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Explication, Language, and Mathematics in Economics: Thinking Like an Economist

In Defense of Funny Diagrams

A great deal of stuff relevant to teaching, reading, and doing economics. Also highly relevant to: Brad DeLong: Optional Teaching Topic: How to Think Like an Economist... (Provided, That Is, You Wish to...) (Pre-Class? Mid-Class?):


Tim Taylor: Some Thoughts About Economic Exposition in Math and Words: "[Paul Romer's] notion that math is 'both more precise and more opaque' than words is an insight worth keeping...

...It reminded me of an earlier set of rules from the great economist Alfred Marshall, who... wrote in 1906 letter to Alfred Bowley (reprinted in A.C. Pigou (ed.), Memorials of Alfred Marshall, 1925 edition, quotation on p. 427): 

But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics; and I went more and more on the rules:

  1. Use mathematics as a shorthand language; rather than as an engine of inquiry.

  2. Keep to them till you have done.

  3. Translate into English.

  4. Then illustrate by examples that are important in real life.

  5. Burn the mathematics.

  6. If you can't succeed in 4, burn 3.

This last I did often.... Mathematics used in a Fellowship thesis by a man who is not a mathematician by nature—and I have come across a good deal of that—seems to me an unmixed evil. And I think you should do all you can to prevent people from using Mathematics in cases in which the English language is as short as the Mathematical...


Paul Romer adds some rules of his own...

  1. The test is whether math adds to or detracts from clarity and precision. A writer can use either the words of everyday language or the symbols from math to make assertions that are clear and precise; or opaque and vague.
  2. The deep problem is intent, not ability or skill.
  3. Writers who want to make predictions use words and math to be clear and precise. Writers who want to make excuses use words and math to be opaque and vague.
  4. Compared to words, math and code tend to be both more precise and more opaque...

I might quibble a bit with his rule #2, because my sense is that many of those who fail to communicate clearly, whether in math or in words, either have simply not put the time and effort into doing so, or lack the ability/skill to do so...


Dani Rodrik... includes the following...

  1. Make your model simple enough to isolate specific causes and how they wor...
  2. But not so simple that it leaves out key interactions among causes...
  3. Unrealistic assumptions are OK...
  4. Unrealistic critical assumptions are not OK...
  5. Do not criticize an economist’s model because of its assumptions...
  6. Ask how the results would change if certain problematic assumptions were more realistic...
  7. Analysis requires simplicity...
  8. Beware of incoherence that passes itself off as complexity...
  9. Do not let math scare you...
  10. Economists use math not because they are smart, but because they are not smart enough.

And, of course, John Maynard Keynes: John Maynard Keynes (1924): What Is the Excellence of an Economist?: "The study of economics does not seem to require...

...any specialised gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician...





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