kitchen table math, the sequel: Arnold Kling on the mathefication of economics

Wednesday, April 30, 2008

Arnold Kling on the mathefication of economics

An Important Emerging Economic Paradigm

By Arnold Kling

"… three types of activity generate a process of continuing and cumulative change. Trading creates new opportunities for innovation and institutional change. Innovation creates new opportunities for institutional change and trading. Institutional change creates new opportunities for trading and innovation. ...the process does not converge on or 'discover' a known or predictable outcome."
-- Meir Kohn

The Dartmouth University economics professor Meir Kohn has identified some important characteristics of an emerging alternative paradigm in economics. This approach, which he calls "the exchange paradigm" and which I prefer to call Learning Economics, is an important new direction in the field. The focus shifts from how an economy allocates a given set of resources to how an economy functions as a learning mechanism, sorting through innovations to find those that provide genuine improvements in living standards.

For those like Kohn and myself, trained in late-20th-century academic economics, appreciating the learning economy has brought with it a skepticism about the value of mathematics as a tool for economic analysis. If Kohn is correct, then economists of the past two or three generations may have committed one of the greatest blunders in intellectual history.

The most distinctive trend in economic research over the past hundred years has been the increased use of mathematics. In the wake of Paul Samuelson's (Nobel 1970) Ph.D dissertation, published in 1948, calculus became a requirement for anyone wishing to obtain an economics degree. By 1980, every serious graduate student was expected to be able to understand the work of Kenneth Arrow (Nobel 1972) and Gerard Debreu (Nobel 1983), which required mathematics several semesters beyond first-year calculus.

Today, the "theory sequence" at most top-tier graduate schools in economics is controlled by math bigots. As a result, it is impossible to survive as an economics graduate student with a math background that is less than that of an undergraduate math major. In fact, I have heard that at this year's American Economic Association meetings, at a seminar on graduate education one professor quite proudly said that he ignored prospective students' grades in economics courses, because their math proficiency was the key predictor of their ability to pass the coursework required to obtain an advanced degree.

The raising of the mathematical bar in graduate schools over the past several decades has driven many intelligent men and women (perhaps women especially) to pursue other fields. The graduate training process filters out students who might contribute from a perspective of anthropology, biology, psychology, history, or even intense curiosity about economic issues. Instead, the top graduate schools behave as if their goal were to produce a sort of idiot-savant, capable of appreciating and adding to the mathematical contributions of other idiot-savants, but not necessarily possessed of any interest in or ability to comprehend the world to which an economist ought to pay attention.

Where Math Works

Kohn points out that mathematical economics describes a world with a given set of goods to trade. The mathematical models answer the question: when all opportunities for profitable trade have been exploited, what will be the end result? This approach is a perfect fit for international economics, where we often are interested in tracing through the implications of opening a previously-closed country to trade. Many of Samuelson's classics are in this area, as are the works of Eli Heckscher, Bertil Ohlin (Nobel 1977), and James Meade (Nobel 1977).

The theory of finance offers another opportunity for mathematical economics to shine. By looking at how various financial claims will pay off under different circumstances, economists can make useful predictions about the relationships among various security prices. The portfolio theory of Harry Markowitz (Nobel 1990) and William Sharpe (Nobel 1990), the corporate finance model of Franco Modigliani (Nobel 1985) and Merton Miller (Nobel 1990), and the option pricing model of Fischer Black, Robert Merton (Nobel 1997), and Myron Scholes (Nobel 1997) combine mathematical elegance with empirical validity and practical application.


Schumpeter and Hayek

Friedrich Hayek (Nobel 1974) captured some aspects of the learning economy paradigm. Appreciating the importance of moving from the unknown to the known, Hayek focused on the "discovery procedure" embedded in market processes.

In some respects, the evolutionary mechanism of the learning economy was anticipated in Joseph Schumpeter's phrase creative destruction. As University of Reading, England economics professor Mark Casson put it,

"In their mathematical models of economic activity and behavior, economists began to use the simplifying assumption that all people in an economy have perfect information...That leaves no role for the entrepreneur..."

According to Schumpeter, the entrepreneur is someone who carries out 'new combinations' by such things as introducing new products or processes, identifying new export markets or sources of supply, or creating new types of organization. Schumpeter presented an heroic vision of the entrepreneur as someone motivated by the 'dream and the will to found a private kingdom'; the 'will to conquer: the impulse to fight, to prove oneself superior to others'; and the 'joy of creating.'"

The creative destruction that took place in Schumpeter's day was a relatively gradual process. As this Wired story reports,

"'Schumpeter probably was right all along,' says [then FCC Chairman] Michael Powell, 'but it's only now, at Moore's law speed, that you can actually observe it.'"

The theories of Schumpeter and Hayek do not translate well into mathematics. One can write down an equation and call it a "Schumpeterian" model or a "Hayekian" model, but such sterile exercises lose the flavor of their theories. As a result, there is not much room for their theories in the conventional economics Ph.D program.

The Role of Government

Many (but not all) disciples of mathematical economic theory are quite paternalistic. Markets result in the best allocation of resources only under a narrow and implausible set of assumptions. Most real-world markets possess features that make them unlikely to produce such an optimum, even after all opportunities for profitable trades are exhausted. By taking a sufficiently optimistic view of government's ability to correct such "market failures," one can become quite expansive about the scope for government involvement in the economy.

On the other hand, many (but not all) of the proponents of the learning economy are quite adamant that government's role ought to be reduced. I am in that camp.

My view is that innovation by trial-and-error is the most valuable economic process, and government intervention tends to be inimical to such innovation. Even when the market is producing unsatisfactory outcomes, my view is that eventually innovators will come along with better ideas. In that way, the market's errors tend to be self-correcting. Government's errors tend to perpetuate and to deepen.

Bureaucracies tend to resist innovation. [ed.: you can say that again] In fact, in a corporate setting, that is their function. External companies have lots of goods and services to sell to corporate America. Their own middle managers have lots of ideas. How can a company sift through all of these possibilities? The answer is bureaucracy.


However, simply being large and bureaucratic is not the chief problem with government. The main way that government impedes innovation is by siding with those who are threatened by innovation. The incumbents in an industry always look to government for protection. When their wishes are granted, economic progress is thwarted.

When you see a sector in the economy that lags in economic performance, either in relation to other sectors or to similar sectors in different countries, chances are that incumbent protection is at the root of the problem. In the United States, the biggest cost increases are in industries where government combines protection of incumbents against competition with subsidies in demand.


In higher education, no well-known university or college has gone out of business in my memory. Over this same period, countless corporate giants have bitten the dust. To me, this says that the incumbent protection racket in higher education works really well. There is hardly any entry, and hardly any exit. No surprise, then, that dousing this sector with subsidies leads primarily to inflation.

Mathematical Hazing

One of the best incumbent-protection rackets going today is for mathematical theorists in economics departments. The top departments will not certify someone as being qualified to have an advanced degree without first subjecting the student to the most rigorous mathematical economic theory. The rationale for this is reminiscent of fraternity hazing. "We went through it, so should they."

Mathematical hazing persists even though there are signs that the prestige of math is on the decline within the profession. The important Clark Medal, awarded to the most accomplished American economist under the age of 40, has not gone to a mathematical theorist since 1989.

These hazing rituals can have real consequences. In medicine, the controversial tradition of long work hours for medical residents has come under scrutiny over the last few years. In economics, mathematical hazing is not causing immediate harm to medical patients. But it probably is working to the long-term detriment of the profession.

I believe that I've observed -- and lived through -- the same process in the humanities, the difference being that in the humanities the move is toward theory.


le radical galoisien said...

Calculus was a necessity for studying economics only after 1970?

It just seems kind of weird, because the whole idea of increasing marginal cost, decreasing marginal benefit (and [dis]economy of scale effects) is basically begging for derivatives and the calculations of optima.

If AP Physics C can implement calculus, why not AP Economics (both exams)?

Anonymous said...

Wait, Kling says that in the wake of Samuelson's 1948 thesis, economists needed to know calculus. So before the 1970s, certainly. Probably widespread acceptance by the 60s.

but you're right, derivatives were invented by Newton, and financial derivatives were known to people investing in financial markets at the time of Newton, so why in the world wouldn't it have been present in economics until 1948 anyway?

I think the answer is academic economics wasn't exactly finance then. Academic economists of early the twentieth century were basically Galbraith and the Austrians. They were talking business cycles, economic growth, advertising, the role of government, etc. Words, words, words, ideas ideas ideas.

They taught the calculations of optimization with little differentials but basically gave their undergraduates the curves and the formulas without expecting them to derive them.

And don't mistakenly think that knowledge of math makes one a finance wizard. Someone here pointed to Long Term Capital Management to explain how modern trading houses use phds in math and physics, but of course, that just proves what arrogant idiots they are, as they went bankrupt because its projections for derivatives didn't foresee that the future is not the past. (They were even quoted as saying "the economic collapse of Russia was not in our model.")

Tracy said...

I emotionally agree with much of the concern over mathematical hazing, and then every now and then in an economics paper I read an assertion that really cries out for a mathematical proof behind it. For example, a paper about the existance of castes in India claimed that there was an economic advantage to "higher" caste people refusing to perform certain functions for themselves, as it improved their bargaining position compared with the lower castes. But nothing was given to support this argument. So it didn't convince me at all.

Mathematics means you have to be precise about what you are assuming, and you have to provide some argument. It's a good discipline.

And as for understanding Kenneth Arrow - well he's fundamental to social choice policy, he explains, mathematically, why all voting systems are imperfect. Then he also produced general equilibrium theory. It makes perfect sense to expect economics graduate students to understand him. If nothing else, if you don't understand GE theory you don't understand the basis on which other economists criticise it.

Catherine Johnson said...

I think I'll mention that I was quite friendly with some of the Long Term Capital folks for a time. They were great.

Gosh, now I wish I could repeat the line one of them told me......

But that would be wrong.

Mark said...

"I think I'll mention that I was quite friendly with some of the Long Term Capital folks for a time. They were great."

I have never met any of them, but the *did* help me to refinance my house into a lower interest rate mortgage in 1998, so I've always figured that I owed them a mental 'thank you.'

"Gosh, now I wish I could repeat the line one of them told me......

But that would be wrong."


Give! Give! Give!


-Mark Roulo

Anonymous said...

I'll accept they were great, and great fun, and great mathematicians, too.

But living in a bubble where you think your model is reality can happen to the brightest quite often, and with unfortunate results.

The map is not the territory.