Arnold Kling  

Sowell on Math and Economics

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A while back, we discussed whether math is necessary for economic education. Thomas Sowell gives his view.


Introductory economics is too often taught as if the students in it were all potential economists who had to be introduced to the standard graphs, equations and jargon that they will need in higher level courses or in the profession.

With all the time that is devoted to equipping these students with tools that they will never use again, some may leave an introductory economics course with little more understanding of real world economic issues than they would have had if they had never taken the course.


There have been various attempts to do this, from Sowell's Basic Economics to Russell Roberts' romance novel The Invisible Heart.

UPDATE: David Warsh offers an appreciation of Paul Samuelson, the pivotal figure in the movement toward mathematics in econoimcs.

For Discussion. Do you recommend any nontechnical introductions to economics?



COMMENTS (38 to date)
Steve writes:

I reccomend another Russell Roberts book ("The choice") for those who are not formally educated in Economics but would like to learn more about free trade.

I've read it, and it helped temper my anger over the current situation, but didn't fully change my mind over free trade vs fair trade because it doesn't address the long term unemployment situation that arises when a communist or socialist government tries to export its deflation problem to an otherwise prosperous capitalist country such as our own.

Gautam writes:

Henry Hazlitt's "Economics in One Lesson"

and a recent text which I have not read

Gene Callahan's "Economics for Real People"

David Thomson writes:

The exaggerated emphasis on math is due to the inferiority complex of many professional economists. They wish to delude themselves that they are hard scientists and not members of the liberal arts community. It’s really as simple as that. Understanding human nature is of far greater importance than pure mathematics. Alas, the mystery of what makes people tick is inherently difficult to investigate in a test tube.

Chevalier writes:

Steven Landsburg's 'The Armchair Economist' as well as 'Fair Play'. Accessible to anyone, even kids with the later title.

Luke writes:

For general economics introduction, I can fully endorse Basic Economics by Sowell.

After taking two economics courses in college, I changed my major to Economics. The technical aspects are very interesting to me, but the books to read for getting a grasp of economic causes and effects on practical life are:

Basic Economics, Sowell.
Free to Choose, Friedman.
Road to Serfdom, Hayek.

Rob writes:

Hidden Order: The Economics of Everyday Life. David D. Friedman. It has graphs and it is not dumbed down but everything is explained in English. I think David has a pretty unique ability to explain economics in plain English. Maybe it is because he grew up with it and has never had any formal training in Econ.

Lawrance George Lux writes:

Arnold,
You should not give me opportunity to plug my own books. lgl

Ramiro Loureiro writes:

As a student I would like to state that I disagree with those economist who have something against math. Math is a tool, a useful tool; and although it may not supply us with all the answers we would expect, maybe it´s because we haven´t developed it enough. I always remember a proffesor I once had, quoting Samuelson "Math is a languaje, just that it´s more precise" (sorry about my english, obviously not a native speaker)

Monte writes:

Hubert Humphrey once said he learned more about economics from one South Dakota dust storm than he did in all his years in college. Maybe we need more bad times and less books on the subject.

David Thomson writes:

“I always remember a proffesor I once had, quoting Samuelson "Math is a languaje, just that it´s more precise"”

I hope to God that you are joking. Are you sure that Samuelson actually said something that stupid? Could you possibly be taking him out of context? Math is definitely not a language.

dsquared writes:

"Almost Everyone's Guide to Economics", by JK Galbraith and Nicole Salinger.

How can you not like a book which has lines like:

"Social tranquility at all times and in all countries is always advanced by the cries of anguish of the affluent. They have a much deeper sense of personal injustice than the poor and a far greater capacity for indignation. And when the poor hear the primal screams of the well-to-do, they imagine that the fortunate are really suffering and became more contented with their own lot. Good statesmanship has always required not only the comforting of the afflicted but the afflicting of the comfortable."

Lawrance George Lux writes:

I personally found 'Jesus' by reading Jacques Ellul. His works (major) were published in English in the early 1960s. The reason I liked him lay in the fact he was pre-New Age Economics. He did not specifically write on Economics, but dealt with modern Political/Social/Economic developments from the prospective of pre-Modernism in a methodological manner. lgl

David Thomson writes:

“How can you not like a book which has lines like....”

It’s very easy to dislike a book that fails miserably to make the proper distinctions. One must not forget that the affluent often unwittingly cause far more harm than good. Has everybody forgotten Friedrich Engels? Good intentions are not alone sufficient. You also must have your head on straight.

John Kenneth Galbraith has done enormous damage to the world. His socialist policies have inadvertently brought about much suffering. The Kennedy administration, for instance, sent Galbraith to India. This was a terrible thing to do.

Arnold Kling writes:

"Hubert Humphrey once said he learned more about economics from one South Dakota dust storm than he did in all his years in college. "

I was an intern for Senator Humphrey in 1973, when I was a sophomore in college. Even though in those days I was a McGovernite liberal, I could see Humphrey's economic proposals were madness. One of his pet projects was the creation of a national development bank which would have taken capital allocation decisions out of the private sector and given them to a government agency.

I can believe that he learned little or no economics in college--or at any other time. I was appalled by Humphrey's ignorance of the subject.

Seeing Congress close up was a major step in creating doubts in my mind about the efficacy of government.

David Thomson writes:

“I can believe that he learned little or no economics in college--or at any other time. I was appalled by Humphrey's ignorance of the subject. “

Hubert Humphrey is a quintessential example of someone who had a good heart---and a messed up intellect. We constantly hear about his kindness and concern for the poor. Unfortunately, this is simply not sufficient. The man failed to have a clue about economic matters. Thus, he caused enormous damage. It’s as simple as that.

Monte writes:

“I can believe that he learned little or no economics in college--or at any other time. I was appalled by Humphrey's ignorance of the subject.”

I hope you understand I was being somewhat facetious (I’m conservative to the point of believing that even the rich deserve a square deal). I don’t know enough about Senator Humphrey to comment one way or the other on his knowledge of economics, as he was a little before my time (apologies, Arnold). But his point is well taken.

Economics provides no reason for us not to believe that experience is the best teacher.

Ramiro Loureiro writes:

DAVID THOMPSON: "During the early 50s, in a meeting organized by the American Association of Economy, Machlup and Samueelson debated about the use of math in the economical analisys. Samuelson supported the idea that math is a languaje, just more precise. Then Machlup asked him: "So math is a languaje. How do u say I love you in math terms?""
(Fein, R:"Eli Ginzberg: listener and scribber", in Horowitz, I.L.: ELI GINZBERG, THE ECONOMIST AS A PUBLIC INTELLECTUAL, 2002)

I do not think I took him out of contest!!

There was a discussion about this topic (good, non-math-y starter econ books) over at my blog. Here's the link to the posting and its comments:

http://www.2blowhards.com/archives/000703.html

Monte writes:

A good introductory text that I cut my teeth on is "Economics" (Samuelson & Nordhaus, 13th edition). Despite the gross oversimplifications and one major faux pas ["...the Soviet economy is proof that, contrary to what many skeptics had earlier believed, a socialist command economy can function and even thrive" (pp. 837)], it's an otherwise excellent treatise.

It encompasses all the fundamentals, and the math is only ankle deep for those who fear they may be getting in over their heads.

Scot Johnson writes:

I vote for _Hidden Order_ by David Friedman and _The Armchair Economist_ by Steven Landsburg as mentioned above. Excellent books, both.

David Thomson writes:

“I do not think I took him out of contest!”

I have not spent much time learning about Paul Samuleson. However, my tentative views are extremely negative. Language is the exact opposite of mathematics. The latter is a hard science while the former is based solely on prudential judgment. Words constantly change in meaning whereas numbers remain static. If Samuleson fails to understand this point---then he is a fool and his Nobel Prize is unearned and fraudulent.

William Utley writes:

"address the long term unemployment situation that arises when a communist or socialist government tries to export its deflation problem to an otherwise prosperous capitalist country such as our own."

What deflation? All I see is inflation coming down the pike. Also, how is the tremendous commodity demand from China contributing to deflation?

Steve writes:

About 500 million unemployed people clamoring to work for $1,000/year will temper your inflation fears.

Eric Krieg writes:

"New Ideas from Dead Economists". Not a lick of math in the entire book! It is economics (and history!) for the lay person.

Eric Krieg writes:

>>"Social tranquility at all times and in all countries is always advanced by the cries of anguish of the affluent. They have a much deeper sense of personal injustice than the poor and a far greater capacity for indignation. And when the poor hear the primal screams of the well-to-do, they imagine that the fortunate are really suffering and became more contented with their own lot. Good statesmanship has always required not only the comforting of the afflicted but the afflicting of the comfortable."

God no!

Everyone has a certain "interest". Our republican (small r) form of government ensures better than most that no one interest, be it rich or poor or whatever, can become dominant without at least SOME support from other interests.

As a result, programs like the New Deal were implemented with the support of aristocrats, not the least of which was FDR himself.

Today we have something of the reverse. Republican policies are seen as being good for "the rich", but there isn't a Republican in America who could be elected without the support of the Wal-Mart set, people who are fiscally poor, but socially conservative.

And Democrats, who are supposedly the defenders of the poor, have come to represent people with very high incomes: municipal bond traders, academics, public employees, trial lawyers, and teachers.

The person who really seems to be out in the cold these days is the traditional Democrat. A trade unionist who is socially conservative really has no place in either political party unless he compromises either on economics or social policy.

Steve writes:

->And Democrats, who are supposedly the defenders of the poor, have come to represent people with very high incomes: municipal bond traders, academics, public employees, trial lawyers, and teachers.

Eric Krieg writes:

>>How do you figure muni-bond traders? Those are the folks who are in the vaunted "investor class" who get all the benefits.

Come on, Steve. Think about it.

I'm not talking about your Grandma here, who is trying to minimize her taxes. I'm talking about guys like Jon Corzine and Robert Rubin, the guys who work on Wall Street and bring the bonds to market.

Eric Krieg writes:

>>Academics have high incomes? PLEASE
Public employees have high incomes? Perhaps after 30 years of service.
Trial lawyers--I'll give you that one
TEACHERS?!!?! TEACHERS?!??! I guess in bizzaro world where $25k/year is "high" income.

Just because academics and teachers don't start out with high incomes does not mean that, on average, they don't have high incomes. On average, they have very high incomes (relative to most Americans, not to Donald Trump).

And don't forget that academics and teachers don't work 50 weeks a year like most schlubs. They have other employment prospects in addition to their main job.

I'm really thinking of the NPR crowd. People who listen to NPR are Democrats, and they have very high incomes. They are NOT you grandfather's kind of Democrat.

Steve writes:

John Corzine and Robert Rubin are politicans to me. I had no idea of prior employment.

The NPR crowd? Do you think that my left-leaningness is because I listen to NPR? I'm asking from a serious standpoint here. I've always thought their reporting was center of the road and even-handed. Perhaps I've been brainwashed by my car radio? Is Paul Krugman right (in your eyes) about anything he says? He says some pretty scary stuff, and I believe him because I see what he is saying with my own eyes.

Is there any place on the dial where I can get a more conservative economic viewpoint to try to sway me to your side?

One thing is sure. This country is becoming more and more polarized. Fewer people are making more of the money and attaining more and more of the wealth.This was PK's point today on NPR. It's like the 1920s. Nobody is disputing this on either side. Is this my leftist-brainwashed side talking or is what I'm seeing for real?

Eric Krieg writes:

>>John Corzine and Robert Rubin are politicans to me. I had no idea of prior employment.

Well maybe you should look into it.

And while you are investigating, please explain to me how Rahm Emmanual could earn 16 million dollars as an "investment banker" from the time he left as Clinton's Chief of staff in 2000 to the time he was elected Congressman from Chicago in 2002.

>>The NPR crowd? Do you think that my left-leaningness is because I listen to NPR?

Absolutely not. Nobody who listens to NPR is going to vote for anyone other than Dean. That's not you.

>>I've always thought their reporting was center of the road and even-handed. Perhaps I've been brainwashed by my car radio?

And I think Rush is center of the road and evenhanded. What's your point? We are ALL comfortable with media soures that fit our political profile.

>>Is Paul Krugman right (in your eyes) about anything he says?

No. I wouldn't even say that Krugman is right about economics! Certainly, when it comes to politics, he is clueless. Everything he has written about Dubya has been proven wrong with time.

>>He says some pretty scary stuff, and I believe him because I see what he is saying with my own eyes.

www.poorandstupid.com

Krugman is a documented liar.

>>Is there any place on the dial where I can get a more conservative economic viewpoint to try to sway me to your side?

Come on, man. The dial IS conservative! Listen to ANYTHING. Except NPR, of course (and that would be conservative too if the government weren't funding it).

>>One thing is sure. This country is becoming more and more polarized.

Politically, yes. We are VERY polarized politically.

>>Fewer people are making more of the money and attaining more and more of the wealth. This was PK's point today on NPR. It's like the 1920s.

And his proof is, what, exactly? I don't think that the statement can be proven as fact.

Not that I don't think we have some real problems in this country. Socialist Insecurity, Medicare, and affordable housing are big on my list. But where are those on PK's radar? In fact, I would be willing to bet that PK is part of the problem on those 3 issues.

>>Nobody is disputing this on either side.

That's only because you aren't listening. People ARE disputing every last thing that PK says.

>>Is this my leftist-brainwashed side talking or is what I'm seeing for real?

The former.

I've started to listen to NPR again. I had stopped during impeachment, because they were such little pro-Clinton blowhards (with the emphasis on BLOW). But the lack of commercials is just too tempting. Commercials drive me nuts.

I got a TiVo like device for Christmas that makes mp3s off the radio (RadioYourWay is the product). Hopefully I can start taping the programs that I like and eliminate the commercials.

Steve writes:

Rush, Hannity, and O'Reilly. What do they all have in common? None has a PhD in Economics and none went to MIT. I want to hear from an Economist, not a right-winger who spouts taking-points all day long.

Eric Krieg writes:

>>I want to hear from an Economist, not a right-winger who spouts taking-points all day long.

PK is proof that being an economist does not preclude one from regurgitating talking points.

Charlie writes:

I will grant that as a mathematicians of sorts (officially my PhD work was computer science) I end up seeing it the opposite way from David Thompson: I can't see how you can possibly say anything sensible, rigorous, and predictive in economics without mathematics.

As to "how do you say 'I love you' in mathematics?" -- fair enough. But how do you state the Central Limit Theorem without it? Or discuss random walks and the Gambler's Ruin? All of them are essential and central to understanding economics.

Scott M. Harris writes:

"I can't see how you can possibly say anything sensible, rigorous, and predictive in economics without mathematics."

The operative word here is "predictive." Yes, mathematics is the best means of expressing theories designed to help us predict. However, it is an extremely lame means of explaining what goes on in economies. If you don’t believe this, consider how we might model Toyota’s rapid tool setting strategy, which lies at the heart of their learning-by-doing production strategy:

We can model Toyota’s rapid tool setting strategy by combining a marginalist economic order quantity (EOQ) model with a learning curve. Solving this little learning-by-doing model requires assigning a value to the knowledge created. Given that knowledge is inexhaustible, i.e., using knowledge doesn’t deplete it, how does one assign this value? One can’t without knowing exactly when and where the new knowledge will be used in the future. (Don’t forget the other fifty identical machines and five hundred similar machines in your production system and the “social” benefit of two hundred thousand similar machines around the world!) The possibility of learning through experience changes the tractable closed-ended EOQ problem into an intractable open-ended one.

Even though we can’t solve this little learning-by-doing model, we can nevertheless learn from it: it is wise to setup more frequently than what the EOQ model says is “efficient.” What is “economic” is not wise. (Frank Knight wrestled with this dilemma for decades.)

The possibility of solving our problems by creating knowledge compels us to think about our ultimate ends, what it is that we ought (owe to ourselves) to seek. Exactly how does one model this problem mathematically?

Whether we recognize it or not, we humans are compelled by our internal programming to learn to live good lives. We are compelled to be both researchers and research subjects in an ongoing human program to discover and test knowledge useful in living good lives. Until all of us act wisely, managing this program well requires distinguishing between theories designed to help us predict, which help us evaluate alternatives, and theories designed to help us explain, which help us formulate alternatives. It’s just good common sense.

S.M.Wobbe writes:

I think the importance of mathematics in teaching economics relies on the intentions of the course. While, a principle or introductory course is required for young, aspiring economists, it is sometimes chosen as an elective by non-econ majors. For the economic students, I feel that mathematics is necessary, since it is an integral part of economic theory. On the other hand, for a student who does not wish to major in economics or plan to take an economics course beyond the introductory level, math should be peripheral to theory. Many people are scared off by the math that is associated with econ, and it is very important that everyone have a general idea what economics is and how it penetrates our lives on a day to day basis. Far too many professors emphasize graphs, math, and models; this leads to a lot of students hating their econ elective and not learning very much. For example, an undergraduate student (non-econ major, taking principles of micro as an elective) recently complained to me about doing poorly on a quiz. He said that his professor wanted him to graphically explain what would happen to supply and demand for coffee if there was a sudden crisis in Colombia, hurting coffee bean crops. He couldn't do it, and said "I know what would happen, and I can explain it in writing, but I cannot draw a graph." Then he told me he hated microeconomics. It is too bad that economics, in a way, excludes people who don't understand math, because there is a lot more to it than that. And if more people were educated on general concepts, we would have a better informed society which could better make sense of things that happen in our nation.

Scott M. Harris writes:
For example, an undergraduate student (non-econ major, taking principles of micro as an elective) recently complained to me about doing poorly on a quiz. He said that his professor wanted him to graphically explain what would happen to supply and demand for coffee if there was a sudden crisis in Colombia, hurting coffee bean crops.

The operative word here is "explain." Clearly, the professor wanted the student to demonstrate his knowledge of Alfred Marshall's comparative static tool kit. As Milton Friedman pointed out in 1953, the purpose of these tools is to help us evaluate alternatives. Unfortunately, the professor used “explain” rather than “predict.” We use explanations to help us think about what happens in economies. In other words, we use explanations to help us formulate alternatives. Whether the professor intended to or not, he was telling his students to use Marshall’s tool kit normatively. This is a recipe for disaster. Marginalist efficiency cannot long compete against managerial excellence. Where the latter embraces solving our problems by creating knowledge, e.g., learning through experience, the former ignores it. Using the concept of marginalist efficiency to formulate alternatives is not rational. It is foolish.

I agree that the economics profession ought to do a better job teaching the public about economics. In fact, one of my professors, George Leland Bach, made this a major part of his life’s work. To succeed at this task, the profession must provide the public with the right tools. Marshall’s tool kit is the right tool for helping us evaluate alternatives. It not the right tool for helping us formulate alternatives.

Scott M. Harris writes:

I should add that I sympathize with the student. When I was an undergraduate, I was forced to learn Hicks’s IS-LM model. Learning it was as much of a chore as memorizing Lewis Carol’s nonsense poem, “Jabberwocky.” At the time I thought I hated macroeconomics. In retrospect, I just hated nonsense. Hicks, much to his credit, eventually recognized how simplistic his model was.

The moral here is that the more useful a model is, the easier it is to learn. Economists ought to explain the very real limits of marginalist economics.

Marina writes:

What can you say about the popular "Economics" by Campbell, MacConell and Brue?
Could it be the best economic guide for the students of such speciality?

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