# income inequality

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## Reparations? How Can You Justify That?

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The movement against modern policing has renewed the call for reparations to descendants of slaves.

## What Trait Affects Income the Most?

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If the history of science has taught us anything, it’s that we can’t trust our preconceptions about how the world works. All human societies have developed stories about their place in the cosmos. Almost without exception, these stories were wrong.

True, we’ve killed many of the old myths. But the process was slow and excruciating. Humans have existed for hundreds of thousands of years. Yet it’s only in the last 0.1% of our existence that we’ve discovered the truth (we think) about our place in the cosmos.

This revolution in our knowledge comes down to one thing: evidence. As we looked closely at the cosmos, our origin stories became increasingly tenuous. They simply could not explain the evidence. And so, with great effort, we abandoned these stories (many of us, anyway).

Why is it so difficult to abandon old myths? One reason is that these myths are used to rationalize social order. Take, as an example, the Earth’s orbit. It took the Catholic church nearly 400 years to admit that the Earth revolves around the sun. Why so long? Because the church’s power was at stake. The church tied its dogma — and hence its authority — to a geocentric view of the universe.

Faced with a challenge to its authority, the church acted predictably. After convicting the heliocentric proponent Galileo of heresy in 1633, the church banned heliocentric teachings for another two centuries (until 1822). It took another 170 years for the church to formally admit (in 1992) that Galileo was right. Think about that. Almost four centuries of denial for an idea that had no effect on daily life. All because it threatened the authority of those with power. The lesson here is simple. When ideas challenge authority, evidence will be ignored, denied and suppressed.

That brings me to economics.

The discipline of economics is the modern equivalent of the church. To legitimize authority, neoclassical economists preach dogmas that are manifestly false. But unlike the ethereal debate about the Earth’s place in the cosmos, economic dogmas have a huge impact on day-to-day life. They make the difference between tolerating inequality versus being enraged by it.

Neoclassical economics preaches that all is fair with the distribution of income. Income differences, the theory claims, stem from differences in productivity. As long as markets are competitive, people earn their ‘marginal product’. And so there’s no reason to redistribute income.

The reality is quite different. Income, I believe, is determined not by productivity, but instead largely by rank within a hierarchy. In other words, power begets income. The role of economics is to deny this uncomfortable reality. Economists reinforce hierarchies by denying their existence.

As Galileo showed, the way to combat dogma is to confront it with evidence. With that in mind, I’m going to show you evidence that challenges the neoclassical faith. Looking at the United States, I find that the single most important determinant of income is something that neoclassical economists refuse to study. It’s not education. It’s not occupation. It’s hierarchical rank.

### Measuring effect size

Here’s the road ahead. I’m going to make a list of different human traits. Then I’m going to measure how strongly each trait affects income. But before we get to the evidence, we need to talk statistics. What does it mean for a trait to have a ‘large’ effect on income? Conversely, what does it mean for a trait to have a ‘small’ effect on income? How do we measure this effect size?

Here’s what statisticians have proposed. To measure effect (on income, or anything else) we compare variation between groups to variation within groups. If a trait has a large effect on income, the income differences between trait groups should dwarf the differences within groups. Conversely, if a trait has a small effect on income, the income differences within trait groups should dwarf the differences between groups.

To get an intuitive understanding for this measure of effect size, we’ll begin with something more immediate than income. Let’s step on the scale and see what affects human weight. We’ll use Americans as our guinea pigs.

#### A small effect

Americans tend to grow heavier with age — likely due to the obesity epidemic. But while this epidemic is devastating to human health, weight gain with age is actually quite small. Figure 1 shows the data. Here I plot the mass distribution of two groups of Americans: those ages 18–24, and those ages 65 or older. You can see that seniors are slightly heavier than young adults. But the effect is small. (You may be complaining that I’m not tracking the same cohort over time, so I can’t judge trends. Fair point. But my purpose here isn’t to rigorously study weight gain. It’s to visualize effect size.)

Figure 1: Adult age has a weak effect on weight. Here’s the mass distribution of two adult age cohorts of Americans in 2018. Data is from the Behavioral Risk Factor Surveillance System.

How do we quantify the size of this age-weight effect? To measure effect size, we compare weight differences between groups to weight differences within groups.

Let’s start with differences between groups. In Figure 1, the vertical lines show the average weight of each cohort. American seniors weigh on average 79 kg. Americans age 18–24 are slightly lighter, weighing on average at 76 kg. So seniors are about 3 kg heavier (on average) than their younger counterparts.

Now we ask — is this 3 kg difference large or small? The answer depends on variation within each cohort. Before getting to the math, think about it this way. If I was comparing the mass of two types of ant, a 3 kg difference would be huge. But if I was comparing the mass of two types of elephant, a 3 kg difference would be tiny. The difference between groups gains meaning only when compared to variation within the group.

To measure variation within groups, we’ll use the standard deviation. This measure quantifies the relative spread of the distribution. The larger the standard deviation, the greater is the variation within the group. Looking at our age cohorts, we find that the standard deviation within each group is about 19 kg. Compared to this variation within groups, our 3 kg difference between groups is small. You knew this intuitively when you looked at Figure 1 and saw that the two distributions almost completely overlapped. But now we have a metric to quantify your intuition.

#### A medium-sized effect

Let’s move on to a medium-sized effect. Men are, on average, heavier than women. This effect turns out to be larger than the age-weight effect. Figure 2 shows the data. American men weigh on average 90 kg. Women weigh on average 75 kg. So men are about 15 kg heavier (on average) than women.

Figure 2: Sex has a medium-sized effect on weight. Here’s the mass distribution of adult male and female Americans in 2018. Data is from the Behavioral Risk Factor Surveillance System.

How large is this 15 kg difference between sexes? To judge its size, we compare it to the weight variation within each sex (measured using the standard deviation). This within-group variation is about 19 kg. So our 15 kg difference between sexes amounts to almost one standard deviation. In other words, sex has a medium-sized effect on weight.

#### A large effect

Now let’s move on to a large effect. We’ll compare the weight of adults to the weight of newborns. Figure 3 shows the data. The average American adult weighs 82 kg. The average newborn weighs 3 kg — a difference of 79 kg.

Figure 3: Growing up has a large effect on weight. Here’s data for the mass distribution of American adults and newborns in 2018. Adult data is from the Behavioral Risk Factor Surveillance System. Newborn data is from the National Center for Health Statistics. Note that I’ve rescaled the newborn density plot. If plotted true to scale, the newborn density curve would be 30 times taller.

It’s obvious, from Figure 3, that we’re dealing here with a large effect. But let’s quantify it. To do so, we compare the 79 kg difference between newborns and adults to the variation within each group. This variation, measured by the standard deviation, is about 11 kg. So the variation between groups is about 7 times greater than the variation within groups. That’s a large effect.

### Comparing the signal to the noise

When we compare variation between groups to the variation within groups, we’re comparing a signal (the effect) to the noise (the non-effect). The ratio of the two is called the signal-to-noise ratio. It’s how we’ll measure effect size.

$\displaystyle \text{signal-to-noise ratio} = \frac{ \text{variation between groups} }{ \text{ variation within groups } }$

Table 1 shows the signal-to-noise ratio for how our three traits affect weight. Adult age has a weak effect on weight. Sex has a medium-sized effect. And growing from newborn to adulthood has a large effect. [1]

Table 1: Measuring how traits affect weight

Trait
Difference in average mass (kg)
Average mass variation within groups (kg)
Signal-to-noise ratio

2.7
19.3
0.14

male vs. female
15.5
19.4
0.80

78.7
10.7
7.33

The signal-to-noise ratio in Table 1 is called Cohen’s d. It’s useful when we want to measure an effect between 2 groups. But what if we have many groups? Then we can’t take as the signal the difference between groups (it’s ill-defined for three or more groups). We need another approach.

The solution is to switch from measuring the difference between groups to measuring the variation between groups. If we use the standard deviation to measure this variation, the resulting signal-to-noise ratio is called Cohen’s f. The numerator changes (from Cohen’s d), but the interpretation remains the same. A larger signal-to-noise ratio indicates a larger effect.

When studying effect on income, however, it’s more convenient to use a slightly different signal-to-noise ratio. Income variation is usually reported using the Gini index (not the standard deviation). So it’s more convenient to construct our signal-to-noise ratio using the Gini index.

Here’s how I’ll measure effect on income. I’ll compare the Gini index between groups to the Gini index within groups:

$\displaystyle \text{signal-to-noise ratio} = \frac{ \text{Gini index between groups} }{ \text{ average Gini index within groups } }$

As before, a larger signal-to-noise ratio indicates a greater effect on income. (For more details about the metric, see this paper.)

### How traits affect US income

Now that you’ve had a crash course in the statistics of effect size, let’s get to the data. Figure 4 shows how various traits affect the income of Americans. The list of traits isn’t exhaustive. It’s merely the traits for which I could find data. (If you think of a trait that I missed, leave a comment.)

Let’s walk through how to interpret Figure 4. The y-axis shows the various traits. I’ve used color to classify these traits into three types: geographic, physical, and social. The x-axis shows each trait’s effect on income, measured with the signal-to-noise ratio. The boxplots indicate the variation (mostly over the last two decades) in the signal-to-noise ratio. (Here’s how to interpret a boxplot. The vertical line indicates the median of the signal-to-noise ratio. The ‘box’ shows the middle 50% of the data. And the horizontal line shows the data range. A single vertical line indicates that there’s only one data point.)

Figure 4: How various traits affect individual income in the US. I plot here the signal-to-noise ratio for how various traits affect income. The ‘signal’ is the Gini index between trait groups. The ‘noise’ is the Gini index within trait groups. The data (mostly) covers the last two decades. For sources and methods, see Personal Income and Hierarchical Power.

#### Physical traits

Now that you understand the chart, let’s walk through the results. We’ll start with physical traits — properties of the individual’s body and brain. These traits have a surprisingly weak effect on income. Take cognitive score (i.e. measured IQ). Americans love to believe that intelligence is rewarded, meaning they live in a meritocracy. Unfortunately, the evidence squashes this myth. Cognitive score, it seems, has a trivial effect on income. [2]

Interestingly, race (as categorized by the US government) also has a weak effect on income. This doesn’t mean that racism isn’t a problem. It’s just that the income difference between races is relatively small compared to the income variation within each race. (Side note: the categorization of race is obviously subjective. The way the US census has classified race has changed over time, reflecting changing politics.)

Moving up the ladder, sex has a stronger effect on income. Women tend to earn less than men. Why? There are probably three reasons. First, women are more likely to work part time. Second, women tend to work at lower-paying jobs. Third, women are generally paid less than men even when they do the same job.

Moving to the top of the ladder, the physical trait with the strongest effect on income is age. That’s easy to understand. Baby boomers, you’ve probably noticed, tend to out-earn millennials. If you believe human capital theory, this happens because people become more skilled (and hence, more productive) with age. But I’m skeptical of this idea. I think that people earn more with age largely because they get promoted in the corporate hierarchy. (We’ll come back to hierarchy in a moment.)

#### Geographic traits

Let’s move on to geographic traits (i.e. the place where you live). It turns out that geography affects income quite weakly. This finding is somewhat surprising, given the segregated nature of US society. There’s no doubt that the US has rich areas and poor areas. But no matter how you slice up space, the income effect of geography is comparatively small. (Sidenote: it would be interesting to see if this geographic effect was greater when segregation was an official policy, rather than an unspoken norm.)

Looking at the data, it seems that dividing the US into counties has the weakest effect on income. The divide between urban dwellers and rural dwellers is slightly larger. (People in cities tend to outearn their rural counterparts.) As we shrink the geographic area, the effect on income grows. The effect of grouping people by census tract slightly trumps the income effect of age. Shrinking the geographic area to census block groups (the size of a few city blocks) increases the income effect a bit more.

What this result tells us is that US spacial inequality is fine grain. Over large spaces (like counties), income differences are small. But as we shrink down to the city block, income differences grow. If you’ve ever walked through a city like New York, this result makes sense. The transition between a wealthy neighborhood and poor neighborhood can happen in a few hundred feet. While highly visible, this geographic effect on income is dwarfed by the effect of many social traits. So despite the segregation of US society, geography has a fairly weak effect on income.

Figure 4 (again): How various traits affect individual income in the US. Here’s Figure 4 again, so you don’t have to scroll while reading.

#### Social traits

If humans were solitary animals, we’d expect that physical and/or geographic traits would affect income the most. (The lone wolf that’s bigger or has better territory gets more resources.) But humans are not solitary animals. We’re a social species. As such, we expect that social traits should most strongly affect income.

The US evidence confirms this expectation. The 6 traits with the largest effect on income are all social. And social traits are the only ones to cross the one-to-one threshold in our signal-to-noise indicator. In other words, they’re the only traits that have a ‘large’ effect on income.

Let’s discuss these 6 traits with the largest effect on income. We’ll start with occupation. It’s a fact of life that some jobs pay more than others. Doctors earn more than janitors. Lawyers earn more than nurses. Why this happens is matter of debate. If you’re a neoclassical economist, you’d say that lawyers have more human capital than nurses. (Interestingly, few economists have the guts to state this bluntly in the current pandemic.)

If you don’t believe the neoclassical fantasy, you’d probably say that there’s many factors at work. Better-paying jobs are often protected by guilds that maintain a barrier to entry. Poor-paying jobs are open access. Good-paying jobs are often unionized. Minimum-wage jobs are not. Some jobs are prestigious, others are not. And perhaps most importantly, some jobs (like CEO) are at the top of the corporate hierarchy. Others are at the bottom. I could go on, but you get the point. There’s probably many reasons that income varies by occupation.

Let’s move up the effect-size ladder to education. It’s worth pausing here to discuss the role of education in the neoclassical theory of income. According to human capital theory, training (of any kind) makes you more productive, and hence earn more income. The most obvious type of training is formal education. In 1958, neoclassical economist Jacob Mincer proposed that years of formal education could explain individual income. Since then, Mincer’s approach has become neoclassical gospel.

The problem (which Mincer himself discovered) is that education can’t explain income. The correlation between income and education is actually quite small. Here’s Mincer writing in 1974:

Simple correlations between earnings and years of schooling are quite weak. Moreover, in multiple regressions when variables correlated with schooling are added, the regression coefficient of schooling is very small.

Now, on its own, this low correlation between income and education isn’t fatal to human capital theory [3]. The fact is that most traits weakly affect income. This is evident in Figure 4. The income effect of most traits is well below the one-to-one level (meaning within-group variation trumps between-group variation). So yes, income is weakly correlated with education. But as long as education has the strongest effect on income, there’s no fatal blow to human capital theory.

The problem is that education doesn’t have the strongest effect on income — not even close. The income effect of education is dwarfed by the effect of hierarchical rank (discussed in detail below). So it seems that human capital theorists have hitched their train to the wrong trait.

Let’s move further up the effect-size ladder. Firm membership, I find, is the first trait to pass the one-to-one threshold in our signal-to-noise indicator. This means that income variation between firms is greater than income variation within firms. What this means is that, regardless of your position, you’ll tend to earn more at Goldman Sachs than at McDonald’s. The caveat here is that this estimate is based on a model. So treat it with appropriate uncertainty. (For details about the model, see this paper.)

Let’s move up the effect-size ladder again. Working full time versus working part time strongly affects income. This finding is easy to understand. Part-time employees work fewer hours than their full-time counterparts. And part-time wages also tend to be worse.

Moving up one more effect-size rung and we get to labor versus property income, which very strongly affects income size. You may think that this large effect happens because property owners (i.e. capitalists) tend to outearn workers. But it’s actually the reverse. The average property owner earns far less than the average worker.

What’s going on here? This result has to do with how property income is distributed. The vast majority of property owners earn almost nothing — a few dollars in interest from their savings account, and some meager dividends on their investments. For most people, this is hardly enough to survive on. That’s why they work. Sure, there are people like Bill Gates who earn all their income from property. But these people are exceedingly rare. Because most property owners earn almost nothing, labor income tends to dwarf property income.

If you’re a Marxist, this result should give you pause. Formulated in the 19th century, Marxist theory envisions a clean division between capitalists and workers. In reality, no such division exists. Most people earn a tiny bit of capitalist income. A few people earn a lot. So being a capitalist (or not) is a matter of degree. (As an aside, it turns out that this degree of being a capitalist is closely related to hierarchy. I discuss how here.)

Figure 4 (again): How various traits affect individual income in the US. Here’s Figure 4 again, so you don’t have to scroll while reading.

### The effect of hierarchy

We’ve finally arrived at the raison d’être of this post — the income effect of hierarchy. My hypothesis is that hierarchy is central to how humans distribute resources. The reasoning is simple. Our social relations govern how we divide the pie. And hierarchical relations are by far the most potent. The testable consequence of this hypothesis is that hierarchical rank should effect income more strongly than any other trait.

Before getting to the results, I’ll clarify what it means to group individuals by hierarchical rank. Figure 5 shows a conceptual example. Here we have different hierarchies, with distinct hierarchical ranks. To measure the income effect of hierarchical rank, we group people by rank across all hierarchies.

Figure 5: Grouping individuals by hierarchical rank.

In conceptual terms, it’s easy to measure how hierarchical rank affects income. But in practical terms, it’s quite difficult. The problem is that few people have gathered the relevant data. Although ubiquitous in human societies, hierarchy has not been well studied.

To estimate how hierarchical rank affects income, I cobble together three different sources. Each source comes with caveats, and none are ideal. The data labeled ‘Mueller et al.’ (in Figure 4) comes from a study of UK firms. The data labeled ‘Heyman’ comes from a study of Swedish firms, and carries the ‘*’ because it doesn’t include all hierarchical ranks within firms. The data labeled ‘US model’ is a model-based inference, based jointly on data from firm case studies and the pay of US CEOs. (For details about the model, see this paper.)

This data on hierarchy is admittedly ragtag. But that’s part of wading into uncharted empirical territory. What’s important here are two things. First, despite their ragtag nature, the three estimates for the income effect of hierarchy are consistent with one another. Second, these estimates dwarf the effects of all other traits.

So the evidence, which is admittedly uncertain, suggests that hierarchical rank has the strongest effect on income.

### And yet it moves

Upon being convicted of spreading heresy, Galileo is said to have remarked: “And yet it moves.” He was referring of course, to the Earth. Galileo had mustered the first evidence that the Earth revolves around the sun. The evidence, though, was indirect. Galileo had closely watched the motion of Venus, and found that it had phases — just like the moon. He concluded that this could happen only if Venus orbited the Sun. By extension, he inferred that the Earth also moved around the Sun.

The Church thought differently. Of the heliocentric model, the church inquisitors concluded:

… this proposition is foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture …

New evidence, unfortunately, is often greeted with this reaction — especially by people with a lot (of power) to lose. While my research pales in comparison to Galileo’s, it’s been greeted with similar resistance. ‘Formally heretical’ … ‘contradicts scripture’. This is essentially the reaction to Figure 4 that I’ve received from neoclassical economists.

Now, I’m the first to admit that the evidence is uncertain. Moreover, this evidence doesn’t establish causation. It doesn’t tell us that hierarchical rank causes income. Still, the evidence suggests that something is deeply wrong with the neoclassical understanding of income. It suggests that treating hierarchical rank as the strongest determinant of income is a hypothesis worth exploring.

Neoclassical economists will have none of this. The idea that hierarchical rank most strongly affects income, I’ve been told, is ‘foolish and absurd’. Why? Because it explicitly contradicts neoclassical scripture. Income, scripture says, must stem from productivity. So behind hierarchical rank, there must lurk some unmeasured skill. Silly me — I’m naive enough to take my results at face value, just as Galileo did when interpreting the phases of Venus.

The case for hierarchy’s effect on income is tentative, yes. But if we accept dogma, we’ll never know the truth. The task for hard-nosed scientists is to gather more evidence and see what happens. Either the case will grow stronger with more evidence, or it will disappear. Join me in this search.

### Notes

[1] Whether we call an effect ‘large’ or ‘small’ is arbitrary. It depends on the type of phenomena we’re studying. In psychology (where effect sizes are generally small), the common thresholds for Cohen’s d are: small effect = under 0.2, medium effect = between 0.2 and 0.8, large effect = over 0.8. When it comes to income, my preference is that we shouldn’t call an effect ‘large’ unless the variation between groups is larger than the variation within groups. This threshold corresponds to a signal-to-noise ratio larger than 1.

[2] Is cognitive score a ‘physical’ trait? I use the term ‘physical’ here not in a genetic determinist sense, but in the sense of ‘residing in the person’s body’. Every property of the brain, whether inborn or learned, is a ‘physical’ trait because it’s a property of the matter inside the person. (OK, this isn’t true if you believe in mind-body dualism.) There’s no doubt that practice can improve your performance on IQ tests, in the same way that exercise can improve your athletic performance. But both types of performance still reside in the body.

[3] There are many other blows to human capital theory that are fatal. Most importantly, the theory posits that productivity explains income. But economists never measure productivity independently of income. Instead, all of their evidence for productivity is, in fact, circularly tied to income. For details, see these posts: No, Productivity Does Not Explain Income, Productivity Does Not Explain Wages, Debunking the ‘Productivity-Pay Gap’, and Productivity and Income … Again.

Fix, B. (2019). Personal income and hierarchical power. Journal of Economic Issues, 53(4), 928–945. Preprint at SocArXiv

Wright, E. O. (1979). Class structure and income determination (Vol. 2). New York: Academic Press. (Wright was, as far as I know, the first person to explicitly study the income effect of hierarchical rank.)

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## Guest on the Debunking Economics Podcast

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Last week, Steve Keen and Phil Dobbie were kind enough to invite me on their Debunking Economics Podcast. We discussed my research on income inequality and hierarchy. You can listen to the episode here:

You can also listen at Steve’s patreon page.

Some back story. Reading Steve Keen’s book Debunking Economics was one of the reasons I got interested in economics. So it’s always exciting to talk to one of your intellectual heroes.

I was also lucky enough to have Steve serve as the external examiner for my PhD defense. Since then, he’s been a tireless advocate for my research. When you’re taking on the economics orthodoxy, it’s always nice to have someone on your side. What’s more, Steve was my very first patreon supporter. Thanks Steve!

#### Support this blog

Economics from the Top Down is where I share my ideas for how to create a better economics. If you liked this post, consider becoming a patron. You’ll help me continue my research, and continue to share it with readers like you.

Keep me up to date

## Even During the Pandemic Many Billionaires Are Snatching Windfalls

In early April this year, as 22 million Americans lost their jobs and the U.S. employment rate approached 15 percent, the combined wealth of America’s billionaires had increased from March 18 by $282 billion — nearly a 10 percent increase. Continue reading The post Even During the Pandemic Many Billionaires Are Snatching Windfalls appeared first on BillMoyers.com. ## John Lewis Marches On Published by Anonymous (not verified) on Tue, 03/03/2020 - 3:15am in ### Tags On August 6, 1965, Rep. John Lewis looked on as President Johnson signed the Voting Rights Act. In this video, he reflects on how the March on Washington led to key civil rights laws. Continue reading The post John Lewis Marches On appeared first on BillMoyers.com. ## Some Sunshine on the Ontario Job Hierarchy Published by Anonymous (not verified) on Tue, 04/02/2020 - 7:03am in ### Tags Income, I’ve come to believe, is shaped largely by rank within a hierarchy. If you’re at the top of a hierarchy, you’ll earn a handsome sum. But if you’re at the bottom of a hierarchy, you’ll earn a pittance. As a hard-nosed scientist, I’m always looking for ways to test this hypothesis. The problem is that it’s difficult to do. Although hierarchy surrounds us, we have almost no data about it. So if we want to study how income grows with hierarchical rank, we need to be creative. In this post I use an unlikely source to study hierarchy — the Ontario Sunshine List. Maintained by the Canadian province of Ontario, the Sunshine List reports the income of public-sector employees who earn more than$100,000. On the face of it, the Sunshine List has nothing to do with hierarchy. It’s a database of individual income. But with a little creativity, we can use it as a window into the world of hierarchy.

Our looking glass will be job frequency. Here’s how it works. Imagine we could take everyone in a society and line them up from lowest to highest income. Then, starting at the lowest earner, we ask each person their job title. As income grows, we track the changing frequency of different jobs.

To make things concrete, suppose we track two jobs — ‘nurse’ and ‘CEO’. How might the frequency of these jobs change with income?

Here’s what you probably expect. Nurses will be common among low earners. But they will be rare among top earners. CEOs, in contrast, will be rare among low earners. But they will be common among top earners.

Now here’s the question. Why do you expect this behavior?

You expect it, I believe, because you have an intuitive understanding of hierarchy. You know that nurses work mostly at the bottom of hierarchies where they get paid relatively little. And you know that CEOs work at the top of hierarchies where they get paid a lot. Because you know this, you expect that nurses will become less frequent as income grows, while CEOs will become more frequent.

In this post, I test this intuition. I first use a model of hierarchy to predict how the frequency of differently-ranked jobs should change with income. Then I compare the model’s prediction to real-world trends.

The results are exciting.

The trends on the Ontario Sunshine List closely match what the model predicts. Low-ranking jobs (like ‘nurse’) become less frequent as income grows. But top-ranking jobs (like ‘CEO’) become ubiquitous as income grows.

I’m thrilled by this result because it means that the income effects of hierarchy are hiding in plain sight. They’re waiting to be teased out from any database that reports both income and job descriptions.

### Using new theory to rethink old evidence

Good scientific theories often give new meaning to old evidence. Take Darwin’s theory of evolution. It gave new meaning to the fossil record. Before Darwin, fossils were just the bones of long-dead creatures. But after Darwin, fossils were a testament of life’s evolution.

On a less grand scale, I propose here that a banal public-sector database (the Ontario Sunshine List) is actually a record of how hierarchy shapes income. As with the reinterpretation of the fossil record, this reinterpretation of public-sector pay depends on new theory — a theory of how hierarchy affects income.

In a series of recent papers (here, here and here) I’ve argued that income is shaped largely by one’s hierarchical rank. As part of this theory, I’ve developed a model of hierarchy. The model uses evidence from a variety of sources (firm case studies, CEO pay) to simulate the hierarchical structure of the US private sector.

Figure 1 shows what the model looks like. Here each pyramid represents a firm. Moving up the pyramid represents moving up the hierarchy. Color indicates individual income.

Figure 1: The US hierarchy model as a landscape. Each pyramid represents a firm. Size indicates the number of employees. Moving up the pyramid represents moving up the hierarchy. Color indicates individual income.

The purpose of the model is to indirectly study how hierarchy affects income. It works like this. First, we use the model to predict an income effect that is caused by hierarchy. Then we look for this effect in the real world. If we find it, we infer that real-world income grows with hierarchical rank as it does in the model.

We can use the model to make many different types of predictions. In a recent paper, for instance, I predicted that top-earning individuals should work for large firms. Then I showed that in the real-world, top-earning individuals actually do work for large firms, just as predicted.

In this post, I study how job frequency changes with income. I first use the model to predict how the frequency of three classes of employees should vary by income. Then I look for the predicted trends in real-world data.

### Three classes of employee

Large hierarchies have many ranks. But because I’m going to use coarse-grain information (job titles) to infer hierarchical rank, here I’m interested in three broad classes:

1. Low-ranking employees
2. Mid-ranking employees
3. Top-ranking employees

As the names suggest, these classes relate to position in a hierarchy. Low-ranking employees are at the bottom of the hierarchy. Mid-ranking employees are in the middle. And top-ranking employees are at the top.

With these classes in mind, here’s the road map ahead. First, I’m going to use the hierarchy model to predict how the frequency of each class of employee should vary with income. Then I’ll show that this variance is due to hierarchy. Last, I’ll look for the predicted trends in real-world data (on the Ontario Sunshine List).

Predictions

### Low-ranking employees are less frequent as income grows

Low-ranking employees are the poor saps (like me) who work at the bottom of hierarchies. They’re the red individuals in Figure 2.

Figure 2: Low-ranking employees in a hierarchy

Before getting to quantitative predictions, let’s first think qualitatively. How might the frequency of low-ranking employees change with income? If income grows rapidly with rank, low-ranking employees should be mostly at the bottom of the distribution of income. So low-ranking employees should become less frequent as income grows.

Figure 3 shows our quantitative prediction. On the horizontal axis I’ve plotted income percentile. For each percentile, the vertical axis shows the relative frequency of low-ranking employees.

Figure 3: Frequency of low-ranking employees by income percentile. The horizontal axis shows income percentile in the model. The vertical axis shows the relative frequency of low-ranking employees within each percentile.

As expected, the model predicts that low-ranking employees become less frequent as income increases. Almost everyone in the bottom 1% is a low-ranking employee. But almost no one in the top 1% is a low-ranking employee.

Figure 4 shows a different way of looking at the same prediction. Instead of plotting income percentile, on the horizontal axis I plot income size (relative to the average income). Note that I’ve used a logarithmic scale, so each axis tick indicates a factor of 10.

Figure 4: Frequency of low-ranking employees by income size. The horizontal axis shows income in the model (relative to the mean). The vertical axis shows the relative frequency of low-ranking employees at the given income.

Again, we find that low-ranking employees become less frequent as income increases. Almost everyone who earns less than 10% of the average income is a low-ranking employee. Conversely, almost no one who earns more than 10 times the average income is a low-ranking employee.

### Mid-ranking employees are most frequent in the middle

Mid-ranking employees work in the middle of hierarchies. While the exact rank of these workers is open to interpretation, here I assume that they work in the second hierarchical rank.

Figure 5: Mid-ranking employees in a hierarchy

Although mid-ranking employees are only one step above low-ranking employees, our model predicts that they are dispersed quite differently in the distribution of income.

Figure 6 shows the prediction for mid-ranking employees. These workers are most frequent in the middle 80% of incomes. They’re rare below the 10th percentile and above the 90th percentile.

Figure 6: Frequency of mid-ranking employees by income percentile. The horizontal axis shows income percentile in the model. The vertical axis shows the relative frequency of mid-ranking employees within each percentile.

Figure 7 shows the same prediction, but this time plotting income on the horizontal axis. The model predicts that mid-ranking employees are most frequent around the average income. Again, this tells us that mid-ranking employees are the middle class.

Figure 7: Frequency of mid-ranking employees by income size. The horizontal axis shows income in the model (relative to the mean). The vertical axis shows the relative frequency of mid-ranking employees at the given income.

### Top-ranking employees are more frequent as income grows

Top-ranking employees work at the top of their respective hierarchies. Figure 8 shows a top-ranking employee in a small hierarchy.

Figure 8: A top-ranking employee in a hierarchy

Moving from the middle to the top of the hierarchy may seem like a small shift. Yet it drastically changes how individuals are dispersed in the distribution of income.

Our model predicts that top-ranking employees are located overwhelmingly at the top of the distribution of income. As Figure 9 shows, few people below the 99th percentile are top-ranking employees. But above the 99th percentile, almost everyone is a top-ranking employee.

Figure 9: Frequency of top-ranking employees by income percentile. The horizontal axis shows income percentile in the model. The vertical axis shows the relative frequency of top-ranking employees within each percentile.

Figure 10 (below) shows how this explosion of top-ranking employees relates to income size. Below the average income, almost no one is a top-ranking employee. This changes at about double the average income, where the frequency of top-ranking employees begins to grow.

Figure 10: Frequency of top-ranking employees by income size. The horizontal axis shows income in the model (relative to the mean). The vertical axis shows the relative frequency of top-ranking employees at the given income.

At 100 times the average income, half the people are top-ranking employees. At 1000 time the average income, virtually everyone is a top-ranking employee.

In hindsight, this prediction is easy to understand. We’ve assumed that income grows rapidly with hierarchical rank. Flipping things around, this means that if you have a large income, you likely have a high rank. And the higher your rank, the more likely it is that you sit at the top of your hierarchy. [1] The result is that top-ranking employees become more frequent as income grows.

### Yes, these predictions stem from hierarchy

Before we test our predictions against real-world evidence, we want to be sure that these predictions actually stem from hierarchy. The way we’ll do this is by simulating a counterfactual world. In this world there are no returns to hierarchical rank. So CEOs earn no more than bottom-ranked employees.

As Figure 11 shows, the results of this counterfactual model are strikingly different than the original model.

Figure 11: A counterfactual world with no returns to hierarchical rank. This figure shows the results of two models. One model has income returns to hierarchy, the other does not.

In a world with no returns to hierarchical rank, our model predicts that job frequency shouldn’t vary by income. Our three classes of employees are equally frequent for all incomes. This stands in marked contrast to our original model. It’s only when there are returns to hierarchical rank that our predictions hold. Only then do top-ranking jobs explode among top incomes.

To test our predictions, I’m going to use the Ontario Sunshine List. Created in 1996, the Sunshine List discloses the salaries of all public-sector employees in Ontario who earn more than $100,000. The Sunshine List is unique for two reasons. First, it’s a complete list of top-earning workers in the Ontario public sector. Second, the database isn’t ‘top coded’. Top coding is the practice of capping the size of incomes that you report. In many databases, for instance, incomes are top coded at$100,000. So anyone who earns more than this amount gets reported as earning ‘more than $100,000’. Top coding is used to shield the identity of survey respondents. But because the Ontario Sunshine List was created to reveal the identity of top earners, it reports top incomes in full. This is important because we’ve predicted that the most spectacular effects of hierarchy occur among top earners. To test our predictions, I pick three jobs that appear on the Sunshine List and equate them with the three classes of workers used in the model. Here are my choices: Class in Model Sunshine List Job Low-Ranking Employee ‘Nurse’ Mid-Ranking Employee ‘Professor’ Top-Ranking Employee ‘President/CEO’ ### ‘Nurses’ on the Ontario Sunshine List I use ‘nurses’ to represent low-ranking employees. The caveat here is that nurses in Canada are paid fairly well — far better than other low-ranking jobs like ‘janitor’. I choose ‘nurse’ because it’s a low-ranking job that pays well enough to appear on the Sunshine List. Figure 12 shows the results. I find that the frequency of nurses declines as income increases — just as the model predicts. Figure 12: Frequency of ‘Nurse’ on the Ontario Sunshine List by income percentile. The horizontal axis shows income percentile on the Sunshine List. The vertical axis shows the relative frequency of ‘nurses’ within each percentile. The inset plot shows the model predictions. A caveat is that the empirical data in Figure 12 isn’t directly comparable to the model. In the model, income percentiles rank all individuals. But in the empirical data, income percentiles rank only the members of the Sunshine List (public-sector employees earning more than$100K).

Figure 13 (below) shows the same data, but plots job frequency against income size. The frequency of nurses declines rapidly as income grows. Most Ontario nurses (on the Sunshine List) earn close to the average Canadian income. Almost none earn more than twice the average income. Our model predicts a similar trend — the frequency of low-ranking employees should decline rapidly as income grows.

Figure 13: Frequency of ‘Nurse’ on the Ontario Sunshine List by income size. The horizontal axis shows income relative to the Canadian average. The vertical axis shows the relative frequency of ‘nurses’ on the Ontario Sunshine List. The inset plot shows model predictions. [2]

### ‘Professors’ on the Ontario Sunshine List

I use ‘professors’ to represent mid-ranking employees. In Canadian universities, professors often command a few subordinates (in the form of teaching assistants and post docs). Professors also have some administrative power through faculty senates.

Figure 14 shows how the frequency of ‘professors’ changes with income on the Sunshine List. Unlike nurses, the frequency of professors is roughly constant with income percentile. This is similar to the predicted behavior of mid-ranking employees (inset).

Figure 14: Frequency of ‘Professor’ on the Ontario Sunshine List by income percentile. The horizontal axis shows income percentile on the Sunshine List. The vertical axis shows the relative frequency of ‘professors’ within each percentile. The inset plot shows model predictions.

Figure 15 (below) shows the same data, but plots job frequency against the size of income. Most Ontario professors (on the Sunshine List) earn between 1 and 5 times the Canadian average. In this case, the model isn’t particularly accurate. It predicts the tapering of mid-ranking employees for large incomes, but it doesn’t predict the tapering (evident among professors) for incomes close to the average.

Figure 15: Frequency of ‘Professor’ on the Ontario Sunshine List by income size. The horizontal axis shows income relative to the Canadian average. The vertical axis shows the relative frequency of ‘professors’ on the Ontario Sunshine List. The inset plot shows model predictions. [2]

### ‘Presidents/CEOs’ on the Ontario Sunshine List

I use ‘presidents/CEOs’ to represent top-ranking employees. Figure 16 shows the trends on the Ontario Sunshine List. Among the bottom 99%, almost no one is a CEO. But among the top 1% (of Sunshine earners), CEOs are ubiquitous. This explosion of top-ranked employees is exactly what our model predicts (inset).

Figure 16: Frequency of ‘President/CEO’ on the Ontario Sunshine List by income percentile. The horizontal axis shows income percentile on the Sunshine List. The vertical axis shows the relative frequency of ‘presidents/CEOs’ within each percentile. The inset plot shows model predictions.

Figure 15 (below) shows the same data, but plots job frequency against the size of income. Below average income, CEOs are basically non-existent. But as income reaches 10 times the Canadian average, CEOs become ubiquitous — approaching 100% of of Sunshine-List members.

Figure 17: Frequency of ‘President/CEO’ on the Ontario Sunshine List by income size. The horizontal axis shows income relative to the Canadian average. The vertical axis shows the relative frequency of ‘presidents/CEOs’ on the Ontario Sunshine List. The inset plot shows model predictions. [2]

The model (inset) predicts this explosion of top-ranking employees. However, the model predicts the saturation of top-ranking employees at about 500 times the average income (see Figure 10). In contrast, saturation on the Sunshine List happens at 10 times the average income.

Why the discrepancy? It’s because the model is based on the US private sector, where pay is far more unequal than in the Canadian public sector. Top US CEOs often earn hundreds of times the average income. In contrast, top public-sector CEOs in Canada rarely earn more than 10 times the average income.

The key here is that top-ranking employees become ubiquitous among the largest incomes — however large these may be.

### A new window into hierarchy?

I’m excited by these results for a few reasons. First, there’s something tantalizing (and insidious) about knowing that CEOs become ubiquitous among top earners. It shows that all jobs are not created equal.

What’s more exciting is that we can predict this trend using a simple model of hierarchy. If income grows with hierarchical rank, then top-ranking employees will become ubiquitous as income grows. There’s no way around this prediction — it’s a basic consequence of hierarchy.

But what’s most exciting are the doors opened for future research. Hierarchy surrounds us. Yet we know virtually nothing about it. The results here suggest that evidence for how hierarchy affects income is staring us in the face. It’s sitting there (waiting to be analyzed) in any dataset that records income and job titles.

### Notes

[1] As rank grows, why is it more likely that you sit at the top of your hierarchy? This results from a joint property of hierarchies and the size distribution of firms.

Imagine two people, Alice and Bob. They both have a rank of 8. But Alice is the CEO of her firm, while Bob is a Vice President in his firm. How common are our hypothetical Alice and Bob?

It turns out that someone like Alice is far more common than someone like Bob. This is because hierarchies tend to grow exponentially with the number of hierarchical levels. Because Bob’s firm has one more hierarchical level than Alice’s firm, we’ll guess that its roughly double the size.

Now, the size distribution of firms follows a power law. The probability of finding a firm of size x is roughly proportional to the inverse square of x (see this post for more details). This means that Bob’s firm, which is twice as large, is about 4 times rarer than Alice’s firm.

So even though Alice and Bob have the same rank, our hypothetical Alice is about 4 times more common than our hypothetical Bob (because the size of her firm is about 4 times more common). The result is that as your rank grows, it becomes increasingly probable that you occupy the top rank in your firm.

[2] I calculate average Canadian income by dividing GDP by the size of the labor force (using World Bank series NY.GDP.MKTP.CN and SL.TLF.TOTL.IN).

Fix, B. (2018). Hierarchy and the Power-Law Income Distribution Tail. Journal of Computational Social Science, 1(2), 471–491. SocArXiv Preprint.

Fix, B. (2019). How the Rich Are Different: Hierarchical Power as the Basis of Income Size and Class. SocArXiv Preprint.

Fix, B. (2019). Personal Income and Hierarchical Power. Journal of Economic Issues. 2019; 53(4): 928-945. SocArXiv Preprint.

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## Debunking the ‘Productivity-Pay Gap’

### Tags

Have you heard of the ‘productivity-pay gap’? It’s the (apparently) growing gap between the productivity of US workers and their pay. Here’s what it looks like:

Figure 1: The Productivity-Pay Gap. Source: Economic Policy Institute.

In this post, I debunk the ‘productivity-pay gap’ by showing that it has nothing to do with productivity. The reason is simple. Although economists claim to measure ‘productivity’, their measure is actually income relabelled.

As a result, the ‘productivity-pay gap’ isn’t what it appears. It claims to be a gap between productivity and wages. But it’s not. It’s really a gap between two types of income — (1) the wages of workers and (2) the average hourly income of all Americans. This gap is an important measure of inequality. But it has nothing to do with ‘productivity’.

### How economists measure productivity

To understand the problem with the ‘productivity-pay gap’, we first need to understand how economists measure productivity. Economists define ‘labor productivity’ as the economic output per unit of labor input:

$\text{Labor Productivity} = \displaystyle \frac{\text{Output}}{\text{Labor Input}}$

To use this equation, we’ll start with a simple example. Suppose we want to measure the productivity of two corn farmers, Alice and Bob. After working for an hour, Alice harvests 1 ton of corn. During the same time, Bob harvests 5 tons of corn. Using the equation above, we find that Bob is 5 times more productive than Alice: [1]

Alice’s productivity: 1 ton of corn per hour

Bob’s productivity: 5 tons of corn per hour

When there’s only one commodity, measuring productivity is simple. But what if we have multiple commodities? In this case, we can’t just count commodities, because they have different ‘natural units’ (apples and oranges, as they say). Instead, we have to ‘aggregate’ our commodities using a common unit of measure.

To aggregate economic output, economists use prices as the common unit. They define ‘output’ as the sum of the quantity of each commodity multiplied by its price:

$\text{Output} = \displaystyle \sum \text{Unit Quantity} \times \text{Unit Price}$

So if Alice sold 1 ton of corn at $100 per ton, her ‘output’ would be: Alice’s output: 1 ton of corn ×$100 per ton = $100 Likewise, if Bob sold 5 tons of potatoes at$50 per ton, his ‘output’ would be:

Bob’s output: 5 tons of potatoes × $50 per ton =$250

Using prices to aggregate output seems innocent enough. But when we look deeper, we find two big problems:

1. ‘Productivity’ becomes equivalent to average hourly income.
2. ‘Productivity’ becomes ambiguous because its units (prices) are unstable.

### ‘Productivity’ is hourly income relabelled

By choosing prices to aggregate output, economists make ‘productivity’ equivalent to average hourly income. Here’s how it happens.

Economists measure ‘output’ as the sum of the quantity of each commodity multiplied by its price. But this is precisely the formula for gross income (i.e. sales). To measure gross income, we multiply the quantity of each commodity sold by its price:

$\text{Gross Income} = \displaystyle \sum \text{Unit Quantity} \times \text{Unit Price}$

To find ‘productivity’, we then divide ‘output’ (gross income) by the number of labor hours worked:

$\text{Productivity} = \displaystyle \frac{\text{Gross Income}}{\text{Labor Hours}}$

When we do so, we find that ‘productivity’ is equivalent to average hourly income:

Productivity = Average Hourly Income

So economists’ measure of ‘productivity’ is really just income relabelled. The result is that any relation between ‘productivity’ and wages is tautological — it follows from the definition of productivity.

### Ambiguous ‘productivity’

In addition to making ‘productivity’ equivalent to average hourly income, using prices to measure ‘output’ also makes ‘productivity’ ambiguous. This seems odd at first. How can ‘productivity’ be ambiguous when income is always well-defined?

The answer has to do with prices.

We expect prices to play an important role in shaping income. Suppose I’m an apple farmer who sells the same number of apples each year. If the price of apples doubles, my income doubles. That’s how prices work.

If ‘output’ is equivalent to income, it seems that my ‘output’ (of apples) has also doubled. But here economists protest. Your apparent change in ‘output’, they say, was caused by a change in price. To find the ‘true’ change in output, you need to hold prices constant. When you do, you’ll find that your ‘output’ remains the same.

On the face of it, this ‘adjustment’ for price change seems reasonable. But it actually leads to a measurement quagmire. To see this quagmire, we’ll return to Alice and Bob.

Suppose that Alice grows 1 ton of corn and 5 tons of potatoes. Bob grows 5 tons of corn and 1 ton of potatoes. Whose output is greater? The answer is ambiguous — it depends on prices.

Suppose that corn sells for $100 per ton and potatoes sell for$20 per ton. We find that Bob’s output is about 250% greater than Alice’s:

Alice’s Output: 1 ton corn × $100 per ton + 5 tons potatoes ×$20 per ton = $200 Bob’s Output: 5 tons corn ×$100 per ton + 1 ton potatoes × $20 per ton =$520

Now suppose that corn sells for $20 per ton and potatoes sell for$100 per ton. We now find that Bob’s output is about 60% less than Alice’s:

Alice’s Output: 1 ton corn × $20 per ton + 5 tons potatoes ×$100 per ton = $520 Bob’s Output: 5 tons corn ×$20 per ton + 1 ton potatoes × $100 per ton =$200

What’s going on here? When we aggregate output using prices, these prices determine the relative weighting given to corn and potatoes. When this weighting changes, the measurement of ‘output’ changes.

As a result, our measure of ‘output’ depends on the particular prices we choose to hold constant. This is a big problem. It means that standard measures of productivity are inherently ambiguous. (For more details about this ambiguity, see my work with Jonathan Nitzan and Shimshon Bichler and with Erald Kolasi.)

To summarize, using prices to aggregate ‘output’ leads to bizarre problems. On the one hand, it causes ‘productivity’ to be equivalent to average hourly income. This means that any connection between ‘productivity’ and wages is circular. On the other hand, the same decision causes ‘productivity’ to be ambiguous. Our measure of ‘productivity’ depends on arbitrary choices about how to adjust for price change. As a result, productivity trends (like the one in Figure 1) are riddled with uncertainty.

### Dissecting the ‘productivity-pay gap’

Now that you understand the problems with how economists measure productivity, let’s return to the ‘productivity-pay gap’. I’m going to dissect the evidence in Figure 1.

This chart comes from the Economic Policy Institute (EPI). By dissecting it, I don’t mean to pick on the EPI authors. They use methods that are standard in economics. Instead, I want to show why these standard methods are flawed.

“Net productivity” [of workers] is the growth of output of goods and services less depreciation per hour worked.

To non-economists, this sounds like the EPI is measuring some physical quantity of output. But they’re not. Instead, the “output of goods and services” is economists’ code for the value of goods and services, as measured by Gross Domestic Product (GDP). ‘Depreciation’ is code for the financial depreciation of capital.

When we subtract capital depreciation from GDP, we get something called ‘Net Domestic Product’:

Net Domestic Product = GDP – Capital Depreciation

So the EPI defines ‘economic output’ in terms of Net Domestic Product.

Now here’s the rub. The national accounts are based on the principles of double-entry bookkeeping. This means that for every sale there is a corresponding income. So when you build a house and sell it for $1 million, you record the sale in one ledger as ‘output’. On the opposite ledger, you record the same sale as ‘income’. So ‘output’ is formally equivalent to income. In the national accounts, Net Domestic Product is the sales side of the ledger, recorded as ‘output’. It’s equivalent to the income side of the ledger, which we call ‘National Income’ — the income of all individuals in the country: Net Domestic Product ≈ National Income I’ve put the ‘≈’ here to mean ‘almost equivalent’. There are some small differences between Net Domestic Product and National Income (some business taxes, for instance). But in practice, the two quantities are nearly identical, as shown in Figure 2. Figure 2: US Net Domestic Product And National Income. Data is from the Bureau of Economic Analysis Table 1.7.5. To calculate workers ‘productivity’, the EPI divides Net Domestic Product by the number of labor hours worked: $\text{Productivity} = \displaystyle \frac{\text{Net Domestic Product}}{\text{Labor Hours}}$ But this is equivalent to dividing National Income by the number of labor hours worked: $\text{Productivity} = \displaystyle \frac{\text{National Income}}{\text{Labor Hours}}$ When we divide National Income by total labor hours, we’re actually measuring average hourly income. So the EPI’s measure of ‘productivity’ is identical to average hourly income: Productivity = Average Income per Hour Given this equivalence, any connection between ‘productivity’ and average hourly income isn’t surprising. It’s a tautology. ### How can wages diverge from ‘productivity’? If productivity is equivalent to average hourly income, how can wages diverge from ‘productivity’? In other words, how can the ‘productivity-pay gap’ exist? Let me explain. ‘Productivity’ (as measured by the EPI) is equivalent to the average hourly income of all US earners. Since average income can’t diverge from itself, average income and ‘productivity’ can’t diverge. However, if we select a subpopulation of US citizens, their income can diverge from the average. This is just a mathematical truism. If I select a non-random sample from a population, the properties of this sample need not match the properties of the whole population. To make this thinking concrete, suppose we select only CEOs. Must CEO income track with the national average? The answer is no. CEOs are a unique subpopulation, so their income can diverge from the national average. And as you probably know, CEO income has done just that. Over the last 40 years, the income of US CEOs has grown drastically relative to average income. ### Wages of production workers In Figure 1, the EPI studies the wages of ‘production/nonsupervisory workers’. Because these workers are a subpopulation of the US, their income can (and does) diverge from the national average. Over the last 40 years, the wages of production workers have declined relative to the average hourly income. This decline, however, has nothing to do with productivity. Instead, it owes to a redistribution of income — a redistribution that has two parts. First, the labor share of national income has declined over the last 40 years. Second, over the same period, US wages and salaries have become increasingly unequal. ### The declining labor share of income In the national accounts, there are two basic types of income. If you earn income from property, you earn ‘capitalist income’. If you earn income from wages and salaries, you earn ‘labor income’. The two types of income sum to National Income: National Income = Capitalist Income + Labor Income If we select only ‘laborers’, it’s possible for the average hourly income of this subpopulation to diverge from the average income of the population. For instance, if capitalist income grows relative to workers’ income, it pulls up the average income. This causes a gap between the wages of workers and the hourly income of the whole population. Looking back at Figure 1, we see that the ‘productivity-pay gap’ emerges after 1970. Not surprisingly, it’s around this time that the labor share of US income began to drop: Figure 3: Labor’s Share of US National Income. Data is from the Bureau of Economic Analysis Table 1.12. Labor’s share is calculated as the ‘compensation of employees’ as a fraction of national income. This decline of labor’s share of income is partly why the EPI finds a ‘productivity-pay gap’. Remember that ‘productivity’ (as measured by the EPI) is equivalent to the average hourly income in the US. Since 1970, US workers have received a declining share of this income. Consequently, their wages have declined relative to the average US income. ### The growing inequality of labor income The other reason that the EPI finds a ‘productivity-pay gap’ is because US wages and salaries have become increasingly unequal. Since 1970, the income share of the top 1% of wage/salary earners has grown steadily: Figure 4: Top 1% of Wage/Salary Earners, Share of US Labor Income Data is from the World Inequality Database (average of series flinc and plinc). It may not be clear how wage inequality would affect the relative income of production workers. To help understand, we’ll divide labor income into two parts: Labor Income = Production Workers Income + Non-Production Workers Income Suppose that the income of non-production workers increases relative to the income of production workers. This increase pulls up the average labor income, causing it to outpace the average income of production workers. Still, it’s not clear how this redistribution relates to wage inequality. This is where hierarchy comes in. I propose that ‘production workers’ occupy the bottom two ranks in firm hierarchies. The bottom rank consists of ‘shop floor’ workers. The second rank consists of ‘working supervisors’. Everyone in ranks three and above is a ‘non-production worker’ (i.e. manager). Figure 5: Production workers in a hierarchy. Production workers (blue) occupy the bottom two ranks in a hierarchy. The first rank contains ‘shop floor’ workers. The second rank contains ‘working supervisors’. Ranks three and above are ‘managers’. In this simple model, ‘production workers’ make up about 77% of total employment. That’s not far from the actual US figure of 82%. Figure 6: Production workers’ share of US private employment. Data is from the Bureau of Labor Statistics, series CES0500000001 and CES0500000006. What does our hierarchy model tell us about the income of production workers? In hierarchies income increases steeply with hierarchical rank. (I review the evidence here and here.) So if production workers occupy the bottom of the corporate hierarchy, they should also occupy the bottom of the income distribution. Let’s suppose that production workers occupy the bottom 80% of US labor incomes. If labor income inequality increases, we expect the relative income of production workers to decline. Figure 7 shows a simple model of what this might look like. Here I’ve defined ‘production workers’ as everyone in the bottom 80% of a hypothetical distribution of income. I then calculate the average income of these production workers and compare it to the average income in the whole population. Figure 7: A model of the relative income of production workers. Here I model ‘production workers’ as the bottom 80% of earners in the population. As inequality (measured by the top 1% share of income) grows, the average income of production workers declines relative to the average income of the population. For the math people, I’ve modeled the distribution of income with a lognormal distribution. Because production workers are at the bottom of the income distribution, we expect their income to be below the population average. (That’s why the y-axis values in Figure 7 are below 100%.) But just how far below depends on income inequality. As we increase inequality in the population (shown on the horizontal axis in Figure 7) the relative income of production workers declines. When inequality is minimal, production workers’ relative income approaches the population average. When inequality is extreme, production workers’ relative income approaches zero. In Figure 7, the vertical red lines show the US top 1% share of labor income in 1970 and 2012. Given this growing inequality, our model predicts that the relative income of production workers should drop by about 50%. This is on par with the pay gap shown in Figure 1. In short, the growing inequality of labor income can explain a large part of the apparent ‘productivity-pay gap’. Again, this gap isn’t about productivity. It’s about the declining relative income of production workers. ### The price-index problem While most of the apparent ‘productivity-pay gap’ has been caused by income redistribution, part of this gap is caused by price index shenanigans. In Figure 1, the EPI uses two different price indexes to ‘adjust’ for inflation. To understand the problems with the EPI’s method, we need to backtrack a bit. I’ve already noted that ‘productivity’ is equivalent to average hourly income. But this wasn’t quite correct. ‘Productivity’ is equivalent to real average hourly income: Productivity = ‘Real’ Average Hourly Income Unlike ‘nominal’ income, ‘real’ income adjusts for inflation. To get ‘real’ income, we divide ‘nominal’ income by a price index — a measure of average price change: $\text{Real Income} = \displaystyle \frac{\text{Nominal Income}}{\text{Price Index}}$ There are many different types of price indexes. Some track a few commodities. Others track many commodities. Because price change varies wildly between commodities, different price indexes can vary wildly. Here’s where the EPI errors. It uses the (implicit) Net Domestic Product deflator to measure ‘productivity’ (i.e. real average income per hour). But it uses the Consumer Price Index (CPI) to measure the ‘real’ wage of production workers. This is a problem. The two price indexes have diverged since 1970 — the very period where the EPI finds a growing ‘productivity-pay gap’. Here’s what the divergence looks like: Figure 8: The US Net Domestic Product deflator relative to the Consumer Price Index. CPI data is from Federal Reserve Economic Data, series CPIAUCSL. The implicit NDP deflator data is from BEA Table 1.17.6 (the ratio of nominal NDP to real NDP). To put this in perspective, the EPI’s method is like using different price indexes to compare the ‘real’ income of two people. Suppose Alice and Bob both start out with$100. Over 40 years, both of their incomes grow to \$200. We then use the NDP deflator to find Alice’s real income. But we use the CPI to find Bob’s real income. Although their nominal incomes are identical, we find that Alice’s real income outpaced Bob’s by 20%.

The crime here is that we don’t need price indexes to compare incomes. We can compare Alice and Bob’s incomes directly. Similarly, the EPI could have compared the nominal income of production workers directly to the nominal hourly income in the US.

### The declining relative income of workers

The problem with the ‘productivity-pay gap’ is that it proclaims to be something it’s not. It’s not a gap between workers’ productivity and their income. Instead, it shows the declining relative income of workers.

The best way to look at this decline is to measure the relative income of production workers:

$\text{Relative Income of Production Workers} = \displaystyle \frac{\text{Average Wage of Production Workers}}{\text{Average Hourly Income of Population}}$

Figure 9 shows this relative income over the last 50 years. In 1964, US production workers earned 60% of the average hourly US income. By 2015, this declined to 35%.

Figure 9: The relative income of US production workers. Average hourly earnings of production workers is from FRED series AHETPI. Average hourly US income is calculated by dividing National Income (BEA Table 1.7.5) by the number of labor hours worked by US persons engaged in production (FRED series EMPENGUSA148NRUG × series AVHWPEUSA065NRUG).

What’s important here is that we haven’t dressed up income as ‘productivity’. We’re explicitly comparing two types of income — the income of production workers relative to the national average.

The relative income of production workers has nothing to do with ‘productivity’. It’s actually a measure of income inequality. As shown in Figure 10, production workers’ relative income correlates strongly with the income share of the top 1%. As income inequality increases, the relative income of production workers decreases.

Figure 10: The relative wages of production workers decline as US inequality increases. For the sources for relative wages, see Figure 8. Data for the top 1% share of income comes from the World Inequality Database.

### Is ‘productivity’ still increasing?

The tale told by the ‘productivity-pay gap’ (Figure 1) is that workers’ productivity has increased steadily but wages have not. This is a powerful piece of propaganda. It says to workers “look, the tide has risen, but it didn’t lift your boat”.

The problem, though, is that it’s not clear that the tide has actually risen. We can say for certain that workers relative wages have declined (Figure 9). But what about their productivity? Has it gone up as Figure 1 suggests?

To believe the ‘productivity’ trends in Figure 1, you have to put on a brave face. You have to believe that the myriad of subjective decisions made by statistical agencies (reviewed here) are the ‘correct’ decisions. You have to believe that prices ‘reveal’ utility, and that monetary income is the same as economic ‘output’.

I, for one, don’t believe these things. Consequently, I treat official measures of ‘productivity’ as garbage.

How should we measure productivity? It depends on what we think the economy ‘does’. Personally, I like the view taken by atmospheric scientist Tim Garrett. He treats the economy as a heat engine. Garrett uses the analogy of a growing child. It takes energy to maintain the child’s body. And if the child is to grow, it needs to consume increasing amounts of energy. The same is true of the economy.

When you think this way, you realize that ‘useful work’ (the amount of energy put to an end use) is a good indicator of economic output. I propose that we treat useful work per labor as an alternative measure of labor productivity.

How does this alternative measure compare with the standard measure of productivity? Figure 11 shows a comparison. Here I use real GDP per labor hour as the standard measure of productivity. I contrast this with Benjamin Warr and Robert Ayres’ estimate for useful work per labor hour.

Figure 11: How a physical measure of US productivity compares to the official measure of productivity. Data is from Benjamin Warr’s REXS Database.

It’s not hard to spot the difference between the two series. The standard measure of productivity tells a tale of steady growth. In contrast, our physical measure suggests that productivity has stagnated since 1970. Interestingly, this is the period when the relative wages of production workers began to decline (i.e. when the apparent ‘productivity-pay gap’ appears).

Here’s an interesting question. Is the stagnation in useful work output related to the decline of workers’ wages? Biophysical economist Carey King thinks so. He recently built a model to investigate this connection.

The important point is that it’s far from clear that US productivity has increased steadily over the 20th century. In energetic terms, productivity has stagnated since 1970. I, for one, think that this physical measure of productivity is far more meaningful than the official measure. ‘Useful work’ is based on the laws of thermodynamics. The standard measure of productivity, in contrast, is based on the dubious assumptions of neoclassical economics.

### The productivity problem

‘Productivity’ is used by both major schools of economic thought. Neoclassical economists use productivity to claim that the distribution of income is just. They argue that in a competitive economy, workers get what they produce. Marxists, in contrast, use productivity to claim that the distribution of income is unjust. They argue that in a capitalist economy, workers receive less than they produce (because capitalists extract a surplus).

What’s interesting is that these two opposing theories commit the same sin. They define productivity in terms of income. Neoclassical economists do so explicitly, as I’ve described in this post. Marxists do so implicitly because they haven’t developed their own system of national accounts. Instead, Marxists who do empirical work use neoclassical measures of productivity (As an example, see this fascinating exchange between Paul Cockshott, Shimshon Bichler and Jonathan Nitzan.)

The result of this circular definition is that the analysis of productivity is a sleight of hand. ‘Productivity’ is just income relabelled.

The ‘productivity-pay gap’ is a textbook example of this relabelling. It claims to show a growing gap between what workers ‘produce’ and what they get paid. But workers’ ‘productivity’ is actually measured in terms of income — the average hourly income.

This relabelling of income gives the analysis ideological potency. Instead of saying that workers’ relative wages have declined, it says that workers don’t get paid what they produce. The latter, as Marx long ago realized, is far more potent propaganda.

### Productivity propaganda cuts both ways

The problem with productivity propaganda is that it cuts both ways. The EPI uses income to measure ‘productivity’ at the national level. But why stop there? Why not equate income and productivity at the sector level, or at the individual level? Curiously, the EPI warns against doing so (see the technical appendix here).

The problem is that the more finely we equate income with productivity, the more we’ll find that everyone ‘gets what they produce’. This is because as we study smaller and smaller groups, we remove the possibility of sampling subgroups whose income diverges from the group’s average income.

As a progressive think tank, the EPI wants to show that workers do not get paid what they produce. So it warns against equating income and productivity at the sector and individual level.

The problem is that the EPI wants to have its cake and eat it too. It wants to equate productivity with income when the results suit it — when the analysis shows a productivity-pay gap. But the more fine grain the analysis, the more this gap will disappear. And so the EPI warns against equating income and productivity at lower levels of analysis.

To be fair, the EPI is doing what many heterodox economists do. They reject the ‘crude’ neoclassical assumption that individual income is equivalent to productivity. Yet they then equate income and productivity at the national level.

This double standard is unjustifiable. Either we side with neoclassical theory and equate income and productivity wholesale. Or we reject neoclassical theory and so reject the accounting system that economists use to measure productivity.

Many heterodox economists are uncomfortable with the latter choice. And it’s not hard to see why. When you reject equating income and productivity, you reject the heart of macroeconomics. You reject the entire suite of measures that macroeconomists use to measure economic output and productivity. In so doing, you reject almost all that you (as a macroeconomist) are taught to hold dear. That’s a scary prospect.

The uncomfortable fact, though, is that if we want to create an alternative to neoclassical economics, we can’t use methods that have neoclassical assumptions baked into them. So a major part of being a heterodox economist is looking for new ways to quantify the economy.

Let’s bring this post to a close. I’m all for reducing inequality. And I think that workers’ wages have grown increasingly unfair. But I’m also a hard-nosed scientist who dislikes analysis with dubious assumptions baked into it. For that reason, I think the ‘productivity-pay gap’ needs to be called what it actually is — a decline of workers’ relative income.

### Notes

[1] “Bob is more ‘productive’ than Alice”. Note that this doesn’t mean that Bob caused his greater output of corn. Maybe Bob had better land. Or maybe he had a bigger tractor. Our measure of productivity says nothing about Bob’s abilities.

Ayres, R. U., & Warr, B. (2010). The economic growth engine: How energy and work drive material prosperity. Edward Elgar Publishing.

Bivens, J., Gould, E., Mishel, L. R., & Shierholz, H. (2014). Raising America’s Pay: Why It’s Our Central Economic Policy Challenge. Economic Policy Institute.

Bivens, J., & Mishel, L. (2015). Understanding the Historic Divergence Between Productivity and a Typical Worker’s Pay: Why It Matters and Why It’s Real. Economic Policy Institute.

Cockshot, P., Shimshon, B., & Nitzan, J. (2010). Testing the Labour Theory of Value: An Exchange. Nitzan & Bichler Archives.

Fix, B. (2019). Personal Income and Hierarchical Power. Journal of Economic Issues, 53(4), 928–945. SocArXiv preprint.

Fix, B. (2019). The Aggregation Problem: Implications for Ecological and Biophysical Economics. BioPhysical Economics and Resource Quality, 4(1), 1. SocArXiv preprint.

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## From Jane Austen to haunting memoirs: books to open your eyes to inequality

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In the second part of our series, we asked Sarah Perry, Jeffrey Sachs, Sebastian Barry, Monica Ali, Richard Wilkinson, Julian Baggini, Kate Pickett and Afua Hirsch to tell us which titles helped shape their views on inequality

Keynes’s message is essentially that societal wellbeing is fragile and that we are all in it together.

Peter Singer's argument does make me acutely aware of the injustice of economic equality and deeply uncomfortable that I am a beneficiary of it

Unhealthy Societies didn’t just open my eyes to the impact of inequality, it showed me how research can be used to have an impact of its own

## PEOPLE’S CLIMATE MARCH and the U.S. ENVIRONMENTAL MOVEMENT: Still disproportionally white and wealthy?

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Updated April 25th, 2017

In the fall of 2014, the largest climate protest to date occurred at the People’s Climate March in New York City. An estimated 400,000 people marched demanding action on global warming. On April 29th, 2017 Washington, DC and dozens of other cities around the country and world will host the second People’s Climate March: March for Climate, Jobs and Justice.

See the celebratory video of the 2014 New York People’s Climate March by clicking on the image below.

While the march was declared a success by the organizers, questions remain about whether the climate change movement is successfully overcoming past criticism that the mainstream environmental movement is too white, too wealthy, and too male.

Various media outposts have pointed out that the environmental movement, in general, is lacking diversity, that is, it is too white. In particular, Brentin Mock wrote about it extensively as a columnist for Grist (he recently moved to The Atlantic).

This is far from a new issue, but rather is something that organizations have supposedly been working on since at least the 1970s.

This lack of diversity has also been documented by several academics, most notably Dr. Dorceta Taylor at the University Michigan. Her 2014 report, The State of Diversity in Environmental Organizations, examines mainstream environmental NGOS, foundations, and government agencies for their degree of diversity of race/ethnicity, class, and gender.

The trends in Taylor’s data show that the percentage of minorities in leadership position in the environmental movement have increased since the 1990s but may have plateaued at a rate lower than the percentage of racial and ethnic minorities in the US population. See a key figure from her report below:

However, the report focuses on the organizations’ leadership, not the members.

Concerns about the diversity of the environmental movement more broadly continue as we head into the People’s Climate March in DC.

According to Lindsey McDougle, “The number of environmental groups has increased in recent years, growing nearly 20 percent from 11,233 in 2003 to 13,283 in 2013. Despite this growth, people from communities of color engage in environmental volunteerism at lower rates than whites, according to the Bureau of Labor Statistics. In 2015, for instance, 3.1 percent of white Americans volunteered for green causes, while only 1.6 percent of Latinos and 1 percent of black Americans did so.”

Others have been critical of Earth Day, as lacking an appropriate edge, based on the current state of the planet. Emily Atkin writes in the New Republic, “Why is Earth Day so benign and toothless when the immediate threats to the planet—particularly to its most vulnerable populations—are so severe?”

Previously, in response to Trump’s executive orders and proposed budget decimating the EPA, she wrote, “Largely missing from [the] attacks were fears about how Trump’s executive order could disproportionately hurt people living in low-income, minority, and indigenous communities. Environmental justice advocates say they’re used to this issue being overlooked. And perhaps there is some logic to the broader focus on global warming; after all, if the planet gets too hot, we’re all doomed.

What about the people who are being mobilized in the streets demanding action on climate change. Who’s voices are these?

Are organizations doing enough to ensure the movement represents the increasing racial and gender diversity of US society? As income inequality grows in our society, is the climate change movement an income-diverse movement or is it the wealthier voices that are being heard?

With the help of a team of nearly 20 research assistants I collected just over 1,000 surveys from a random sample of protestors at the 2014 People’s Climate March. Anecdotally, looking at the crowd that was in New York City that day it was diverse in a number of ways: race, gender, issue orientation, and age. However, random sample survey data provides more accurate information than one’s individual observations.

The general population of the US is a majority white (at least for another decade or two), so we would expect that whites are still the most predominant in number at such an event. However, we can look at the proportions of different races and ethnicities in the US as a whole and compare that to the proportions at the 2014 People’s Climate March to examine the level of diversity at the march.

Despite the awareness that the environmental movement has historically lacked diversity, the People’s Climate March was still disproportionally white. In 2014, whites (according to US Census estimates) represented 62% of the population as a whole, yet they were over-represented as 71% of the protesters at the People’s Climate March. Hispanic and Latinos were well underrepresented as they make up 17% of the US population but only 7% of the protesters that day in New York City. Blacks made up only 7% of the People’s Climate March activists, while making up 13% of the total population in 2014. Native Americans were also underrepresented as only 0.5% of the marchers but 1.2% of the US population. Asians were slightly over-represented as 6% of the marchers and 5% of the overall population. The “other” category represents bi-racial identities and (in the data below) Native Hawaiian and Pacific Islanders.

It is not just racial and ethnic diversity that is of concern, but also economic diversity. Is the climate change movement, like the mainstream environmental movement, disproportionally upper-middle and upper class? One way of measuring the income distribution is dividing the population by five, or into clusters of 20% of the population (quintiles). The survey data indicates that participants in the 2014 People’s Climate March disproportionally fell into the upper two quintile income brackets in the US. The income ranges in the figure below each represent 20% of the US population. If the protesters were evenly distributed across incomes, each of the bars in the figure below would be at 20%. Instead, the data shows that just over 50% of the protesters were from the top two US income quintiles in the US. Just 32% of the protesters were from the bottom two quintiles.

. . .

Lastly, the gender distribution within environmental organizations has also been criticized as disproportionally male. Dorceta Taylor’s research shows that the boards of organizations remain disproportionally male, while the staff are disproportionally female, as seen in her charts below.

The participants in the historical 2014 People’s Climate March were split in roughly the same gender proportions as the US population (see the figure below). The gender distribution of marchers shows greater equality than either the race/ethnicity or income distribution.

Regarding leadership, 350.org is the main organizer of the People’s Climate March both in 2014 and 2017. A quick count of the staff listed on 350.org’s web page (as of October 2015) indicates that 57% of their global staff are women. Of their seven board members, four are women.

. . .

Climate organizations need to make a greater and continued effort to ensure that all the communities being negatively impacted by climate change have a voice and are present in the mass mobilizations. We continue to live in a racialized society (see my previous posts if in doubt, here, here and here among others) and overcoming that will take intentional effort, reaching out to minority groups with specific rather than open invitations, and ensuring that they are part of the planning not just invited at the last minute. As Naomi Klein, prominent author and board member of 350.org writes in the article linked to below:

“What does #BlackLivesMatter, and the unshakable moral principle that it represents, have to do with climate change? Everything. Because we can be quite sure that if wealthy white Americans had been the ones left without food and water for days in a giant sports stadium after Hurricane Katrina, even George W. Bush would have gotten serious about climate change. Similarly, if Australia were at risk of disappearing, and not large parts of Bangladesh, Prime Minister Tony Abbott would be a lot less likely to publicly celebrate the burning of coal as “good for humanity,” as he did on the occasion of the opening of a vast new coal mine. And if my own city of Toronto were being battered, year after year, by historic typhoons demanding mass evacuations, and not Tacloban in the Philippines, we can also be sure that Canada would not have made building tar sands pipelines the centerpiece of its foreign policy.”

This piece has focused on the movement in the US and around one particular mass mobilization. It is important to remember that the lack of diversity at the People’s Climate March was not because the working class and racial minorities don’t care about the issue (nor was it that the organizers did not care about diversity). The NAACP has a campaign called the Climate Justice Initiative that “works at addressing the many practices that are harming communities nationwide and worldwide and the policies needed to rectify these impacts.” Nations of the Global South, predominantly not white and less developed than the advanced industrialized Western nations (read greenhouse gas emitters) have been mobilizing against climate change for some time now. On the African continent, there is the Pan African Climate Justice Alliance (PACJA). Others include Focus on the Global South, La Via Campesina, and many others. See some survey data on the views of organizational members of the Pan African Climate Justice Alliance here.

The US climate movement must stay focused on the principles of climate justice if it wants to be inclusive and not just the mass mobilization of wealthy, white, males. While improvements in this area have been made, much remains to be done.

I’ll have another research team collecting survey data at the 2017 march in both DC and Chicago. Watch for updated data as those results come in. See you at the protest!

Teach well, it matters.

. . .

A couple of “thinking critically” caveats about the data that need to be considered. First, in conjunction with the main event, the People’s Climate March in New York City, there were a few hundred other smaller protests held in cities throughout the country and world. My data is limited to the New York City event. While we could speculate that these other events may have been more racially and economically diverse (but we have to reason to believe so), the bulk of the organizing efforts seemed to go into the march in New York City. The main march, with an estimated 400,000 people is the event that received the media attention, the primary purpose of the event. So, even if the smaller, more local events were of greater diversity, they were peripheral.

Secondly, the event was held in New York City and the income distribution within the metropolitan area is skewed slightly upward relative to the nation as a whole. While the organizers made a herculean effort to bring in people from all over the country, there is a still a chance that the crowd was predominantly from New York City. If we only considered the income distribution in NYC, this would likely result in a more even distribution among income quintiles.

. . .