Paul Krugman

graciously responds to my

economath post, but demurs:

It turned out -- and still turns out -- that people's economic intuition,
if untutored by models, missed a major possibility that is in fact
probably the main story.

My question for Paul:

*Who* precisely are the people that intellectually benefit from being "tutored by models"?

1. Econ blog readers? Clearly not. Paul's blog has as little math as mine because we both know most people can't or won't follow the math.

2. Econ undergrads? No. Econ profs very rarely use economath in undergraduate classes because even upper-division students can't handle it.

3. First-year econ Ph.D. students? Probably not. When they arrive, they're perfectly able to follow intuitive economic arguments.

4. Advanced econ Ph.D. students? Maybe. But only because they've been brainwashed to dismiss intuitive arguments.

5. Econ professors? Often. But only because they're true believers in their own dogmatic methodology. Paul had to use math to explain his ideas to these people because they mentally raspberry any new idea unless it's expressed mathematically.

My challenge for Paul: Name three important economic insights you think we owe to economath. I will explain each insight without economath at a level accessible to any good undergraduate economics major.

P.S. Funner, high-cost challenge: Randomly assign econ undergrads to two classes. I teach one; a defender of economath teaches the other. Paul gives each teacher an hour to explain three important ideas we allegedly owe to economath. Then Paul tests our students to see how well they understand the ideas he picked. Prediction: Paul will name me the victor.

Notice that Krugman didn't make his response in algebra.

It seems he's offering himself as an example. My take away from his post is that sometimes you don't have an intuition about something, but having a simple model can help you get there. Krugman is saying that very few people intuited some of the main findings of New Trade Theory.

So Krugman's own work is a model showing how increasing returns implies specialization produces free trade gains to all countries, not just countries specializing in industries featuring increasing returns.

The idea was not new, but seeing it modeled explicitly convinced folks of its truth.

But given that a model can be produced for virtually any proposition, why is the ability to create a model implying the truth of a proposition convincing?

Bryan asks whose thinking is clarified by modeling.

My question is why the ability to model an idea counts as evidence the idea is true.

I agree with you, but Ricardo's Law of Comparative Advantage is very difficult to sell without a concrete numerical example.

I also find that the Fisher equation illuminates monetary theory better than intuition alone.

Perhaps these are not what you meant by "economath" though.

It will be interesting to see how Krugman responds to your challenge. Paul Samuelson reportedly said that the only non obvious, non trivial insight from economics was the law of comparative advantage, which can be understood and explained with a little arithmetic.

"Name three important economic insights you think we owe to economath. I will explain each insight without economath at a level accessible to any good undergraduate economics major."

Even if you can do it, it's irrelevant to the issue at hand. What you're talking about here is giving a hand-waving, conceptual argument after the fact. It's easy to rationalize things in this way. But actually coming up with the idea, being truly convinced by it, and convincing others that it's true usually doesn't happen without mathematical modeling.

To put it another way, anyone can use an iPad, but it takes an engineer to create one.

Here's a test for you--how mnay econ textbooks (at any level) are presented with no equations or model-based graphs? I'll bet there's none. That alone implies that a cost-benefit test strongly favors mathematical modeling, since equations and graphs are much harder to make and publish than mere words.

I don't think arithmetic or graphs are what anyone means by "economath".

It is impossible to not have a model in mind when discussing some economic problem. Any economic insight is based on a very simplified view of the world: one's own.

This discussion is centered around whether you should write down that view explicitly. It is easy to hide the economic model you are arguing with if you present it in words; it is much more difficult to do so in the mathematical language.

A very wrong verbal argument can appeal to my intuition by cleverly hiding the assumptions of the argument. If I am forced to write down the assumptions of my model in a precise language (like mathematics), this becomes more difficult.

That test won't show what you think it will show. Nobody will dispute the notion that you can take an insight provided by math and explain it in words. That's what most papers do. The question is, how likely is it that you would have arrived at that insight without first seeing it in math? Your test won't answer that question.

Of course the benefit of math varies between concepts. But seeing something in math then explaining it in words, as you say you'll do, supports the notion that math is useful as much as it discredits that notion.

Name three important economic insights that have been subsequently shown to be specious. I will explain each insight without economath at a level accessible to any good undergraduate economics major.

PK: "But that was not at all the point of New Trade Theory, which ended up suggesting that concentration of production due to increasing returns is generally beneficial to importers as well as exporters of increasing-returns goods, that it generally reinforced the case for open trade, rather than undermining it."

1) The math doesn't make the idea clearer, the way that, say Ricardo's model of comparative advantage does, or how Black-Scholes makes more sense than some rule of thumb. The idea in its entirety is amenable to a blog post.

2) If one believes in increasing returns to scale as a common general phenomenon, in my experience that person is more inclined to believe in selective tariffs, counter to his assertion that his New Trade Theory is "probably the main story" in import-export arguments for increasing trade.

The important thing is not whether or not you communicate using actual mathematical syntax. What is important is whether you think with the requisite level of precision. Perhaps laying out your thoughts with some algebra helps you to do that. In my case it doesn't as I already basically think purely in math even if I don't talk in math, but probably for a lot of people it does help.

In my daily life I am constantly surrounded by smart people who make claims about concepts that at root do have mathematical meanings, with a level of sloppiness that, if they had applied it to their high school algebra homework, would've prevented them from eventually getting the degrees that they now have. Clearly they have stepped up their logical coherence to a vastly higher level when called upon to write down their thoughts in mathematical language.

I think you won this battle.

Even with the liquidity trap, the basic idea that nominal interest rates can't be below zero (or much below zero) b/c why would anyone lend money today to get back less tomorrow, and thus places a constraint on normal Fed activity is a perfectly easy thing to explain and understand using simply the concept of zero rather than a new keynesian model.

Paul's papers are littered with real insights, but I suspect in most or not all cases he had the insight first and then designed the clever model second.

How about we back it up to most basic Laws (and I do mean capital-L Laws) of Economics: Demand and Supply.

Law of Demand: ceteris paribus, an increase in price results in a decrease in quantity purchased (and vice versa)

Law of Supply: ceteris paribus, an increase in price results in an increase in quantity offered for sale (and vice versa)

These are the most powerful propositions in economics. As I am fond of describing them, they are ironclad and unyielding. They have no exceptions (no, Giffen and prestige goods do not count).

Does ANYONE need, or even benefit from, a mathematical exposition of these ideas? In my brief encounter with grad school we went through the proofs of these Laws. Aside from being able to use these results in further economath, I benefited from this exercise not at all.

I took Math Econ at GMU, and every time Roger C described and set up a model (usually from a newspaper story) I would always have the right "intuition", would recognize all substitution and income effects, before Roger even began to solve the model. Since Roger's solutions to these models *always* matched my intuition I concluded that mathecon works, but is unnecessary. This, of course, supports the idea that it is a matter of comparative advantage: I taught at one school where most of my students were in engineering or Marine Sciences- lots of them found it better to think of demand and supply as a-bp and c+dp. Math has been unhelpful at every other school where I have taught econ in the past 19 years.

The one thing I would add to what Bryan posted is that "scientism" provides an incentive to over use math in econ. Models look impressive and scientific, many are impressed by the appearance of sophistication and intellectual superiority that models provide. Of course, verbal economics is often very hard too, but it looks less impressive to the casual observer.

How about a non-mathematical explanation of Black-Scholes pricing of a European option and why you don't need a forecast for stock price movements in it (which seems like a plausible intuition to me)?

Or Merton's model for pricing corporate debt and how it can be used to evaluate credit risk in structural credit risk models without going through balance sheet data (except debt to assets)?

Is it really so that you can bypass the mathematics, stochastic differential equations, etc. with intuition alone? I'd be interested.

True, both models aren't perfect, especially in the hands of those who believe in mathematics rather than understand it with all its limitations. But they aren't useless either.

@Finegold:

"Krugman is saying that very few people intuited some of the main findings of New Trade Theory."

Yes, and that those who *did* intuit those findings were not believed until the math came along.