Friday, July 23, 2010

First Approximations

Greg Mankiw posts a letter from an editor friend in response to a blog post of his sharing Robert Solow’s views on modern macroeconomics. The editor writes:
“I was particularly interested to read the following sentence:

"But this is not a bad FIRST APPROXIMATION in many cases."

I don't think I have edited one econ manuscript that has not used the phrase "first approximation" many, many times. When econ PhDs are given out, are you all required to sign a secret agreement that says you must use this phrase in anything you write? Note that I have not found a similar phrase in the other disciplines for which I've edited several books (chemistry, biology, anatomy, physiology, genetics, physics, political science, and history).”
This concern caught my eye because I noticed this phrase “first approximation” in another well known piece of economics I was reading recently: the General Theory of Employment, Interest, and Money. In Keynes’s discussion of the time structure of production, he introduces the section with:

“It follows from this that the assumption upon which we have worked hitherto, that changes in employment depend solely on changes in aggregate effective demand (in terms of wage-units), is no better than a first approximation, if we admit that there is more than one way in which an increase of income can be spent. For the way in which we suppose the increase in aggregate demand to be distributed between different commodities may considerably influence the volume of employment. If, for example, the increased demand is largely directed towards products which have a high elasticity of employment, the aggregate increase in employment will be greater than if it is largely directed towards products which have a low elasticity of employment.”

I’m not sure if Greg Mankiw’s friend is offering a criticism or what, but I think this is a good thing. I don’t think you see “first approximation” talk in chemistry, anatomy, physics, or genetics because the material these sciences deal with is either (1.) sufficiently precise that talk of “first approximations” is irrelevant, or (2.) sufficiently sensitive that “first approximations” aren’t useful to talk about (you don’t want to build a nuclear reactor on the basis of a “first approximation”).

We know that economics studies an extremely complicated system with lots of feedback loops, and that the components of the system are harder to measure than those other disciplines. It’s also reasonable to think that “first approximations” are still useful in economics. Even economists who eschew policy intervention eschew it on the understanding that, for example, expansionary monetary policy will cause some imprecisely known degree of inflation. Lack of precision as to how much doesn’t weaken the negative response to the policy (nor the positive response, for that matter).

I think you don’t see talk of “first approximation” in biology, political science, and history because these fields usually aren’t rigorous enough in their modeling to even need it. When they do model (think, for example, population dynamics or epidemiology) I’m not sure if they say “first approximation” – but it would certainly be appropriate for them to qualify that such models are first approximations. Same with meteorologists and other scientists that do rigorous modeling of complex systems.

So I agree with Mankiw’s friend – the origin of the use of the term is probably cultural as much as anything else. But we should be glad economists are conscientious enough to approach their work in this way! They know the qualifications that hem in their work. Whether journalists, politicians, or the public get the picture is a different matter, of course.


  1. Sounds like a CYA phrase - all disciplines have such.

    "I think you don’t see talk of “first approximation” in biology ... because these fields usually aren’t rigorous enough in their modeling to even need it."

    You are wrong about this ... there has been a modeling explosion in the biological sciences in the last twenty years.

  2. I'm not wrong, Xenophon. Once again, me making a comparison to economics is not me saying that there is no or there is trivial modeling in biology. I even cited several.

    Of course there is. For that matter, there is modeling in history and especially political science too.

    But in none of these disciplines is modeling of phenomena as rigorous or as relied upon as it is in economics, which is the point.

    You often read comparative statements as absolute statements - I'm not making an absolute statement here.

  3. "But in none of these disciplines is modeling of phenomena as rigorous or as relied upon as it is in economics, which is the point."

    And you are wrong with regards to biology. You are just wrong.

    So clue me in ... when was the last time you read a modelling study on morphology?

    This is the key part of your statement BTW:

    "When they do model..."

    Biologists model *everything* now.

  4. Look, I just don't think you are aware of the changes that have happened in biology since the 1980s regarding modeling. Really, there has been a dramatic leap in the field.

  5. Xenophon, I'm aware of the advances. Two of my math professors were mathematical biologists. You assume everyone is ignorant because, yet again, you interpret statements in the most extreme way you can conceive of. I'm ending this. I'm not going to continue to argue with you over your misinterpretation of what I'm communicating here.

    As for the comparative use of modeling between economics and biology, I just spent some time reviewing recent articles in Ecology, the Journal of Biology, and Cell. You do the same exercise and try to tell me with a straight face that the modeling is comparable. I don't know how Journal of Biology compares, but Ecology and Cell are very prominent journals in their sub-fields and I picked them because those sub-fields are particularly likely to utilize modeling.

    Cell didn't have much of anything in this respect.

    Ecology did, most was mahalanobis distance work, and cluster analysis - not surprising for an ecology journal. But this stuff (1.) is nothing you wouldn't see in economics, (2.) nothing that you need anything more than an undergrad degree for (I did this stuff before getting a graduate degree), and (3.) it's not even really modeling - it's mostly empirical work.

    Another place to check would of course be epidemeology which would probably come up with a picture similar to the ecology journal - moderate to common modeling, not especially complicated, but certainly tougher stuff, mostly data characterization and empirical work.

    Morphology, perhaps, is another route.

    Empirical work is a different story entirely - biostatistics has a long history, and it has contributed a lot to empirical social science. But sophisticated empiricism is very different from modeling. It doesn't require the same sorts of qualifications and "first approximation" caveats. I didn't think we were talking about empirical work - but perhaps you're confusing the two (if you are talking about rigorous empirical work in biology, that goes back considerably farther than the 1980s).

    I encourage you - not necessarily even to use the same journals as I did - just three top journals in biology and three top journals in economics, and tell me which relies more heavily on modeling behavior. You can't be serious about this comparative point (and as I've walked you throuh, you're misinterpreting my absolute point). To quote you, you're just wrong.

    Think about it - why do economists end up taking more math than biologists do?

    It's intuitive, and if you just take some time to look through the literature it's blatantly obvious.

    Unless you're still convinced I'm saying biologists don't model, in which case (1.) you're wrong, and (2.) I suppose I could understand why you drone on and on over the same point.

  6. *I don't know what you read in economics too, and that could make a difference. If you spend a lot of your time reading Austrian stuff, I could understand how you might come to this conclusion.

  7. I am more than aware of what is in the journals that I read.

    "Think about it - why do economists end up taking more math than biologists do?"

    I would argue that they don't. In my experience the 1980s it was possible to get a degree in biology without a very strong background in math; that is just no longer the case.

    I read mostly Austrian stuff; and some of the work of Friedman.

  8. I'm going to keep pointing this tendancy of yours out, Xenophon, so hopefully you can improve upon it...

    Nobody said that you can be a biologist without a very strong math background. Nobody said that. So why are you treating it like you're presenting a counter-argument?

  9. "Nobody said that you can be a biologist without a very strong math background."

    Actually, that is exactly what you sound like.

  10. Anyway, I do agree with you that it is perfectly appropriate to use the "first approximation" phrase. Though you might want to liven things up with a few different phrases for making the same point.

  11. "Though you might want to liven things up with a few different phrases for making the same point."

    Ya, but it was just a first approximation.

  12. Does anyone ever get around to doing a second approximation?


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