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Was there anything to the Cambridge capital debates?
Many readers raise this topic in the comments. Sadly I must characterize the Cambridge capital debates as a fruitless diversion. The non-neoclassicals won virtually every point on the modeling, but it doesn't much matter when it comes to the substance. The critics showed that:
1. There is no unique measure of roundaboutness or capital intensity which is independent of the interest rate (i.e., market prices).
2. Since equations with exponents often have multiple roots, sometimes more than one interest rate can serve as an equilibrium in a simple capital theory problem.
On #1, I say so much the worse for roundaboutness. (By the way, I tried to find a good definition of "roundaboutness" on-line but I couldn't; that is indicative.) The concept of risk is in any case far more useful for macro, capital theory, and finance. While the risk idea has its own problems, no credit goes to the Cambridge critics there.
On #2, multiple equilibria of the Cambridge sort are not a major problem or issue in modern capital markets. A variety of forces -- including money markets, loanable funds and institutional frictions -- hold interest rates in place. No real world interest rate is determined solely by the solution to a single equation with exponents. Empirically, interest rates do not suddenly leap to another equilibrium under stable basic conditions. The single-equilibrium supply and demand model for interest rates, modified possibly by credit rationing, seems to explain the real world reasonably well. Whatever puzzles exist do not seem attributable to the existence of multiple roots for an equation with exponents.
If you readers are not careful in your comments, you might soon get a post on the contributions of Piero Sraffa.
Posted by Tyler Cowen on May 31, 2007 at 05:45 AM in Economics | Permalink
Comments
Rather than Piero Sraffa, it would be more fun to have a post on the Critical-Paranoic School of Economic Thought:
http://www.columbia.edu/~xs23/critical.htm
Posted by: chug at May 31, 2007 6:42:54 AM
"If you readers are not careful in your comments, you might soon get a post on the contributions of Piero Sraffa."
Please, please, please, give us such a post.
On another note, a quadratic equation isn't an example of an exponential equation.
Posted by: Johan Richter at May 31, 2007 6:49:51 AM
Thanks, corrected...
Posted by: Tyler Cowen at May 31, 2007 7:02:16 AM
AS usual, Tyler is completely correct. Anyone interested in further analysis should take a look at Mark Blaug's short book The Cambridge Revolution: Success or Failure? It's out of print but is by far the best summary of the debate.
Posted by: Alex Tabarrok at May 31, 2007 8:06:15 AM
Tyler,
There is more to the problem of capital aggregation than the Cambridge (UK) objections.From a purely technical point of view, capital aggregates and the aggregate production function are mmeaningless except under extremely stringent conditions. This has been established by Franklin Fisher more than three decades back (1971, Econometrica). Here is recent paper that summarizes the issues:
http://are.berkeley.edu/courses/ARE241/fall2005/Felipe.pdf
The paper also addresses the "substance" issue that you state favors the current status quo.
Posted by: srinivas at May 31, 2007 9:04:45 AM
There is a lot more, but I am about to leave town and don't have time for
much. But some other implications include that dynamic discontinuities in
growth paths are more likely, and that profits cannot be explained as the
"marginal product of capital."
I would also note as an aside that Hayek realized the problems with defining
"roundaboutness" in his Theory of Capital, which kind of coincided with him
giving up on "Austrian capital theory" and shifting over to the economics
of information and many of his later concerns, with some of those problems
indeed resembling those raised by Sraffa, such as unusual time patterns of
production, costs, and returns.
My more general view on this can be found in Chap. 8 of my From Catastrophe to
Chaos: A General Theory of Economic Discontinuities, Vol. I, Mathematics,
Microeconomics, Macroeconomics, and Finance, 2nd edn, 2000, Kluwer.
Posted by: Barkley Rosser at May 31, 2007 9:31:29 AM
Tyler,
Thanks for an interesting post.
Alex,
Thanks for the reference, I was just about to ask for something like that.
Posted by: Commenterlein at May 31, 2007 9:33:21 AM
Aren't the Cambridge (UK) arguments just a special case of the index number problem?
Posted by: Brad DeLong at May 31, 2007 10:05:21 AM
Barkley,
What do you think of the Blaug book? And, with no offense intended, do you have something shorter of your own writing than that huge (and really expensive) book? I am sure it's worth it, but I won't have time to read it.
Thanks.
Posted by: Commenterlein at May 31, 2007 10:13:40 AM
Yes, especially when it comes to Fisher's work on capital aggregation.
Posted by: Tyler Cowen at May 31, 2007 10:13:41 AM
I don't know what Tyler is talking about.
I think both Cambridges recognized that talking about one interest rate is an analytical simplification, abstracting from a whole complex of rates with varying levels of risk. The UK folks would want to distinguish between risk and uncertainty. And they have Kalecki in their camp for the analysis of finance.
I don't know what it would mean for an equation to determine an interest rate. I suppose such talk makes sense if bond traders or the Fed chairman use a model to inform their decisions.
The correct claim of the UK folks is that neoclassical (and Austrian) theory does not provide any basis for using well-behaved factor demand curves in an explaination of prices and distribution. This claim applies to "money markets" for "loanable funds", as well as labor markets.
The claim that we don't typically see massive instability in interest rates (what about Oct 1929?) is consistent with the proposal of alternative theories of distribution. For example, perhaps, at any moment, bond traders have a balance of bulls and bears forecasting what the Fed will do to set interest rates. (That suggestion draws on both Sraffa and Keynes). And perhaps the 1970s stagflation in the US had something to do with conflicting norms on pay raises and Fed policy.
Barkley draws on the CCC in his use of complex dyanmics. I've thought somewhat about this myself. Barkley has also contributed to empirical literature on Sraffa effects.
One who confines their introduction to the CCC to Blaug's tract suffers from a lack of perspectives. Good surveys include books and papers by Harcourt, Bliss, Burmeister, Hahn, Ahmad, and Harcourt and Cohen. I've mentioned some textbooks before.
Posted by: Robert at May 31, 2007 10:20:44 AM
What do UK-Cambridge arguments have to do with the index number problem?
Posted by: Person at May 31, 2007 10:35:30 AM
If you have an intellectual con job to sell--such as path dependence or The Great Conspiracy to Destroy the Streetcars--it's most likely the Post-Keynsians who will buy it. (You know who you are.)
Posted by: Patrick R. Sullivan at May 31, 2007 10:36:50 AM
Oh, and one more thing: I normally try to post more humbly, but ...
Anyone who thinks that 5% interest rates (2% real) are "keeping the poor man down" ... is an idiot.
That's ultimately the implication of UK's anti-usurism.
Of course, the "poor man" pays *more* than the interest rate on treasuries, but that's because of the
default rate and transaction costs -- and who considers those costs "exploitation"?
Posted by: Person at May 31, 2007 11:41:43 AM
Have not quite grabbed that plane for that complexity conference in Turin,
Italy, where among other things Sraffa's main acolyte, Luigi Pasinetti,
will be honored, who recently retired from Catholic University in Milan.
Commenterlein,
It is just Chap. 8, and you can get most of it in the same chap. in the
first edition, 1991, which is in a lot of university libraries, yours
could probably get it by interlibrary loan. Yes, the book is too expensive.
A short version of part of the dynamic discontinuities argument is in my
1983 paper in the Journal of Economic Theory, "Reswitching as a Cusp
Catastrophe." Sorry, don't have my vita or anything with it by me at
the moment for the exact details, but that should do it.
I have problems with Blaug's account, but do not have time to go into it
now. Check out Cohen and Harcourt in JEP recently, although that has a lot
of limitations in different directions.
brad,
The line that it is "just an index problem" is an old one that got said a
lot at MIT and Yale, but is incorrect, and I think Uncle Paul (A. Samuelson)
would agree. Index number problems arise due to varying the quantity weights
on the different capitals. The problem here is the fact that net returns
can go positive and negative at different points in the future, hence the
present values can get scrambled and do odd things relatively as the interest
rate changes. The hard core Cambridge, England people would disagree, but
it has links to the "multiple roots problem" of capital valuation that was
recognized as far back as Irving Fisher.
BTW, for those who argue (another widely repeated argument) that the
alternative is "empirically irrelevant" ("look, ma, at our wonderful
aggregate neoclassical production functions that have all these residuals
when we try to use them to explain growth!") I would note that among the
dynamic discontinuities one can observe in such a model (like in my 83
JET paper), are sudden large changes in the value of capital due to a
very tiny change in the interest rate. Now, standard financial economics
theory allows for jump-diffusion processes that discontinuously change
prices in response to large new pieces of information, but this is different.
And does anybody want to say that we have never seen large and sudden
changes in asset values in response to nearly imperceptible changes in
the objective economic environment?
And, for the record, it was Pasinetti who first understood and pointed
out in print this issue of discontinuities as the underlying issue implied
by the capital theoretic paradoxes.
Posted by: Barkley Rosser at May 31, 2007 12:05:20 PM
Thank you, Barkley. I will get the book.
I read the Cohen and Harcourt paper and it summarizes pretty well what I still remember learning about the CCC. Now I am looking for something that helps me remember all the things I forgot, and all the things I never understood.
Oh, and for the record, I found Pasinetti's book really difficult to understand.
Posted by: Commenterlein at May 31, 2007 12:13:12 PM
You say that the East Anglicans won the technical debate but that it makes little substantive difference. But surely the substance was whether the distribution of income was determined by technology, (marginal product of capital) or by raw political power. If the marginal product of capital is a circular concept, definable only after we know the rate of return, then the whole edifice of marginal distribution theory would seem to fall.
Posted by: Tom at May 31, 2007 12:15:52 PM
But surely the substance was whether the distribution of income was determined by technology, (marginal product of capital) or by raw political power.
Even if "marginal product of capital" is a tautological concept, the rate of interest is set in the market for loanable funds. "Raw political power" can only result in a temporary discoordination.
Posted by: guest at May 31, 2007 1:42:00 PM
By the way, Mark Blaug has acknowledged errors in his summary of the Cambridge Capital Controversy. He later wrote a negative review of the New Palgrave in a review pamphlet for the same right-wing think tank.
Posted by: Robert at May 31, 2007 5:50:56 PM
quest,
The CCC is not about how the interest rate is set. It is about what happens
when the interest rate changes, irrespective of how it is set. Yes, it is
"set" in the market for loanable funds, but in the real world, central banks
intervene on a daily basis to set the rate, at least for the shortest time
horizons, such as the overnight interbank federal funds rate that is the main
immediate policy target of the US Federal Reserve. While there are days when
things go blooey and the rate can shoot up briefly as high as 100%, generally
by the next day the Fed has gotten it back to about its target through its
interventions in the repo market for fed funds.
Posted by: Barkley Rosser at Jun 5, 2007 1:09:04 PM
BTW, a real bottom line, and one of the major annoyances by most
heterodox observers is that in effect the bottom line is that
explaining the profit rate as being determined by the "marginal
product of capital" at the macro level is about as meaningful
as using the phlogiston theory to explain fire. However, mainstream
journals proceeded to pretend that the whole thing did not happen,
and one sees plenty of papers in leading journals that continue
to use the marginal productivity theory to explain profit rates.
Posted by: Barkley Rosser at Jun 5, 2007 1:11:17 PM
It is about what happens when the interest rate changes, irrespective of how it is set.
This is largely an empirical question, e.g. whether capital reswitching occurs in practice.
continue to use the marginal productivity theory to explain profit rates, [which] is about as meaningful as using the phlogiston theory to explain fire
These papers are not "explaining" anything: they're simply stating an equivalence. Are you saying that modern finance theory was devised by heterodox economists?
Posted by: guest at Jun 7, 2007 12:41:43 AM
Multiple roots clustered near each other could explain the random walk seen in markets.
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