In my recent critique of Paul Romer’s attack on Joan Robinson, I pointed out that Romer was wrong. Even Paul Samuelson admitted that Robinson had won the Cambridge-Cambridge debate. One of the big issues is whether you can aggregate capital. You can’t.
But that hasn’t stopped economists from trying.
One commenter, Thaomas, says:
The Capital controversy is just the index number problem in other guise. There is not [sic] perfect way to aggregate prices and yet economists and politicians continue to do so. So what?
The index number problem is a problem. But I don’t think it’s the main problem.
The main problem is that with the assumption of homogeneous capital, which is in the Solow-Swan growth model, you’re necessarily led to the conclusion that there is diminishing marginal product of capital. But, as economist Jeff Hummel points out in a yet to be published article, heterogeneous capital, which is what we have, allows for complementarity between different types of capital. And we observe complementarity. The big bottom line for growth theory that’s different from Solow-Swan is that with heterogeneity and the implied complementarity, there is no necessity for diminishing marginal product of capital.
That’s why I say that if Solow and others hadn’t assumed homogeneous capital, we would probably be further along in growth theory.
READER COMMENTS
Jim
Feb 21 2020 at 10:13pm
You’re right about heterogeneity. The A term in Solow just bundles everything together. Explicit knowledge, tacit knowledge, organizational efficiency (structure), capital structure, institutions etc… Can we even pretend to disentangle capital from the knowledge that it embodies and that its structure embodies? If not, this is a bigger problem than Solow-Swan…
Thaomas
Feb 22 2020 at 7:35am
So growth in output that in a Solo model gets dumped into scale or technology gets dumped into capital ‘heterogeneity.” It might make an interesting model but how do you know it’s better? If it can be used to make better policy recommendations, what are they? If better predictions what are they?
Jon Murphy
Feb 22 2020 at 8:01am
Read the bit about Jeff Hummel: it provides a better explanation of observable reality. Part of any good model is to explain reality; the Solow-Swan model doesn’t do that; it cannot explain the complementary nature of capital, which in turn leads to all sorts of poor policy recommendations (especially in the realm of development economics. See, for example, much of the writing by Bill Easterly or my colleague at GMU Chris Coyne’s book Doing Bad by Doing Good).
If your theory of growth is necessarily based on an incorrect assumption, you’re going to have a poor theory of growth.
Thaomas
Feb 22 2020 at 11:58am
Sorry, I have not read Hummel’s yet to be published paper. 🙂
As for assumptions and models, I refer you to Milton Freedman on billiard players who cannot do integral calculus yet manage to hit balls into pockets.
Development economics? Hmm. My field. I always thought of our main job (I worked for the World Bank) as getting countries to adopt better policies — to raise the Solo residual, if one bothers to couch it in those terms. Frankly I can’t see how a model of heterogeneous capital would have made any difference to my work. Of course there’s the seen and the unseen. Who can say that having more heterogeneous capital models out there wouldn’t have helped.
But the claim that they WOULD is yours. I remain skeptical.
Thaomas
Feb 23 2020 at 9:36am
When someone asks you a questing in class do you always just refer them to the readings? Modesty about not being the originator of knowledge is great, but not, I think, when it impedes communication.
As long ago as Milton Friedman we’ve know that unrealistic assumptions do not invalidate a model. That seems like a red herring.
When I ask how do you know that a heterogeneous model of capital is better, I was expecting an example of where use of the latter gave “better” results along some dimensions.
I’m a big fan of Easterly but I don’t see the relevance, a defect of your “citation” method of exposition, I’m afraid.
Jon Murphy
Feb 23 2020 at 10:15am
Yes, especially when the readings are explicitly about the question they asked. If the student gives an indication that they did the pre-class readings and didn’t understand it, then I am happy to elaborate. But when they give an indication they didn’t even do the readings, I just refer them back to it.
In fact, I’ve started knocking off points if students ask me questions that can be found on the syllabus.
Jon Murphy
Feb 22 2020 at 1:46pm
Larry White reminded me of another way that the difference between homogenous and heterogenous capital is crucial: war.
If capital really is homogenous, it wouldn’t matter where bombs are dropped. Blowing up a storefront is no different than an oil refinery.
Philo
Feb 25 2020 at 9:49am
How is war special? Suppose I want to produce gasoline (a peaceful activity); if capital were homogeneous it wouldn’t matter whether I bought a refinery or a grocery store–they’re both “capital.”
Obviously it does matter–obviously capital is not homogeneous. But if, in a simple model, one assumes otherwise, what avoidable error is one likely to make in drawing conclusions about the economy as a whole?
Deirdre Nansen McCloskey
Feb 24 2020 at 8:49am
Dears,
Jim, the first commentator, made a good point (this among many in response, and the original post): the heterogeneity, which Larry White amusingly illuminates with the bombing example, comes from having different ideas for projects. If I invest in a second gas station embodying exactly the same idea (location, size, design etc.) as the first, there will indeed by diminishing returns. If, though, my second idea is rather a (complementary) restaurant next door to the station, no returns diminish, supposing it to be anyway a good idea. (I have gradually gotten the Austrian point, you see.) So what? It is the environment for fresh ideas that makes for economic growth, not “K”. So I have argued at length in, say, Bourgeois Dignity and other writings. What’s the policy implication? Leave people alone, mainly. Give them if you will good tools for thinking up useful fresh ideas–elementary education, probably, but not necessarily; a free religious and intellectual environment, surely; permission, for sure. Evidence? Growth since 1800, and the recent histories of China and then India.
Clifford Bryan
Feb 25 2020 at 3:49am
I agree, we probably would be further along in growth theory.
Roger McKinney
Feb 25 2020 at 11:19am
Be careful! You guys sound very Austrian! Welcome! The besy way to improve growth theory is to read Mises and Hayek.
Knut P. Heen
Feb 26 2020 at 11:51am
There is an area in finance called real options which suggests that capital is more flexible than one may think. I love Deirdre’s writings, but I think a gas station may be turned into a restaurant pretty quickly. Indeed, here in Norway, I am not completely sure whether I am at a gas station or a restaurant when I fill gas. It looks like a McDonald’s with pumps outside.
Larry White’s point is funny, but the war-economy is an economy in which the participants exchange losses rather than goods. It may be significantly cheaper in terms of own losses to blow up a storefront than a well-defended oil refinery. The Vikings went for the monasteries, not for the castles.
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