A Second Look at Hierarchy

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.

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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 1: The relative income of CEOs grows with firm size. [Source: Compustat and Execucomp]

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, by the way, was the CEO of McDonald’s. Jonathan Steinberg 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. 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. 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), 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 2: Income within case-study firms grows with the number of subordinates. [Color indicates the case-study source. For methods, see Personal Income and Hierarchical Power]

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

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

Mincer, J. (1958). Investment in human capital and personal income distribution. The Journal of Political Economy, 66(4), 281–302.

Roberts, D. R. (1956). A general theory of executive compensation based on statistically tested propositions. The Quarterly Journal of Economics, 70(2), 270–294.

Simon, H. A. (1957). The compensation of executives. Sociometry, 20(1), 32–35.

7 comments

  1. Anecdotal evidence: I was in charge of pay in firms ranging from 4 to 15,000 over the course of 35 years and in my experience the hierarchy is true. I had a “bookkeeper” at the 4 person firm who was paid just a bit more than the average accountant at the large firm where there were dozens of accountants who came at various levels (Accountant 1,2,3), supervisors, managers, directors, VP’s and CFO. Each level clearly has to be paid more.
    The second function is bracket creep which is driven by a standard process used everywhere called “benchmarking”. You justify pay levels by comparing to other firms of similar size and of course, your people are as good as if if not better than the rest of the herd, so they should get paid at the upper end. You can see where this goes… It exploded on an exponential curve from about 2000 onwards.

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    • Thanks Robbie. Fascinating stuff. Although I study them, I actually have no lived experience in corporate hierarchies. I’ve been in small business and/or the public sector my whole life. So I love to hear from people who’ve been part of these hierarchies.

      About benchmarking, I don’t doubt that firms do this. The question is, what did they do when CEO pay was so much lower than today? In the 1950s and 1960s, CEOs didn’t dare pay themselves the spoils that modern CEOs take home. Why? Obviously a culture shift has occurred. But the reasons for it are poorly understood.

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  2. Pay vs hierarchy correlates well in the private sector, but I wonder if it does in other sectors? How about clergy, military, and public sector pay scales? What about criminal organizations such as mafias? Of course, some of those sectors have no income to distribute, but if hierarchy were truly important to (justified) salaries, one would think the correlation would also be found virtually everywhere. If so, I suspect that the slope of the hierarchy vs pay curve depends on the amount of money flowing through the organization involved.

    In that vein, has anyone tried to refine executive pay by adjusting for corporate cash flow (not profit) plus hierarchy? I would think that salary would depend not only on the power to skim but also on the pool of cash available for skimming.

    Liked by 1 person

    • Hi Joe,

      Good question. I’ve found the same pattern in the US military: https://economicsfromthetopdown.com/2020/01/04/the-power-ethos-in-the-us-military/

      Note that the scaling exponent between pay and number of subordinates is much lower in the military. Top generals make about 10 times more than the bottom rank. Top CEOs can make 1000’s of times more than bottom-ranked employees.

      Like you, I suspect that the correlation between number of subordinates and income is universal. What will change is the slope of the relation. This is something that is begging to be studied in more detail.

      Yes, salaries also correlate with sales per employee. When firms earn more, every employee (including the CEO) tends to have a higher salary. This part of salary is not directly related to hierarchy, at least not the hierarchy within individual firms.

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  3. Have you considered your findings in relation to fractal relationships? You as much as say that hierarchies are fractal, and that pay is relative to the level in the hierarchy. But then you switch over to comparing based on the number of subordinates.

    A hierarchy is a tree-shaped graph, which is characterized by the number of branches. In an ad hoc tree like an organizational hierarchy, there is no rule about how much branching happens: how wide or narrow the tree is; nor about how tall or short it is. Branching degree can vary at different levels, and at the same level on different branches (in different divisions, say). But they could be averaged out for all the branches below a given node.

    After averaging, a short wide tree has fewer levels than a tall narrow one, for the same number of employees. Does the height of the tree (the distance, optionally statistically weighted, from the root nood to the leaf nodes) affect the degree of difference between compensation for nodes at each extreme? This is what I mean by “fractal”: each level of the hierarchy is a new tree.

    There is going to be some correlation between tree size and tree height, affected by branching. So it would be interesting to know how the shape of the tree affects the compensation distribution, and whether the jump between levels is non-linear, and in aggregate has even more impact on executive pay than simply number of employees.

    It would also be interesting to know how pay is generally distributed throughout the hierarchy, and how it varies from industry to industry. Although it is taken for granted that bankers all make more money than, say, agricultural workers, it seems necessary that compensation is also affected by the size of a company. Income has to be distributed to all employees according to some function, but there is a limit of how much is available, as a percentage of the firm’s revenue. These factors would all determine how compensation varies at different levels of the organizational hierarchy, I think.

    Do you think proving this will affect how pay is determined? Can more transparency expose unfairness and bias? Will it force economists to pay more attention to reality and society? Or will it be considered a curiosity? Or poor taste, even dangerous, to question the assumption that everyone “deserves what they get”, and risk the threat to vanity that might cause?

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    • Important comments. Corporate hierarchies are a type of network. In real life, they’re certainly not a pure hierarchical network. Here’s the problem. I’m not aware of any organizations that release their complete chain of command (who answers to who) along with salaries. This type of data would be an absolute gold mine. But I’ve never seen it.

      The kind of studies that exist group people into aggregate ranks. So that’s my analysis is based on the data that’s available — comparing average pay to average number of subordinates. If better data comes along, we could make the analysis much more sophisticated.

      To get at your question, we simply don’t have the data yet to tell if the ‘shape’ of a hierarchy affects income distribution. How are ‘flat’ hierarchies different than ‘tall hierarchies’ in terms of pay? We have no good data. People need to be interested in hierarchy and go out and collect this data!

      About your last question, do I think showing how pay is distributed within a hierarchy will affect its distribution. No and yes. No, in that knowing something academically often doesn’t change behaviour. Yes, if enough people learn the truth and get angry about it, then things will change.

      Liked by 1 person

  4. Really interesting, thank you for this post.

    In one of my final year undergraduate modules, when explaining rising wage differentials in the West, my lecturer straight up gave “CEOs have become more shameless” as a reason – linked to the benchmarking comment made by another commenter. The more conventional reasons like globalisation, falling trade union power, etc were also given. Of course, the shameless/greedy comment is the one that stuck.

    In light of your (and Simon’s) evidence, it’s interesting to think that growing CEO pay may instead be down to the growth of firm workforces, allowing executives to be paid more.

    Like

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