither and thereby starved to death. What this example overlooked is that there is a third choice, which presumably the ass liked the least: starving to death. So that it was therefore “perfectly rational” not to starve to death but rather to choose one of the two bundles even at random (and then to proceed to the second bundle).

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Adam Smith and his Inflated Reputation

Adam Smith is widely regarded as the progenitor of all economics–the singularity, the common ancestor of all economists, the beginning.

This is wrong.

Turgot, Cantillon, mercantilism, scholasticism, and Aristotle predate Smith among many other economic ideas and people who wrote about economics. All are featured in part one of Rothbard’s history of economic thought, aptly titled Economic Thought before Adam Smith, where you find this gem of a quote:

Adam Smith is a mystery in a puzzle wrapped in an enigma. The mystery is the enourmous and unprecedented gap between Smith’s exalted reputation and the reality of his dubious contribution to economic thought.

And in Wages and Capital, you can almost hear F.W. Taussig sigh when he says,

During the first half of the present century […] it was the custom to treat all earlier contributions to economic thought as of little account, and to begin the history of the subject with the Wealth of Nations.

He goes on to delineate Smith’s versus others’ contributions in a kinder way than Rothbard:

On some subjects, and notably on those which most attracted the attention of his contemporaries, Adam Smith gained much and directly from his predecessors. The mercantile ideas, in their cruder forms, had been refuted by a long series of writers, by North and Hume among the English, by Boisguillebert, Cantillon, and the whole line of the Physiocrats. The functions of money in domestic and in international trade had been fully and adequately discussed by these writers ; and much had also been done toward clearing up the subject of money by writers who, like Locke and Steuart, were still befogged on international commerce and the balance of trade. On credit, paper money, and banking there had been active discussion since the close of the seventeenth century, when banks began to exercise their functions on a considerable scale, and paper-money experiments came to be tried in almost every form. Adam Smith was abundantly familiar with the literature of his subject, and accepted without hesitation what had been accomplished by his predecessors. The famous attack on the mercantile sys- tem bears, indeed, the unmistakable marks of his vigorous and independent mind, in the reasoning as to the limitation of industry by capital, and in the general discussion of foreign trade. But the ground had been prepared for it by a long line of writers; and the upper tier of the educated public was prepared to accept ‘his views at once.

The subjects of production and distribution show Adam Smith, not perhaps at his best, but at his freshest. Here he broke new ground. On the division of labor and its causes and effects, the functions of capital, the partition of income into wages, profits, and rent, the causes determining the amount of each form of remuneration, on all these topics he started economic thought on new lines, and on lines that have been substantially followed since his time. The very novelty of his investigation made it inevitable that his results here should be more crude than on the subjects which had been worked over by two or three generations of previous thinkers ; a defect which, rightly considered, makes the debt of science to him so much the greater.

Even on these subjects, it would be a mistake to consider Adam Smith as an unaided pioneer. The division of labor, and its consequences in bringing exchange and necessitating a medium of exchange, had been noted by a long series of writers, from ancient times to modern. Further, some stimulus to his thought on capital doubtless came from the general reaction against the treatment of interest and money by the mercantile writers. The older and cruder notions as to the importance of an abundance of specie had been effectually exploded before he began. As these exaggerations in regard to the importance of plentiful specie crumbled away, it was inevitable that other ideas connected with them should be overhauled and reshaped. The function of money having become clear, interest could no longer be explained as affected simply by the abundance or scarcity of money. The better understanding of the medium of exchange, again, directed attention to the nature and qualities of the commodities whose barter was seen to be facilitated. All this paved the way to the consideration of real capital, and the real machinery of production. In such indirect ways Adam Smith probably got a stimulus to his speculations on capital and interest, and so, by a natural progression, on capital and wages.

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Thou Shalt Not Overcomplicate Things

Justin Fox has a short piece at Bloomberg View that asks “What’s Wrong With ‘Mathiness’ in Economics?

He begins by characterizing (caricaturizing?) the pre-math economics profession as confused and garrulous philosophers:

Once upon a time economists made their arguments in long, discursive, often contradictory books…

Thankfully, Paul Samuelson brought math to the field like Moses brought the Ten Commandments down from Mount Sinai to the lost and wayward Israelites.

In the 1940s Paul Samuelson of the Massachusetts Institute of Technology brought enlightenment, in the form of elegant mathematical treatments of the major concepts in economics.

[…]

Samuelson’s approach gave the discipline a, well, discipline that it had previously lacked, and enabled economics to make great leaps in coherence and rigor.

But, just a few words later, Fox admits that

It also made the field incomprehensible to laypeople, but that turned out to be more a feature than a bug. Economists were seen as possessing unique scientific knowledge, and came to play increasingly prominent roles in public life in the U.S. and elsewhere.

Although I disagree with his first characterization of the pre-math economics and his regard for Samuelson’s influence, this last bit is where I want to parley with Fox.

The incomprehensibility of the math to the laypeople is the primary piece of evidence in the indictment against the current “mathiness” of economics. Economics is the study of those regular, ordinary laypeople making choices. Ordinary people make choices all the time, and so describing the nature or logic of their choices should be intuitive to them.

This does not mean that everybody automatically knows all of the deep and varied conclusions of economics just by making choices. It means that any explanation of how choice and interaction with other people making choices (like in markets) should be digestible without an advanced degree in another field like math or statistics. Choice and market interaction are so mundane and ubiquitous, explaining how they work should be simple, right?

I use this example frequently but it fits in well here: When you walk down the grocery store aisles, are you taking derivatives of utility functions? Or are you weighing your preference for each good against others and the money you are prepared to spend at the register?

Which of these two explanations for how people make choices would serve as a better foundation for the science that purports to study individuals making choices?

Fox doesn’t really answer the question posed in the title of his article: “What’s wrong with ‘mathiness’ in economics?” He just comments on Romer’s beef with the way mathematical models are overused and abused by even Nobel-winning economists. Fox quotes Romer:

Presenting a model is like doing a card trick. Everybody knows that there will be some sleight of hand. There is no intent to deceive because no one takes it seriously. Perhaps our norms will soon be like those in professional magic; it will be impolite, perhaps even an ethical breach, to reveal how someone’s trick works.

And I say no more magic. Drop the smoke, the mirrors, the rabbits, and their hats. Let’s drop the pretense–it is, after all, a violation of the Ninth Commandment.

You shall not bear false witness against your neighbor. (Exodus 20:16 ESV)

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The Broken Window Fallacy, Broken Down

Published on Medium.

It’s a longer piece, but with pretty pictures and some humor sprinkled in.

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