Does hierarchy mediate the growth of top incomes?

Blair Fix

Download PDF Abstract   Although the determinants of income are complex, the results are surprisingly uniform. To a first approximation, top incomes follow a power-law distribution, and the redistribution of income corresponds to a change in the power-law exponent. Given the messiness of the struggle for resources, why is the outcome so simple?

Redistributing Income Through Hierarchy

In 1957, Herbert Simon proposed that CEO pay had a simple explanation: it stemmed largely from rank in a hierarchy. His model was largely forgotton. Here’s a second look.

Last fall, I wrote a short article for [The Mint
Magazine](https://www.themintmagazine.com/){target="_blank"
rel="noopener"} about how income relates to hierarchy. The Mint, if
you're not familiar, does great work promoting pluralist thinking in
economics. Check out their on-going [Festival for
Change](https://festivalforchange.global/){target="_blank"
rel="noopener"} --- a festival devoted to building a better economy.

Back to my aricle. I submitted a manuscript called 'A Second Look at
Hierarchy'. It got published in The Mint as [Down to
Size](https://www.themintmagazine.com/down-to-size){target="_blank"
rel="noopener"}.

Here's my original manuscript.

::: {style="text-align:center;"}
✹ ✹ ✹
:::

In 2016, Steve Easterbrook had a good year. Easterbrook --- a CEO of an
American firm --- earned about *600 times* the pay of the average worker
in his company. In the same year, Jonathan Steinberg wasn't so lucky.
Steinberg --- another American CEO --- earned just *8 times* the pay of
the average worker in his firm.

Why did Easterbrook earn so much more than Steinberg?

The reason, it turns out, owes mainly to company *size*. Easterbrook
helmed a multinational corporation with some 375,000 employees.
Steinberg, in contrast, helmed a small firm with about 200 employees.
Although neither Easterbrook nor Steinberg likely knew it, each man's
pay was part of a broader trend. The relative income of CEOs, it seems,
grows reliably with firm size.

Figure 1 shows this trend. Each dot represents an American CEO (observed
between 2006 and 2016). The vertical axis shows the pay of each CEO,
measured relative to the average worker in their firm. The horizontal
axis shows the number of employees in each firm. From this data, you can
see that CEO pay tends to grow with firm size. You can also see that
Easterbrook and Steinberg lie close to the best-fit trend.

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/09/ceos-1.png?w=723&amp;ssl=1"
class="wp-image-1894" decoding="async" data-attachment-id="1894"
data-permalink="https://economicsfromthetopdown.com/2020/07/17/living-the-good-life-without-killing-the-planet/energy_life_expect_resid/"
data-orig-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/07/energy_life_expect_resid.png?fit=3600%2C3600&amp;ssl=1"
data-orig-size="3600,3600" data-comments-opened="1"
data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}"
data-image-title="energy_life_expect_resid" data-image-description=""
data-image-caption="&lt;p&gt;diff life countries&lt;/p&gt;
"
data-medium-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/07/energy_life_expect_resid.png?fit=300%2C300&amp;ssl=1"
data-large-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/07/energy_life_expect_resid.png?fit=723%2C723&amp;ssl=1"
data-recalc-dims="1" />
<figcaption>Figure 1: The relative income of CEOs grows with
firm size. [Source: Compustat and Execucomp] 
</figcaption>
</figure>

This trend raises an interesting possibility. Both Easterbrook and
Steinberg likely had preconceptions about their income --- that it
stemmed, for instance, from things like performance, skill or education.
And yet knowing none of these things, an unassuming scientist could have
predicted Easterbrook's and Steinberg's relative income. The scientist
need know only one thing: the size of each man's firm.

([Steve
Easterbrook](https://en.wikipedia.org/wiki/Steve_Easterbrook){target="_blank"
rel="noopener"}, by the way, was the CEO of McDonald's. [Jonathan
Steinberg](http://ir.wisdomtree.com/management/jonathan-steinberg){target="_blank"
rel="noopener"} was the CEO of a small firm called Wisdomtree
Investments.)

### A road not taken

If you're surprised that CEO pay grows with firm size, you're not alone.
Few people know about this trend. And yet it's not a new finding. The
economist David Roberts [discovered it in
1956](https://academic.oup.com/qje/article-abstract/70/2/270/1900180){target="_blank"
rel="noopener"}. In the years that followed, other correlates of income
(like education) became well known. But the fact that CEO pay grows with
firm size remained obscure. Why?

The answer has to do with the road taken by economics.

In the late 1950s (when Roberts published his CEO findings), economists
were putting the finishing touches on their theory of income
distribution. The roots of this theory dated to the turn of the 20th
century. At the time, John Bates Clark had argued that in a competitive
market, people earn what they produce. This idea became known as the
'marginal productivity' theory of income.

In its initial form, marginal productivity theory applied only to
*groups* of people (capitalists and workers). It left *individual*
income unexplained. For 50 years, this problem went unaddressed. Then,
in 1958, Jacob Mincer [found a
solution](https://www.journals.uchicago.edu/doi/abs/10.1086/258055?journalCode=jpe){target="_blank"
rel="noopener"}. He argued that every individual had something called
'human capital' --- a stock of skills and knowledge. This human capital
explained individuals' productivity, And productivity, in turn,
explained income.

Mincer's ideas spread like wildfire. Soon most economists proclaimed
'human capital' a core part of marginal productivity theory. With their
newly-minted theory in hand, economists argued that everyone's income
stemmed from productivity.

It was in these heady days that Roberts published his CEO findings. His
results, not surprisingly, were mostly ignored. Why? Because they were
hard to square with marginal productivity theory. (Roberts himself tried
to attribute executive pay to productivity, but his reasoning was
torturous.)

While not easily attributable to productivity, the growth of CEO pay
with firm size did have a simple explanation. It was the polymath
Herbert Simon who first hit upon it. CEO pay increased with firm size,
Simon argued, because of *hierarchy*.

Here's his reasoning.

Firms, Simon proposed, are organized using a hierarchical chain of
command. The CEO commands a handful of subordinates. And these
subordinates, in turn, command their own subordinates. This chain of
command creates a pyramid structure, with many people at the bottom of
the hierarchy and few at the top.

On its own, this pyramid says nothing about income. But with one simple
assumption, Simon made a startling prediction. If income grows with
hierarchical rank, CEO pay will increase with firm size. This is because
larger firms have more hierarchical ranks. So the CEO of a large firm
has a greater rank --- and hence greater income --- than the CEO of a
small firm. Thus, CEO pay grows with firm size.

Simon published this result in 1957. While the paper had an unassuming
name (he called it [*The Compensation of
Executives*](https://www.jstor.org/stable/2786111){target="_blank"
rel="noopener"}), it dropped a bomb on economic theory. Income, Simon's
model claimed, didn't stem from productivity. Instead, it was largely a
function of hierarchical rank. But because Simon was more mathematician
than social radical, he couched this bomb in opaque language. Here's how
he put it:

> \[O\]nly an improbable coincidence would bring about equality between
> salaries determined by the mechanism described here \[pay based on
> hierarchical rank\] and salaries determined by the marginal
> productivity mechanism.

> \[Translation: this model conflicts with marginal productivity
> theory.\]

Was Simon correct? Is income within firms largely a function not of
productivity, but of hierarchical rank? Unfortunately, it's difficult to
say. Now, as in Simon's day, we have little data about hierarchy.

Although Simon's paper opened a new road for economic theory, economists
chose not to explore it. Instead, they stayed on the trodden path of
attributing income to productivity. In the years after Simon's paper was
published, economists rushed to accept human capital theory. The
possibility that hierarchy affected income was ignored.

Here's an example of this blinder. Gregory Mankiw's textbook *Principles
of Microeconomics* mentions 'human capital' 27 times. It mentions
'productivity' (and its derivatives) 74 times. Hierarchy is not
mentioned once.

### Revisiting hierarchy

As a graduate student, I stumbled onto the evidence shown in Figure 1.
The relative pay of CEOs, I found, grew with firm size. Thinking this
was a new discovery, I set out to explain it.

Imagine my surprise when I found Simon's 1957 paper. My 'discovery' was
not new. It had been first documented 25 years before I was born! What's
more, my 'discovery' had an incendiary interpretation that had long been
forgotten. The CEO evidence suggested that income within firms was
largely a function of hierarchical rank.

Intrigued by this abandoned road of economic theory, I searched for data
on hierarchy. To my dismay, little existed. In the 60 years since
Simon's paper had been published, few economists had bothered to study
hierarchy. After a year of searching, I eventually found a handful of
studies that measured hierarchy within firms. While sparse, this
case-study evidence suggested that Simon was on the right track.

To make sense of the evidence, we'll first generalize Simon's model.
Simon argued that because firms are hierarchically organized, CEO pay
grows with firm size. If he was correct, something similar should hold
not just for CEOs, but for *all* employees within the firm.

To generalize Simon's model, we'll reflect on what firm size means in
the context of a hierarchy. As corporate leaders, CEOs command everyone
else in the firm. So the *size* of the firm indicates (roughly) the
number of *subordinates* below the CEO. The CEO of a 10-employee firm,
for instance, has 9 subordinates. And the CEO of a 100-employee firm has
99 subordinates.

Using this insight, we can reinterpret the CEO evidence in Figure 1. It
suggests that CEO income grows with the number of subordinates they
control. If Simon's model is correct, the same pattern should hold for
*all* members of the firm. Income should grow with the number of
subordinates.

So does income behave this way? The evidence suggests that it does. In
the existing case-studies of firm hierarchy, relative income grows with
the number of subordinates. Figure 2 shows the trend.

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/09/case_results-1.png?w=723&amp;ssl=1"
class="wp-image-1894" decoding="async" data-attachment-id="1894"
data-permalink="https://economicsfromthetopdown.com/2020/07/17/living-the-good-life-without-killing-the-planet/energy_life_expect_resid/"
data-orig-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/07/energy_life_expect_resid.png?fit=3600%2C3600&amp;ssl=1"
data-orig-size="3600,3600" data-comments-opened="1"
data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}"
data-image-title="energy_life_expect_resid" data-image-description=""
data-image-caption="&lt;p&gt;diff life countries&lt;/p&gt;
"
data-medium-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/07/energy_life_expect_resid.png?fit=300%2C300&amp;ssl=1"
data-large-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/07/energy_life_expect_resid.png?fit=723%2C723&amp;ssl=1"
data-recalc-dims="1" />
<figcaption>Figure 2: Income within case-study firms grows with
the number of subordinates. [Color indicates the case-study
source. For methods, see <a
href="https://osf.io/preprints/socarxiv/pb475/" target="_blank"
rel="noopener">Personal Income and Hierarchical Power</a>] 
</figcaption>
</figure>

### CEOs: superhumans or despots?

It's time, I believe, to revisit the road opened by Simon's model of
hierarchy. What's at stake is both the scientific understanding of
income and the justification (or lack thereof) for mitigating
inequality.

To see why our theory of income matters, let's revisit our friend Steve
Easterbrook. As CEO of McDonald's, Easterbrook earned 600 times more
than the average worker. If mainstream theory is correct, Easterbrook
earned this windfall because he was *superhuman*. He was 600 times more
productive than the average McDonald's employee. If true, most of us
would agree that Easterbrook's income was fair. So there's no reason to
give part of it to someone else.

Now consider the alternative. What if Easterbrook's income stemmed not
from his productivity, but from his command of subordinates? If true,
Easterbrook wasn't superhuman. He was a *despot*. Much like the kings of
old, Easterbrook used his power to enrich himself. So we have every
reason to take part of his fortune and give it to the needy.

As you can see, theory matters. Because the stakes are high, I think
it's worth taking a second look at hierarchy.

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### Further reading

::::::: {#refs .references}
::: {#ref-fix_personal_2019}
Fix, B. (2019). Personal income and hierarchical power. *Journal of
Economic Issues*, *53*(4), 928--945.
:::

::: {#ref-mincer_investment_1958}
Mincer, J. (1958). Investment in human capital and personal income
distribution. *The Journal of Political Economy*, *66*(4), 281--302.
:::

::: {#ref-roberts_general_1956}
Roberts, D. R. (1956). A general theory of executive compensation based
on statistically tested propositions. *The Quarterly Journal of
Economics*, *70*(2), 270--294.
:::

::: {#ref-simon_compensation_1957}
Simon, H. A. (1957). The compensation of executives. *Sociometry*,
*20*(1), 32--35.
:::
:::::::

Last fall, I wrote a short article for The Mint Magazine about how income relates to hierarchy. The Mint, if you’re not familiar, does great work promoting pluralist thinking in economics. Check out their on-going Festival for Change — a festival devoted to building a better economy. Back to my aricle. I submitted a manuscript called ‘A Second Look at Hierarchy’. It got published in The Mint as Down to Size. Here’s my original manuscript.

Messaggi di Rogue Scholar

Redistributing Income Through Hierarchy

A Second Look at Hierarchy