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.