a curmugeon’s journey through economath…Posted: 2013-08-26
For the many of us who have long left chalk or magic markers in the class room, and who still have vague memories of AER and its dense math some good news. And yes, from RGD Allen to Taro Yamane, as Edith Piaf would sing, ‘Je regrette rien’.
Here are a few posts, a rich smorgasbord, on the use of mathematics in economics that should provide some enjoyment and incentive for some maths calisthenics. And as we see from the quality of writing, and literary and intellectual reach, of the writers we appreciate the importance of communicating with clarity and concision, and, at times, doing so with dollops of irreverence – the likes of Month Python and The Princess Bride have enlivened many an otherwise rigorous post.
Just one post from Noah Smith on the usefulness of mathematics, or, rather, his disenchantment with much of its use, in economics is all it took. That post, A few words about math, on Noahopinion, harmless sounding enough, was sufficient to get the ball rolling, prompting posts on other blogs.
Krugman would jump in with his, The Point of Economath And Bryan Caplan jumps in response to Krugman, Economath Fails the Cost-Benefit Test, which prompts Krugman to jump back in response to Caplan, More Economath
Now, macro. Suppose somebody says something like “Well, government borrowing drives up interest rates, and higher interest rates depress private investment, so increasing government spending in a slump is actually contractionary.” People who try to do economics without any kind of mathematical modeling do indeed say things like that — and it’s very hard to explain why it’s self-contradictory nonsense without a bit of math.
All that said, yes, there’s a lot of excessive and/or misused math in economics; plus the habit of thinking only in terms of what you can model creates blind spots. I gave a set of lectures about that. (Actually, the reason I read Haberler back when was because I wanted to see if there were “lost” insights in macro comparable to the ones that had been temporarily suppressed in geography and development. I couldn’t find any; pre-Keynesian macro was just a mess).
This post comes across as a fairly comprehensive, very informative post in Magic, Maths and Money, Oedipus and the difficult relationship between maths and economics This gem of a post would takes us on a journey where we meet the ideas and contributions of illustrious personages such as Aristotle, Fibonacci, Bachelier, Descartes, Bertrand Russell and Samuelson. Rewarding reading.
From his earlier post Noah did highlight the usefulness of useful mathematics in economics. What is math, and why should we use it in economics?
So what do I think is a useful definition? When it comes to scientific methodology, I think of “math” as basically being the same thing as “precision of meaning.” This working definition is not a yes-or-no sort of thing; it’s a sliding scale. Methods can be more math-y or less.So what do I mean by “precision of meaning”? Basically, something with a precise meaning has fewer alternative things that it could mean. For example, compare the two scientific propositions:1. If you push something, it will push you back.2. Momentum is conserved.[snip]So why should we use math in economics? Well, I can think of a number of reasons:1. We may want to make precise predictions about what will happen in a market.2. We may want to make precise predictions about the conditions under which things will happen in a market.3. Precise statements often help resolve debates, avoiding the phenomenon of “talking past each other”.4. Precise statements often lead to unintuitive but logically inescapable results.5. It is usually easier to check sets of precise statements for logical inconsistencies.I think all of these reasons are good reasons sometimes and bad reasons sometimes (note how imprecise of a statement that is!). I have no hard-and-fast rule about how much precision to use, and when. But I do know that if you tried to implement a Shapley-Roth matching algorithm without mathematically precise statements about what happens when, it would be hopeless.
And Comments, many worth a read, do give the viewpoint of the empirical analyst and the critical-thinking reader.
Of course, the overall point comes through, for example, with the frequent, sloppy use in the media of ‘increase in demand’ for ‘increase in quantity demanded’.
In all this, just as SHAZAM or STATA or R is never far, so too ever close are authors such as Kindleberger, JK Galbraith, Adam Smith, Findlay and O’Rourke… And on this we have the recent post by Krugman, as he ‘introduces’ Steve Ballmer to 14th Century philosopher Ibn Khaldun – no math there, but more enlightenment and incentive to continued curiosity for us all.
The joys of the gift from Tim Berners-Lee…