Friday, July 8, 2011

A quick question on ABCT

Why are Hayekian triangles the shape of a triangle? Why not two axes with an irregular line between them?

Let's pretend the yield curve doesn't exist and there's actually a linear relationship between time and the interest rate. That still doesn't guarantee that it should be a triangle. Although in that case the marginal cost of capital is linear over time, the marginal cost of capital at the point that it is equal to the marginal product of capital need not have this linear relationship with time.

Another way of posing the question is, why can't higher order processes be very heavy in the addition of factors of production, lower order processes be very light in the addition of factors of production (but perhaps time intensive). Or vice versa to such an extreme extent that the capital structure is hyperbolic rather than triangular.

This seems to make a big difference when we get around to:

1. Empirically looking at changes in the capital structure, as Andrew Young does in his forthcoming RAE article, and

2. Thinking about how the capital structure rebalances during a downturn.

And yet I've never heard anyone really ask this question - why is the Hayekian triangle a triangle? I'm not sure if there is a good answer, and if the answer is "there's no reason for it to be", I'm still not quite sure what all the implications of that are.

Thoughts?

1. Not quite sure what you are looking for, but this might be helpful:

http://www.auburn.edu/~garriro/b3beyond.htm

2. Unfortunately Garrison's book and every article of his that I've read pretty much follows Hayek's Prices and Production. This is a good example from your link:

"Hayek makes use of several heuristic assumptions that cause production time and non-consumption spending to be more tightly linked in his graphics than in reality. He assumes, for instance, that the production process consists of stages of production such that output of one stage sells as input for the next and that the number of stages varies directly with production time."

I'm not quite sure why though.

It's precisely the rigidity of the hypotenuse that drives a lot of the Austrian adjustment process, so this is not a trivial issue.

3. The Hayekian triangle is not meant to be an accurate portrayal of any economy. Hayek explicitely says that he trades accuracy for simplicity in Prices and Production. More accurate models are presented in The Pure Theory of Capital.

"It's precisely the rigidity of the hypotenuse that drives a lot of the Austrian adjustment process, so this is not a trivial issue. "

I'm not sure why you say this.

4. Why the hypotenuse of a Hayekian triangle is what it is seems like a very advanced topic to me.
Does this mean you have mastered all the more basic stuff, such as why Say's Law is 100% correct, why increasing the money supply cannot ever be beneficial, why it is impossible to "stimulate the economy" or to "create jobs", why GDP growth measures nothing but price inflation, why increasing consumption during a recession will deepen the recession?

5. Jonathan Catalan is correct, the Hayekian triangle isn't triangular. There have been many papers about this and it's mentioned in several books.

In more sophisticated presentations the point comes down to this.... Technology, existing capital, the long-run interest rate and customer demands determine a particular configuration of production. Then, monetary expansion beyond demand causes this configuration to come into an unsustainable state.

Mises didn't use the triangle in "Theory of Money and Credit" or in "Human Action". In TOMAC he used the older subsistence fund idea, which has it's own problem that are similar to the problems with Hayek's triangles. Hayek attempted to remedy this in "Pure Theory of Capital". Rothbard used that presentation in "Pure Theory of Capital" in "Man, Economy and State" but modified it to fit his pure-time preference theory of interest and his dislike of fractional reserve banking.

6. To build on what Current writes regarding Mises, Mises actually doesn't agree with Hayek that monetary distortion necessarily causes the structure of production to lengthen. In this sense, Mises is more of a "radical subjectivist" than Hayek is, to borrow Lachmann's and Shackle's terminology.

7. This might help:
mises.org/journals/scholar/block18.pdf

8. Current -
My concern is that the reason most people talk about a linear hypotenuse is because they presume the capital structure to be highly sensitive to the interest rate. If it were (and if we abstract from the yield curve for a moment), we WOULD expect a linear hypotenuse, no questions asked.

But obviously it's not - as you say its sensitive to considerably more prices than the interest rate.

But merely admitting this seems to make it harder to identify the elongation of the capital structure associated with interest rate changes as a determinant factor in the business cycle.

Let me put it this way - if the interest rate is not a major force in the determination of the time structure of production and the hypotenuse is a wet noodle, would ABCT hold up? A lot would change - a lot would depend on its interest rate sensitivity, and high interest rate sensitivity implies a relatively linear hypotenuse.

Which ultimately makes it an empirical question - if it is highly sensitive, then there's no concern here.

9. To put it another way, I'm not sure what's so Austrian (much less interesting) about ABCT without a high level of interest rate sensitivity, so this seems like something that ought to be well established.

10. Thanks anonymous - it does.
I'm working through some of Young's work now and I cites that, but I haven't been able to pull it up and read it yet.

11. First, the Hayekian triangle is technically not Hayekian. It was taken from Jevons, and Hayek frequently referred to it as the "input function" or "investment function".

Second, after P&P, Hayek almost invariably assumed the hypotenuse to be non-linear - a half-parabola. He did this to be empirically more consistent. Generally speaking, more labor is devoted to the output of the near future than is devoted to the distant future. The number of people working on stuff that will be the output of 50 years from now are very small compared to the number people working on the output of 1 year from now. A linear hypotenuse would be consistent with same amount of labor applied at all dates.

Third, to think about the interest rate Hayek employs a third dimension. The issues involved get more complicated. In any case, before you can even think about potential problems with the frame work, you've got to get deeper into the theory.

Last, Hayek does discuss processes in which more input is applied earlier. He also discusses when later stages are more time intensive. Neither vitiate the general theory.

I know you've got a lot of reading on your plate, but if want to be serious about these kinds of problems you've really got to read the relevant literature.

Background:
Bohm-Bawerk: Positive Theory of Capital
Rothbard: MES - Capital Theory chapters.
Wicksell: Value, Capital, & Rent

The Guts:
Hayek: "The Relationship Between Investment & Output"-Economic Journal
"Utility Analysis and Interest"-Economic Journal
Or just go to JSTOR and search Hayek from 1930-1940. It's everything he was working on up to the Pure Theory.
"The Pure Theory of Capital"

Later on:
Lachmann: "Capital & Its Structure"

12. Daniel,

The Austrian business cycle is a factor of the rising price of capital goods relative to consumer goods. It really doesn't matter if the structure of production elongates "perfectly" (assuming perfect sensitivity to changes in the rate of interest) or not; investment in capital goods, in general, runs the risk of being malinvestment.

13. It should also be pointed out that when economists of the Austrian tradition use the term "interest rate" they frequently do not mean your basic monetary loan rate of interest - this can be especially confusing with Hayek. What's considered more important is the "rate of profit" - what the monetary loan rate of interest conforms too in the long run.

14. I second edarniw's suggestion to read Lachmann's book. Lachmann's book on capital is a simplication of what Hayek tried to get across in the Pure Theory of Capital, so it's a good book to read first.

15. "GDP growth measures nothing but price inflation.

A new one!

16. argosy,

Once in a while, a new nugget is found here on FOST.

17. A few points...

Firstly, I think the references edarniw gives are good, but I haven't read them all.

Jonathan Catalan says:
"The Austrian business cycle is a factor of the rising price of capital goods relative to consumer goods. It really doesn't matter if the structure of production elongates "perfectly" (assuming perfect sensitivity to changes in the rate of interest) or not; investment in capital goods, in general, runs the risk of being malinvestment."

The first-order split between investment goods and consumer goods does have some problems. In an ABCT boom those who benefit from the initial low real interest rates are not fully aware of the situation. So, instead of investing more capital owners may decide to spend more as they are confident of high future profits.

"My concern is that the reason most people talk about a linear hypotenuse is because they presume the capital structure to be highly sensitive to the interest rate. If it were (and if we abstract from the yield curve for a moment), we WOULD expect a linear hypotenuse, no questions asked.

But obviously it's not - as you say its sensitive to considerably more prices than the interest rate.

But merely admitting this seems to make it harder to identify the elongation of the capital structure associated with interest rate changes as a determinant factor in the business cycle."

The ABCT theory can be made into any number of simple theories. As Jonathan suggests a simple break can be made between the capital/investment side and the wages/consumption spending side. That would be similar to Keynesian "overheating" in some ways.

AFAIK the theory continues to work as long as there is interest rate sensitivity and as long as there are specific capital goods that must be committed to particular employments. What changes is what kind of capital is malinvested and of-course, how much.

Notice also, that another important thing about the "linear hypotenuse" problem is how much capital is non-specific at each production stage. We should expect a linear hypotenuse on a graph of total capital employed in every stage of production, not a graph of specific capital. Again, that is as far as I can tell.

18. Another of my posts has been eaten.

19. I demonstrate that ABCT cannot be sustained:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1671886
I have heard this paper referred to as being about triangles that are not triangles.

You cannot get ABCT from Hayek's Pure Theory of Capital.

I recognize that many you will meet on the internet going on about the ABCT, including in previous comments on this thread, don't know what they are talking about.

20. I just read Vienneau's paper. It's erudite, but vacuous - essentially a long ( and rather pompous) analog to the "reswitching refutes Bohm-Bawerk" notion that a naive reading of Samuelson's article on the topic seems to imply, only here applied to Hayek and Garrison. Not worthy of serious attention.

21. I just read Vienneau's paper. Erudite, but rather vacuous - he essentially applies the "reswitching refutes Bohm-Bawerk!" notion (that a naive reading of Samuelson's original article on the topic seems to imply) to Hayek and Garrison. Contrary to his rather arrogant claim above, he seems to be operating at a lower level of understanding than the rest of the commenters here when it comes to the real issues surrounding ABCT.

1. Thanks for the thoughts Daniel - sorry on the delay publishing. The older posts don't publish comments automatically.

All anonymous comments will be deleted. Consistent pseudonyms are fine.