Piketty’s Can Opener

by Jim Manzi

I’m late to the party in commenting on Thomas Piketty’s best-selling book, Capital in the Twenty-First Century. This is because it’s taken me a while to work my way through the whole thing, and then read the footnoted papers that back up the key claims that most interest me.

In retrospect, this turns out to have been a wise approach. In the past couple of months, significant controversies have arisen over both the data (especially with respect to wealth inequality) and calculations (especially with respect to returns to capital).

I have a longstanding interest in Piketty’s subject. I believe that the first thing I ever wrote for print was an attempt to describe why income inequality had become so extreme in America. Since then, I’ve written repeatedly about the related problems of rising inequality, the increasing cultural gap between those with and without college degrees, slowing middle-class wage growth and insufficient social mobility. I have argued – usually in conservative publications – that conservative thinkers, activists, and politicians have frequently downplayed such problems, and have implemented policies that tend to exacerbate them. 

I support many right-of-center economic policies in spite of this, because I view these negative effects as the bad side of a trade-off in which we must accept some amount of social dislocation in return for innovation to drive increases in productivity that, in turn, drives long-run improvements in living standards for the broader society. I see managing this tension between innovation and cohesion as perhaps the fundamental task of domestic political economy in wealthy modern societies.

Piketty’s Argument
Piketty posits a simpler world. He argues that there is no such trade-off, at least in any practical sense that would drive policy decisions. 

I’ll focus on the case of America, and start by stipulating to all of his data. The work of claim and counter-claim that has arisen on the subjects of wealth inequality and returns to capital is useful and productive, but isn’t very relevant to the causes of rising inequality to date in the United States. The American super-wealthy are not primarily living off returns to capital; they are mostly people who work for an extremely lucrative living. Piketty is direct about this, saying:

Let me return now to the causes of rising inequality in the United States. The increase was largely the result of an unprecedented increase in wage inequality and in particular the emergence of extremely high remunerations at the summit of the wage hierarchy, particularly among top managers of large firms.

He dubs these people the “supermanagers,” and points to the U.S. as the exemplar of what he terms “meritocratic extremism.”

Piketty then presents a straightforward solution to reducing the resulting income inequality: an 80 percent top marginal income-tax rate plus a progressive global wealth tax.

He believes that this increase in taxes would not affect economic output, saying that “the evidence suggests that a rate on the order of 80 percent on incomes over $500,000 or $1 million a year not only would not reduce the growth of the US economy but would in fact distribute the fruits of growth more widely while imposing reasonable limits on economically useless (or even harmful) behavior.” In fact, in this quote he hints that we might not just get a free lunch, but might get paid to eat as well, since such very high taxes would reduce only two kinds of activities: those that produce zero extra output (“useless” activities) and those that actually reduce welfare (“harmful” activities).

Tax rates are not the only thing that drives behavior, but the idea that you could institute tax rates at this level and have no impact on output is a pretty extraordinary claim. This is what explains his repeated insistence on a very specific mechanism that has created the so-called supermanagers in the US: In plain English, that large company CEOs and their cronies have gamed the compensation process.

Piketty first attacks the idea that there is a rational basis for setting executive compensation (page 331)

Since it is impossible to give a precise estimate of each manager’s contribution to the firm’s output, it is inevitable that this process yields decisions that are largely arbitrary and dependent on hierarchical relationships and on the relative bargaining power of the individuals involved.

He comes back to this point again on page 334, referencing the “absence of a rational productivity justification for extremely high executive pay.”

On page 509, he explains how this has enabled too managers to seize value:

Because it is objectively difficult to measure individual contributions to a firm’s output, top managers found it relatively easy to persuade boards and stockholders that they were worth the money, especially since the members of compensation committees were often chosen in a rather incestuous manner.

Importantly, this applies to firms that have both separation between ownership and management (otherwise the top managers are stealing from themselves), and distributed shareholders with independent directors (otherwise top managers would be negotiating with a small number of sophisticated owners). In practice, this mostly means public companies. When we get to Piketty’s research papers, we will see that all of it is, in fact, based on public companies. 

He terms this the “bargaining power model” for executive compensation, and is clear a few pages later that this has been the root of the increasing pay for top managers, which in turn has been the primary driver of growing U.S. inequality writ large.

Our findings suggest that skyrocketing executive pay is fairly well explained by the bargaining model (lower marginal tax rates encourage executives to negotiate harder for higher pay) and does not have much to do with a hypothetical increase in managerial productivity.

At least with respect to America to date, then, “r > g, the “reemergence of a patrimonial society,” and all the rest is just a sound and light show. Piketty’s argument with respect to America is simple and linear: (1) Top managers of large companies have gamed the compensation system to seize more income; (2) this activity has not added any economic value; and therefore, (3) the government can take this excess income back through taxes and redistribute it without any loss in economic output.

But when thus seen clearly, his entire case rests on his “finding” that growing wage inequality is explained by executives gaming the compensation system.

Three Problems with Piketty’s Key Assertion
I don’t believe that his asserted finding is credible, for three reasons. First, there just aren’t enough top managers of relevant companies to account for most of the growing incomes at the top. Second, executives of public companies represent a shrinking share of top incomes. And third, Piketty’s “bargaining power model” for executive compensation in public companies is extremely naïve. 

Consider first the issue of the number of senior executives theoretically in a position to game their compensation. Piketty gestures at this problem when he says on page 302 that:

If we look only at the five highest paid executives in each company listed on the stock exchange (which are generally the only compensation packages that must be made public in annual corporate reports), we come to the paradoxical conclusion that there are not enough top corporate managers to explain the increase in very high US incomes, and it therefore becomes difficult to explain the evolutions we observe in incomes stated on federal income tax returns.  But the fact is that in many large US firms, there are far more than five executives whose pay places them in the top 1 percent (above $352,000 in 2010) or even the top 0.1 percent (above $ 1.5 million).

But he never gets into the numbers beyond this, which turns out to be important. Start with some simple dimensional arithmetic. There about 150,000 people in the top 0.1 percent. Piketty claims on page 303 that 60 to 70 percent of these, or about 100,000 people, are “top managers.” There are about 5,000 public companies in America. If Piketty is correct, therefore, an average of something like 20 people per company should be pulling down more than $1.5 million per year. 

The problem is that while this is true for the very largest companies, it’s not remotely true for a majority of public companies. I looked at companies 491–500 in the Fortune rankings. The average number of executives with total comp reported through SEC filings above $1.5 million in this group is 4. For those ranked 991–1000, the average is 2.8.(The actual numbers per company might be higher than this in these tiers: Three of the companies ranked 491–500, and two of those ranked 991–1000, have 5 executives above $1.5 million, and therefore could well have more than 5 total; some executives close to the threshold could have outside non-capital income that pushes them over the line, and so on. But there are nothing like an average of 20 people per company making more than this amount among companies of this size.)

Illustratively, a very aggressive estimate would be 100 people per company make more than $1.5 million in the top 100 companies; 20 people per company in the next largest 400 companies; 10 people per company in the next 500 companies (where, remember, we count an average of 3–4 people per company at this income level from proxies); and 5 people per company for the remaining roughly 4,000 public companies. This adds up to 43,000 people, or 29 percent of the count of those in top 0.1 percent. These assumptions are very aggressive, and we are still nowhere near Piketty’s assertion of 60 to 70 percent.

Keeping this back-of-envelope estimate in mind, the details of the research that Piketty cites as evidence for this assertion are illuminating.

In 2005 (the most recent year reported in the paper), 42.5 percent of these top earners were “executives, managers and supervisors” in non-finance industries, and 18 percent were “financial professions, including management.” The other categories are not those to which Piketty’s model realistically applied – things like lawyers, doctors, “business operations” (at this level of income, basically high-end management consultants), entrepreneurs and so forth. 42.5 + 18 = 60.5 percent, so thus far it looks like evidence in favor of Piketty’s claim.

But down in the addendum to Table 3, the paper breaks out the non-finance “executives, managers and supervisors” into those who work for closely held companies versus those who are “salaried.” Basically, the salaried are those who work in the classic public company with a distributed shareholder base and elected board of directors that is purportedly subject to gaming by Piketty’s bargaining model. Of the 42.5 percent, 23.6 percent work for closely held companies, leaving only 19 percent who are salaried. “Finance professions” are not broken out in this way in the paper, but even if we assume that they have roughly the same split between closely held and salaried (and given the structure of the high end of the finance industry, this likely over-estimates the number of salaried earners), this would mean another 8 percent of the top 0.1 percent would be salaried. Adding these two together, we have about 27 percent of the top 0.1 percent to which Piketty’s model could realistically apply. So, a careful reading of the paper Piketty cites results in an estimate closely in line with the prior estimates I made.

So, to be clear, however you estimate it, Piketty’s theory doesn’t even apply to something like three-quarters of top 0.1 percent.

Which brings us to the second problem.

One could argue that the top executives of public companies set the tone for compensation, which then propagates out to other professions. They are like the locomotive pulling the train. The big problem with this theory is that salaried executives are the one group that has had a collapsing share of the top 0.1 percent over the past several decades.

By the narrowest definition, reading straight from the addendum to Table 3 in the paper, salaried executives in non-finance industries were 32 percent of the top 0.1 percent in 1979, and declined to 14 percent in 2005. This is, by a long shot, the biggest absolute loss in share of any group reported in the table. By the broader definition I established earlier (all salaried employees in non-finance industries plus the estimated salaried employees in finance), those large company employees subject to Piketty’s asserted mechanism of gaming the comp system declined from 47 percent of the top 0.1 percent in 1979 to the 27 percent in 2005 cited earlier.

Who is grabbing this share that these large company employees are giving up? It’s not predominantly lawyers, doctors, entrepreneurs, and the like, but rather, mostly executives, managers, and supervisors of closely held companies, and finance as an industry (again, without a breakout in the paper between public and closely held companies).

In summary, according to Piketty, top managers of public companies are driving the explosion in executive comp among the top 0.1 percent, despite being something like one-fourth of the people in it, and despite being the exact group that is rapidly losing share to those who are not subject to the bargaining model he asserts.

And this brings us to the third problem: Piketty’s description of how top executives of large companies have gamed their own compensation is extremely naïve, and his evidence for it is extremely weak, even among the small group to which it could theoretically apply.

As I indicated earlier, Piketty makes a huge deal of the fact that as a realistic matter we can’t measure executive productivity in the way that we can measure the output of a manufacturing line. This is undoubtedly true. What is more questionable is his resulting assertion that this means that increases in executive compensation over the past several decades have been the result of “lower marginal tax rates encourage[ing] executives to negotiate harder for higher pay.”

In his book, Piketty cites a key paper that he co-authored as evidence for this assertion. In it, he evaluates the causes of increasing public company CEO pay, In Piketty’s paper, he cites macro evidence for the U.S., then international macro evidence, and then micro evidence based on CEO pay. 

Here is the conclusion of his section on macro U.S. evidence: “Therefore, this evidence based on a single country is at best suggestive. Hence, we next turn to international evidence.” 

Here is his conclusion of that section on international macro evidence:

As an important caveat, those regressions rely on a very strong identifying assumption, namely that any deviation of GDP growth from its trend not caused by top tax rates is uncorrelated with the evolution of top tax rates. Many potential factors could invalidate this assumption. . . . To provide more compelling evidence, we next turn to micro evidence using CEO pay.

So, by Piketty’s own reasoning, none of the macro evidence is sufficiently compelling. 

We then turn to the micro evidence of CEO pay. (I’ll note in passing that any evidence presented under this rubric can cover no more than about 5,000 people in the U.S. – so even if we were to accept the forthcoming evidence, it would be relevant for about 3 percent of the people in the top 0.1 percent.)

In this section, Piketty uses a methodology presented in a well-known 2001 paper by Bertrand and Mullainathan. In effect, Piketty (as did the 2001 paper) builds a regression equation which evaluates whether CEO-pay increases for companies that were in industries that experienced overall improvement, even if the CEO of that specific company did not improve versus industry peers. Both papers term this “pay for luck,” and conclude that it is evidence that CEOs have gamed the compensation system.

The problems with this kind of methodology are enormous. Start with the observation that you have a few hundred data points as the raw data upon which you are trying to build a theory that explains a fairly complex human behavior. As I’ve described in more detail in a prior article on CEO compensation, the whole process of decomposition of sources of variance cannot be definitively established by such an approach.

And amusingly, at the end of the section on the empirical validation of his model for CEO pay, Piketty has this to say about his empirical test of this theory: “Naturally, this test is not definitive as luck shocks could affect differently the productivity of CEOs vs. other workers. Hence, the possibility remains that CEOs’ true marginal product of effort could vary with the performance of the industry.” In other words, as with the prior two lines of evidence, he can’t rule out an obvious alternative theory that would also explain the data – in this case, that it may be that when times are booming in an industry, it’s worth more to keep the CEO on board. In fact, there multiple papers that provide evidence for exactly this effect this that is as strong (or really, as weak) as Piketty’s.

Further, there are numerous other plausible theories for rising CEO pay, including agency explanations, the managerial labor market, technological shocks driving corporate strategy and change, and misperceptions about stock options. One of the clearest is that between 1980 and 2003 U.S. CEO pay increased by a factor of six, and over that same period, large company capitalization increased by . . . a factor of six. This makes sense if you think that the CEO will now affect, to whatever degree CEOs affect things, six times as much economic value. Piketty’s response to this very widely discussed result was:” The problem is that this theory is based entirely on the marginal productivity model and cannot explain the large international variations observed in the data…” But Piketty has previously described the U.S. as the land of “meritocratic extremism,” and so this is hardly an argument for why this would not apply to the U.S.

Other than this passing and unpersuasive comment down in a footnote, Piketty confronts none of this. And beyond not considering realistic alternative explanations for rising CEO pay, Piketty asks the wrong question to test the idea that CEOs have gamed the process, which is not, “Are CEOs paid for marginal productivity?” but more practically, “Would shareholders make more money if CEOs were paid less?”

Piketty argument that CEOs are “paid for luck” because they are granted options or restricted stock that pays out for them even if they are just riding an overall industry wave, would be better stated from a shareholder’s point of view as, “Would paying the CEO with performance-indexed instruments make the shareholders better off than paying with straight options or stock?” He doesn’t consider the well-known problem that indexed options and other similar methods can create a large accounting charge, and this can outweigh other advantages. He doesn’t consider that attractive CEOs can quit at any time, and that it is often when an industry gets hot that they will have the most tempting other offers, and therefore it can be wise to make sure they are well-compensated even if this looks like luck. He doesn’t consider that in some cases identifying an ex ante peer group is simple, and in other cases, it is very unclear.

Most crucially, he doesn’t really consider the details of the employment contracts that he is characterizing at an abstract level in his model. At the end of 2006, the SEC mandated the disclosure of relative performance evaluation in CEO compensation. Recently, a couple of enterprising academics used this data to construct what is a direct test of Piketty’s hypothesis. Their conclusion was that there is “little evidence” to support hypotheses based on managerial power. What explains why firms use more or less of the strategy of tying CEO pay to indexed performance?  The degree of uncertainty in establishing a peer group.

Piketty, in his own words, has lines of evidence for his theory of why CEO compensation has increased so much that range from not-compelling to not-definitive. He has ignored obvious alternative explanations, and has ignored data and analysis that contradicts his theory.

In summary, Piketty has weak evidence to support his theory for why CEO pay has increased in America. What evidence he has covers only CEOs of public companies, and hence about 3 percent of the top 0.1 percent. His whole model, even if correct and extended beyond what is supported by the evidence could only apply to about one-fourth of the top 0.1 percent. And this very group that he claims is responsible for driving income inequality in America is collapsing as a share of the top 0.1 percent.

Piketty’s explanation for rising inequality in America plays to many people’s predispositions, but he has no real evidence that it’s true. Therefore accepting the predictions he makes for the effect of his policies would be incredibly dangerous.

Piketty, like the proverbial economist in an old joke, has addressed the problem of how to open a can of food when stuck on a desert island with no tools by assuming the existence of a can opener – just tax away the large incomes with no significant trade-off or cost. We are stuck, unfortunately, with a problem that doesn’t have such an easy answer: How do we maximize the amount of innovation and growth we achieve while minimizing the social disruption that this causes?

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