Home > Uncategorized > No, productivity does not explain income

No, productivity does not explain income

from Blair Fix

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’.

  1. John deChadenedes
    October 14, 2019 at 6:17 pm

    Well said, Mr. Fix. It seems to me the whole thing comes down to a false premise sneaked in and then treated as true, a typical economist move. Bates said, “this law, if it worked without friction…” But of course the so-called law does not work without friction. All of the money generated from sales slips effortlessly into the accounts of the business owners. The portion that is pried out to pay the workers takes great and ongoing efforts, since the owners control the friction at that point. They have many ways to increase the friction: union-busting, threatening to move production to other countries, actually moving production to other countries, and so on. For a hilariously illogical exposition of this method, using an “as if” proposition as a fact, see Friedman’s marvelous “Methodology in Positive Economics”. He goes so far as to pretend that this is what real scientists do, treat something as if it were true and then base their arguments on it. Ha!

  2. October 15, 2019 at 3:51 pm

    From my blog, 5y ago:
    https://ppapageorgiou.wordpress.com/2014/06/01/marginal-contribution/

    “The moral for economists is that marginal contribution is nonsense. A meritocratic market can rank contributions with plausible veracity but says nothing about the magnitude of contributions. Earnings are an emergent result of technology, ownership, legal structures, trust, marketing, and other factors. These factors determine the shape of the earnings curve – how much winners win and losers lose. A meritocracy, at best, defines who the winners are.”

    • Rob
      October 16, 2019 at 8:49 am

      An enduring civilization cannot be built upon the practice of defrauding the laborer of his hire.

  3. Herbert
    October 15, 2019 at 5:25 pm

    Any sane person understands that neo-economists are no closer to understanding the economy than cavemen. It is worthwhile to deal with macroeconomic profit and income, then productivity will make sense. Without a doubt, there is no direct connection between income and productivity, because the question itself is incorrect; Whose income are we discussing? Ask yourself a simple question; Does increasing productivity increase revenue as a whole before we start sharing it by cost?
    And by the way, there is a universal profit calculation formula applicable in both macro and microeconomics.

    • Robert Locke
      October 16, 2019 at 5:03 pm

      Do you mean that I have to go through the methdologies of neocllassical economics, all the education, and I’ll end up with the understanding of a caveman. How could I recommend any young person study such a subject.

      • Rob
        October 17, 2019 at 10:32 am

        Do you mean that I have to go through the methdologies of neocllassical economics, all the education, and I’ll end up with the understanding of a caveman. How could I recommend any young person study such a subject. ~ Robert Locke

        .
        I would never recommend my children become economists, but I have made sure they know they must understand the history and danger of economics for their future well being.
        .

        Last year, Ursula K. Le Guin gave an impassioned speech in accepting the National Book Foundation’s Medal for Distinguished Contribution to American Letters. She declared that her “beautiful reward” was accepted on behalf of, and shared with:

        . . . Writers of the imagination who, for the last fifty years, watched the beautiful rewards go to the so-called realists.

        I think hard times are coming, when we will be wanting the voices of writers who can see alternatives to how we live now. Who can see through our fear-stricken society and its obsessive technologies to other ways of being, and even imagine some real grounds for hope. We will need writers who can remember freedom—poets, visionaries; the realists of a larger reality. Right now, I think we need writers who know the difference between production of a market commodity and the practice of an art. . . .

        We live in capitalism; its power seems inescapable. So did the divine right of kings. Any human power can be resisted and changed by human beings. Resistance and change often begin in art, and very often in our art: the art of words. . . . The name of our beautiful reward is not profit. Its name is freedom. (Fleming, David. Surviving the Future (Kindle Locations 188-199). Chelsea Green Publishing. Kindle Edition.

        .
        I hope I am wrong, but I wonder others see the coming interregnum? The coming collapse of civilization and the inevitable dark ages that shall follow. Capitalism has become a greater threat to humanity than totalitarianism. Consider the fact that China, a totalitarian state, is using capitalism as its economic engine with the aid of global corporatism’s transnational loyalty to shareholder profit even at the expense of democracy and freedom.
        .
        No doubt many are aware of what is happening in the U.S. and the fact that because of cultural degeneration and the rise of market fundamentalism wedded with religious fanaticism (evangelicals were a large part of Trump’s debased base) largely brought about by mainstream economics, the 200 plus year experiment in democracy has turned into an elective despotism with a wicked demagogue as its leader.
        .
        This can destabilize the world if not swiftly rectified, for otherwise it will potentially lead to global conflict, even WW III. Ignorant and blind nationalism has been tried before, and when only a few superpowers are following the same pattern, it doesn’t take a genius to see the possible outcome.

      • Craig
        October 17, 2019 at 4:58 pm

        Capitalism is not the correct target. Not because it doesn’t have multiple stupidities and ethical shortcomings, it does, but because it is used by finance to invoke the false dualism of capitalism vs socialism and so endlessly distract everyone from the REAL problem, namely finance’s monopolistic paradigm of Debt Only as the sole form and vehicle for the distribution of credit and/or money.

        We need to focus on the real, the deepest, the broadest problem….the monetary and financial paradigm which will transform the economy by resolving the long standing problems of monetary scarcity and chronic price and asset inflation, increase our survivability by immediately enabling us to begin a bottom up consumer move toward ecological sanity and equally enable the fiscal projects necessary for our ecological survival.

      • October 19, 2019 at 1:20 pm

        Thanks for the replica! I want to say that studying economics in the form in which it exists now is meaningless, just like studying religion to search for answers about the development of society. Everything that the modern economy teaches does not correspond, even in the first order, to the real state of things. Economic development, which is an emission process, is limited only by the level of productivity. But when the question arises of removing this limitation by increasing productivity and opening the economy to increased profit, it turns out that profit is not dependent on productivity. And economic growth itself (as an emission process) is declared an enemy of economic sustainability. Economists, like idiotic runners, tend to break their legs in order to run faster. In this sense, the caveman had more idea of ​​the economy than the modern economist.

  4. Ken Zimmerman
    October 20, 2019 at 12:34 pm

    Fundamentally, in real capitalism rights of ownership to newly created value are based on ownership of the tools used in the production of value, not the labor used to create value. Labor is not seen as the source of property rights, capital ownership is. The result is the private concentration of capital and the widespread adoption of wage-labor, resulting in the widespread use of labor markets to determine labor compensation. Labor markets do not, in any way, guarantee that worker compensation is comparable to the value that workers produce.

    Capitalist economic theory dictates that wages are determined by labor markets, so how much each employee gets paid is not determined by their contribution, but rather by the market value of their labor.

    The purpose of hiring an employee is for that employee to generate value for the employer. Every employer is making a profit from the work of their employees, in theory. For an employer to run a profit then their employees as a whole have to be creating more value than that for which they are compensated.

    Though the manufacturer has his wages advanced to him by his master, he, in reality, costs him no expense, the value of those wages being generally restored, together with a profit, in the improved value of the subject upon which his labor is bestowed.
    – Adam Smith; The Wealth of Nations

    The question for wage-laborers is: “How much is my employer making off me?” That is a legitimate question, and one that every worker should be able to answer. It is only when every worker can answer that question, and be comfortable with the answer, that economic justice can be discussed as a part of the capitalist system.

    Thus, it isn’t labor markets, worker productivity or merit, or even worker loyalty that determines worker wages in most situations. It is rather the relative political, economic, and often police power differentials between capital owners and workers. So long as this differential is kept small, workers have the strength to demand and receive a living wage, no matter the situation in either the labor “markets” or the political makeup of the nation or region in which the workers are employed.

    • yok
      December 21, 2019 at 5:57 pm

      Ken, your thinking is the most clear.

  5. ghholtham
    November 3, 2019 at 6:14 pm

    I don’t want to defend marginal productivity theory as an explanation of incomes. There are lots of reasons why it is no good: factor specificity, joint products, monopoly, circular definitions of capital, aggregation errors..I coud go on. But there’s a baby in this discussion that seems to be going out with the bathwater. If we define production as the sum total of goods and services produced commercially, i.e for sale, and we arrive at a total production figure by aggregating using market prices, conceptually that total production must equal total incomes, including wages, profits and monopoly rents. Total commercial income in the system (which I am not confusing with total welfare or happiness) is therefore dependent on total production. As defined in national accounts they are the same thing. Conventional economics is lousy at explaining income distribution. Yet it is not wrong to say that aggregate income depends on aggregate productivity. Politicians have been keen to emphasise productivity of labour because if it grows, total production can grow and everyone can get better off so distracting attention from issues of income distribution. Those become much starker in the absence of productivity growth. In the past, economics has tended to ignore the input of raw materials into production and the the output of pollutants but as evidence of the seriousness of this omission accumulates it must be addressed.

    • November 4, 2019 at 10:42 am

      “Conventional economics is lousy at explaining income distribution. Yet it is not wrong to say that aggregate income depends on aggregate productivity.”

      Only if you discount the ability of one sector of the economy to produce money from thin air. See what I just wrote about complex numbers in the thread on Econometrics. Discussing the distribution of income in terms of national GDP’s, one of the most telling comment by Geoff Davies in his new book (advertised to right. p.286) is to the effect that in compiling the GDP’s, the mathematics of economists is so poor that they cannot even tell the difference between positive and negative numbers.

      “[However], it is clear that even at the level of elementary accounting, mainstream economics is quite deficient. Even to refer to ‘elementary accounting’ is to understate the problem. Adding things that should be subtracted does not begin to qualify as accounting”.

      • Ken Zimmerman
        November 4, 2019 at 12:53 pm

        Dave, energy companies do this sort of mathematics routinely. As do many sovereign funds and, of course organized crime.

  6. Gerald Holtham
    November 5, 2019 at 3:23 pm

    I do discount the ability to produce money from thin air because it is irrelevant to the point at issue. “If we define production as the sum total of goods and services produced commercially, i.e for sale,” was the key qualification. Does production of nerve gas aid human welfare? Arguably not. But no-one does it for nothing. They get paid so it is in GDP – just like the police force, armed forces and other activities that are supposed to mitigate harms rather than directly promote welfare. National accounts statisticians did not invent capitalism; they just try to record it, There are other measures produced by “mainstream economists”, eg so-called ISEWs, which attempt to subtract such activities, subtract depletion of non-renewable resources and adjust for unequal income distribution. They are a better measure of welfare and have been around for 30 years but have never caught on with politicians or the public.

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