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The Overuse of Mathematics in Economics – Article by Luka Nikolic

The Overuse of Mathematics in Economics – Article by Luka Nikolic

Luka Nikolic
September 2, 2019


If you enrolled at university today, you would find economics modules filled with mathematics and statistics to explain economic phenomena. There would also be next to no philosophy, law, or history, all of which are much more important to understanding the way our world works and how it impacts the economy.

The reason is that since the end of the 19th century, there has been a push toward turning economics into a science—like physics or chemistry. Much of this has been done by quantifying phenomena and explaining it through graphs. It has been precisely since this shift that there has been such a poor track record of public policy, from fiscal to monetary.

What many contemporary economists fail to realize is that economics is as much of a philosophical pursuit as a mathematical one, if not more so.

Modern economics was first introduced as a formal subject called “history and political economy” in 1805. Economics was a three-decade-old discipline then, as Adam Smith had published his Wealth of Nations in 1776. The earliest economists were philosophers who used deduction and logic to explain the market. Smith deployed numerical analysis only as a means of qualitatively assessing government policies such as legislated grain prices and their impact. No graphs or equations were used.

Even earlier, 17th-century philosopher John Locke contributed more to economic liberty than any mathematician has since. Likewise, philosopher David Hume successfully explained the impact of free trade with his price-specie flow mechanism theory, which employs pure logic. John Stuart Mill’s book On Liberty likewise furthered the cause for free markets without using math.

In 1798, Malthus mathematically predicted mass starvation due to population growth, but he could not quantify the rule of law and free markets.

The first substantial misuse of mathematics was by Thomas Malthus. In 1798. He predicted mass starvation due to population growth, which was exponential and outpacing agricultural production, which was arithmetic. Malthus was evidently wrong, as contemporary free-market Japan’s population density towers over collectivist sub-Saharan’s Africa. Malthus could not quantify the rule of law and free markets.

Alfred Marshall’s Principles of Economics (1890) was the first groundbreaking textbook to use equations and graphs. One of Marshall’s students, John Maynard Keynes, would further the cause of quantifying economics by mathematically linking income and expenditure and how government policy could impact this. Keynes’ General Theory (1936) would serve as a blueprint for 20th-century economic policy as more scientific methods of economics gained favor in the coming decades. Friedrich Hayek summarized this shift in his Nobel Prize acceptance speech.

It seems to me that this failure of the economists to guide policy more successfully is closely connected with their propensity to imitate as closely as possible the procedures of the physical sciences—an attempt which in our field may lead to outright error. It is an approach which has come to be described as the “scientistic” attitude—an attitude which is decidedly unscientific in the true sense of the word, since it involves a mechanical and uncritical application of habits of thought to fields different from those in which they have been formed.

It is impossible to quantify human action. Although equations, such as utility measures, do exist to quantify human behavior, they are faulty when examined. How can an equation tell me when I am no longer satisfied with a certain good? Mathematically speaking, it is when marginal utility becomes negative. This may be true. However, the problem is how to determine how much chocolate will give me a stomach ache—mathematically speaking, what amount will produce negative marginal utility. A doctor could not figure this out, let alone an economist.

There cannot be “catch-all” formulas due to the complexity of economic phenomena. Measuring the elasticity of demand for a certain good is at best a contribution to economic history. Elasticity will hardly be constant in the same country throughout time, let alone in other countries. However, the economists pursuing this analysis do not do it to update economic history—it is done for the purpose of having government micromanage demand for these goods. In reality, government should allow the free market to produce a certain good. The market will determine the demand/supply.

Economics is more related to jurisprudence than math.

Economics, among other things, is the study of the allocation of scarce resources. If there is a limit of a certain good, it’s not the government’s job to utilize an equation to distribute it. Rather, governments must ensure that the property rights of that good are clearly defined. It is then up to the person who owns the good to allocate it. As such, economics is more related to jurisprudence than math.

The Solow-Swan growth model is a perfect example of quantifying economics. It claims to explain long-run economic growth based on productivity, capital accumulation, and other variables. It is unquestionable that these factors impact growth, however, it oversimplifies the complex interactions between various qualitative factors.

For example, English Common Law has allowed countries such as the US or Hong Kong to prosper more than African nations with no basis for the rule of law and where corruption is still widespread. Protestant nations were historically more favorable toward capitalism compared to other religions. Both of these factors undoubtedly affected the variables in the Solow-Swan model—the problem is quantifying them. Productivity and capital accumulation do not “just happen.”

Monetary policy has suffered the worst. Today, central banks manipulate interest rates to stimulate the economy due to a false belief in purely theoretical mathematical models. Such sophisticated analysis would be welcoming if it offered a better track record. By artificially lowering interest rates, central banks create malinvestment in the economy, creating a bubble.

Once the economy is deemed to be “overheating,” the rates are raised, causing the bubble to burst. This is precisely what has happened since the introduction of discretionary monetary policy in many instances. The 2008 crisis is the most recent example.

However, such policy was not possible with the gold standard because there was no need for a central bank nor monetary policy, as a tool, to even exist. Likewise, the economy was much more stable. Why did gold work? It could not be manipulated easily by the government, and furthermore, it was spontaneously chosen by people because it fulfilled the necessary criteria. Mathematical formulas cannot replicate this. One economist jokingly described it:

Instead of trading away your valuable pigs for horses, why not accept some smooth stones? Don’t worry that you don’t want them, someone else will give you horses in exchange for them! If we could just all agree on which smooth stones are valuable, we’d all be so much better off!

While serving as Hong Kong’s financial secretary from 1961 to 1971, John Cowperthwaite was skeptical about government collecting statistics outside what was necessary, claiming, “If I let them compute those statistics, they’ll want to use them for planning!” Hong Kong remains one of the richest and freest economies.

It should be recognized that mathematically-driven economics is a divergence from the foundation of traditional economics.

Sadly, Cowperthwaite’s skepticism of central planning based on models is rarely heeded today, evidenced by the Keynesianism that has reemerged in the intellectual sphere. Furthermore, considering that publishing in mathematically-driven economics journals is needed to secure tenure, it is questionable whether mainstream economics will be changed by such incentives.

Mathematics has a place at best for budgets and debt servicing—but it should be recognized that mathematically-driven economics is a divergence from the foundation of traditional economics.

That Cold-Hearted Discipline – Article by David J. Hebert

That Cold-Hearted Discipline – Article by David J. Hebert

The New Renaissance Hat
David J. Hebert
November 6, 2013

But of all the duties of beneficence, those which gratitude recommends to us approach nearest to what is called a perfect and complete obligation. What friendship, what generosity, what charity, would prompt us to do with universal approbation, is still more free, and can still less be extorted by force than the duties of gratitude. —Adam Smith, The Theory of Moral Sentiments

A recent article by Wharton Professor Adam Grant has been popping up here and there, most recently in Psychology Today. Grant suggests that studying economics breeds greed, and he cites several studies to support his claim. The studies conclude economics professors give less money to charity than other professions, economics students are more likely to deceive others for personal gain, and people who study economics have less of a concern for fairness and tend to think that “greed” is okay.

To his credit, Grant does consider the alternative: that maybe economics actually attracts greedy people or that greedy people tend to thrive by studying economics. He dismisses these possibilities by noting that “there is evidence for selection . . . but this doesn’t rule out the possibility that studying economics pushes people further toward the selfish extreme.” He goes on to chide practitioners of the discipline for teaching self-interest in the classroom.

Finally, he concludes with four points that are meant to provide evidence of the social harm in studying economics, which can be summarized in two overarching points:

1) Economics justifies greedy behavior, and

2) Studying economics makes people less altruistic.

I want briefly to discuss these two points here.

Economics Justifies Greedy Behavior?

Studying economics, and specifically the role of incentives, teaches us that relying on altruism is a brave assumption that has but limited applicability. For example, among people we know, we can rely on a certain degree of altruism or benevolence. I know, for example, that my family and friends will be there for me not because I pay them to do so, but because they care about me. Similarly, they know I will be there for them. However, I don’t know the same thing about random people I encounter on the street.

And yet in order to enjoy the immense wealth that the division of labor affords us, society demands that we have interactions both with people we know well and people we do not know at all. These two distinct spheres of activity require two distinct forms of cooperation, which one might get from reading Adam Smith’s twin pillars of economics: The Theory of Moral Sentiments and The Wealth of Nations.

More tidily, perhaps, F. A. Hayek describes this situation in The Fatal Conceit by noting the difference between the macroeconomy and the microeconomy. Macro, in this context, refers to society as a whole, while micro refers to just the people to whom we are close. Hayek says that if we were to apply the same rules of the family unit to the macro, as would be the case if we were to allocate resources altruistically, we would destroy the macro. This is because there would be a complete lack of economic calculation, resources would be misallocated, and plans would fail to be coordinated (see these articles for more on economic calculation).

Hayek also notes that the reverse is true: If we were to apply the rules of the market to the family, we would destroy it as well. We don’t need prices and incomes at the dinner table to allocate the food. Even the most ardent defender of markets would agree that having prices and such as the means of allocating food at the dinner table would be wrong, just like paying your friends to help you move across town would be strange. (Beer and pizza don’t count.)

Instead, students of economics recognize not that greed is good, as the saying goes, but that greed can be transformed into the service of others given the proper institutional setting. That institutional setting, which has been thoroughly discussed elsewhere, is one that celebrates the role of property rights, prices, and profits (and losses) and recognizes their role in creating the incentives to properly husband resources, generates the information about the relative scarcities of various goods and transmits this information to consumers and producers in a quick and efficient manner, all of which provides a feedback mechanism to drive continued innovation.

Economics Makes People Less Altruistic?

Grant cites a 2005 article by Neil Gandal et. al. as concluding that “students who planned to study economics rated helpfulness, honesty, loyalty, and responsibility as just as important as students who were studying communications, political science, and sociology,” but that by the third year, economics students rated these values “significantly less important than first-year economics students.”

While the Gandal study does include such conclusions, it also includes much more. For example, economics students attribute less importance to fairness. Evidencing this, Gandal points out that, when questioned about the allocation of radio frequencies to different mobile-phone service providers, students who study economics are more likely to advocate selling the rights to the highest bidder while students of other disciplines are more likely to advocate for allocating the rights to “anybody who meets some minimal eligibility criteria.”

Students of economics do not advocate for property rights because we are greedy; we advocate for property rights because we understand and take seriously potential incentive problems in politics. The notion of minimal eligibility requirements may sound nice, for example, but problems may lie in who gets to draw that line, by what process that line gets drawn, and the incentives faced by the line-drawers. As Madison points out in Federalist 51, “If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary.”

Economics students know men are no angels. And as Nobel laureate James Buchanan points out, government officials are human beings, too, with their own hopes, dreams, and aspirations—and yes, forms of avarice. Supporting the allocation of resources to the highest bidder sidesteps the issues raised by these potential incentive problems. This means that the choice of how to allocate resources fundamentally comes down to a choice of institutions.

We can have a central authority establish guidelines by which anyone who wants can use the radio frequencies, or we can let the market decide. The former leads to a standard tragedy of the commons problem, whereby the radio frequency gets overused. In the case of cell phones, this means that the frequency would be crowded with multiple conversations simultaneously; imagine trying to shout to your friend across a crowded bar. The latter leads to the frequencies being allocated to the person who is best able to utilize them to serve the general population. So AT&T, for example, gets exclusive rights to a certain bandwidth and then tries to figure out how to best serve its customers. In this case, the customer gets to enjoy a clear phone call without the distraction of several other conversations in their ear simultaneously.

In any case, these are not examples of quelling altruism, but of keeping it in its place.

Less Greed, More Cooperation

Viewed in this light, economics does not so much teach greed but rather the beauty of cooperation. How else could we explain how a woolen coat gets made, how Paris gets fed, or how a pencil gets made? And if allocating, say, radio frequencies based on highest valued use makes people learn to discard fairness, well, how exactly is that a bad thing?

David Hebert is a Ph.D. student in economics at George Mason University. His research interests include public finance and property rights.

This article was originally published by The Foundation for Economic Education.


Editor’s Note by Gennady Stolyarov II: Mr. Hebert’s article is excellent in focusing on the true significance of economics and the need for private property rights. In one important respect, though, my position differs from his when it comes to the allocation of radio frequency to highest bidders such as AT&T and other entities exercising similar coercively granted monopoly and quasi-monopoly powers.

My position, arising out of similar libertarian principles, is that the allocation of radio frequencies to AT&T (and similar local/regional telecommunications monopolies) through the political process would not result in an economically optimal allocation, even if AT&T were the highest bidder. The reason for this is that AT&T’s very bidding ability arises out of (1) its decades-long history as the telephone monopoly in the United States and (2) the protections from competition that it enjoys in certain jurisdictions as a local or regional monopoly provider of certain services wrongly considered “natural monopolies” – such as high-speed cable services. In a pure free-market system, there would likely need to be some sort of allocation process for radio frequencies, so long as the use of radio frequencies by some parties has the physical ability to interfere with the use of the same frequencies by other parties. However, the outcome of such a free-market allocation process would differ considerably from the outcome of a bidding process in today’s status quo, conditioned by decades of deleterious path-dependency arising out of the privileges granted to AT&T and similar local/regional monopolists. Probably, an auction of radio spectrum on a purely free market would result in many smaller firms buying up many smaller ranges of spectrum and competing with one another more vigorously to provide superior customer service than do a handful of large, politically privileged telecommunications companies (AT&T, Comcast, Verizon, et al.) today. In this path-dependent, partially unfree environment it may be, in some cases, that allocations to lower bidders would result in better uses of resources and improved consumer outcomes, as long as institutional political privilege (e.g., enforced monopolies or historical insulation from competition) of the higher bidders can be incorporated into the bidding process in the form of some reasonable handicap used in considering their bids.