Wednesday, July 7, 2021

Zachariah’s “Labour Value and Equalisation of Profit Rates”: A Critical Review

D. Zachariah’s paper “Labour Value and Equalisation of Profit Rates: A Multi-Country Study” (Indian Development Review 4 [2006]: 1–20) seeks to prove Marx’s Labour Theory of Value (LTV) by examining empirical data on factor input costs and final prices of finished goods from 18 nations in a period from 1968 to 2000.

Zachariah concludes that “market prices and labour value of industry outputs are highly correlated for a fairly broad sample of economies” (Zachariah 2006: 18), and that the idea of “prices of production” (used by Marx in volume 3 of Capital) is an inferior theory to the simple Labour Theory of Value in explaining prices, especially since Zachariah finds strong evidence against a tendency to equalisation of profit rates (Zachariah 2006: 18). In essence, Zachariah also concludes that the Transformation Problem appears to be irrelevant, given his findings.

So it is clear that Zachariah is trying to defend a version of the LTV used by Marx in volume 1 of Capital.

We must remember that Marx had no single, consistent Labour Theory of Value. The “law of value” (a phrase which Marx used to refer to the LTV) in volume 1 of Capital contradicts the “law of value” in volume 3.

In order to clarify this problem, we can review Marx’s two versions of the Labour Theory of Value, as follows:
(1) The “Law of Value” in volume 1 of Capital
In volume 1 of Capital, Marx defended in his text a “law of value” in which homogeneous socially-necessary labour time units were the anchor for the price system in modern capitalism. That is to say, individual commodity prices are supposed to gravitate towards their labour values (but volume 1 contained two footnotes hinting at the different theory of price determination in Marx’s draft of volume 3, so that volume 1 was not even internally consistent).

By volume 3 of Capital, Marx thought this only happened in the pre-modern world of commodity exchange, but he describes the process as follows:
“The assumption that the commodities of the various spheres of production are sold at their value implies, of course, only that their value is the center of gravity around which prices fluctuate, and around which their rise and fall tends to an equilibrium.” (Marx 1909: 208–210).
For this LTV to work and be empirically proved, all human labour of different kinds must be measurable in a homogenous unit of basic socially-necessary labour time and then compared.

(2) The “Law of Value” in volume 3 of Capital
In volume 3 of Capital, Marx abandons the view that commodity prices tend to equal pure labour values. Instead, Marx defended the view that the “law of value” only ultimately and indirectly explains prices, and defended three aggregate equalities:
(1) the sum of surplus value = sum of profits;

(2) the sum of values = sum of prices, and

(3) the value rate of profit = the money rate of profit.
These aggregate equalities were asserted as true as Marx’s attempt to defend labour value. But Classical “prices of production” became the anchors for the real-world price system.
Now Zachariah in his article is essentially rejecting the “law of value” in volume 3, and trying to defend the crude LTV in volume 1.

The trick that Marxists like Zachariah use is this: by showing empirically that there is a high correlation between the labour cost of fundamentally different labour types to the prices of their respective output goods, Marxists think they have proven the LTV. But this is a spectacular non sequitur. The reason is this: Marx’s Labour Theory of Value is much more than this simple correlation.

Zachariah’s contends that it is “the need for companies to meet the wage-bill that forces market prices to gravitate around prices proportional to labour values” (Zachariah 2006: 4). But this does not follow at all, because we cannot even properly measure the objective labour values of all different goods produced by heterogenous kinds of human labour. The very concept of labour value as used by Zachariah has not been properly defined in the way Marx used it.

No Marxist has ever convincingly shown how to overcome the problem of reducing all different types of human labour-time and measuring it in a homogeneous unit. For example, one hour of labour by a highly-skilled engineer is different from one hour of labour by a brick layer on a construction site.

This devastating problem with even properly defining the LTV has been noted by economists from different schools. Joan Robinson correctly pointed out that Marx needed to reduce all heterogeneous human labour time to a meaningful homogenous unit (Robinson 1966: 12), but this “leaves open the problem of assessing labour of different degrees of skill in terms of a unit of ‘simple labour’” (Robinson 1966: 19).

Marx faced the problem of reducing all heterogeneous human labour to a homogeneous abstract socially-necessary labour time unit, but Marx did not properly explain how this happens. You cannot prove a theory when your fundamental concept cannot be empirically defined or measured.

Eugen von Böhm-Bawerk identified the same problem. Böhm-Bawerk stated:
The fact with which we have to deal is that the product of a day’s or an hour’s skilled labor is more valuable than the product of a day's or an hour's unskilled labor; that, for instance, the day's product of a sculptor is equal to the five days’ product of a stone-breaker. Now Marx tells us that things made equal to each other in exchange must contain ‘a common factor of the same amount,’ and this common factor must be labor and working time. Does he mean labor in general? Marx's first statements up to page 45 would lead us to suppose so; but it is evident that something is wrong, for the labor of five days is obviously not ‘the same amount’ as the labor of one day. Therefore Marx, in the case before us, is no longer speaking of labor as such but of unskilled labor. The common factor must therefore be the possession of an equal amount of labor of a particular kind, namely, unskilled labor.

If we look at this dispassionately, however, it fits still worse, for in sculpture there is no ‘unskilled labor’ at all embodied, much less therefore unskilled labor equal to the amount in the five days’ labor of the stone-breaker. The plain truth is that the two products embody different kinds of labor in different amounts, and every unprejudiced person will admit that this means a state of things exactly contrary to the conditions which Marx demands and must affirm, namely, that they embody labor of the same kind and of the same amount!.” (Böhm-Bawerk 1949 [1896]: 81–82).
Marxists like Zachariah cannot even defend the “law of value” in volume 1 of Capital without solving this problem, but there is no convincing solution to the problem even mentioned in Zachariah’s paper.

The normal technique used by Marxists is to correlate mere labour costs in money prices with output prices, but this is a practice that cannot possibly overcome the problem of aggregating the different types of labour with a homogenous unit. To prove that prices are determined by labour values, you would have to calculate the homogeneous socially-necessary labour time units required to produce every commodity where all skilled labour and unskilled labour can be measured in the same homogenous unit, and then compare these quantities with prices. But Zachariah and other Marxists do not do this.

What Zachariah has proven is that there is, indeed, a very high correlation between labour factor input costs and prices, since labour costs are, generally speaking, a huge part of total production costs in most sectors. But Post Keynesian economics also accepts this, as do all non-Marxist cost-based theories of price determination.

The problem with all these Marxist attempts to empirically prove the LTV is identified by Nitzan and Bichler:
“The other problem with [sc. Marxist] empirical studies has to do with values – or rather the lack thereof. To our knowledge, all Marxist models that purport to correlate prices with values do no such thing. Instead of correlating prices with values, they in fact correlate prices with . . . prices!

The reason is simple enough. Recall that, according to Marx, the value of a commodity denotes the abstract labour time socially necessary for its production. Yet, as we already mentioned …, this quantum is impossible to measure. And so the researcher makes assumptions.

The most important of these assumptions are that the value of labour power is proportionate to the actual wage rate, that the ratio of variable capital to surplus value is given by the price ratio of wages to profit, and occasionally also that the value of the depreciated constant capital is equal to a fraction of the capital’s money price. In other words, the researcher assumes precisely what the labour theory of value is supposed to demonstrate. ….

Since values are forever unknown, we need to first convert prices into ‘values’ and then correlate the result with prices. It seems reasonable to expect the outcome to be positive and tight. After all, we are correlating prices with themselves. What remains unclear is why one would bother to show this correlation and, more puzzling still, how the whole excise relates to the labour theory of value.” (Nitzan and Bichler 2009: 96–97).
Apart from labour-time data from Sweden, Zachariah states clearly that the rest of his data simply uses monetary “labour costs... as a proxy for labour input” (Zachariah 2006: 6), so that virtually all Zachariah’s data is subject to the critique above.

While some Marxists have in fact used labour hours or labour time in trying to calculate value, not even this proves Marx’s LTV, because the Marxists never calculate the homogeneous socially-necessary labour time units necessary for comparing different types of labour.

In reality, the finding that labour costs are strongly correlated with output prices is actually one of many strong proofs of the Post Keynesian cost-based mark-up theory of pricing, which has no need for a Labour Theory of Value at all.

And one can only note that when Marxists try and prove the crude LTV in volume 1 of Capital, they are in effect admitting that the aggregate identities that constitute the “law of value” in volume 3 must be false, which Zachariah effectively does.

However, one very interesting finding from this paper, as noted above, is that Zachariah found strong evidence against a tendency to equalisation of profit rates (Zachariah 2006: 18). It logically follows that Classical “prices of production” cannot be anchors for the real-world price system, because a tendency towards an equal profit rate is a necessary condition of “prices of production.” So the Classical, Sraffian and Marx’s theory of price determination as used in volume 3 of Capital cannot be true.

Further Reading
“The Critical Responses to Volume 3 of Marx’s Capital and the Early Development of Marxism,” February 9, 2016.

“Joan Robinson on Marx’s Labour Theory of Value: A Few Points,” August 11, 2015.

“Marx’s ‘Law of Value’ in Volume 1 of Capital,” February 4, 2016.

“Why Marx’s Labour Theory of Value is Wrong in a Nutshell,” June 28, 2015.

“Empirical Studies showing that Prices are Correlated with Labour Costs do not Prove the Classical Marxist Labour Theory of Value,” December 23, 2015.

“Böhm-Bawerk on Marx’s Problem of Aggregating Heterogeneous Human Labour,” March 7, 2016.

“Marx’s Capital, Volume 1, Chapter 11: A Critical Summary,” February 7, 2016.

“Alexander Gray on the Two Contradictions in Marx’s Theory of Surplus Value in Volume 1 of Capital,” February 8, 2016..

BIBLIOGRAPHY
Böhm-Bawerk, Eugen von. 1949 [1896]. “Karl Marx and the Close of His System,” in Paul M. Sweezy (ed.), Karl Marx and the Close of His System and Böhm-Bawerk’s Criticism of Marx. August M. Kelley, New York. 3–120.

Marx, Karl. 1909. Capital. A Critique of Political Economy (vol. 3; trans. Ernst Untermann from 1st German edn.). Charles H. Kerr & Co., Chicago.

Nitzan, Jonathan and Shimshon Bichler. 2009. Capital as Power: A Study of Order and Creorder. Routledge, Milton Park, Abingdon, UK and New York.

Robinson, Joan. 1966. An Essay on Marxian Economics (2nd edn.). Macmillan, London.

Zachariah, Dave. 2006. “Labour Value and Equalisation of Profit Rates: A Multi-Country Study,” Indian Development Review 4: 1–20.

14 comments:

  1. “A barrel of conventional crude oil contains the equivalent of roughly 4.5 years of continuous human labour; or around 11 years at 35 hours per week, 48 weeks of the year.  But the capitalist doesn’t pay for the value of the fuel, merely the cost of extracting it.  For a mere £49 (at pre-pandemic prices) the capitalist purchases £330,000 worth of work (at the current UK median wage).  It is the exploitation of fossil fuels rather than the exploitation of labour which generates the vast majority of the surplus value in an industrial economy. . . .

    As Nicole Foss once put it – if conventional oil was like drinking draught beer from a glass, fracking was the equivalent of sucking the spilled dregs from the carpet.”

    https://consciousnessofsheep.co.uk/2020/05/26/two-money-tricks/?fbclid=IwAR1rOz0jexO2dIIldSlseh-8-EqES4oYZcBTvHMtW-JyBgMHB6xgfOOsbBI

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  2. All your accusations, such as those of Nitzan and Bichler, were analyzed by Cockshott, Cottrell and Baeza in the article Empirics of the Labor Theory of Value: Reply to Nitzan and Bichler. If you were at least minimally familiar with the topic, you would not carry such nonsense that your post is filled with.

    https://www.econstor.eu/bitstream/10419/157802/1/bna-496_cockshott_cottrell_valle_baeza_2014.pdf

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    1. Rubbish. Cockshott et al. (2014) does not refute the core of my argument above.

      Cockshott does not demonstrate how to measure a homogenous unit of socially labour time. The best this Marxist hack can do is argue that wage bills (measured in money prices) give a "reasonable proxy for Marx’s socially necessary labour time" which is rubbish since he has not demonstrated how to measure all heterogenous types of human labour.

      His other apologia is that in *some limited cases* you can use raw labour hours, but that doesn't prove anything either, since only homogeneous socially-necessary labour hours can measure the actual value of any good.

      What is especially comical here is that in volume 3 of Kapital Marx doesn't even think individual commodities have prices equal to their labour values. Roughly half of prices produced in industries with a proportion of constant capital above the average sell at a price above their labour value, and in the contrary case they will sell below their value. So even your attempt to defend the LTV in vol. 1 means volume 3 is B.S.

      Enjoy your Marxist insane asylum.

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    2. I'm convinced by your argument. Labour theory is wrong. But I'm not convinced that Marxism is destined for the dustbin of history, because Marxism has parts which are NOT based on labour theory of value. For example the marxian theory of crises according to Simon Clarke, the foremost expert on this area, is independent from the labour theory of value.

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  3. Very interesting post, I am waiting for more such analyzes. Maybe something about the failure of the socialist economy in Cuba

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  4. The notion that Volume 1 and 3 of Capital "contradict" each other is either sheer incompetence or mendaciousness. First of all, Volume 3 and Theories of Surplus Value (wherein Marx discusses Prices of Production at length) were written prior to V1 thus Marx was well aware that in "mature" capitalism commodities do not actually sell at their value.

    So why does Marx assume that everything sells at its value in Volume 1? Because Volume 1 is about the production of value (the book is subtitled "The Production of Capital), not its distribution after its creation. Nowhere does Marx say that in currently existing capitalism (ie: 1860s) products sell at their values. However to introduce the concept of prices of production would be contrary to the purpose of Vol. 1 in which Marx puts forth no theory of price. It is necessary for the reader to understand value before he can understand price because value serves as the basis both historically and logically which is why he delays discussion of price until V3.
    Anyway according to Marx in commodities that are produced with the average organic composition of capital value is equal to price of production, therefore the reader can merely assume that in the examples Marx gives in Vol. 1 are composed of the average composition of capital if he is in anyway concerned with a "contradiction" (which doesn't actually exist, anymore than any other simplifying assumptions in science are "contradictions.")

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    1. "Nowhere does Marx say that in currently existing capitalism (ie: 1860s) products sell at their values."

      LOL!!:

      (1) Marx states in Chapter 1 that it is possible to accurately measure the value of skilled labour by looking at the exchange values of products of skilled labour as against products of unskilled labour (Marx 1906: 51–52), but that makes no sense unless Marx really believes that commodities tend to exchange at pure labour values.

      (2) Marx also says that gold or silver, when initially brought to market, is exchanged with other commodities with an equal socially necessary labour time value as a barter transaction (Marx 1906: 122). That requires exchange at pure labour values.

      (3) Marx states there is an equilibrium process at work by which prices are driven back towards their true labour values:

      “It is true, commodities may be sold at prices deviating from their values, but these deviations are to be considered as infractions of the laws of the exchange of commodities, which, in its normal state is an exchange of equivalents, consequently, no method for increasing value.” (Marx 1906: 176–177).

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  5. szalaim@hotmail.comAugust 13, 2021 at 12:26 PM

    Dear Bubble! Even if there is no contradiction between Vol I. and VOl. III: this means only that LTV is consistent, but not that it is TRUE. LTV (in its original, marxian form, according to which only living labour creates new value) is unable to explain the prices. To reduce to, or explaing with the value of non-labour inputs with the value of labour inputs is an unnecessary and complicated procedure. Capitalism exploitative, becaouse workers don't possess means of production, and are forced to sell their labour-power to the capitalists on unequal terms. But Marx derived from this undeniable fact, that all social surplus are created by the workers. And this is a non-sequitur.

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  6. I continue to think that the whole topic is based on a giant misunderstanding: it not about the "Labour Theory of Value", but the "Labour Definition of Value", that is in the classics "value" is simply defined as being labour, especially by Marx. This is rather clear in his pointing out that the labour of slaves and animals does not create any "value". The only things that create value are "land" (e.g. when a corn seed in planted, 100 corn seed are created), more properly called "rent" than "value", and "labor" (of free humans only), and "land" creates "rent" only in conjuction with labor, however minimal (e.g. to collect a fruit spontaneously grown by a wild tree before eating it).

    The purpose of the definition of "value" as labor is simply cost accounting: it is not a theory of prices. The cost accounting is used to delve into distributional issues, not into price issues, that is to show how labor flows from employees to employers, because in conditions of capital being relatively scarcer to labor, the exchange-value of labor-power is lower than the "value" of labor (for example employers can buy 8 hours of work by offering commodities that cost 6 hours of labor to make). If the conditions were reversed, that is labor is relatively scarcer than capital, then the exchange-value of labor-power would be higher than the "value" of labor (for example employers to buy 8 hours of work most offer commodities that cost 10 hours of labor to make); this means that employers lose capital until conditions are reversed.
    The above applies only to "economic goods" of course.

    There have been attempts at turning the "labor definition of value" into a "labor theory of value" by asking whether exchange-values would converge to labor costs, but that is to say the least far from trivial, because mostly labor costs in most cases define a lower bound to prices, and not necessarily always, depending on the relative scarcities of labor and capital and land, and how they change with time. My personal impression is that in most cases prices are not too far for too long from labor and land "values".

    I will repeat here my impression that the classicals wrote largely before it became evident just how enormous is the contribution of "land", in the form of coal and oil, to value added, that is how enormous is the consumer surplus of those fuels, so they blithely "labor" as the only source of "motive force"; for a wider approach to cost-accounting in modern economies some people think that instead of "labor" content it is more insightful to use "energy used". whether consumed by humans, animals, or coal and oil fueled machines.

    PS: as to the the various reswitching issues I think that they are obvious as it is obvious that the optimization landscape in general case is "bumpy", that is it has various local maxima, which also move with time.

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  7. Part of the story here is what determines consumer surplus, and why it exists at all (a good view of marxian "surplus value" is that it is the consumer surplus that employers get when purchasing the labor-power of free employees for (wage-commodities embedding) less labor than that labor-power can give).

    To get a theory of prices one has to build both a theory of costs (in terms of the labor of free people or whatever else) and then along with it a theory of consumer surplus. I suspect that our dear dr. Sraffa when writing "Prelude to a Critique" was quite aware that his work was limited to the "cost accounting" topic only.

    PS The funny thing is that neoclassical Economics does not have a theory of prices, even if ostensibly that is all that it has, because it does not have a theory of the price of capital, so it cannot even begin to do cost accounting.

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  8. «2021_Sraffa__s__Reduction__of_the_Prices_of_Basics.pdf»

    Interesting, I read that without paying too much attention to the maths and my impression is:


    * It has always been obvious to me that re-switching arises from path dependency which is inevitable if one allows "capital" to be a link between past and present and future, so the main effort of neoclassical theory is to in effect hand-wave away capital and time.

    * My intuitive understanding of why in practice re-switching is often not a big deal is JM Keynes observation that almost all capital is long term.

    * The paper to me seems to argue something similar, the way I summarize it to myself is that cumulative capital values decay at a fast enough rate for path-dependency to be not a big deal, because the older parts of the path have rapidly vanishing influence.

    But these are just first impressions.

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  9. «The only things that create value are "land" (e.g. when a corn seed in planted, 100 corn seed are created), more properly called "rent" than "value"»

    I feel ashamed (regardless of nobody reading that comment or this one) that I have not been clear in my naming convention, and the above can be read wrong: When I wrote "create value" I should have made it clear that I meant the intuitive meaning of the word "value", as "economic worth", not the technical meaning as in "the labor of free men". I try to remember using the convention of quoting terms-of-art that differ from the ordinary meanings, but I guess it was not clear,

    So I should have written better: The only things that create economic worth called "exchange-value" are "land" (which really means "natural phenomena") and is then called "rent" and "labor" (of free humans only) and is then called "value" without qualifications.

    «that re-switching arises from path dependency which is inevitable if one allows "capital" to be a link between past and present and future, so the main effort of neoclassical theory is to in effect hand-wave away capital and time.»

    And that is why during the Cambridges Capital Controversy it was shown that Arrow-Debreu models works only with a single capital commodity, while they work even with multiple consumer commodities, and why JB Clark defined "capital" as a single metaphysical essence that imbues "capital" commodities: path dependency is then waved away as "capital" is then essentially "leets"/"putty".

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  10. «Does The Existence Of Wine Refute The Labor Theory Of Value?»

    As a pithy summary, consider the similar question: "Does the fruiting of apples on a wild apple tree refute the Labor Definition of Value?".
    «Part of the story here is what determines consumer surplus, and why it exists at all (a good view of marxian "surplus value" is that it is the consumer surplus that employers get when purchasing the labor-power of free employees for (wage-commodities embedding) less labor than that labor-power can give).»

    That can be considered a theory of the exploitation of labor that any neoclassical Economist could propose, even JB Clark:

    * Consumer surplus can be defined as the gap between the price of market commodity and the highest price the price would be willing to pay for it.
    * When paying wages employers must have a consumer surplus, because the highest wage they would be willing to pay is the one that makes them merely break even, so they not not bother.
    * That employers have a consumer surplus would not be considered "exploitation" because it is considered quite right for market participants to buy low and sell high, whether or not that is the result of adding value, or receiving rent.
    * Regardless, employees also "exploit" in "consumer surplus" terms the employers, because as a rule they pay for the commodities they consume a price well below the highest that they would be willing to pay.

    The last two points however are quite disingenuous because there is a very big difference between the "consumer surplus" of employers who buy labor from employees, and employees who buy commodities from employers:

    * The "consumer surplus" that employees gain from buying commodities is *notional*, it is purely in terms of "utility", it is not additional money income, they cannot spend that "consumer surplus" to buy more commodities.
    * The "consumer surplus" that employees gain from buying labor is not notional, it is in terms of money, it is actual money income, that they can spent do buy commodities. That is because employers buy labor from employees paying money to resell it to employees for money, embedded in the commodities the employees buy with their money wages.

    The difference is obvious considering the ridiculous arguments of "tech cornucopian" who argues that thanks to web services the living standards of the working class have been booming, for example:

    https://href.li/?https://www.theguardian.com/business/2018/jul/22/why-uk-economy-needs-leap-of-imagination-harry-potter
    “our use of search engines, email and other products like social media and digital maps should cost as much as $25,700 (£19,560) a year”

    The buyers of those web services are not actually receiving an extra $25,700 per year of money income, they cannot spend that "consumer surplus", but employers can surely spend their "consumer surplus", their profits are money income, to buy any commodities they want. The same of course for "land" (etc.) rentiers, their "consumer surplus" is actual money income.

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  11. While reading Cohen and Harcourt's "Retrospective" I noticed that the major example the give for Wicksell effect involves purely labour and time in wine-making:

    https://www.aeaweb.org/articles?id=10.1257/089533003321165010

    “Why do reswitching and capital-reversing occur? Samuelson (1966) provides the intuition using the Austrian conception of "capital as time", so that the productivity of capital is the productivity of time itself. Figure 1 illustrates two techniques for making champagne using only labor and time (and free grapes). In technique 'a', 7 units of labor make 1 unit of brandy in one period, which ferments into 1 unit of champagne in another period. In technique 'a', 7 units of labor make 1 unit of grape juice in one period, which ripens into wine in another period. Then 6 units of labor shaking the wine produce 1 unit of champagne in a third period.”

    Note: as to “capital as time” while it is possible to *define* "capital" as "time", I don't think that it is useful to consider "capital" as "time", anymore than it is useful to imagine "capital" as the quality of "capitalness" as J. B. Clark did.

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