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..

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.