No, Productivity Does Not Explain Income

Did you hear the joke about the economists who tested their theory by defining it to be true? Oh, I forgot. It’s not a joke. It’s standard practice among mainstream economists. They propose that productivity explains income. And then they ‘test’ this idea by defining productivity in terms of income.

In this post, I’m going to show you this circular logic. Then I’ll show you what productivity differences look like when productivity is measure objectively. They’re far too small to explain income differences.

Marginal productivity theory

The marginal productivity theory of income distribution was born a little over a century ago. Its principle creator, John Bates Clark, was explicit that his theory was about ideology and not science. Clark wanted show that in capitalist societies, everyone got what they produced, and hence all was fair:

It is the purpose of this work to show that the distribution of the income of society is controlled by a natural law, and that this law, if it worked without friction, would give to every agent of production the amount of wealth which that agent creates. (John Bates Clark in The Distribution of Wealth)

Clark was also explicit about why his theory was needed. The stability of the capitalist order was at stake! Here’s Clark again:

The welfare of the laboring classes depends on whether they get much or little; but their attitude toward other classes—and, therefore, the stability of the social state—depends chiefly on the question, whether the amount that they get, be it large or small, is what they produce. If they create a small amount of wealth and get the whole of it, they may not seek to revolutionize society; but if it were to appear that they produce an ample amount and get only a part of it, many of them would become revolutionists, and all would have the right to do so. (John Bates Clark in The Distribution of Wealth)

So the neoclassical theory of income distribution was born as an ideological response to Marxism. According to Marx, capitalists extract a surplus from workers, and so workers get less than what they deserve. Clark’s marginal productivity theory aimed to show that this was not true. Both capitalists and workers, Clark claimed, got what they deserved.

The message of Clark’s theory is simple: workers need to stay in their place. They already earn what they produce, so they have no right to demand more.

The human capital extension

Clark created marginal productivity theory to explain class-based income — the income split between laborers and capitalists. But his theory was soon used to explain income differences between workers.

In the mid 20th century, neoclassical economists invented a new form of capital. Workers, the economists claimed, owned ‘human capital’ — a stock of skills and knowledge. This human capital made skilled workers more productive, and hence, made them earn more money. So not only did productivity explain class-based income, it now explained personal income.

With the birth of human capital theory in the 1960s, the marginal revolution was complete. All income differences, economists claimed, could be tied to productivity differences. And from then onward, there was an endless stream of empirical work that ‘confirmed’ that productivity explained income.

A sticky problem: how do we compare different outputs?

Before we look at how economists ‘confirm’ marginal productivity theory, we have to backtrack a bit. We have to understand a basic problem with the concept of productivity.

Imagine we want to compare the productivity of a corn farmer to the productivity of a composer. The corn farmer produces corn. The composer produces music. How do we compare these two outputs?

I think it’s obvious that we cannot do so objectively. Any comparison will require a subjective decision about how to convert corn and music into the same dimension. The lesson is simple. We cannot objectively compare the productivity of two workers unless they produce the same thing.

Think about how severely this problem undermines marginal productivity theory. The theory claims that productivity differences universally explain income differences. But we can never actually test the theory, because productivity differences cannot be universally measured.

Even worse, it’s possible to earn income without producing anything. Think about the practice of patent trolling. Patent trolls are people who buy the patent for a product that they neither invented nor produce. These individuals don’t ‘produce’ anything. But they still make money. How? Because they get the government to enforce their property rights. Patent trolls sue (or just threaten to sue) anyone who infringes on their patent. Viola, they earn income without producing anything.

My point here is to show that marginal productivity theory is plagued by a simple problem. We can’t compare the productivity of people who produce different things. And some people don’t ‘produce’ anything at all. This problem seems to severely limit any test of marginal productivity theory.

Economists’ sleight of hand: defining productivity using income

Given the problems with comparing the productivity of workers with different outputs, you’d think that marginal productivity theory would have died long ago. After all, a theory that can’t be tested is scientifically useless.

Fortunately (for themselves), neoclassical economists don’t play by the normal rules of science. If you browse the economics literature, you’ll find an endless stream of studies claiming that wages are proportional to productivity. Under the hood of these studies is a trick that allows productivity to be universally compared. And even better, it guarantees that income will be proportional to productivity.

To understand the trick, we have to look at some basic accounting definitions. Figure 1 shows how a firm’s income stream gets split. The firm earns income in the form of sales (right). Part of this income is paid to the firm’s owners as ‘profits’, and part of it is paid to workers as ‘wages’. The rest goes to other firms as ‘non-labor costs’.

Dividing an income stream

Figure 1: Dividing an income stream. Accounting principles dictate that a firm’s sales get divided into profits and wages.

The point here is that the income on the right (sales) is the source of the income on the left (profits and wages). So a larger income on the right translates into larger incomes on the left. Thus sales per worker will obviously correlate with wages. Given our accounting definition, it has too.

With our accounting definition in hand, we’re ready for the trick used by neoclassical economists. To test their theory, they define ‘productivity’ in terms of income! They assume that a firm’s sales indicate its ‘output’.

Figure 2 shows this slight of hand. Neoclassical economists take the firm’s income stream and reverse it’s direction. Presto! Sales now indicate output! [1]

Using sales to measure output

Figure 3: The neoclassical slight of hand. Neoclassical economists assume that sales measure ‘output’. Presto! They show that wages are proportional to productivity. Or rather, they show what we already knew was true from Figure 2: the income on the right explains the income on the left.

With this slight of hand, we can endlessly confirm that productivity ‘explains’ income. We find that productivity — as measured by sales per worker — is highly correlated with wages!

The key here is to forget that we are dealing with an accounting truism. Sales are no longer ‘income’. Sales are now ‘output’. And this output miraculously ‘explains’ wages!

I wish I could tell you that this is a joke, since it doesn’t pass the laugh test. But it’s not. Measuring ‘productivity’ using sales (or value added) is standard practice in mainstream economics.

And so economists test their theory of income distribution by assuming it is true. They measure productivity in terms of income. Then they find (unsurprisingly) that productivity ‘explains’ income.

How to show that productivity ‘explains’ income:

I’ve taken the liberty of creating a step by step guide for how to test marginal productivity theory and guarantee that the theory succeeds:

  1. Find an income-accounting equation that is true by definition.
  2. Forget that you are dealing with an accounting equation.
  3. Pick a form of income (in your equation) that you want to explain.
  4. Given your choice, look at the opposite side of your accounting equation.
  5. Convince yourself that this opposite side no longer measures income. It now measure output.
  6. Regress the two sides of your accounting equation.
  7. Celebrate when you find a strong correlation.
  8. Claim you that have found evidence that productivity explains income.
  9. Never tell anyone that your results were guaranteed because they followed from an income-accounting equation. (This step is unnecessary if Step 2 is successful).

Productivity differences cannot explain income inequality

Neoclassical economists resort to slight of hand to measure productivity differences, and so endlessly confirm their theory. But what happens if we try to measure productivity differences objectively?

We find that productivity differences cannot possibly explain income inequality.

To measure productivity objectively, we can only compare workers doing the same task. For instance, we can compare the productivity of two workers who make rivets. Or two workers who both deliver mail. Since the workers have an output with the same dimension, we can objectively compare their productivity.

Here’s an interesting question: how much does productivity vary among workers doing the same task? The psychologist John E. Hunter spent much of his career answering this question. According to his results, the answer is ‘not very much’.

Productivity Dispersion

Figure 3: How productivity differences between workers doing the same task compare to income inequality within countries. Source: The Trouble With Human Capital Theory

Figure 3 takes Hunter’s data and compares it to data on income inequality within countries. Let’s break down the results. First, I measure inequality using the Gini index, which varies from 0 (no inequality) to 1 (maximum inequality). In Figure 3, the x-axis shows the Gini index. The y-axis shows the ‘density’, or relative frequency, of the particular Gini value.

The red curve in Figure 3 shows the Gini index for workers’ productivity. For each task reported by Hunter, I’ve converted the workers’ productivity differences into a Gini index. The red curve shows the distribution of Gini indexes for all of the reported tasks. According to Hunter’s data, differences in workers’ productivity clump tightly around a Gini index of 0.1.

Next to this productivity data, I’ve plotted the distribution of inequality within all the countries of the world (the blue curve). The average Gini index within these countries is about 0.4.

The lesson here is that differences in workers’ productivity are tiny compared to differences in income. So it’s inconceivable that productivity differences (as measured here) can explain income inequality.

Let’s kill the productivity-income thought virus

The idea that income is caused by productivity is a dead end. Marginal productivity theory only survives because economists never test it objectively. Instead, they resort to slight of hand. They measure productivity using income, and claim that this ‘confirms’ their theory.

Let’s not mince words. Marginal productivity is a thought virus that is sabotaging the scientific study of income. It needs to die.

Notes

[1] Economists will often subtract non-labor costs from sales to calculate ‘value-added’. They’ll then claim that value-added measures firm output. It’s the same slight of hand, since they’re still converting an income stream into an ‘output’.

33 comments

  1. Thank you, this was most interesting. I’ve noticed the circular reasoning before, but the ideological roots of the marginal productivity theory were new to me – though I’m not surprised in the slightest.

    One question, though: are there more recent measurements of individual productivity? The common counterargument is that in some fields like software engineering, a “star” can really be many times more productive than the “average” employer. For instance, contributions to codebase are typically highly skewed.

    (I have my reservations about such claims, as they partly result from what kind of tasks these people are assigned with or gravitate towards, these stars do not come about in a vacuum, and for more realistic results we probably ought to measure the team effort more than individual productivity.)

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    • Hi J.M.

      Yes, there is a common claim that productivity has a skewed distribution, and that there are a few superstars that produce much more than the average individual. Most people cite the work of O’Boyle and Aguinis (THE BEST AND THE REST: REVISITING THE NORM OF NORMALITY OF INDIVIDUAL PERFORMANCE).

      The problem is that their findings are mostly an artefact of measurement. Beck et al. have a fantastic rebuttal (On the Distribution of Job Performance: The Role of Measurement Characteristics in Observed Departures from Normality).

      Here’s a simple example. Among scientists, the distribution of published articles is highly skewed. This makes it look like the distribution of productivity is also highly skewed. But here is the crucial point. Scientists do many different tasks. Some focus on teaching, some do a lot of administrative work, and so on. When we look only at published output, we give 0 weight to this other work. The point is that the subjective choice for productivity metric affects what you find. There is no objective way to compare teaching output to research output. They are incommensurable.

      When people do different tasks, it is not meaningful to talk about a ‘distribution of productivity’.

      Liked by 1 person

  2. As always, super interesting work.

    I’m probably missing something so please forgive me. I think of the Gross Domestic Product as a financial measure of an increase in the length and density of civilization networks, those required to enable dissipative energetic flows. Power can then be tied through a constant to the historical accumulation of GDP.

    In that context, productivity is pretty agnostic to whether the production is of corn or music. Both can sustain networks, even neural networks, to a degree that is reflected in the amount of money that is spent to access them. If no one likes the music, it is low productivity. If there is a glut of corn, any extra is low productivity, and this will be reflected in a financial productivity measure.

    So as long as we recognize that money is implicitly linked to physical power, without consideration of the specifics of humanity, why care about the details? Are traditional economists really that wrong (in this regard)?

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  3. I’m assuming you’ve come across the “term” ZMP worker where ZMP stands for “zero marginal productivity”. Do you think we can safely say this particular term is not only pseudoscientific, but an intentional smear-word?

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  4. Hi Blair:

    Just came across your work. Great stuff. Excuse me if I go on a bit here…

    First, exactly, thank you: I’ve always been flummoxed by the idea that spending measures production. Maybe it’s the only numerable measure (?), but…

    Say we’re producing and selling 50 $20K Toyotas. Then instead, we produce and sell one $1M Lamborghini. Have we produced the same amount of stuff?

    I think obviously not. (Which is why I think extreme wealth and income concentration “distorts” the production mix, resulting in massive deadweight loss — measured in utils as deadweight lost inevitably must be, though it’s cloaked as a dollar figure.)

    Measuring the “value” of heterogenous goods is vexing. I don’t have any simple answer to this conundrum, can only point out that mainstream econ (even heterodox, really) doesn’t even address it. Grrr, when (ordinal) price theory replaced (cardinal) value theory… https://bit.ly/2JssvUQ

    Relates directly to the whole issue of differential inflation. But I cast it in more mundane frame: inflation for lower- versus higher-income people/households.

    Inflation indexes are based on the cost of (population-average) market baskets. But clearly, different classes have different market baskets. Shouldn’t we have different inflation indexes for the poor and the rich? Seems obvious and simple. But of course it’s not.

    The problem: Substitution — which (along with hedonics) is the most troublesome thing to estimate over time.

    Key point, IMO: lower-income people are generally already purchasing the lower/lowest-cost substitute available. They can’t change their market basket (much) by substituting down.

    If you don’t have much money, you live in Seattle, and you want to go to a top university, there is no substitute for the University of Washington. You can’t avoid its cost increases by adjusting your market basket.

    I’ll leave it at that, but again: great post. Thanks.

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  5. Very good comments here. n8chz, I had not heard of “zero marginal productivity” workers. I think I will reserve that term for economists who, as I see it, add nothing but toxic ideology to society.

    Tim, I’m not sure I understand, but I’ll try to reply. As I see it, anyone is free to define productivity however they want. But the point is that this definition is subjective. If I value music more than corn, then the composer is more productive than the corn farmer. But others — say starving people — likely disagree.

    The crux of the matter is that whenever we pick a dimension for productivity, we automatically devalue all other dimensions. So if being productive means earning money, then the stay at home mom is no longer productive.

    Regarding your work on the thermodynamics of human society, I see no reason to bring the word “productivity” it. If you’re interested in the growth of structure, then measure this structure however you like. Personally I like the word “throughput”. It nicely captures that we are putting resources through the social system. Whether these resources are used “productively” is a value judgement, not a scientific one.

    My point in this post, though, was a very specific one. It’s fine if economist simply define productivity in terms of income. Again, we’re all allowed our opinions about the dimension of productivity. But having done this, you cannot turn around and say that productivity “explains” income. That’s just circular reasoning.

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  6. i’m always amused by the divergence of the standard productivity measurement as opposed to GDP divided by labor hours. There was a long period during the recovery when the GDP kept growing but the number of hours worked stayed the same. Meanwhile, productivity was flat.

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  7. Interesting post. Thank you.

    I think there is some self-correction involved with the relationship between productivity and income, but it’s asymmetric. One cannot vastly overpay employees without the external, objective consequence of going bankrupt. (Using your diagram above: If Wages exceeds Sales, you need to cut wages (rates or number of staff or both) or increase sales – quickly.)

    On the other hand (“Get me a one-armed economist!”), one can get away with vastly underpaying (a subset of) employees, and redirecting those savings to executives and/or profits, without facing inherent consequences. A cottage industry defending this status quo would probably be required to prevent rebellions of various kinds. That there exists vigorous defenders of the current state of affairs could mean that you are entirely correct in your assessment, or that the plurality of economists are reasonably accurately describing the ratio of economic value produced and wages.

    One final thought: I don’t know how to measure the productivity of a corn farmer and a composer on the same dimension in a rigorous manner. How does one compare the relative merit of food vs. art? If there is an answer to this question, I don’t know what it is. But the composer has one advantage over the farmer: creating an additional unit requires time, capital, and/or effort on the part of the farmer, but nothing from the composer – the only difference to the composer in selling one copy and one hundred million copies of an album is the size of the royalty cheque. Surely there is no more “productive” industry (at the margins) than selling intellectual property. But all intellectual property is a monopoly enforced by law, which is a human (and thus arbitrary) convention. We could, if we so chose, vastly reduce the duration of copyrights and patents, or eliminate these sources of income altogether.

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  8. I’d be happy to be shown wrong on this, but I feel that you are performing some sleight-of-hand here by glossing over the rather important *profits* figure on the left hand side of the equation.
    It is by no means a accounting truism that an increase in a firm’s income leads to an increase in the wages it pays. It could equally well go to an increase in profits. Indeed the neoclassical argument is that labor is getting its fair share of the income and capital is getting its fair share. i.e. the argument is about the distribution of the numbers on the left hand side.
    I don’t for a moment believe that the distribution of income between capital and labor is equitable today, but I don’t think the claim can be so easily dismissed as you do here.

    Liked by 1 person

    • I am surprised this escaped both the author and the commentators here. Your point isn’t only correct – it’s obviously correct.

      Consider the following example which exactly mimics the point in this post (and in the paper):
      1. All household income is either (1) spent on groceries (2) spent on other consumption or (3) saved. This part is an accounting truism.
      2. It’s therefore an accounting truism that as household has more income it spends more on groceries.

      But of course 2 isn’t an accounting truism, and in fact it’s likely often empirically wrong. For many households, as they grow richer, they spend less on groceries (in absolute terms, not just as a share of income) and eat more outside. If you don’t believe there are such households, at the very least you can easily imagine such households. So, a correlation between income and spending on groceries cannot be an accounting identity.

      Moreover – this is the whole freakin’ point! how hard is it to imagine – seriously, how hard is it – that a firm will increase its sales but will not increase wages? I mean, people are arguing that this is the case in many firms, many countries, and in at least some years. But set aside for a second whether or not such firms exist. Of course you can imagine such firms, and the claim of it’s an accounting truism that if sales are higher then wages are higher is obviously flat out wrong.

      There’s another point here. We all do so intuitively, and it’s also the right way to go – the more astonishing is a claim, the more we do, and should, examine it very closely. The claim in this post, if true, is truly astonishing: that for a hundred years or so, a whole profession is being either a fool or a crook. Thousands of people either miss an obvious point or they realize it but are lacking intellectual integrity. I ain’t saying it’s impossible, but it’s astonishing, and so a claim that this is the case should be heavily scrutinized. That you all missed such an obvious error in the argument, is a bi troubling.

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      • assfzim and The Sixth Replicant,

        Imagine the following accounting identity.

        x + y = z

        Now, suppose we test for a correlation between x and z.

        We have two options.

        Option 1. If the variation in y is far larger than the variation in x, then there won’t be a correlation between x and z. In our example, that would mean that we don’t find a correlation between wages and sales. So we falsify the neoclassical idea that “productivity” (as measured by sales) explains wages.

        Option 2. Variation in x dwarfs variation in y. We therefore find a correlation between x and z. This would mean we find a correlation between wages and sales. But this is a case of auto-correlation, since z is composed of x. Neoclassical theory seems “confirmed”. But it’s confirmed by auto-correlation, nothing more.

        So either the accounting identity doesn’t help you, because the empirical evidence already falsifies marginal productivity theory. Or, the empirical evidence appears to support marginal productivity theory. But this evidence is just an auto-correlation.

        Unless you measure productivity independently of income (which economists seldom, if ever do), then you are stuck with this problem. Neoclassical theory is either wrong or circular. Either way it’s garbage.

        Like

      • This is a completely different argument from what you stated in the post, or the article. I am glad you now agree that what you state in the post is incorrect, and that there is no “accounting truism” in a correlation between wages and sales (or added value), and that it is incorrect that there “has to” be a correlation between them because of how they are defined. Everything else you say later in your reply here is secondary to that point. and it’s encouraging that you are willing to own your error – there is no accounting truism that means there “has to” be a correlation between wages and sales.

        You then go on to how you would interpret two extreme possible empirical findings. Why only these extremes? Why not the realistic case of similar variation in X and Y?

        Anyway, you are wrong even on these extremes. let’s go over your cases:

        1. If variation in profits is much larger than variation in wages then you do not get a strong correlation between wages and revenue. Right. And in this case the theory should be rejected (subject to some nuances, differences between marginal and average, etc.). But “variation in profits” isn’t something that just happens. It exactly means that as revenue changes, profits changes, but wages do not. This (again, subject to some nuance) is correctly interpreted as evidence against the theory.

        2. If variation in wages is much larger than variation in profits you do get a strong correlation between wages and revenue, and it should be correctly interpreted to support the theory. Your starting point – variation in wages is larger than variation in profits, isn’t some innocuous mathematical option. It’s the whole point! It means that as revenue varies, it is wages that change with it, not profits. If the world was such, for example, that wages are more or less fixed, regardless of revenue, then variation in wages would not be larger than variation in profits. If it is indeed larger – it means something. This is the whole point.

        Generally, if x is part of z, it means nothing to the correlation between x and z. Like in the example I gave – spending on groceries is part of total household income, by definition. Yet, the correlation between spending on groceries and income can be positive, negative, or zero. And each case is instructive about the nature of the economic forces that shape the relationship between spending in groceries and income.
        Same for wages – the fact that they come out of the firm revenue, per se, means nothing about the correlation between wages in revenues. If variation in wags is smaller or larger than variation in profits is meaningful and useful information to understand the economic forces that shape them.

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      • One more point (sorry for multiple comments):

        There is an obvious symmetry between “wages” and “profits” in your explanation. X and Y are completely symmetric. It therefore fails some very basic logic to argue that if X is strongly correlated with Z then it’s “auto-correlation” and meaningless, but that if Y is strongly correlated with Z it is meaningful, and is evidence against the theory. This, again, is quite obvious. Of course X and Y are perfectly symmetric, and of course it’s impossible to say something about Y but something different about X!

        And again, I am amazed that based on such obviously flawed argumentation so many people are happy to believe that a whole field of study is intellectually corrupt…

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    • Hi Blair,
      Can you please post the correspondence around this objection?
      I heard the same objection from an economist whom I’ve asked to comment on this post and he did, but I can’t see the exchange.
      You may recall the heuristics I’ve mentioned once (under a different post) for determining which expert to trust. A major one is how an expert responds to counterclaims from other experts.
      I think it would be extremely valuable (especially for laypersons) to see mainstream objections to your argument openly discussed.
      Best,
      Yigal

      Like

      • Hi Yigal,

        I approved the comments. I’m not sure why they don’t appear here. Appears to be a WordPress glitch. I’m looking into. Also, I don’t consider the exchange over, as I I only briefly responded. But will try to fix this.

        Blair

        Like

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