Post-Industrial Reality of Marxist Economics (Short Marxist Literature Review)

Abstract

There are few debates that are as polarizing as Marxist economics against the world. More specifically, Marxist claims about the Labor Theory of Value (LTV) and the Tendency of the Rate of Profit to Fall (TFROP or LTFROP). To be clear, Marxists must demonstrate that the rate of profit falls as the organic composition of capital changes, as opposed to simply falling, which is compatible with classical and Austrian economics theories.

In this short(ish) essay, I examine several strands and interpretations of the Marxian economic literature that supposedly prove both TFROP and the LTV, often instrumental to the immiseration of the proletariat. I focus on the more popular Marxist arguments, from Michael Roberts’ “proof” of TFROP to Basu’s use of the WIOD dataset, to Anwar Shaikh’s empirical proof of the Labor Theory of Value.

Although I am largely anti-Marxist, anti-communist, and anti-collectivism, I would not encourage libertarians or other critics to simply handwave Marxist economics. The Marxist tradition contains a vast body of influential works that constitute at least some engagement. Frustratingly enough, lots of Marxist literature, in my experience, is pseudo-rigor to justify their wholly absurd theory. I’ll be critiquing the empirical and methodological foundations contained in some of the literature.

Section I: Marxist Philosophy and Theory

The first thing to address is the popularity of Marxist philosophy and Marxist economics. Much of what Marx wrote can be considered to be in the continental school of philosophy, predating the rise of analytical philosophy. Marx’s writings on class struggle, viewing history under a Hegelian class lens, coercion, the downfall of capitalism, and the specialty of labor, all resonate deeply in the average man, who toils while a billionaire seemingly contributes little but commands the proletariat for their own profits. Much of Marxist literature is resentment pointed at the Capitalist Bourgeoisie class, who owns the means of production, i.e., capital goods (factories, etc.), to extort the proletariat.

Marx and modern Marxists wholly believe that the proletariat and bourgeoisie operate entirely in their own class self-interest, such that any type of fiscal policy to help the proletariat may only delay the inevitable.

Thus, the belief of communists alike was that class dictated your self-interest, even in the case of Hegel, who lived a rather bourgeois lifestyle.

The Marxist thesis, which draws from elements of Hegel, predicts that such an internal contradiction between the proletariat and the bourgeoisie will inevitably cause a falling rate of profit, which then squeezes the proletariat. With nothing but the chains of Capitalism to lose, this gives rise to the revolution, a new synthesis, in which the means of production are once again given to the working class, a liberated class, one class.

The first basic critique to roll out is that historicism generally isn’t great, and as interesting as Hegel is, we could easily use a deductive class lens between state and man, something often touted by Austrian and Anarcho-Capitalists. What’s to say that the Austrian lens, which runs contrary to the Marxist lens of class conflict, isn’t correct? In this, we must move on to a different methodology, that is, empiricism, which I wholly believe Marxist Economists have failed badly.

Section II: Methodological Errors in Shaikh’s LTV Paper

As a quick preface, this section is quite math-heavy, and I had to consult a lot of friends and refresh myself on Linear algebra-related stuff in order to write this, but if you’re just looking for a clean response, don’t let the math bog you down too much; the methodological errors are very straightforward. As I’ll point out, my entire critique of this paper is that it fails to even test for the thing it seeks to test.

It’s important to first refute the Labor Theory of Value (LTV) since the falling rate of profit rests on the Labor Theory of Value being true. This ideological theory of value is the idea that labor generates value; thus, the capitalist class does nothing aside from taking from the value created by the labor. It’s probably good to look at this kind of counterintuitive type of thing with high levels of skepticism, though we should still look deeply into the arguments for it.

There are many Marxist scholars and a great body of Marxist literature. Anwar Shaikh, a PhD at UMass Amherst, has done extensive empirical work on the Labor Theory of Value (LTV) and published papers with supporting empirical evidence. My main critique of his paper is that, given his empirical evidence, it is more parsimonious to go with other theories of value which not only have more explanatory power but also more simplicity.

Shaikh runs a linear transformation to map output in the business sector (value) with firm labor inputs (to be honest, it’s been years since I took linear algebra, but this is somewhat like exponentiating a matrix, which I did once for a social mobility paper, and the math stack exchange linked above may help). As a second side note, his paper mentions that they did not use a least squares type of linear regression because correlation measurements were weak.

Below, we can see the table that establishes the relationship between the labor value and the price of production. These two factors map onto each other tightly, which is not the case with the price of production. From 1947 to 1972, we see that there is an average percentage deviation of 0.44 with the labor value vs price of production and an average percentage deviation of 0.082 with the price of production vs market price.

The first question is whether the data he sources (from Ochoa) is trustworthy. The second, but more important, critique is that figures 15.2 and 15.3 show rescaled prices plotted against total labor hours and aggregate price of production plotted against total labor hours.

It literally just looks like a linear function since it’s been log-scaled. Unfortunately, the quality of the paper I got isn’t great, but if you look carefully, you’ll see several tiny dots which are just going to be plotting an industry. The rescaled market prices here are actually more tightly held to the output levels. To Shaikh, this is irrefutable evidence of the LTV being true. Unfortunately, the entire experiment is uninsightful since a strong relationship between labor input and gross output is meaningless when you fail to account for the size of the industry plotted. As reddit user u/robthorpe puts it, “It’s a case of omitted variable bias. In this case, the omitted variable is the size of the sector. The principal problem is that this breaks the independence assumption in regressions.”

Obviously, large sectors employ a large number of people, and small sectors employ a small number of people. Figures 15.2 and 15.3 do not empirically test the LTV hypothesis. It is nothing more than a graph of larger firms using more labor while also having a higher gross output. This theory is completely compatible with other theories of value, such as Marginalism, the theory that states value is derived from marginal utility. What Shaikh has found is nothing more than a spurious correlation. For instance, ice cream production is correlated with shark attacks, yet that doesn’t mean that ice cream production raises shark attacks. Similarly, labor output being correlated with industry output tells us next to nothing. To conclude that the LTV is an accurate quantitative tool would be absurd statistical malpractice.

On a side note, here’s a fun marginal utility debate: link.

Section III: Various Critiques of the Labor Theory of Value

Central to the Marxist Labor theory of value was that living capital, ie, human labor, as opposed to dead capital, ie, machinery, had these sorts of metaphysical mystical properties which dictated the value of a commodity. In the case of a bus driver, the surplus value is generated solely by the labor of the driver, not the dead capital like the bus. Of course, as special as humanity might be, this claim is very dubious to say the least.

I also have to ask, the labor theory of value (LTV), being a quantitative tool for value, seems to lose its purpose when socially necessary labor hours are very much subjective. Labor may be a good heuristic; however, that could just as well be a spurious correlation.

By virtue of parsimony, I have no reason to adopt the view that labor has any time of unique features that generate surplus value, unlike other forms of capital. In fact, such a thesis takes up an enormous burden of proof, that is, to provide evidence that this Marxian thesis has more explanatory power to make up for its lack of simplicity.

Sraffa’s Joint Production Critique

There are a few views here that are more plausible than the Labor Theory of Value. One postulated by the Post-Keynesians is that material relations / physical conditions determine market prices (as opposed to the magnitude of labor). The second is the more Libertarian view, originally.

Pierro Sraffa’s unpublished notes grant much insight and critique on the debate. Sraffa called the idea that “labor is a quantity commensurate with value” a “fatal error”. He claimed that Smith, Ricardo, and Marx had simply substituted labor time for these inputs. Sraffa viewed the relationship between inputs and output, ie, how much steel or wool is inputted to create other goods.

For example, in the case of 2 wool spools and 1 needle to create a shirt, the worker receives 1 wool spool as wages. In the Sraffian model, this is what determines prices and profit, not labor value. In the Sraffian model, you can have zero labor values, yet still have a surplus value because what matters are the physical surpluses, not the level of labor. Sraffa demonstrated this by using high school-level Algebra 2. Take, for instance, this example:

2 spools of wool + 1 spool of yarn = 1 sweater

4 spools of wool + 2 spools of yarn = 1 t-shirts

Workers get half a spool of yarn as wages

Mathematically, this is expressed by:

2W+1Y = 1S

4W+½ Y=2T

I think you might see what Sraffa was getting at here. You quite literally do not need to calculate labor values in this system of equations. Surplus value (profit) emerges from the physical relationships of goods.

In other words, all you need are physical input and output relations and distribution rules to calculate value. Labor is wholly irrelevant, and thus labor is not special as Marxists would like to believe.

Marginalism and Subjective Value Theory

The second, more prominent theory of value, which refutes Marx’s Labor Theory of Value, occurred during the marginal revolution. Carl Menger, the founder of the Austrian school of economics, pointed out that socially necessary labor hours were quite irrelevant as to why a commodity has value. Consider the following scenario:

You have both a bottle of water and a Rolex. Which one do you value more? Well, intuitively, you might say the Rolex since it intuitively and typically has more value. But why is that the case? Is it because of the “socially necessary labor time” put into the watch?

Menger pointed out that it makes more sense when you consider the setting of being stranded in the desert. In this scenario, the bottle of water could be life-saving, and quenching your thirst while stranded in the desert grants much more satisfaction than having a watch. This is the concept of marginal utility.

Thus, Menger concluded that value is wholly subjective. Where the Labor Theory of Value serves as a quantitative tool for measuring a commodity’s value based on labor, the Subjective Theory of Value uses marginal utility functions in order to measure value, though this is also indexed to subjective values. Value is not inherent to the product itself or labor-based.

Is the Rate of Profit Falling?

It is important to note that Marx not only saw the rate of profit falling as a prediction, but as an a priori truth due to the internal contradictions of the system.

“The progressive tendency of the general rate of profit to fall is, therefore, just an expression peculiar to the capitalist mode of production of the progressive development of the social productivity of labor. It is, therefore, a law, in the sense that it expresses an a priori necessity.” (Capital Volume 3, Chapter 13). In a less roundabout way, it is the law of the rate of profit to fall.

The formula for the rate of profit is given by:

Where r is the rate of profits, s is the surplus value, or unpaid labor, c is the constant capital, such as capital goods, machinery, raw materials, non-living capital, and variable capital, i.e,. The cost of living labor (ie, the proletariat hires). The Marxist thesis postulates that the denominator (c+v) would grow faster than the numerator of s, thus the rate of profit would fall over time.

There’s a lot to unpack here, especially with the surplus value bit and why Marx considers it unpaid labor. As previously covered, surplus value is generated by labour; thus, any profits are due to the laborer, not the machinery or fixed capital.

Furthermore, a falling rate of profit is completely compatible with Austrian and Neoclassical theory since the rate of profit can fall due to falling time preferences. Thus, the burden of the Marxist school is to demonstrate that the rate of profit falls as the organic composition of capital falls, that is, dead capital (machinery) rises as living capital (labor) falls.

C: So the long story short, it’s really inconclusive. To my knowledge, every paper has large methodological errors. It doesn’t make sense for anyone to say definitively that the rate of profit of falling, though what we can say broadly is that a capitalist mode of production has done outstanding things for living standards in society.

Refuting Roberts (Empirics of Declining Rates of Profit)

Michael Roberts wrote a paper/blog seemingly supporting the idea of TFROP. I won’t need to write a long refutation; simply, Marxists must demonstrate that the rate of profit declines as the organic composition of capital changes. More importantly, Roberts sources from the Penn World Tables, which don’t have access to the data that measures the quantity of capital. Instead, what they do is impute (estimate) the quantity of capital through the perpetual inventory method.

Additionally, the starting interval is at 40% in the 1940s, which seemingly is a malicious methodological choice. For example, a stock might have an average return of 10% per year since 1940; however, most of the growth is skewed towards the front end (1940–1960) of the growth, thus to expect 10% returns in the present would be an incorrect assumption since the 10% only holds due to very old trends.

The falling rate of profit that Michael Roberts “discovers” is simply a depreciation baked into the data.

Basu’s World Input Output Data (WIOD)

A friend of mine recently sent me some of Basu’s works as well, which are sourced from the WIOD tables. Unfortunately, the dataset only contains about 40 countries.

We can first look at Australia, which seemingly has a rising and then falling rate of profit.

Then, looking at the rate of profit for the United States, it shows the exact opposite.

Anyways, the way they compile the twenty countries into the world’s rate of profit is by this:

All it’s doing is weighing countries by output (GDP?) to aggregate the “world’s” rate of profit. This is consistent with the typical Marxist pseudo-rigor in order to make these trivial findings seem profound. The methodological suicide this paper commits by only looking at the time interval between 2000 to 2014 is also dubious. Really? This 14-year trend is “proof of TFROP”? To be fair, Basu is explicit about this. I thought Marx distinguished this to be some sort of economic law; surely there is better evidence available.

The world’s rate of profit consists of more than just a handful of countries. Because the WIOD data includes only a small fraction of the world’s countries and the world’s population, we can dismiss it entirely.

Furthermore, the Marxoids must demonstrate that the falling rate of profit occurs as the organic composition of capital changes, which they have not whatsoever, leaving me wholly convinced of any of Marx’s predictions.

Section IV: Falling Rates of Profit & Firm Behavior

Now that we have the empirical claims out of the way, can we make an inductive case of traditional firm behavior given a falling rate of profit? Conditional on TFROP being true, does it then follow that the plight of the proletariat will be expedited? I think we all would share the intuition that a falling rate of profit in and of itself isn’t harmful.

The reason why immiseration of the proletariat may follow from a falling rate of profit, as the organic composition of capital might follow, is that only labor creates surplus value (false but okay). With higher dead capital and a lowering of living capital, profit rates tend towards 0% thus, the proletariat is allocated less and less. What’s important to note is that the bourgeoisie would also likely be squeezed out if this were true. Of course, this all presupposes the LTV being true, which is false!

Conclusion

Marxism tells a fictional story of labor and exploitation, eventually leading to an inevitable collapse, but the evidence simply runs contrary to all the claims. Either that or there is insufficient evidence to justify any Marxist ideas. Empirical studies are often methodologically weak, and the theoretical critiques demonstrate that labor is not unique or necessary to explain prices or profits. The LTV and TFROP may seem interesting, but they fail rigorous economic proof. Capitalism, on the other hand, is not on the verge of collapse.

Acknowledgments

Big thanks to the people over at r/AskEconomics and u/RobThorpe for chatting with me about some of these papers and providing several insightful reads.

Useful Readings into TFROP and LTV Debate

Shaikh, “The Empirical Strength of the Labour Theory of Value”

Penn World Table documentation

Paul Cockshott’s assessments of the LTV

Econometric work from Basu (2010), “Is There a Tendency for the Rate of Profit to Fall?”

Kilman (TSSI) and Pro-TFROP studies