The Astonishingly Poor Empirics of the Tendency of the Rate of Profit to Fall
I’ve been meaning to follow up on my video about theories of value. I know it was released in November 2022, but I had (1) intensive teaching responsibilities (2) other videos/papers/books to be writing and (3) respect for my own time and mental health. Despite those interceding issues, I did want to clarify quite how bad the situation is for the empirics of the Tendency of the Rate of Profit to fall (TRPF). After my video I realised the average (online) Marxist economists’ understand of statistics is far worse than I thought.
The tendency of the rate of profit to fall (TRPF) is one of the key empirical implications of the Labour Theory of Value (LTV). I’ve had some fruitful, as well as many not-so-fruitful, interactions with people about this. Overall, I have been astonished by the poor level of statistical analysis. To put it bluntly, many seem to believe that eyeballing noisy time series trends and making loose statements the history of the displayed time period is sufficient to illustrate the TRPF empirically. It isn’t.
The Basics
To back up, the basic outline of the LTV is that only labour can create more value than capitalists pay for it. Capitalists pay for labour power, the commodity form of labour, but appropriate the value newly produced by the workers — that is, the value that labour creates. The amount paid for labour power is lower than the value the labour creates for the capitalist and the difference between the two is called surplus value, which is the source of capitalist profits. Capitalists compel the worker to produce more than they consume; workers are exploited because they produce more value than they receive as wages. The rate of exploitation e is surplus value S divided by the value of labour power V, or e= S/V.
Marxists sometimes call non-labour inputs into production ‘constant capital’, and constant capital only generates as much value as is paid for it. In the Marxist LTV, constant capital is not exploited in the same way as labour (which is sometimes also called ‘variable capital’ — yes, the terminology is a nightmare). This means constant capital is a wash as far as surplus goes; a net zero. If I buy a truck of coal for use in my electricity plant, it contributes to the value of the output exactly the amount I pay for it. Capital is not exploited in the same way as labour, so total profits are both determined and limited by the surplus value extracted from labour alone.
Using this analysis, we can easily predict the TRPF. If labour is the only source of value, then the more variable capital relative to constant capital used in production, the more surplus value and the higher profits. The relative ratio of constant capital to variable capital is C/V and is known as the Organic Composition of Capital (OCC). If we assume that C/V rises over time because capitalists try to invest in labour-saving technology, capitalists’ costs will contain more constant capital C relative to variable capital V. This results in less surplus value produced relative to costs, lowering the Rate of Profit (RoP): Surplus Value divided by total costs, or RoP = S/(C+V).
There are fair few attempts to calculate the rate of profit out there. It is usually done at the level of the whole economy and there are good theoretical reasons for this, though it does rob the theory of potential explanatory power. On first look, you might be forgiven for thinking that the LTV implies that industries which are more labour intensive, such as construction, will have higher rates of profit, since they have a lower OCC and therefore more surplus value. The converse applies to those industries with high capital intensity, such as oil extraction: they’ll have lower rates of profit. We could test this implication on microeconomic data.
Yet Marx assumed that profits tend to equalise across sectors due to competition, which is a reasonable assumption. This competition would effectively ‘share out’ surplus value to equalise the rate of profit, so the observed rate of profit in specific industries would deviate from the ‘value rate of profit’ implied by their industry-level OCC. This dynamic is the essence of the transformation problem which plagued Marxist economics for so long. In practice, the Temporal Single System Interpretation (TSSI) provides a resolution to the transformation problem which means that the TRPF will only be observed at the level of the whole economy, which is quite a weak test with lots of so-called ‘researcher degrees of freedom’ — as we’ll see.
One of the main Marxist scholars people cite online is Michael Roberts, who has a website devoted to discussions of Marx’s theory, focusing largely on the TRPF and the role it has played in contemporary crises. An illustrative example of his comes from a 2015 note on the UK rate of profit. He produces the following graph for 1855–2007:
It’s clear from Figure 1 that there is a decline in the RoP over the whole period, but also that there are a lot of fluctuations. In fact, there are 2 periods of relative stability in the RoP towards both the beginning and the end of the time period, with a fairly precipitous decline in the middle. Following the solid black line, which depicts the estimates using data from the Office for National Statistics (ONS) and Bank of England (BoE), the RoP starts at around 21% in 1855. It then rises up to a peak of almost 27% in 1871, before falling down to 19% by 1879. It is roughly stable for a few decades, but drops suddenly to a local minimum of just under 15% in the 1920s. From there, it rises again slightly and peaks at just over 21% at the end of WW2, before declining precipitously from the 1940s until the 1970s, when it goes as low as 10%. From 1975 to 2007 it was stable on average, with fluctuations of a few percentage points in either direction.
Figure 1 indicates that although the TRPF may assert itself during some periods, it is not universally observed. And Marx knew a measure like the RoP cannot be expected to fall neatly and uniformly. He outlined several “countervailing tendencies” which may act against the TRPF. As per usual, Marx took too long explaining them to quote him here, but they were described clearly by Basu and Manolakos (2012):
“(1) the increasing intensity of exploitation of labor, which could increase the rate of surplus value; (2) the relative cheapening of the elements of constant capital; (3) the deviation of the wage rate from the value of labor-power; (4) the existence and increase of a relative surplus population; and (5) the cheapening of consumption and capital goods through imports.”
Countervailing tendencies are completely reasonable in principle: everything in economics is complex and the effects we want to isolate are often swamped by many others. We need to be sure that the mechanism we have identified — in this case the LTV, rising OCC, and resultant TRPF — is the one which explains the movements in the data. After all, most movements in data can be explained in multiple ways. This is one reason modern mainstream economists are obsessed with research design which isolates the causal effects of one variable on another (and maybe too much so).
Unfortunately, the clear progress in this area seems to have passed many Marxists by and they think that ‘countervailing tendencies’ are something they can selectively invoke when the data do not demonstrate the TRPF. Instead, they are something which should be actively accounted for by good research design, which simply cannot be done by eyeballing graphs.
Assuming the Theory to Test the Theory
In my experience after my numerous interactions with Marxists, when you produce a graph of the rate of profit falling, Marxists will claim that this confirms the TRPF. However, when you produce a graph where the RoP rises or stays stagnant, they will insist (without clear evidence) that the countervailing tendencies are to blame, and therefore the TRPF (and LTV) are saved. This practice obviously renders any testing of the TRPF unfalsifiable, since any outcome can be rationalised in terms of the theory. It is ‘begging the question’ to assume that the LTV and TRPF are true when interpreting the data, yet this is exactly what so many Marxists do.
The reality is that without concrete measures of them, we simply have no idea if the countervailing tendencies are moving one way or the other. My favourite way of illustrating this comes from the same Roberts paper, where he takes a few different measures and, in the process, splits up the time period from Figure 1. Firstly, he takes the second half of the 19th century on its own:
The RoP doesn’t decline in Figure 2 and for the first few decades it actually rises. Now here’s a test: does this make you think “well clearly the RoP is not falling so the countervailing tendencies are dominating”? In that case, stop right there. You are doing precisely what I’m warning against: assuming the theory in your test of the theory. The above graph does not contain measures of the countervailing tendencies so we cannot conclude anything about the Marxist TRPF, at least as long as we acknowledge the countervailing tendencies are important.
In fact, we cannot conclude anything about the rate of profit after accounting for the countervailing tendencies from any such graph, including one where the rate of profit seems to be falling, as it was in the post-WW2 period:
If your first thought looking at this graph is “there is that evidence for the TRPF”, then once again I’m going to have to ask you to stop right there. Stating that the Marxist TRPF is occurring is equivalent to stating that the countervailing tendencies are either too small in magnitude to make much of a difference, or that they are working against the underlying dynamics of the LTV but are being overpowered. You cannot know either of those are true because the countervailing tendencies are not in the graph.
To cement this further, imagine a case where ‘countervailing tendencies’ are actually pushing the rate of profit down. This is entirely possible, since we can’t expect our ‘countervailing tendencies’ to only go in one direction. For example, the price of imports could rise; or the available surplus population could be dwindling due to people withdrawing from the labour force; or the rate of exploitation could be falling due to rising wage demands. In this case these factors would themselves be causing the fall in the RoP, rather than the ‘underlying’ dynamics of the LTV.
Whether in Figure 1, 2, or 3, this could mean that even when they show the unadjusted RoP falling, the RoP adjusted for countervailing tendencies is rising, which is contrary to Marxist predictions. It would also imply that this rise cannot be explained by countervailing tendencies, which had already been accounted for. As with all data, we actually need to check to see which direction these magnitudes are moving!
One argument I’ve seen is that the dynamics laid out by the labour theory of value must come home to roost at some point, which sounds like a reasonable claim at first but is still difficult to test. When people say ‘tendency’ it is not clear which time frame or magnitude of effect they have in mind, which brings us back to unfalsifiability. This claim that the TRPF must happen ‘eventually’ actually amounts to a claim that the countervailing tendencies can only go one way over the long-term, but again that is an empirical claim that needs to be investigated. The sheer volume of unstated assumptions Marxists make when interpreting these frankly flimsy correlations is nothing short of astonishing.
More than one person suggested that the labour theory of value causing the TRPF is comparable to CO2 emissions causing climate change. That is: a tendency which can only be observed over the long-term and with highly aggregated data. I’m sorry, but this is a shallow understanding of the science behind climate change which is not much better than that of the deniers. The greenhouse gas effect has been isolated in the laboratory since the 19th Century. Conversely and as noted earlier, Marxian theory has converged on the idea that it’s impossible to test the TRPF at the microeconomic level, let alone in a controlled experiment. Furthermore, climate scientists have been making quantitively correct predictions about global warming since the 1970s. Marxists struggle to make even qualitative predictions about the rate of profit beyond ‘it will go down for some stretch of time at some point in the future’.
The obvious econometric solution is to control for the countervailing tendencies and see what happens to the RoP. Thankfully, many of the tendencies outlined by Marx are actually observable, which is a good feature for a theory to have. Basu and Manolakos (2012) [hereafter BM] do exactly this and find what they call a “weak” downward trend in the USA from 1948–2007, with the RoP falling by 0.2% every year. This is a much better approach than eyeballing graphs and I hope we see more of it, but it is only one paper and if the replication crisis has taught us anything, it’s that we need about a hundred more (on top of better research practices) to be sure that what we’re seeing is actually there. In addition, there is the question of whether such a slight, aggregate fall is especially interesting, which is perhaps a topic for another time (though see here for a nice post on the matter).
‘Why’ is a Causal Question
Another, more piecemeal approach is to disaggregate the TRPF using Marxist concepts to get an idea of how different magnitudes, such as the OCC or the rate of exploitation, are moving. Recall that the RoP is given by Surplus Value divided by total costs: RoP = S/(C+V). If you divide this whole thing through by V, you get RoP = e/(C/V+1). So the rate of profit is equal to the rate of exploitation divided by the OCC plus one. If you get investment in labour-saving technology then, assuming the rate of exploitation is constant, you get a rise in the OCC and the RoP falls. This would seem like suggestive evidence that capital is being substituted for labour, and that this is resulting in less surplus value, in line with the LTV.
Roberts’ 2015 paper on the UK contains the following table showing exactly this pattern in the data. Ignoring the rate of exploitation S/V for simplicity, we can see that from his Table 3 that the measures of the RoP generally fall while the OCC generally rises:
This is an interesting exercise for sure, but it tells us nothing about causality. Whereas before we were eyeballing one time-series trend, now we are eyeballing two (or three)! Besides, these types of correlations are entirely explainable through non-LTV reasons. Suppose we observe in the data a simple negative correlation between the economy-wide OCC and RoP. I can think of three reasons this could happen, none of which have anything to do with the LTV:
(1) Reverse causality from the RoP to OCC. This is actually plausible: higher profit rates may lead to greater worker retention, since companies can ‘afford’ to keep workers. Or to put it another way, in hard times companies may shed variable capital relative to constant capital to cut costs, meaning that a low RoP causes a higher OCC. It would strike me as bizarre for Marxists to deny capitalists shedding labour during downturns as a possibility.
(2) Some third factor causing both a rise in the OCC and a fall in the RoP. For example, increased competition through a new entrant using shiny new, labour-saving capital tech could increase C/V but reduce profits. This would not be because a higher capital/labour ratio is reducing profits directly a la the LTV, because the new entrant would actually have higher individual profits. But because the new entrant increased competition, other firms would experience a decline in their RoP. (Arguably this is a Kaleckian updating of the TRPF and makes a bit more sense. I’m also aware Marxists would tend to interpret this ‘through the lens’ of the LTV but I’m not convinced there is any need to do so, it’s just straightforward competition).
(3) A more subtle issue of the ecological fallacy. This would be a case where the OCC rises and the RoP falls at the aggregate level, but at the level of individual firms and industries the opposite is going on. I’ve discussed the ecological fallacy in other contexts, for instance the so-called gender equality paradox, and in a future post I may construct a more detailed example to illustrate how this could happen with the OCC. Point (2) may even offer hints as to how this might work. The crucial point is that you could generate a negative aggregate correlation between OCC and RoP while assuming the LTV is not true, thus rendering that correlation not a unique prediction of the LTV.
We could say something analogous for the observed movements in rate of exploitation and other Marxist categories used to ‘prove’ that the LTV is driving the economy. But I’ll leave those as an exercise for the reader.
The boring truth is that the TRPF is just one out of many mechanisms — seven in total according to BM — which may increase or decrease the profit rate. When you say it like this it becomes apparent that you’re saying nothing whatsoever. If we stick to eyeballing aggregate time series graphs, its predictions are no different to having a TRPR, or tendency for the rate of profit to rise. The problem is compounded when you consider that the underlying dynamics of the economy may not be Marxist, for instance that capital potentially generates surplus value, in which case there is no reason to expect the TRPF in the first place. Of course, many Marxists have shown themselves to be constitutionally incapable of imagining a world where the LTV isn’t true, but that’s where the theory becomes a dogma rather than a testable set of propositions about the world.
We can get a couple of useful, if broader predictions out of the TRPF literature. For BM, the tendency is a long-term trend after controlling for countervailing influences and the effect exists but is muted. For others, the TRPF asserts itself during specific historical time periods like the post-WW2 to 1970 in Figure 3, which seems true but has myriad explanations besides Marxian ones, as noted eloquently by David Harvey. Others still basically admit the TRPF is unfalsifiable and is just a lens through which to understand capitalism. Andrew Kliman thinks that the TRPF is falsifiable but has admitted that the underlying LTV is less easy to test. I’m actually okay with the last two ideas, but then don’t pretend it’s a truly falsifiable exercise. You can’t have it both ways.
As I’ve noted, the TRPF is tested only on economy-wide aggregates for good reasons. This means that the LTV doesn’t actually imply anything at the level of individual prices or industries, which greatly reduces its explanatory power and our ability to test it empirically. If the theory made microeconomic predictions, we could look at capital intensity in different industries and how it related to profits, but this is not possible because it makes the theory itself inconsistent. We end up with macroeconomic predictions, which are notoriously difficult to settle definitively. That’s why macroeconomics sucks.
If we were to start from the basics and formulate a clear, testable proposition based on Marxist theory we might come up with something like this:
An influx of labour (relative to capital) causes a rise in the aggregate rate of profit
This kind of statement blows away the tedious layers of jargon and circular reasoning that so many Marxists seem to relish and points us to a clear way to test the causal claims they are making. Now, I’m not saying this hypothesis is easy to test, although it does make me wonder if immigration shocks like the Miami boatlift could be of use. I’m happy to hear any suggestions anyone has about how to put this into action.
As a pluralist who has countless problems with mainstream economics and sees plenty of value (!) in Marxism, I am aware of the historical issues surrounding the marginalisation of Marxism and contemporary mainstream economists’ complete ignorance of its insights, which prevent it from getting a seat at the table and also prevent resources being put into measurement and testing in accordance with Marxian theories.
Yet Marxists are equally clueless about how to carry out credible statistical analysis and in the age of the internet, there is no excuse. Again, I am sympathetic to the notion that mainstream economists are too reliant on this type of analysis and that we can use other types of data than statistics. What annoys me is that Marxists may agree on this point, then carry out this lacklustre statistical analysis anyway. If you don’t believe in statistical analysis as a test of the LTV, then just drop it and the debate can move forward using more historical analysis or whatever you favour.
What I’ve just discussed is the absolute bare minimum expected of people doing empirical, statistical analysis. It doesn’t amount to more than ‘correlation doesn’t equal causation’ and ‘if you say there are important covariates, measure them and include them in your analysis’. These are expressed above in a level of detail I didn’t think I’d have to go into in my original video, but I was wrong. And I haven’t even gotten into how robust the above graphs are to different measurements and datasets; or potential aggregation issues with labour and capital; or more granular issue of how exactly to measure things like the OCC. I haven’t even mentioned statistical significance, which is another thing people like Michael Roberts tend to ignore.
Unfortunately, Marxists seem to think that shoddy statistical analysis can be solved by writing a lot of words which, seemingly to them, ‘prove’ that labour is the source of value. Since I’ve been studying mainstream economics for a long time, I’m afraid that no volume of explanation can convince me that any economic assumption is necessarily true, a point I’ll probably elaborate on in the context of the labour theory of value another time. For me, the LTV is simply the assumption that only labour generates surplus value, and the implications of this have to be borne out using rigorous research design rather than casual eyeballing of a few flimsy correlations.
