Brad DeLong attacks Krusell and Smith for using in some of their thought experiments a depreciation rate of 10%, which is probably too high. Fair point but in my post I assumed a depreciation of just 5% and showed that Solow and Piketty give very different predictions about how the K/Y ratio will change with a change in g.
Thought experiments rather than data and context. In other words, meaningless formalism.
Marginal Revolution
Depreciating Capital
Alex Tabarrok | Professor of Economics and Bartley J. Madden Chair in Economics at the Mercatus Center, George Mason University
8 comments:
"... different predictions about how the K/Y ratio will change with a change in g."
Tabarrok commits the fallacy I have warned about several times in applying Piketty's 2nd fundamental law. That law does not imply that when g changes, K/Y changes. It implies only that the value toward which K/Y is converging changes, and also the rate at which K/Y is increasing or decreasing changes.
Dan, have you told Tabarrok this?
Yes, y, in the comments on his blog. Krussel and Smith are doing the same thing.
The way a lot of economists seem to think about limit theorems is that if they have a theorem that says
For increasing x, F(x) converges to G(x)
which licenses the slightly vague statement:
F(x) = G(x) in the long-term
then what they are supposed to do is build a model of some kind of steady-state equilibrium conditions, and build:
F(x) = G(x)
into the model. Somehow they have gotten the impression that this is what Piketty is up to, and this is how he want's the 2nd fundamental law to be used. But it seems to me that Piketty's model of the dynamics of wealth and income does not involve any imposed equilibrium conditions whatsoever.
Based on all of the things he says on pp. 166 - 170, the second fundamental law is supposed to be interpreted as:
For any year i, in which the savings rate is s(i) and growth rate g(i), the capital-to-income ratio W(i)/Y(i) is converging to s(i)/g(i).
But what many of the commentators are doing is reading the law as saying:
For any year i, in which the savings rate is s(i) and growth rate g(i), the capital-to-income ratio W(i)/Y(i) is approximately to s(i)/g(i).
And Piketty explicitly disavows this kind of statement. If you read the law in the erroneous way, then learning something about a change in the growth rate licences an inference to a change in the capital-to-income ratio. But that doesn't follow on Piketty's thinking at all. If you know that the capital-to-income ratio is currently 4, savings is 12%, and growth is 2% and so the capital-to-income ratio is converging toward 6; and then you learn that growth has just fallen to 1%, then all you should infer is that the capital-to-income ratio is still 4, but is now convering toward 12, and growing at a faster rate than it was previously. You can't and shouldn't infer anything at all about changes in the value of s(i).
It's not just Tabarrok and Krussel, but many of the supporters too. They just can't get out of the habit of thinking in terms of equilibrium conditions.
Useful points, Dan.
Sigh. You're exposing the deep flaw of economists thinking in static terms .... and, as usual, most don't even see it.
Who handed down this supposedly inviolable false-law of static conditions endowed to Luddites?
Is there a hidden text somewhere in the ceiling of the Sistine Monetarist Chapel? [Pull my finger?]
You almost have to have NEVER taken an economics course in order to be immune to this supposedly divine axiom of illogic.
And finally, what to do about it?
Maybe make a passing competence in physics, math or dynamic systems engineering a prerequisite for taking economics 101? (Or entering any policy office whatsoever?)
Who could have imagined that "experts" in the most dynamic system ever evolved on Earth - would be the ONLY ones unaware of dynamics.
I wish all the Piketty posts didn't include MMT as category tag so we could have a way to see quickly what is relevant and being published in MMT world without having to read about all the orthodoxy debates du jour. I realize it's fascinating to many readers of your blog, and it has an important place in the content. But I always wind up wasting a half hour or more a day by getting sucked into reading all this Piketty mental masturbation.
I think Robert Solow described pretty well what this anti-Piketty nittpicking is all about:
” Suppose someone sits down where you are sitting right now and announces to me that he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the battle of Austerlitz. If I do that, I’m getting tacitly drawn into the game that he is Napoleon. Now, Bob Lucas and Tom Sargent like nothing better than to get drawn into technical discussions, because then you have tacitly gone along with their fundamental assumptions; your attention is attracted away from the basic weakness of the whole story. Since I find that fundamental framework ludicrous, I respond by treating it as ludicrous – that is, by laughing at it – so as not to fall into the trap of taking it seriously and passing on to matters of technique.”
http://larspsyll.wordpress.com/2014/05/17/solow-telling-chicago-economists-some-home-truths/
I think Robert Solow described pretty well what this anti-Piketty nittpicking is all about:
” Suppose someone sits down where you are sitting right now and announces to me that he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the battle of Austerlitz. If I do that, I’m getting tacitly drawn into the game that he is Napoleon. Now, Bob Lucas and Tom Sargent like nothing better than to get drawn into technical discussions, because then you have tacitly gone along with their fundamental assumptions; your attention is attracted away from the basic weakness of the whole story. Since I find that fundamental framework ludicrous, I respond by treating it as ludicrous – that is, by laughing at it – so as not to fall into the trap of taking it seriously and passing on to matters of technique.”
http://larspsyll.wordpress.com/2014/05/17/solow-telling-chicago-economists-some-home-truths/
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