Wednesday, May 21, 2008

Socratic Solow

Brad DeLong reflects on a semester's teaching with a socratic dialogue on the Solow model; an excerpt:
Akhilleus: So why are you morose then?

Glaukon: Because, looking back over my syllabus this semester, I realized that I spent five full weeks--one third of the semester--teaching them the Solow growth model...

Khelona: It's a fine model...

Glaukon: And yet when the rubber hits the road, it doesn't do us any good. It doesn't tell us anything first-order about the world--aside from post-WWII Japanese convergence from a bouncing-rubble B-29 testfield to a prosperous OECD economy.

Khelona: Actually, I don't think the Solow growth model explains that...

Glaukon: You don't?

Khelona: Post-WWII Japan converged to the OECD norm. And the Solow growth model has some convergence in it--if you start out really poor because your economy's capital stock has been turned into rubble or worse by B-29 strikes, you will grow fast because a low capital stock gives you a high social marginal product of investment and depreciation cannot be a drag on growth if there is no capital to depreciate. But these have always struck me as second- or third-order mechanisms in the story of post-WWII economic growth. Trade. Technology transfer. Institutional reform. The survival of the economic-mobilization components of the fascist Tojo dictatorship. The destruction of the other components of the fascist Tojo dictatorship. The ability of large firms to strike high-productivity bargain with their core workforces by shifting risks onto small-scale producer-suppliers and secondary-sector workers. The neocolonial origins of comparative development--that for Cold War-fighting reasons the U.S. was willing to cut Japan an enormous amount of slack in terms of market access that it was not willing to cut Mexico or Argentina or anyone else outside NATO. You know the story. You know the story better than I do.

Glaukon: Great! So now you've depressed me further--you have gotten me down from one example of the model at work telling us something interesting down to zero....

I also had my students spend quite a bit of time - though not quite a third of the semester - on the Solow model, and I have no regrets. This is partly for the reasons expressed a while back by YouNotSneaky!, who also had the classics on the mind, in a post titled "Socrates would have taught the Solow model":

Socrates thought there were two, maybe three, kinds of people in the world and that you could arrange them in a hierarchy;

1. Those who don't know but think they know.
2. Those who don't know but know they don't know.

and then maybe some lucky ones;

3. Those who know and know they know.

There aren't many people in the 3rd category. But for some reason we always expect our models to move us from the 2nd category to the 3rd. And we're not satisfied if the movement is from the 1st to the 2nd.

The Solow model basically says that "it ain't capital accumulation" which is the cause of sustained growth, it's something else, the magical so called "Solow residual" .....

There've been many people over the years that've concluded that since the Solow model doesn't "explain" growth (because it lumps its major cause into an exogenous residual) it is useless and only an excercise in mathematics.

But people! When you thought you knew (it's capital accumulation!) and then you learn that you don't know (it can't be capital accumulation!) you've learned something just as important and valid as if you've acquired a "positive knowledge"....
Moses Abramowitz called the Solow residual a "measure of our ignorance" - and that is indeed a useful thing. I've posted previously on the joys of growth accounting (measuring the residual).

The Solow model is somewhat unsatisfying because it (i) attributes growth to an exogenous constant and (ii) it does not do a good job of explaining the vast differences in incomes between countries. But it is invaluable as a starting point for teaching economic growth because
  • It forces students to really learn some key economic concepts, like:
    • the implications of diminishing marginal returns
    • the difference between levels and growth rates
  • The subsequent research on economic growth - endogenous growth theory and the neoclassical counter-reformation as well as the renewed emphasis on institutions (which admittedly is not really new) - can be understood as attempts to resolve the dissatisfaction due to (i) and (ii).
So while Solow doesn't really answer the questions that we would like growth theory to answer, it is tremendously useful for learning some economics and about how economics works.


Fixed Carbon said...

Wow, this seems to be saying that economics is all about our ignorance.
But, I'm pretty ignorant about economics.

Bill C said...

There are certainly lots of things that we don't know, or have competing theories about. That's what makes it interesting to be an economist, but it means that people who expect us to be oracles (students, etc.) are sometimes disappointed.