Monday, June 30, 2014

Piketty and the Capital Theory Dustup

I’ve been thinking some more about the odd treatment Piketty gives the capital theory debate on pp. 230-232 of K21.  Its strangeness is summed up in the following sentence:
Controversy continued, however in the 1950s and 1960s between economists based primarily in Cambridge, Massachusetts (including Solow and Samuelson, who defended the production function with substitutable factors) and economists working in Cambridge, England (including Joan Robinson, Nicholas Kaldor and Luigi Pasinetti), who (not without a certain confusion at times) saw in Solow’s model a claim that growth is always perfectly balanced, thus negating the importance Keynes had attributed to short-term fluctuations.  (p. 231)
Anyone who has studied this debate knows that this summary bears no relation at all to what was actually argued over.  Piketty seems like a smart, open-minded guy, so I would have to assume that he hasn’t read the original documents; his take must have been formed by what he was told in grad school.  If so, this passage can be read as a reflection of how the Two Cambridges battle has been turned into official history.  That’s a discouraging thought.

As for myself, I think I disagree with both sides.  The UK Cantabrigians said that the value of capital is determined by its cost of reproduction, which is a function of its composition, the technology of production and the division of income between labor and capital.  Thus the value of capital depends on its return, and this circularity is what makes aggregate valuation underdetermined.  The upshot is that this return is necessarily a political, not a technical factor.  (Cue Marx.)

The Massachusetts Cantabrigians said that the value of capital is determined in general equilibrium, which encompasses cost of production and the productivity of capital goods.  The reproduction constraint of the UK crowd doesn’t apply, because agents can rationally incorporate their expectations of capital’s productivity in market transactions that pertain to future economic states that differ from the present.  (Cue Arrow-Debreu.)

On this issue I would side with Keynes, for whom profitability does depend on the future, but who viewed the future as truly, radically unknowable.  The result is that there is a cost price for capital goods and a constantly fluctuating market valuation of capital-in-use, and there is no theoretically determinate relationship between the two.

Or to put it differently, the owl of realized capital valuation flies at dusk.

5 comments: said...


I hesitate to get into this as I have still to read Piketty's book (will get at it soon, yada yada). However, I think you are misrepresenting the capital theory debate itself, however far off Pikettty is (or is not, and I have taken seriously Jamie Galbraith's critique based on this issue).

For starters, I agree with you that Piketty's statement as provided by you looks like a bad misrepresentation. I checked, and his degree is listed as coming from both EHESS and LSE, so pretty clearly nobody at those places was doing a decent job or teaching this stuff. And, of course he was at MIT as an Assistant Prof for awhile, but it is not surprising that interpretations there are a bit off, although Samuelson was still alive, whose view of it seems to have been better informed and less biased than Solow's, who seems to have been the lead guy in doing the misinterpreting there and getting entrenched.

As for your view, I would simply note that the key to reswitching in fact involves problems of present value calculation, identical mathematically to the "multiple roots" problem actually recognized by Irving Fisher, as it was understood at Yale, if not MIT. Complicated future streams of net returns are at the heart of it, although you are right that the UK Cantabridgians did fall back on political power for how r and w were to be determined.

I agree that Keynes's view is useful, but it misses the point basicall, and is I think irrelevant to this discussion of Piketty, although I need to read him before making such assertions too strongly.

BTW, for anybody who wants a summary of my views on the Cambridge capital theory debate, see Chap. 8 in either the 1991 or 2000 edition of my From Catastrophe to Chaos: A General Theory of Economic Discontinuities, which more or less summarized earlier work I did on this matter.

Peter Dorman said...

Hi Barkley. I figured someone would bring up reswitching. It's true that reswitching shoots down Solow's aggregate capital, and it's also true that Paul Samuelson eventually conceded that reswitching is unavoidable, for exactly the reason you give. However, that was not the reason promulgated by Pasinetti et al. They had a reproduction model in which changes in the interest rate caused changes in the value of capital goods which, when aggregated, produced "perverse" effects on the relationship between the capital-labor ratio and choice of technique. Samuelson (rightly in my opinion) never bought into that. You neither, I'll bet.

While reswitching became a kind of fulcrum for this debate, I think it's not a useful one. The deeper issue is, from the UK-Cambridge point of view, is whether capital can be aggregated apart from a prior determination of the rate of interest. You could argue yes to that and still concede reswitching, as PS did. said...

I really do not want to go on about this too much, but I fear I disagree with substantial amounts you have to say on this.

First of all, go read Sraffa and Pasinetti (and Garegnani) carefully. What brings about the result, as well as the more generally non-monotonicity that can happen without outright reswitching is the pattern of the labor coefficients in the matrix. However, Sraffa and especally Pasinetti in 1966 are very clear that these complicated patterns of labor coefficients in the matrix reflect complicated time patterns of net returns. This is not a one versus the other interpretation. Sorry.

Also, while Solow clearly loved letting people aggregate capital so they could go around estimating Solow growth functions, which underlie much of the supply-side of RBC models, Samuelson granted the theoreticcal problem. Remember, he at first denied the problem for aggregation in 1965, but then was foreced to concede, which he did. In my very first conversation with him, I raised this issue, and he just totally caved, declaring "we must model capital as heterogeneous."

Peter Dorman said...

This isn't an ideal forum for hashing this out, but we see different things. My first diss was on a related topic, and I know my Sraffa pretty well. Yes, I agree that the complex structure of the coefficient matrix is necessary to give you the reswitching result -- and PS accepted this. (The example he gave was so obvious you have to wonder what all the fuss was about.)

But the Cambridge-UK folks were after bigger game. They wanted to argue that capital, as an aggregate, was a politically determined variable, that it depends on the rate of interest/profit which, from an economic point of view, is only bounded, not determined.

The funny thing is that Piketty, without relying on a theoretical model, comes closes to agreeing with the UK position. (Does he know this?) He talks about r being in the 4-5% range as if it were more a social norm than an economically determined result. said...

Not sure we are disagreeing with you fundamentally. I think I said that the UK Cambridge view is that r and w depend on politics. Cannot comment on how close or not Piketty comes to that as I still have not read him, although clearly there is a lot of wrangling going on over his treatment of the theoretical issues in all this.