Attention conservation notice: 2300 words about an odd, un-influential old book on radical political economy and statistical mechanics, plus gratuitous sniping at respectable mainstream economics.
I tracked down this down because I somehow ran across a link to a conference devoted to it. It appears to have emerged from the debates provoked among heterodox economists by input-output analysis, especially as employed by Sraffa and his followers.
A word about input-output analysis. This is a technique, developed largely by the great economist Wassily Leontief, for analyzing the technological interdependencies of different sectors of the economy, and especially physical resource flows. Start with some good, say (because I am writing this as I do laundry) washing machines. Making a washing machine calls for certain inputs: so much steel, rubber, glass, wire, a motor, switches, tubing, paint, ball-bearings, etc.; also electric power for the factory, workers, wear and tear on assembly-line machinery. To provide each one of those inputs in turn requires other inputs. Ultimately, one can imagine (if not actually estimate) a gigantic matrix which shows, for each distinct good in the economy, the physical quantity of all other goods required to produce one unit of that commodity. (At least, in a linear approximation.) Given an initial vector of inputs, this defines the range of possibilities of production. Conversely, given a desired vector of outputs, this defines the minimum required inputs. (It is no coincidence that input-output analysis fits so well together with linear programming.)
If one takes input-output analysis seriously, and assumes (following Marx, and indeed the whole tradition of classical economics back to Adam Smith at least) a uniform rate of profit across industries and even firms, then one runs into insuperable difficulties for the labor theory of value. Put simply, prices, at least equilibrium prices, are then determined by the uniform profit rate and the coefficients in the input-output matrix, with no real relation to how much labor goes into different commodities.
The authors — mathematicians who are, plainly, Marxian socialists, if not perhaps strictly Marxists — deny the premise that the rate of profit is uniform. ("Profit" here is defined as money received for goods sold, minus money paid for wages, raw materials, rent, and wear-and-tear on capital assets. It is thus before taxes, repayment of loans, and investment.) They agree that firms and industries where it is above average will tend to attract investment, and those where it is below average will tend to shed capital, and that these forces tend to equalize the profit rate. But they deny that there is any reason to think that this force should produce complete uniformity, or even very close uniformity. After all, there is a tendency for the speed of molecules in a gas to equalize, but that doesn't mean they all end up with the same speed. This is their main, driving analogy, and they think it so important that they devote chapter two [of eight] to accurately expounding the elements of the kinetic theory of gases and of statistical mechanics. They suggest that there should be a random distribution of profit rates, and that (on the analogy with statistical mechanics again, and no deeper reason that I noticed) that it should be a gamma distribution. (Why not a beta? Why not a log-normal? Why any of the cookbook distributions?)
They then try to mesh this with something very much like a labor theory of value, though they are careful not to actually assert such a theory. Starting from the assumption that "labor" is a universal input into the production of all commodities, they define the "labor content" of a commodity as total amount of labor needed to produce it using current technology (and summing over all the goods needed to produce that technology, all the goods needed to produce those goods, and so on). Because this is defined with respect to current technology, this is not the same as the amount of labor which, historically, happened to have gone into any one good. (By design, it is however reminiscent of Marx's attempt to define the value of a commodity as the quantity of "socially necessary" labor time which went into producing it.) They further claim that there will be a certain characteristic distribution of labor content over the commodities bought and sold in a given economy over a given span of time.
With these two distributions, they then argue as follows.
It is only in the last chapter that they present any sort of empirical evidence whatsoever. This is scanty, and it is not clear that the compilations they found on profit rates really are using a definition of "profit", much less of "capital", which matches theirs, but the comparison between the histograms and their fitted gamma distributions isn't visually painful. It shows that realized profit rates, from firms which are large enough, and live long enough, to be included in directories of companies have a wide dispersion and are somewhat right-skewed. Even this does not quite settle the matter of uniformity of profit rates. Because investments must be made now for profit later, what the forces of competition should equalize are not these realized, ex-post profit rates, but rather predicted, ex ante rates. Even if everyone agreed in their predictions of profitability (obviously not the case), and even if ex ante rates were uniform, one would expect the ex-post profit rates to have non-trivial dispersion, though a stable distribution for the latter is another story.
To sum up what's gone so far: I am happy with the idea that there is no uniform rate of profit, though their case is hardly air-tight. I am utterly unpersuaded of the attempts to rehabilitate even a shadow of the labor theory of value on this basis. There are, it seems to me, to be two key points where it fails. One is the traditional problem that labor is not really a homogeneous commodity. The other is that labor does not have any unique role in their formal framework.
The traditional issue here is that they have to assume there is a single commodity called "labor" (or "labor-power" or "abstract labor"), and that producing one unit of this requires the same inputs, no matter where in the economic system the labor is applied, i.e., what type of work it is really doing. This has long been recognized as a huge problem with labor theories of value; they devote Appendix II to acknowledging it; and they wave it away. This seems to me to make no more economic sense than lumping together all the different fuels produced by an oil refinery, electricity from a wind-mill, and fields of beets as the commodity of "energy" (or even "abstract energy").
Granting, for the sake of argument, that we can treat all forms of labor as equivalent (including equality in what's needed to produce them), there is still another problem. They can define a labor-content for every commodity because labor is "universal", a direct or indirect input to the production of every other commodity. But this is the only feature of labor which they really use in their arguments. So any other universal input would do as well. Water, for instance, is an input into the production of labor, and so one could just as well go through everything in their analysis in terms of water-content rather than labor-content. Indeed, water and electricity, being much more nearly homogeneous physical substances than "labor", would seem to make an even better basis for the analysis. So to the extent that they have a basis for saying that the ratio between the prices of commodities and their labor content is nearly constant, I could equally say the same of the ratio between prices and water content, or electric content1. They were, I think, aware of this objection to at least some degree, since they single out labor on the grounds that economists should be interested in the metabolism of the social organism, which necessarily involves labor. But I fail to see why materialist economists, studying the social metabolism, should not be equally interested in water, or electricity, or indeed thermodynamic free energy in general.
At a deeper level, Farjoun and Machover think economics suffers from assuming economic variables have deterministic relationships, which we just measure imperfectly; they want to take stochastic models as basic. (They want to introduce noise into the dynamics, and not just into observations2.) I am, naturally, very sympathetic to this, but they fail to convince me that it really would make as much difference as they claim. Someone like Haavelmo could, I think, have accepted this postulate with no change at all in his econometric practice. On the other hand, something like John Sutton's approach of finding inequalities which hold across huge ranges of economic models actually seems to lead to real insights into how the economy is organized and evolves, and is a much bigger departure, methodologically, from the mainstream approach than what Farjoun and Machover advocated.
If you want to understand how capitalism works, I think you are no worse off
spending your time reading Farjoun and Machover than,
say, Kydland and
Prescott3. The math is fine, and where sketchy could be
elaborated endlessly by clever graduate students, but in neither case does it
really support a valuable
the mechanisms and processes of the real economy, because the mathematical
structure is raised along lines laid down by a tradition which is irrelevant
when not actively misguided. One might ask, then, why one of these efforts
languishes in obscurity, and the other does not, but
because one of them is very congenial to both right-wing
politics and to a well-entrenched style of economics, and the other is
not a question I will leave to the competence of the historians of
1: This would imply a nearly-constant ratio between labor content and water content, which I suspect would be the ratio of the entries for labor and water in the dominant eigenvector of the input-output matrix. But that's just a guess based on the Frobenius-Perron theorem. (It does not seem worthwhile to pursue this to a definite answer.)
2: Note that in a dynamic stochastic general equilibrium model, the "stochastic" part comes solely from an unobserved, and generically unobservable, "shock" process. (This process may be vector-valued, and its projections along some preferred basis may be given suggestive names, like "technology".) The actions of the agents in such models are however deterministic functions of the state of the system facing them, which leads to the use of complicated, face-saving machinery for observational noise.
3: It may be worth noting that Kydland and Prescott, and their intellectual tradition, also assume homogeneous abstract labor. In fact, the Kydland-Prescott "real business cycle" model further assumes homogeneous abstract "capital", and a single homogeneous abstract consumption good. (One could even argue that it has an embedded labor theory of value.) In fairness, this was to some degree inherited from earlier approaches like Solow's growth model; in further fairness, Solow is too wise to mistake his model for a deep, "structural" description of the economy.
Furthermore, all models in the real business cycle/DSGE tradition have a huge, but generally ignored, measurement problem, since it is by no means obvious that the model variables called "output", "capital", "labor", etc., correspond exactly to standard statistics like GDP, market capitalization, and recorded hours worked (respectively), though almost all attempts to connect these models to data assumes that they do. At most, typically, one allows for IID Gaussian measurement error. (Boivin and Giannoni's "DSGE Models in a Data-Rich Envirnment" is a notable exception, and even they handle this systematic mis-match between theoretical variables and empirical measurements through an ad hoc factor model.) The point being, while Farjoun and Machover's scheme has serious issues with the definition of its variables and their measurement, it is not as though such defects stop economists from adopting modeling approaches they otherwise find attractive, or even bothers them very much.
Update, 12 December 2015: Just to buttress the point about how much work went into making something not being as relevant as how much work would go into replacing it, a quotation from Uncle Karl (Capital, I, ch. XV, sec. 3b, omitting Marx's footnotes):
But in addition to the material wear and tear, a machine also undergoes, what we may call a moral depreciation. It loses exchange-value, either by machines of the same sort being produced cheaper than it, or by better machines entering into competition with it. In both cases, be the machine ever so young and full of life, its value is no longer determined by the labour actually materialised in it, but by the labour-time requisite to reproduce either it or the better machine. It has, therefore, lost value more or less. The shorter the period taken to reproduce its total value, the less is the danger of moral depreciation; and the longer the working-day, the shorter is that period. When machinery is first introduced into an industry, new methods of reproducing it more cheaply follow blow upon blow, and so do improvements, that not only affect individual parts and details of the machine, but its entire build. It is, therefore, in the early days of the life of machinery that this special incentive to the prolongation of the working-day makes itself felt most acutely.
Posted at October 26, 2011 09:45 | permanent link