TCS Daily


Limits to Math?

By Arnold Kling - May 30, 2006 12:00 AM

"at the end of 1985 it was clear only that [1995 Nobel laureate Robert] Lucas had picked a fight with [1987 Nobel laureate Robert] Solow...At that point perhaps only [potential Nobel laureate] Paul Romer thoroughly understood that his old teacher had picked a fight not just with Solow but with Romer too."
-- David Warsh, Knowledge and the Wealth of Nations, p. 248

As the excerpt above from his new book illustrates, David Warsh, a uniquely dedicated journalist, turns economics into melodrama. He takes a number of risks, both in terms of content and style, and not all of them work. But in the end, I believe that the reader will come away from his book with some understanding of how a set of important economic theories were developed and how they relate to one another.

There is another book that can be used to introduce a reader to the literature on economic growth of the past twenty years. Elhanan Helpman's Mystery of Economic Growth, which Warsh cites and praises, has many qualities that Warsh's book lacks. Helpman's work is focused, careful, thoroughly professional in its treatment of the economic issues, and well proofread. It is also a total snoozer. If you want to get excited about economics, read Warsh. If you get so excited that you think you might want to go for a Ph.D in economics, then I recommend Helpman as an antidote.

Speaking of antidotes, however, I cannot resist quoting these sentences from Warsh (p. 219).

"Even in those days [the 1980's] any number of people wanted to talk about knowledge workers and intellectual property. But none had much stomach for working through the transversality conditions in infinite-dimensional spaces."

Warsh tosses out this last phrase with no expectation that the reader will understand. Perhaps not even Warsh himself knows what it means. It could be that he has spent so many years reporting on academic economics that he has become a math snob by osmosis.

The Krugman-Romer Derivative

Warsh centers his story on Paul Krugman and Paul Romer, particularly the latter. If either or both of them should be awarded the Nobel Prize, Warsh's fame also will surge. In financial market terms, Warsh now owns a derivative security in Krugman's and Romer's careers.

In his profiles of Krugman and Romer, Warsh writes

"After graduating from Yale, [Krugman] moved in the fall of 1975 to MIT...MIT was still the single best place in the world to learn economics by a wide margin, thanks to the quality and commitment to teaching of its faculty...Romer had been among the twenty or so economics students who arrived at MIT in the fall of 1977." (p. 182, p. 196)

I myself entered MIT in 1976, but I did not see much of either Krugman or Romer. I remember feeling vaguely jealous of Romer for his good looks and somewhat less jealous of Krugman for his status as a sort of "teacher's pet." In retrospect, the relationship between Krugman and his adviser Rudiger Dornbusch must have been interesting. Dornbusch loved to play cat-and-mouse with the egos of graduate students (see Ken Rogoff's recollections in section D of his tribute to Dornbusch), and it has become clear over the years that Krugman's ego is easily ruffled -- in his own review of the Warsh book, Krugman can barely conceal his resentment that Romer gets top billing.

My own experience with the teaching faculty of MIT was not so positive. At one point, Robert Lucas, from the University of Chicago, came to MIT for a day to represent the Sweetwater school of economics -- this was a bit like coming to Fenway Park with a Yankees cap. I took those issues quite seriously and I was a strong Saltwater fan.

At that time, I was taking a required part of the macroeconomic theory sequence from Stanley Fischer, and I was completely unimpressed by the arcane mathematical topic we were studying, which was "monetary growth models." Before class began one day, Fischer asked what we had thought of seeing Lucas. In a voice laced with sarcasm, I said, "It was not nearly as relevant as monetary growth models."

In retrospect, I gave up on being an academic economist at that point. I was compulsive enough to complete my Ph.D thesis, and it took me a long time to switch to business and then to economic journalism. But when you address a decent, respectable gentleman (Fischer most recently was appointed head of Israel's central bank) with the spite and contempt a teenage girl shows her parents during a tantrum, you are in the wrong occupation. Oddly enough, Warsh points out that Krugman and Romer, in spite of much greater success, also have experienced periods of doubt about their fit with economic research as a profession.

I think that the case for a Krugman-Romer Nobel Prize is credible. I have to separate my views of Krugman the New York Times columnist (execrable) with my views of Krugman the research economist (original and significant).

Breaking the Law of Diminishing Returns

All students of economics learn the law of diminishing returns. The idea is that if you keep throwing more of a resource into a project, you will eventually start to see smaller and smaller gains in terms of results.

What Krugman and Romer homed in on are some phenomena that appear to break the law of diminishing returns. Krugman looked at economic geography, including the tendency for industries to concentrate in a given location. He also looked at the patterns of international trade, in which we observe things like intra-industry trade as well as industries, such as automobiles, where the same country is both an importer and an exporter. Krugman recognized that (a) such patterns are not explained well by traditional trade theory and (b) the reason that traditional theory fails is that it is overly wedded to the law of diminishing returns.

Romer looked at the phenomena related to the standard of living. He focused on the fact that economic growth has been speeding up over the past few centuries and the fact that the standard of living diverges sharply between rich and poor countries. Both facts are inconsistent with the law of diminishing returns.

An ongoing controversy concerns the source of increasing returns that would explain real-world behavior. Krugman and Romer created mathematical models that tied increasing returns to specific objects, such as a firm, a local industry, or a population. The first firm to reach critical mass may accumulate advantages over other firms, primarily by "learning by doing." A local industry, such as Hollywood or Silicon Valley, may accumulate advantages of spillovers between firms. A larger population may accumulate more scientific knowledge and inventions.

For explaining economic growth over time, the accumulation of knowledge represents a plausible source of increasing returns. Unlike labor, machinery, or natural resources, knowledge does not wear out or get used up. By the same token, however, it is difficult to explain how knowledge fails to spread across countries so as to minimize divergence in the standard of living.

New Institutional Economics vs. Mathematical Growth Theory

The challenge of explaining differences in the use of knowledge across different countries has given rise to what Warsh calls (p. 375) "the parallel universe of...literary growth theorists." These are economists who do not see salvation in the mathematical models of increasing returns. Instead, they see more promise in the analysis of economic institutions. In fact, rather than refer to themselves as literary growth theorists, they prefer the name "New Institutional Economics." I have discussed this sort of economics in several essays on TCS, most recently in Group Power.

The New Institutional Economics could be described using mathematical expressions that explain the increasing returns that Krugman and Romer seek to analyze. In What Causes Prosperity?, I suggested that economically successful societies have a work ethic, a public service ethic, and a learning ethic. Mathematically, one could describe this as leading to increasing returns because of interaction effects, threshold effects, and virtuous-cycle effects. However, as I pointed out in that essay, it is extremely difficult for a scientific observer to learn the true dynamics of such a highly nonlinear system. It is a bit like trying to figure out the personal identification number on a bank card in just three guesses. Since we do not believe that we are likely to get so lucky, most of us who take the New Institutional Economics point of view do not think that mathematical formalization is worth bothering about. Frankly, I feel that those who insist that economics must use mathematics are like the proverbial drunk who lost his watch but refuses to search where he lost it, instead looking under a lamp post because "that is where the light is."

My sense is that there are more mathematical growth theorists who are somewhat receptive to the New Institutional Economics than the other way around. I am not certain what to make of that. My sense is that many (but not all) mathematical growth theorists tend to favor activist government, but New Institutional Economists often hang out on the libertarian fringe. I am not certain what to make of that, either.

If you want to balance out your reading of Warsh, with its focus on the mathematical growth theorists, you might try my book, Learning Economics. It does not have the melodrama of Warsh, but it does present the alternative point of view.

TCS Contributing Editor Arnold Kling is an adjunct scholar with the Cato Institute. His most recent book is Crisis of Abundance, concerning health care policy.

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17 Comments

"The Spirit of Enterprise"

In addition to Mr. Kling's book, which I expect would be well written, an interested reader should get a copy of George Gilder's "The Spirit of Enterprise." It is Gilder's finest book.

Concepts like entrepreneurship and the "spirit of enterprise" are utterly foreign to the likes of Krugman. In a lively work, Gilder suggests why stolid mathmatical models are practically powerless to explain or predict economic reality.

what you put in
A real mathematical theory is built from a few simple empirical facts. Mathematical economics has the equations but not the empirics.

There are no famous datasets surprisingly explained by the new theories. (If you observe that demand goes down as price increases then fit a model
D = a/P + r: (Demand) = (fitting constant) X (recripocal of price) + (unexplained variation), you cannot say your model explains the fact that increasing price reduces demand. It's a statement of the fact, not a reason for it.)

The "Laffer curve" is like this, it's someone's belief, not a consequence of something that fits data. The Microeconomics book by Kreps is a case study: not a single empirical number, just philosophy: people make economic decisions to maximize expected utility. Now, there's a whole field of finance (behavioral finance) debunking this idea.

One thing Krugman has shown math is useful for.
Checking the numbers of tax proposals and other legislation, and uncovering deliberate fraud meant to mislead voters. As Krugman has done on numerous occasions.

arithmetic and common sense
I am a big fan of arithmetic and common sense. I believe that they can be applied effectively to criticize the Bush Administration. I also believe that they can be applied effectively to criticize Social Security.

But arithmetic and common sense is not what economics math snobbery is all about. Warsh's phrase about "transversality conditions in infinite-dimensional space" comes closer to capturing the atmosphere.

And Krugman's done just this with Social Security claims
for example:

Social Security turned 70 yesterday. And to almost everyone's surprise, the nation's most successful government program is still intact.

Just a few months ago the conventional wisdom was that President Bush would get his way on Social Security. Instead, Mr. Bush's privatization drive flopped so badly that the topic has almost disappeared from national discussion.

But I'd like to revisit Social Security for a moment, because it's important to remember what Mr. Bush tried to get away with.

Many pundits and editorial boards still give Mr. Bush credit for trying to "reform" Social Security. In fact, Mr. Bush came to bury Social Security, not to save it. Over time, the Bush plan would have transformed Social Security from a social insurance program into a mutual fund, with nothing except a name in common with the system F.D.R. created.

In addition to misrepresenting his goals, Mr. Bush repeatedly lied about the current system. Oh, I'm sorry - was that a rude thing to say? Still, the fact is that Mr. Bush repeatedly said things that were demonstrably false and that his staff must have known were false. The falsehoods ranged from his claim that Social Security is unfair to African-Americans to his claim that "waiting just one year adds $600 billion to the cost of fixing Social Security."

Meanwhile, the administration politicized the Social Security Administration and used taxpayer money to promote a partisan agenda. Social Security officials participated in what were in effect taxpayer- financed political rallies, from which skeptical members of the public were excluded.

I'm writing about this in the past tense, but some of it is still going on. Last week Jo Anne Barnhart, the commissioner of Social Security, published an op-ed article claiming that Social Security as we know it was designed for a society in which people didn't live long enough to collect a lot of benefits. "The number of older Americans living now," wrote Ms. Barnhart, "is greater than anyone could have imagined in 1935."

Now, it turns out that an article on the Social Security Administration's Web site, "Life Expectancy for Social Security," specifically rejects the idea the Social Security was originally "designed in such a way that few people would collect the benefits," and the related idea that the system faces problems from "a supposed dramatic increase in life expectancy in recent years."

And the current number of older Americans as a share of the population is just about what the founders of Social Security expected. The 1934 report of F.D.R.'s Commission on Economic Security, which laid the groundwork for the Social Security Act, projected that 12.7 percent of Americans would be 65 or older by the year 2000. The actual number was 12.4 percent.

continued at:
http://www.pkarchive.org/column/081505.html

Limits to Man
As I see it, there is mathematical economics (the study of growth in a logical universe) and psychological economics (the study of growth as a subset of the logical universe as limited by human genetic and cultural restraints).

As a realist, I can never accept a purely mathematical understanding as a basis for policy or even business. However, I have to emphasize the severe limitations of a psychological understanding -- it must change as we do. So if it's "difficult for a scientific observer to learn the true dynamics of such a highly nonlinear system" -- it's doubly so give the permanence of change.

For example, online gaming: within hours and without regard to geography, communitiees can coalesce to accomplish specific goals via distibuted tasks accroding to non-traditional ethics. Consequently, I encourage those interested in economics to learn from this phenomenon:

ESRC Centre for Research on Innovation and Competition
University of Manchester

The long term conceptual core of the research programme consists of three themes: Distributed Innovation Processes, Competing Concepts of Competition, and Consumption & Innovation.

http://les1.man.ac.uk/cric/

not a good example
I'm afraid this is one of his most mendacious exercises. FDR's people forecast a MUCH lower level of benefits than what we now have. What we have is FDR's program plus Nixon's add-ons plus others.

He is also mendacious in using trust fund accounting as his basis for saying that the program is "intact." The challenge with Social Security is that the level of promises that it makes in the future is much higher than the projected level of taxes, under assumptions of economic growth that are admittedly conservative. Trust-fund accounting says, "Never mind the shortfall in tax revenues. What matters is that there is another set of promises sitting around, called the trust fund."

I don't know a single respectable economist, not even Peter Diamond, Peter Orzsag, or others on the left, who think that Social Security does not need reform. See
http://www.dartmouth.edu/~vox/0506/0109/security.html

On this issue Krugman is as far outside the mainstream as the people who deny evolution. The fact that you found him convincing shows just how poorly-informed the public is on the economics of Social Security.

Not a convincing refutation at all.
Arnold, Krugman brings specific claims in for analysis. One claim was the claim that:

"'m writing about this in the past tense, but some of it is still going on. Last week Jo Anne Barnhart, the commissioner of Social Security, published an op-ed article claiming that Social Security as we know it was designed for a society in which people didn't live long enough to collect a lot of benefits. "The number of older Americans living now," wrote Ms. Barnhart, "is greater than anyone could have imagined in 1935."

Now, it turns out that an article on the Social Security Administration's Web site, "Life Expectancy for Social Security," specifically rejects the idea the Social Security was originally "designed in such a way that few people would collect the benefits," and the related idea that the system faces problems from "a supposed dramatic increase in life expectancy in recent years."

And the current number of older Americans as a share of the population is just about what the founders of Social Security expected. The 1934 report of F.D.R.'s Commission on Economic Security, which laid the groundwork for the Social Security Act, projected that 12.7 percent of Americans would be 65 or older by the year 2000. The actual number was 12.4 percent."

Is he inaccurate about this? Is he inaccurate about the Bush claim about African-Americans.

> On this issue Krugman is as far outside the mainstream as the people who deny evolution. The fact that you found him convincing shows just how poorly-informed the public is on the economics of Social Security.

And we're supposed to believe you because you say so? Krugman's talked about plans like the Dartmouth one you bring forward. I'm afraid you're letting your political animus toward him get in the way of the facts and the issues.

here is what I mean
Krugman's line about the 12.7 percent vs. 12.4 percent is a classic case of rhetorical use of statistics.

The reason that in 1934 the forecast was for a high percentage of people over 65 is *not* that they correctly projected that people would live longer. It's that they failed to foresee the post-war baby boom.

But that baby boom does not represent the salvation of social security. Quite the reverse. By 2020, the over-65 population *will* outstrip what was contemplated in the 1930's.

So Krugman's point is totally misleading. What's more, I believe that he knows it. His accusations that others play fast and loose with the facts are often on target, because he knows how to think about data. But that makes his own behavior even less excusable.

Social Insurance??!
Social Security from a social insurance

I would settle for changing it from a supposed investment/ retirement plan to social insurance.

Insurance against living too much longer than average: increase age that is needed to collect to above the average life expectancy.

Insurance against not earning enough money in a life time off work: people who earned more should get less not more from this social insurance program

The whole thing is a terrible fraud!



totally misleading???
I don't think so.

The Bush administration said the facts were X. The facts are Y. You have a reason why the facts are Y, but that does not make Krugman's point misleadin.The administration in fact said X.

But here's a more complete critique. He is specifically wrong where. Note that he does NOT say that there's no problem. What he does say is:

"Should we consider modest reforms that reduce the expenses or widen the revenue base of Social Security? Sure. But beware of those who claim that we must destroy the system in order to save it."

http://www.pkarchive.org/column/030504.html

A terrrible fraud!
If only those poor dupes forced into Social Security had been able to put their money into Enron and Worldcom stocks.

Other frauds do not make SS honest!
Support making SS into sensible social security insurance

1. Raise the age to required to collect.
2. Make it so the poor collect at least as much per person as the rich and middleclass.
3. Eliminate the SS and Medicare taxes and fund those programs from the general revenue so that people understand that SS is a welfare program not an investment program.

BTW poor people do not generally invest in the likes of Enron and Worldcom they invest in real-estate and family and in banks (thanks to FED money in bank accounts is wasted away). For those middleclass people who invested in Enron and Worldcom most will recover and do fine.

BTW it is your beloved government who keeps corporate person in existence and it is the corporate person that keeps the assets of management from reach of those bilked.

Middleclass and rich people should not be on welfare in retirement.

Bush is a liar. What does that have to do with the desirability of SS eom

one comment
>3. Eliminate the SS and Medicare taxes and fund those programs from the general revenue so that people understand that SS is a welfare program not an investment program.

SS has never billed itself as an investment program nor is it a welfare program.. It is a benefits program in which working people pay for the retirement of people who used to work on the expectation that others will do the same for them after they retire.

You might go to Chile & see
They did away with a SS-like system in favor of a market system - except for the government. It's a slow motion disaster. Check it out.

More Economics Theory
And if you want to read some more ideas on economics, particularly from a systems theory, complex nonlinear dynamics, emergentist point of view, I invite you to read www.zatavu.blogspot.com

It has many other topics, being an interdisciplinary site, but since it is an interdisciplinary site, it should become clear how a particular world view and scientific understanding of the world necessarily leads one to certain political and economic organizations.

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