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April 03, 2008
Why teach the Solow model? (Part II)
This all started with my post on how a computer demonstration allowed me to illustrate a certain technical feature of the Solow model that would otherwise require a lot more setup time. The (unstated) implication being that it allowed me to get to the "good stuff" sooner.
That's a little ironic because both John Palmer and Gavin Kennedy clearly want to focus on the other important institutional aspects of growth. Kennedy wants more attention to a careful and correct reading of Adam Smith (I can't disagree with that), and Palmer wants to focus on reducing transaction costs a la Coase. No doubt that others could come up with entirely reasonable things to add to that list, and no doubt many of those additions are things that, given enough time in the semester, would be beneficial to cover in class.
Yet I think that both John and Gavin overstate the objection to the Solow model (and presumably other models) as just a mathematical exercise--math for math's sake. As John puts it, "Yes the models are a great seive for filtering the students and putting them through the hoops." But in his later post he writes:
Second, the basics of economic growth are extremely important: consumption uses scarce resources that cannot then be available for producing capital goods; saving allows investment, which means more will be available for consumption in the future. We all (I hope) teach something like this in our intro courses when we show that saving today shifts the production possibilities frontier outward for the future.
We agree! And there's probably no better way to quickly and coherently communicate this than a simple undergraduate treatment of the Solow model. You have the most simple dynamics possible. You can talk about investment and depreciation. You can talk about stocks and flows. You can talk about capital seeking a high rate of return. You can talk about the tradeoff inherent in the consumption/saving decision. It's all there in a convenient package that can be covered in one class period.
And really, the Solow model as typically presented at the undergraduate level is not much of a math problem. It reduces to a couple lines of algebra. One does not have to do the full-blown differential equations version.
Perhaps this would be a good time to lay out the way that I approach growth in an intermediate macro course. It is based on the presentation in Steve Williamson's text, but I add my own twist.
1. Overview of growth experiences across the world. Evolution of average world GDP since the industrial revolution. Demonstration of gapminder.org website. Parente and Prescott stylized facts.
2. Malthusian pre-industrial revolution scenario. No growth. Mercantilism.
3. Industrial revolution. Economies begin to accumulate physical capital in a serious way. Solow model is introduced. Growth accounting. Solow model can explain how high marginal product of capital attracts investment. Solow model can't explain why countries take off or why sustained growth occurs. Convergence happens among wealthy countries with similar institutions but no worldwide convergence. Finish with Alwyn Young analysis of TFP in Asia before the financial crisis, which leads directly to...
4. Modern growth. Robert Lucas and Paul Romer style models (sketch... little math). "It's not factor accumulation, it's 'A'" a la Easterly and Levine. Endogenous TFP. Discussion (institutional issues are raised).
It's not particularly math heavy, though there are some opportunities for the motivated student to show off a little. If anyone had the impression that I dwell on the Solow model, I'll clear that up now. But it is a very important part of the context of the whole discussion (not to mention the only way I know to introduce growth accounting). Plus, while the Parente and Prescott approach is not exactly the Solow model, it is of that lineage.
There are so many interesting things to talk about when the time of the semester comes around to discuss growth theories. The simple algebra of an undergraduate version of the Solow model is one of the boring parts, but it is, I believe, necessary. Not as a filtering device (it is a rather coarse filter), but as a way of showing the "measure of our ignorance" (as the Solow residual is sometimes renamed) before moving on to (attempt to) lift the veil of that ignorance.
So anyway, I think we should have more and better presentation tools for streamlining the presentation of the Solow model to make the mechanics clearer and to better allow us to communicate how it revolutionized thinking about growth and how it ultimately showed us that there is so much we don't know without getting our students bogged down in the technical details.
That's what started this whole discussion anyway.
See also: Mike Moffatt (whose comments on the Coase theorem I will take up at a later time), Gabriel Mihalache (who agrees with me while maybe overdoing the case for analytical precision--at least if we're mainly talking about undergraduate pedagogy--but that is to be expected of a soon to be first year Ph.D. student [been there, done that]), and YouNotSneaky (who agrees with me for essentially the right reasons).
Posted by William Polley at April 3, 2008 08:34 PM
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Comments
There is no pleasing you, these days, isn't it? :-)
It's my experience, from a growth presentation I held a while ago to a non-technical crowd, that people have much trouble accepting income comparisons (and, in a sense, welfare comparisons) across countries and especially across time.
One can talk about PPP and chain indexing, but in the end, some of the point estimates that economic historians make are not credible to smarter-than-average non-economists. That being said, they might accept the idea that even with large measurement error (+/- 50-100%) the differences are big enough to still matter...
Posted by: Gabriel at April 4, 2008 03:49 AM
Gabriel,
Read this.
http://findarticles.com/p/articles/mi_qa3620/is_/ai_n8834669
It's getting a little dated. The numbers could use a little updating. But this kind of story sells pretty well to most students I have taught (econ majors or not). As long as they are not completely closed-minded.
Posted by: William Polley at April 4, 2008 09:41 AM
I suggest that the Solow model has a place in the context of a comprehensive theory of economic growth--not as the whole story, but as one component. It is a theory that tells us much about what we don't know (measure of our ignorance) and helps organize our thinking about what we do know.
I suggest that this has pedagogical value apart from being math for math's sake.
I maintain that it is unnecessary to appeal to an argument that the Solow model is a mathematical filtering device. It most definitely need not be so.
I praise the development of presentation methods that reduce the technical burden on the student so that the focus is less on the math, more on the intuition, and so that one can get to the institutional questions faster.
And I'm the one who is hard to please?
And as for the criticism of the model that is rooted in past misuses...
Just because some starry-eyed social planners thought they'd found the holy grail and got carried away does not imply that the model has nothing to teach our students.
Indeed a defense of free trade that appeals *only* to Ricardian comparative advantage would be similarly naïve. Yet Ricardian comparative advantage is certainly a part of a comprehensive view of trade theory. Again, this was my point in my original answer to John.
Posted by: William Polley at April 4, 2008 10:15 AM