Why is the labor share of income declining? An informal meta-analysis

Seven years ago, Thomas Piketty’s Capital in the Twenty-First Century landed on coffee tables across the English-speaking world. With his proclamations about the rise of the rentier class, newfound attention was devoted to the divergent incomes of laborers and capitalists. Google trends data confirms the post-2008 surge in focus upon terms like inequality, labor income, and the median wage. Within this broad category of “concerns about the income distribution,” there are three primary issues:

1) The declining labor share of income.

2) Rising income inequality.

3) The growing gap between productivity and the median-wage.

Each of these phenomena deserves its own investigation; here I’m going to focus on the first issue — labor’s share of income — though there is inescapable entanglement between all three.

What is the “labor share of income”? It is Marx’s favorite economic statistic: it indexes the division in economic reward between toiling labor and idle, acquisitive capital. The idea being that all of the income in an economy should be divisible between that which accrues to capital, and that which accrues to labor. Labor income is the total sum of wages; capital income is the total sum of payments for capital — machines for a factory, office chairs, and cloud storage all count as capital. Any expense of firms which isn’t a salary payment, is a capital payment.

In practice, the economy doesn’t quite work in such a stylized manner. Firms make profits, which is revenue in excess of payments to capital and labor. The world we live in is not one of perfect competition. Big shocker, I know. But in some ways, profits can still be thought of as payments to capital, since profits are usually either re-invested into production capital, or re-distributed to firm shareholders — by definition, “capitalists.”

Compared to income inequality or the gap between pay and productivity, the labor share is a less important indicator of people’s actual economic livelihood. Even if labor takes in a decreasing share of national income, if everyone holds more stocks, or the government gives out increased benefits to all, it might be that no one is worse off than they were in the previous status quo. Income inequality (if you take into account taxes and transfers) is a measure of who gets what in the outcome of the economic production process. Conversely, the labor share can be thought of as a way of thinking about the structure of economic production. It tells us how different inputs are used to produce all the goods and services that make our world spin. If your goal is purely to “understand how the economy works,” the labor share is more informative.

From a policy-making perspective, learning about the labor share helps one think about how taxes and transfers should be designed so as to achieve a desired realization of inequality. It is an input into the system of “what determines people’s economic well-being”; an input that should be coordinated with the levers policy-makers can pull.

Anyway, enough about why you should care about the labor share of income — please do care! The question du jour is what is up with the labor share, why is it declining?

Unsurprisingly, leagues of macroeconomists, after noticing this trend, have assembled datasets, ran marathons worth of regressions, and proffered their explanations to the world. And even more unsurprisingly, they do not all agree. Not at all.

Here is a sampling of sentences from some of the premier macroeconomists in the field today, each purporting to explain the declining labor share.

From Anna Stansbury and Lawrence Summers: “In this paper, we estimate the magnitude of the decline in worker rent-sharing in the U.S. over recent decades, [and] show that it is large enough to be able to explain the entire decline in the aggregate labor share…”1

From Daron Acemoglu and Pascual Restrepo: “our single index of automation...explains 50% of the variation in the change in labor shares and task displacement across industries.”2

David Autor and co-authors (wisely) hedge by producing a few different estimates, which include the following: “By this measure, rising concentration can account for about half of the fall in the labor share” and, more boldly, “using the production function based measures of the markup, we account for essentially all of the labor share change.”3

[Italics mine in all of the previous quotes.]

Those are just three examples of straightforwardly contradictory hypotheses about the declining labor share, all published within the last three years — many more could be found. Across the literature, seven(!) primary explanations have been proposed for the declining labor share:

1) The rise of new capital technologies. These “new technologies” could be explicitly machines that automate jobs that workers used to do, or simply more efficient investment goods, which cause firms to invest more in capital, and require less labor input. If a bunch of firms are spending money on cloud storage that previously would have been spent on workers, that could cause the declining labor share. Some papers focus on automation, some on cheaper investment goods (cheaper=more efficient); both are prominent hypotheses.4

2) Globalization and off-shoring. If the labor input into production can be more cheaply outsourced to developing countries (where wages are lower), it could be that the “capital-intensive” parts of production locate in developed countries like the US, leading to a drop in labor’s share.5

3) Rising firm “market power.” Firms can have product-market power or labor market power. Product market power comes from monopolistic or oligopolistic structures: one firm, or a few firms, are the exclusive producers of some good, allowing them to price the good at a higher cost than would exist in an alternative, competitive world. Higher prices lead to greater firm profits, which, if returned to shareholders, can lead to a lower proportion of income going to labor. Labor market power is when there is a shortage of firms hiring workers in some region, giving the existing firms excess power to set, and suppress, wages.

Both market power explanations have been suggested for the labor share decline.6

4) Decreasing worker power. Stansbury and Summers (2020) provocatively asserted that declining worker power, not rising market power, is the underlying factor which explains the labor share evolution. In some sense, worker power and firm market power are inverses — as one rises the other falls — but they can be distinct drivers of change in wage outcomes. The most obvious sign of worker power is unionization rates—unions give labor increased bargaining power; but there are other contributors to worker power, such as the enforcement of laws surrounding overtime pay, laws about working conditions, or the level of the real minimum wage.7

5) “Super-cycle” effects: as far as I can tell, only two publications focus on super-cycles — this McKinsey report, and Kehrig and Vincent (2021). But each argues that super-cycles are the main explanation of recent labor share trends! Super-cycles are transitory demand shocks to certain sectors, like it just so happening that minerals rose in price because of greater demand from China in the past 20 years. If you want to understand the difference between academic economics’ approach to understanding the world and leading business analysts, just compare that McKinsey report with the way this Acemoglu paper looks. Interpret that as you will!

6) Measurement issues. This is a large category of explanation, with many different proposed measurement problems being responsible for the supposed decline in the labor share. I am about to get into this issue in fuller detail, so will hold off on excursus for now.

7) Increased ability of firms to measure worker productivity. This explanation has not seen much play in the literature but was counter-offered by Tyler Cowen in his comment on Stansbury and Summers. It also is theoretically defended in Bental and Demougin (2010). Under Cowen’s interpretation, firms are now better able to assess the varying quality of different workers, and therefore pay most workers less than before, since most workers do not contribute all that much to production. But a select subset of workers, perhaps 20%, — following the 80/20 rule — do have increased bargaining power, due to firms realizing just how much value they add. A benefit of this explanation is that it straightaway also helps explain growing income inequality.

Of course, the true explanation of what is going on is likely some combination of all of these factors. The economy, like most things, is a polycausal mess, and isolating the contribution of any one particular trend to a macroeconomic statistic almost inevitably comes with large standard errors. Not to mention the fact that these explanations are not wholly distinct; they interact in a bevy of potentially confounding fashions. Imagine a world in which increased automation decreases labor bargaining power; decreased bargaining power leads to a decline in unionization; lower unionization rates allow firms to get away with higher markups; more profits give firms the market power to start building barriers to competition; those barriers are sustained by weaker anti-trust law; firms now have excess money to invest, which they direct towards improved worker-monitoring, further decreasing labor’s bargaining power, and lowering employee compensation. What, then, explains the decreasing labor share? There is a reason the philosophical literature on “causation” is ten fathoms deep!

Yet, these are reasons for circumspection, not reasons to abort the investigative mission. Science must march on! Or, at least, the academic-industrial complex must continue churning out citations in order to preserve their labor share.

My aim in the rest of this post is to try and compare these differing explanations and offer some story about what is going on.

To preview: after taking a machete through the overgrowth of a few measurement issues, it turns out the object of interest is a ~6% labor share decline, experienced solely in the US, and only since 2001. A melange of factors lies behind that change in labor’s share, but, once the scope of the labor share change to explain is so narrowed, we know that the foremost cause must be a US-specific trend. Which leaves us really only with market power and worker power as the two candidates on offer.

In line with Stansbury and Summers, I will argue that declining worker power, far more than rising market power, is the primary driver of US labor share change. But not taken on its lonesome. Only when the interaction between declining worker power, rising software usage, and better productivity measuring is accounted for, do the finer details of the labor share evolution begin to solidify. Showing why that is so is my task in the rest of this post.

A 6% decline in labor share’s of income may not sound like much, but when considered as an economy-wide transfer of wealth away from workers, where that 6% is 6% of all American business revenue, it should begin to resonate.


I titled this post “an informal meta-analysis” to reflect my methodological preoccupations here. I am not well trained enough in economics to build some baroque theoretical model; nor do I have the data-savvy, or data sets, that would allow me to conduct a traditional “meta-analysis.” But I do believe there is a dearth in the literature of attempts to properly compare the existing explanations on offer, and try and synthesize them in a productive fashion.

As many a referendum on the replication crisis has pointed out, academic journals value shiny, new contributions above all else. In the case of something like psychology research, fetishizing the new leads to publishing flat-out incorrect results. In the case of understanding a macroeconomic trend of importance, exclusive attention to new contributions prevents the field from ever reaching any sort of consensus. In defense of econ, new data is continually emerging — making a stagnant consensus unlikely. But that doesn’t mean research should metastasize, ad nauseam. Rather than each paper trying to make the strongest possible case for its own contribution, more papers should evaluate how their contribution fits relative to other elements of the story.

Part of my thought process in this post is the belief that, when it comes to explaining something like “the decline in the labor share,” mathematical gymnastics is not of primary importance. The behavior of the labor share is an empirical phenomenon, where, if we can assemble the right data (a gargantuan if), we should be able to see the precise timing of when and where the labor share declined. With that information, if we also have data on when and where the differing explanations above took off, we should be able to make an inference to the best explanation. Coming up with precise quantitative magnitudes requires regression analyses, and theoretical models can provide useful discipline on proposed explanations — to make sure mechanisms can do what they claim — but the fundamental causal story should mostly follow from assembling the right data. In fact, I would venture to say that a convincing argument for what explains the declining labor share should be able to be made entirely graphically. Just by putting the right figures side-by-side, you would be able to see what gets started when, what gets started where, and make the appropriate inferences. As a result, my focus in the rest of this piece is going to be heavily figure-based.

Now, it may be that the “right” figures have not yet been made — there are undiscovered datasets, or new ways of constructing the data, that would be more telling than anything yet fashioned in the forge of STATA. That is an important caveat, and I will offer some thoughts on data in need of collection. But I do believe that just going by what is already out there, we can come to a reasonable assessment of what is going on.

Measurement issues, or, is the labor share even declining?

Surely one of the most annoying things about macroeconomic research is how important proper measurement of the variables of interest are. You can spend hours upon hours working through theories of some trend, only to realize that what accounts for the trend is not changing real-world patterns, but some varietal of mismeasurement. There is something that feels very “cheap” about measurement explanations, but in many cases, careful measurement really is what matters.

In the case of the labor share, before we start speculating as to why the labor share declined, it is essential to figure out when, where, and by how much it declined. Is the decline a US-0only occurrence, or a worldwide happening?

Karabarbounis and Neiman (2014) was one of the first papers to place the “declining labor share” under the microscope of attention, and it garnered interest, in part, because of the magnitude and the ubiquity of the decline it identified. They found that since 1980, the global labor share had declined 5%, with downward trends in 42 of the 59 countries in their dataset and a 6% decline in the US since 1975.8

Since then, at least a conference’s worth of papers have been written disputing various aspects of the measurement of the labor share. I am going to restrict my attention to a few more recent papers that I believe do the most to clarify the issue.

The U.S. vs. the Rest

Probably the most important paper in this whole measurement mess, if its claims are true, is Gutiérrez and Piton (2020).9 These three sentences from their abstract are almost all you need to know: “While the US excludes all self-employed and most dwellings from the corporate sector, other countries include large amounts of both —biasing labor shares downwards. We propose two methods to control for these differences and obtain ‘harmonized’ non-housing labor share series. Contrary to common wisdom, the harmonized series remain stable or increase in all major advanced economies except the US and Canada.” [bold mine]

And here is the telltale figure:

The black lines are their own measure, the gray lines are those of Karabarbounis and Neiman (2014). As they say, contrary to common wisdom, it turns out the global share is not declining! Which is a hugely important distinction — the factors that would explain a globally declining labor share are very different from what would explain a couple-country-specific decline.

The two relevant measurement issues are how to measure self-employment income, and which “dwellings from the corporate sector” should count as part of corporate income versus non-corporate income. Gutiérez and Piton’s major insight is that these income sources are not treated equivalently across the US and other nations. After standardizing the accounting,10 the decline in non-US labor shares disappears — a mirage that lured many a desert-weary researcher.11

A third factor, easy to overlook at first glance, is that Gutiérrez and Piton’s time-scale extends back five years earlier than Karabarbounis and Neiman’s data. Looking farther back, there was a notable rise in labor’s share of global income between roughly 1970-75. So, whether there has been a global “decline” or not depends on which year you take as your starting point for investigation. And whichever starting point is chosen, the US remains an exception.

Passthroughs

A conceptually similar problem to self-employment, this time US-specific, is how to treat the wages of “S-Corporations” and “partnerships” (from here on out, I am going to refer to these two types of income as “passthrough” income, for terminological convenience). The Tax Reform Act of 1986 made it more favorable with Uncle Sam to classify certain income as S-Corporation or partnership income. But that income still often goes to one or a few employees, functionally acting as their wage. So it is treated as capital income (S-Corps) or non-business income (partnerships), but should be counted as labor income. According to Smith et al. (2021), when you adjust for this tax chicanery, one-third of the decline in the corporate sector labor share goes away.

Note that they say “combining both adjustments” because they do separate adjustments for S-Corporation and partnership income. Taken from Figure 3 in Smith et al. (2021)

The red line is their preferred labor share series.12 Claiming to explain one-third of the labor-share decline, however, conceals an important discrepancy in the contrasting time evolution of the labor share, and time evolution of “how much the BEA labor share series misses out on passthrough income.” You’ll notice that the gap between the BEA series and the corrected series is 1.60% by the end of the data set. But if you look at the year 2001, the BEA labor share is ~.645 and the adjusted series is ~.655 — the gap is already one percent. So 62.5% of the “miscounted” passthrough income occurs from 1987-2001. Yet, the downward movement in the labor share happens entirely from 2001-2017; in fact, the labor share in 2001 is higher than it was in 1987. Using the tried-and-true method of squinting at a graph, this implies that only 9.09% of the actual decline in the labor share is accounted for by not counting passthrough income (calculations in footnote).13 If we introduce uncertainty around this, we can say that 6% to 12% of the post-2001 labor share movement is explained by leaving out passthrough income. By all means an important adjustment! —but nothing close to a complete account of why the labor share has declined.

Equity Compensation

Another issue in this terrain of “stuff that gets counted as capital income but is kindaaa labor income” is equity compensation. Startups are the obvious example — early employees often get most or even all of their compensation via equity; that is a different way of earning income, not a shift from capital—>labor. Some equity compensation is already included in existing measures of the labor share, but not all of it.14 Eisfeldt et al. (2021) attempt to quantify the role surging equity compensation plays in the declining labor share. Their grab-your-attention-in-the-abstract-line is that “including equity-based compensation in high-skilled labor income reduces the total decline in labor income share relative to value added by over 30%.” Alas, that glitteringly straightforward 30% cannot be taken and run with.

The “over 30%” estimate comes from a specific data set — the NBER-CES — which excludes any form of equity compensation in its measure of labor income. More frequently used when discussing the labor share is the BEA’s data set, which does count some equity compensation towards the labor share. To wrangle the BEA data, the authors first subtract an estimate of the amount of equity compensation already included, so that they can then add back their measure of total equity compensation. Here is the figure that results:

Discrepancies with Smith et al. from above are due to a restricted focus on non-service sectors (if you compare the two, you will see that the labor share of non-service sectors has declined more than the aggregate). In this series, including equity compensation accounts for 20% of the decline in the manufacturing-only labor share.

But once again, notice the differential in what happens between 1980-2001 and what happens from 2001-2019. The entire gap between the total income series and the wage (no-equity) series opens up by 2001: from 2001 to today, the two series maintain almost perfect equidistance.15 And this behavior is mirrored by the pure “equity-based compensation” series — it rises dramatically from 1990 to ~2001, but afterward stops increasing. Meaning that while miscounting equity compensation plays a significant role in misrepresenting the labor share trend from 1980-2001, it plays virtually no role in explaining the post-2001 behavior of the labor share.

Depreciation

Before we can get away to the promised land of engaging with “theories that hypothesize some sort of interesting change in economic conditions,” it is worth mentioning depreciation. A few papers have been written on how different accounting for depreciation affects the labor share trend, but, to abbreviate things, they don’t offer us much new perspective on the matter.16

The primary paper in this literature is Bridgman (2014). Even in his corrected net labor share series, there remains a ~6% post-2001 decline. Funnily enough, figure 1 in his paper shows that including depreciation bumps up the 1980-2001 labor share trend (around 1%), but does not alter the post-2001 series.

A US-only, post-2001 decline it is

Having surveyed the Gobi-desert-dry terrain of measurement issues, where are we left? Across the different figures presented thus far, if we restrict our attention to the corporate sector, there is a ~6% decline in labor’s net share of income between 1975 and 2011, with an ever-so-slight uptick since 2011. If you go farther back in time,17 the level of labor’s share was a few percentage points lower in the 50s and 60s, increased from 1970-80, maintained a slightly lower level from 1980-1990, decreased noticeably 1990-95, spiked again in the run-up to 2001, and has seen most, if not all, of its net downward movement since 2001.18

The two primary issues not included in that ~6% are passthrough income and equity compensation. As we have discussed, each contributes a good deal to labor share mismeasurement in the 1980-2001 range. In particular, the lower level of labor income from 1980-90 and the 90-95 downward trend are chiefly an artifact of not including passthrough and equity compensation. If included, the labor share in 2001 would be higher than it was in 1980.19 But, crucially, aside from a small contribution (6-12%) from passthrough income, the post-2001 labor share trend is not explained by any of these factors. And that post-2001 trend is just as significant a ~6% decline as was supposedly in need of explanation for the entire time horizon!

Whew. That is all for measurement. We are still left with a noteworthy labor share decline crying out for theorizing, but it is a US-specific decline, and a post-2001 decline at that. Taken together, those two facts go a long way in helping sift through the different hypotheses on offer for why the labor share has declined. Let’s start working through some implications for the different extant theories.

The worker power hypothesis timeline

Stansbury and Summers’ primary argument in favor of the declining worker power hypothesis comes from a “labor rent index” they construct. The idea here is that we can create some measure to approximate how much “rent” labor is extracting from a firm. Rent, used in this manner, is a tricky concept, based on the difference between the wage labor is being paid and the wage labor would be paid in a theoretical counterfactual world of perfect competition (where the wage-paying firm makes no profits). In order to measure in reality unobservable “rents,” Stansbury and Summers make use of the concept of “observably equivalent workers.” “Observably equivalent” refers to observation through econ-goggles: the classic data points of age, education, location, work experience, and anything else that fits in an excel column. Once you have established observational equivalence, you then look at the dispersion of wages across different firms: if within some firms, or certain industries, workers systematically receive higher wages, that suggests those workers are “rent-sharing.” They are either working with employers who make greater profits, and thereby can distribute more of those profits to workers, or workers within that firm/industry have more bargaining power than their equivalents elsewhere.

Stansbury and Summers’ overall labor rent measure combines three different indicators:

1) Union wage premia: how much more workers who are in a union make than non-union observationally equivalent workers.

2) Industry wage premia: how much more workers in certain industries make than observationally equivalent workers in other industries.

3) Firm-size wage premia: how much more workers at larger firms make than their observationally equivalent counterparts at smaller firms.

With data on these premia stretching back to 1982, Stansbury and Summers unveil the crux of their paper:

The inference they would like the reader to draw, of course, is that the decline in labor rents is responsible for the decline in labor’s share of income. But given what we know from our measurement section, this conclusion can be held in abeyance: while there is a systematic decline in the labor rents index from 1982-2001, there is no such decline in the labor share. You can already mostly see this in their graph, but if adjustments were made for equity compensation and passthrough income, the absence of co-movement would be even more pronounced. And further, 2/3rds of the decline in the labor rent share occurs before 2001; after 2001, the labor rent share declines by 2% (from 70%—>68%), but the labor share declines by 6%. So whatever was going on with labor rents from 1980-2001 did not meaningfully impact the labor share at the time (unless it was offset by some countervailing force?), and even if labor rents started to play some role in the post-2001 decline, they do not appear alone sufficient to explain the decline. It is worth noting that even if you do not make the equity and passthrough income adjustments, this problem persists. Which means that if labor rents did impact the labor share post-2001, some explanation must be concocted for why this influence only began in the post-2001 period.

But don’t discard worker power just yet

More appealing pieces of the worker power hypothesis pie are the state and industry-level regressions of labor rents on the labor share. Regression coefficients are uniformly significant, and the figures they adduce show much clearer relationships:

Not perfect by any means, and your typical correlation != causation disclaimer applies, but these charts at least point to their being common factors behind declining labor rents and declining labor share.20

Given this more fine-grained data, the fact that there is an economy-wide two-percent decline in labor rents since 2001, and the theoretical linkage between labor rents and the labor share — if labor rents go away and no other significant changes happen to the wage distribution the labor share must decline — it seems likely that declining labor rents are a contributor to the declining the labor share. Exactly how much of a contributor, we are not yet in a position to say. An advantage, in some sense, of the worker power hypothesis is that Stansbury and Summers’ labor-rent index is by no means a perfect tracker of true “worker power.” Solely looking at deviations from observationally equivalent workers making equivalent salaries leaves out the possibility that workers’ bargaining power is lower across the entire economy.

Before trying to polish our answer to “how much credit should the worker power hypothesis get” to a reflective sheen, let’s consider some of the alternate theories — starting with automation.

Robot apocalypse?

The primary proponents of the automation hypothesis are Daron Acemoglu and Pascal Restrepo. They have somehow combined to write twelve(!) different papers on the topic in the last three(!!) years.21 Given Acemoglu’s productivity on a range of other projects at the same time, it is entirely fair to wonder whether his interest in the topic of automation comes from having figured out how to automate himself without telling anyone.

But even with this dog cone of attention fixated on the topic, the papers have been theory-heavy, and the empirics they look at are mostly US-specific. This is a problem because the biggest hurdle to getting the automation argument off the ground is the cross-country evidence: automation is something that should have affected advanced economies in a similar fashion, a problematic caesura for those linking the US-only decline with automation.

Probably the strongest evidence Acemoglu and Restrepo present comes from this recent paper. They construct an industry-level “index of automation” — which includes a “penetration of robots” as well as “software and specialized equipment” measure — and regress it on industry-level labor share changes from 1987-2016:

The most important panel here is panel C — which passes the eyeball test! And when they run horse-race regressions of the automation index against import penetration, concentration, markups, and unionization, the automation index conquers all foes, consistently explaining ~50% of the variance in labor share.22 Issues can, unsurprisingly, be raised with these regressions: the automation index is a makeshift construct, creating room for biases to leak in; the industry labor share declines don’t account for equity/passthrough compensation; and it would be nice to see the regressions split into pre and post-2001 periods. Yet, since Stansbury and Summers never include a measure of automation in their regressions, the default here should be that automation is more explanatory than unionization.

What about the cross-country issue — is there a deus ex machina to save the robots? A troublesome paper for the automation hypothesis is Dauth et al. (2017). Look at this graph:

There are more robots per worker in the EU than in the US, and the rate of increase in robots has been greater in Germany than in the US. These are hard facts to fit with automation negatively impacting the US labor share but not other countries, including Germany. Dauth et al. do at least find a negative impact of robot penetration on wages, supporting the labor share effect channel, but again failing to fit with Germany’s overall trend. A puzzle piece is missing here, and I am making no progress on locating it.

Software, not hardware, silly

A more attractive tack in my mind is to focus on the discrepancy between robot penetration and “software and specialized equipment.” The Acemoglu and Restrepo figure above shows that the latter, not robots, has a stronger relationship with labor share changes. In their regression analysis, software and specialized equipment are broken up into their own categories, and software emerges as the winning horse — a.k.a., the largest coefficient.23 Focusing on software evades the otherwise confusing cross-country evidence on robots, and fits our proposed timeline, if software usage intensified post-2001.

But there is still a need for cross-country data that shows unique US exposure to software, on some dimension.

Aum and Shin (2020) provide more direct evidence for this interpretation. They break down US labor share trends into manufacturing trends and service sector trends. The manufacturing sector has seen a declining labor share since 1970, that accelerated post-2001; the service sector, meanwhile, had a rising labor share up until 2001 but has trended downward since. Together, a neat fit with the economy-wide labor share only beginning its descent post-2001.

And in tables 1 and 2, we (finally!) get two regressions on labor share change between 2000 and 2010, with import competition, intermediate offshoring, task offshorability, routineness, computer intensity, and software intensity as independent variables. In dramatic fashion, only software intensity emerges as statistically significant — and not by the hair of some p=0.09 business, but with a triumphant p<0.01. They run two regressions of this sort — one within manufacturing, the other within services — and both have the same pattern of results. Unionization rates aren’t part of this race, but, nonetheless, this is powerful evidence for “software intensity” being a key explanatory variable.24

To estimate magnitudes, we can look at the regression of labor share change on solely software intensity. The R^2 for the manufacturing sector is 0.45; for the service sector, 0.52. Directly, those numbers would imply that software intensity explains about 50% of the labor share movement. Correcting for all of passthrough mismeasurement occurring here (using passthrough’s post-2001 contribution 12% upper bound), adding some uncertainty due to equity compensation, and sprinkling in more general uncertainty that something is being mismeasured would reduce that estimate — say to the 20-50% range — but not eliminate it. Remember that none of these numbers are very precise, but that trying to come up with some numbers is better than simply avoiding the question! Rough numbers are like making your bed: they provide discipline [disclaimer: I don’t make my bed].

The argument against this attribution is the cross-country data: why should software intensity negatively impact the US’s labor share but not other countries? Once again, the only get-out-of-jail-free arguments here are either that the US had unmatched software intensity; that other forces in non-US countries increased the labor share and offset any software-caused decline; or that something about US firm-labor relations changed the way software exposure influenced wages.

I’m not aware of any evidence that exposure to software is higher in the US than in Europe, nor can I think of any particular economic headwind that affected global economies but not the US.

There are, however, a few candidates for the haecceity of the US software experience, vis-a-vis firm-labor relations. The frontrunner, in terms of the play it has gotten in existing accounts, is rising firm market power.

Concentration, 64, no repeats, or hesitations

Shifting the lens of focus from worker power to firm power brings us to the tangled realm of various market power hypotheses. In many ways, this is a distinct literature; examining it with appropriate depth would take us far afield. Lots more measurement debates abound, on what are the basic questions for even framing this issue: on whether or not markups are increasing; and whether or not concentration is increasing. If you follow the links I just scattered like balls upon a floor, you will find highly respected economists writing appendix-filled, robustness checked and double-checked papers that come down on either side of each issue. The fact that it isn’t even settled whether or not concentration is increasing is as if we weren’t sure whether unionization rates had decreased, or whether robot penetration had increased, yet were still trying to evaluate their impact on the labor share. A ripe set-up for creating some grand narrative of what is going on that has no connection to reality.

Rather than get into the weeds, I will pull them up, to clear the ground for a few summary comments. The following three points are, I believe, a reasonable summary of the current (uncertain!) consensus on concentration (I am not an expert on this literature, so please correct me if I’m wrong).

1) Industry concentration at the national level is increasing, while local sales concentration is decreasing.25 This makes sense if new technologies allow big firms to operate more efficiently at scale across the entire country, but must compete more fiercely within a given local market — since it is easier for non-local firms to expand into such markets.

2) The rise in national industry concentration accelerates somewhere in the 1997-2002 range; potentially matching the post-2001 trend break in labor’s share.26

3) Cross-country evidence supports the idea that there has been a distinct amount of increased concentration in the US.27

In conjunction, these three points are an enticing place to begin insinuating a connection between US concentration, software exposure, and labor-share trends.

Note that, within the “concentration is increasing and hurting the labor share” position, there are two further sub-groups: team good concentration and team bad concentration.

The “good concentration” story is what Autor et al. (2020) call the “superstar firm hypothesis”: internet technologies have created new economies of scale and network effects that allow a small set of “superstar” firms to increasingly dominate their markets, make more profits, and rely on capital at the expense of labor. But these firms are highly productive — they attain superstar status through their superior efficiency, thus making the economy as a whole better off.28

“Bad concentration” is Covarrubias et al. (2019)’s name for their version of things, where the rise in firm market power is due to weaker enforcement of anti-trust law, and higher barriers to entry for new firms that entrenched firms have erected. The proverbial “moat” that venture capitalists want their investments to have can be polluted water if powerful firms engage in anti-competitive practices, like stealing IP, or promoting their own products on a supposedly “free” marketplace.

Concentrating hard won’t solve this problem

Alrighty then, can either good or bad concentration explain the singularity of the US labor share? I’m afraid that, based on my consultation of an 8-ball, the answer is “outlook not so good.”

Covarrubias et al. supply no explicit regressions of changes in concentration on changes in the labor share; they merely note the concomitant rise of concentration and decline of the labor share. But, as we know, correlation does not causation make. Autor et al. do run the regressions of interest, which, when compared to the results of other regressions we’ve discussed, do not end up looking very impressive.

In lieu of simply repeating what is said elsewhere, consult Bivens et al. (2018)’s section on Autor et al.’s results for a good discussion.29 The upshot is that even with generous assumptions, concentration explains no more than 33% of the decline in labor’s share.30 But that is in regressions which do not control for trends in worker power or automation.

Acemoglu and Restrepo (2021) and Stansbury and Summers (2020) both include measures of concentration in their labor share change regressions, and both find insignificant, marginal effects when their own variables of interest are included.31 Stansbury and Summers determine that “the average [industry’s] increase in concentration can explain only around 10%” of the changes in labor’s share of income since 1997.32

Until I see evidence that contradicts this last point, it is hard to place too much weight on the concentration hypothesis. This figure from Stansbury and Summers is, arguably, all you need to see:

Compare that figure to the previous figures linking the labor share with automation or labor rents. Quite simply, the relationship is far noisier in the case of concentration!33

But what about rising corporate profits? Increasing markups? Declining investment? Don’t those trends point to an ossification of the market power of big businesses, propped up by lily-livered anti-trust enforcement and incessant, deep-pocketed lobbying for pro-business regulations?

There certainly is evidence to point to for all of those trends. It is likely that for some industries, market power has increased in nefarious ways — Stansbury and Summers’ 10% number only captures the average industry. But how much of the overall trend in labor share is explained by these forces is a different question.

Take profits, for example. From my reading of the evidence, it is genuinely unclear how much profits have increased, though some degree of increase seems to have occurred (also follow the links on markups). Assume that profits have increased. What lies behind that increase? Rising concentration — some of the good kind, some of the bad — is likely part of what is going on. Another element, more often ignored, and maybe more helpful in understanding the evolution of the labor share, is the rise of “super-cycles.”

Sneaky Super-Cycles

As a reminder: super-cycles are demand shocks to a particular industry/sector that drive up prices and profits for some time but don’t reflect longer-lasting, anti-competitive market power. In an increasingly globalized world, these types of demand shocks might be more potent in the energy and commodity sectors than in times of yore.

Super-cycles are most persuasively argued for in the aforementioned Mckinsey report, which attributes 33% of the labor-share trend to “super-cycles”, and in Kehrig and Vincent (2020), who focus on the role of super-cycles within manufacturing. Kehrig and Vincent’s paper is a magnificent investigation of what they call the “micro-level anatomy of the labor share decline.” The reason they fit in the “super-cycle” category is that they find low labor share firms are those “whose labor share fell as they grew in size” but that “they have only temporarily lower labor shares that rebound after five to eight years.”34 [Italics mine]

Their figure 9 starkly registers the super-cycle effect:

This figure is a lot to take in at first glance. If you look at the first panel, what you see is that in the five years prior to a firm falling in the “low labor share” category, they experience a dramatically falling labor share; but by five years after falling within the category, their labor share is barely lower than the average firm. Firms do not tend to sustain their low labor share status. They have transient bouts of a lower labor share when there is a surge in demand for their product. Kehrig and Vincent identify demand shocks as the driver because these meteoric flashes of low labor share status translate into higher prices and only a slight rise in employment. They further chronicle that in comparison to the 1982 start of their analysis (when the manufacturing labor share began its decline), since 2000, demand shocks have become more volatile, while employment responds even less to shocks than it used to.

What this analysis leaves out is the history of how demand shocks used to be responded to before 1982, and how they would have been responded to in the absence of automation and worker power trends. Did it used to be the case that when demand shocks occurred prices rose, but so did salaries, since workers had greater bargaining power? Or did it used to be the case that when demand shocks occurred, employment increased, but greater automation makes employment less responsive? Or is it simply that demand is more globally interconnected, cyclical, and winner-take-all than it used to be, and that neither labor-rent-sharing nor automation plays a role? Further micro-analysis of how differences in automation and unionization levels transmit to firm behavior when demand shocks happen could illuminate these questions, but for now, we are left in the dark.

A similar set of questions apply to the McKinsey analysis. They do less to catalog the precise, firm-level unfurling of super-cycle effects, but they have the advantage of looking at manufacturing and non-manufacturing sectors. Four sectors are singled out for having a labor share decline primarily due to super-cycles: mining and quarrying, construction, real estate, and coke and refined petroleum. In the case of the mineral and commodity sectors, they chalk up the rise in demand to China. Rising prices in these sectors were accompanied by rising output, almost one-for-one, pointing to a super-cycle mechanism.35

McKinsey treats super-cycle effects as distinct from labor bargaining power, but I’m not sure that is justified. Check out Stansbury and Summers’ sector-by-sector relative unionization decline figure.

The two biggest declines occur in manufacturing (which includes petroleum refining) and mining. Construction also sees a substantial — 40% — decline in its unionization rate. Meaning that, the sectors most influenced by super-cycle effects also saw major declines in unionization. I would be pretty darn surprised if that decline in worker bargaining power didn’t alter the way profits were distributed when demand shocks hit!36

So super-cycle effects are real, but how much they are an independent factor, or can be collapsed into worker power or automation stories, remains up for debate. I think considering them in further detail mostly lends support for the worker power hypothesis. Stansbury and Summers’ labor-rent index can’t capture the counterfactual of how much labor would have shared in profits in a world where labor rents had never declined. In that sense, strictly looking at the decline in labor rents since 2001 fails to incorporate the built-up contribution of declining worker power across the 1980-2001 period. Potentially, that legacy of declining worker power only started to really “hit” the labor share in the wake of spiking super-cycles.

Spinning around Software

Our task at the outset of venturing into “market power hypotheses” was to explain the effect of software intensity on the US labor share, via some unique software-to-labor market interaction. Have we accomplished that task? The concentration hypothesis certainly fits what we are looking for: an outlier trend in the US, with a plausible connection to software intensity — firms that use more software establish market power due to technology advantages, and thus make excess profits. But the evidence we scrutinized suggests concentration can only account for some, likely a minority, of what is going on with the software intensity —> labor share relationship. Recall that software intensity explained ~20-50% of the variance in labor’s share decline, while concentration was credited with a mere 10%.

Pairing the low end of software intensity estimates with a high end ~15% concentration estimate leaves concentration explaining most of what is going on; but if we take the “average” case, concentration is explaining <1/3rd of the reason software intensity hurts the US labor share.

And super-cycles are no savior on the software intensity front. There is a case to be made that the “super-cycles” in construction, manufacturing, and commodity sectors identified by Kehrig and Vincent and the McKinsey report were US-specific shocks.37 Therefore, they could explain something like 10-33% of the US labor share trend38 (with that credit being apportioned between changing patterns of automation, worker profit-sharing, and distinct super-cycle effects). Coming up with a linkage between super-cycles and software intensity is a more difficult chain to craft. None of the identified super-cycle industries are particularly software intense.39

Altogether, we’re still in a position of inadequately explaining software intensity’s association with the labor share.

A return to worker power

On its own, the “worker power hypothesis” is fairly capacious. All sorts of cultural norms, laws, and population characteristics can contribute to the bargaining power workers have. As such, worker power is something that can vary immensely country-to-country; and if focusing on firm market power was insufficient, focusing on worker power remains the most inviting avenue for understanding cross-country heterogeneity. Given the sweep of the worker power hypothesis, more baroque, stylized, and refined versions of it await construction.

Part of the motivation for a more intricate worker power story is that declining unionization is not a US-specific force. According to Schmitt and Mitukiewicz (2012), 20 out of 21 OECD countries they look at (Finland is the exception) have seen a decline in union membership from 1980-2007, and eleven of those countries saw larger declines than the US!40 And if you go back and look at the Gutiérrez and Piton cross-country figure from the beginning, you will note that many of these countries — such as Germany, Japan, Italy, and the UK — saw increases in their labor share since 1975. That is, to say the least, a bloody glove in need of not fitting to exculpate those defending the worker power hypothesis!

That being said, even with the dramatic declines in other country union membership, the US remained the OECD country with the lowest membership rates across the whole period — only Japan is even close. More pointedly, there are good reasons to think that unionization rates are not a great index of European worker power, since collective bargaining agreements function in place of unions in many European countries. It is also true that regulations in the US tend to be less labor-friendly than in Europe.

So perhaps the trend in US union membership only impacts the labor share in conjunction with lower absolute unionization and weaker accompanying labor institutions. Investigating the union wage premium in European countries and trying to construct similar “labor rent indexes” for non-US countries would help clarify this issue.

Regardless, worker power cannot be reduced to labor laws. Norms around how much CEOs make relative to workers, how dogmatically focused companies should be on turning profits for shareholders, how much of a problem inequality within a workplace is, and many other intangible, micro-norms about how workers should be treated influence companies’ final balance sheets. Relative to Europe, there is less concern about inequality in the US, and thereby, less advocacy for government redistribution — almost undoubtedly, these attitudes spillover into influences on wage-setting.41

The power of productivity monitoring

I think it is with these facts in mind that Cowen’s hypothesis — on firms increasing ability to measure worker productivity — begins to crystallize. Taken alone, there is no reason that increasing ability to measure worker productivity should be a US-specific trend, making it unfit to explain a US-only labor share decline. But when gulped down with a swig of special US wage-setting norms, it makes sense: better productivity measures create downward pressure on median wages, which in Europe are successfully resisted by fairness norms and labor power, but in the US, lead to lower median wages, greater income inequality, and a lower labor share.

Another essential piece of this story is that it is precisely software intensity that allows for improved productivity measuring. This is explicit in the case of something like a coding job, but also think of Amazon’s ability to measure warehouse employees’ work rates (which applies across many warehouse-based manufacturing jobs).

This story is unavoidably conjectural, unavoidably a bit of a “just-so” story; as far as I know, there is no measure of how well different industries/firms track worker productivity. But it fits a number of the criteria we are looking for, and quite nicely at that.

Productivity measuring or productivity itself?

A productivity measuring narrative can be complemented with a more traditional “skill-biased technological change” (SBTC) mechanism.42 SBTC is straightforwardly a theory of rising income inequality: technology changes such that there is greater demand for, and a greater premium paid to, high-skilled workers. The labor share changes in a similar manner as Cowen’s theory — software intense workers are made better off, yes, but the median worker ends up getting paid less. Aggregate payments to labor decline.43 The effect is restricted to the US because inequality averse Europe resists such stratification.

How to divvy up explanatory accolades between SBTC and productivity-measuring is not something I’m in much of a position to evaluate. If evidence could be found that labor share declines are equally pronounced in industries that primarily use software to monitor productivity (like warehouses) as jobs that demand software skills, that would be support for productivity-measuring over SBTC. Given that most jobs do not demand intense software skills, I would default to productivity-measuring being of greater import, but uncertainty here is of the Duke Ellington, Woody Herman kind: big bands.

Dare we conclude?

Somehow, we have wriggled our way into being able to tell a story about the US-specific decline of the labor share. From 1980-2000, the primary labor share trend of interest was a decline in manufacturing’s labor share, without an accompanying economy-wide decline. Increasing automation (robot-caused) and declining unionization likely were co-evolutionary: one begets the other, and visa-versa; together they caused the manufacturing decline. A small role could be assigned to import-competition, but all the recent regressions I’ve seen find little if any significance for import-competition variables.44 Workers who lost out on manufacturing jobs found new jobs in the growing service sector, which, due to its growth, was able to give a larger share of income to labor than beforehand.45 Some of this growth in service sector income is undercounted by time-series that leave out passthrough income and equity compensation; adjusting for them leaves us with an aggregate fluctuating but net trend-less labor share.

Things changed post-2001’s tech bubble burst: software proliferated, concentration surged, super-cycle shocks to construction and commodity sectors occurred, unionization continued declining, and cut-throat, pro-business management practices only grew in popularity. The infiltration of software led to greater worker productivity measuring and a premium for high-skilled software workers. Within the US, those trends resulted in greater income inequality and a worse off median-worker — in manufacturing and services. Some combination of fairness norms and pro-labor laws prevented those trends from impacting wages to the same degree in Europe. Concentration likely played some of its own starring role, and some of an interacting role with software intensity: service-sector businesses acquired new economies of scale, partly through software technologies — resulting in greater per-worker productivity, but lower total salary expenses.

Super-cycle demand shocks probably hit the US more acutely than other OECD nations. Firms responded to those shocks with higher prices, but not higher wages. Profits were for shareholders. If there were similar shocks elsewhere, disparities in labor’s bargaining power could have “hidden” those shocks through greater profit-sharing.

Alongside everything else, the steady erosion of worker power and ratcheting toughness of management took away from labor’s share of income in the US, across all comers: non-software intensive and non-super-cycle sectors included.

Finally, a small portion of the blame lies on mismeasured passthrough income — perhaps an indicator of rising income inequality, but, either way, liable for ~9% of the labor share decline.

Summing up, we have five initial buckets of explanation for the 6% post-2001 labor share decline: responsibility goes, 6-12% passthrough income, 10-33% super-cycles, 10-33% labor rents (as an independent, economy-wide channel), 10-15% concentration, and 20-50% software intensity. That gives us a range of 56-143% explained; a slight overstatement, because some of the concentration explanation “credit” likely interacts with, and overlaps with, software intensity. Further breaking things down, both super-cycles and software intensity demand a good deal of “worker power” analysis: I would guess that anywhere from 33-75% of the super-cycle profits could have been returned to labor in a nation of greater worker bargaining power; and that productivity measuring and SBTC interacting with software intensity accounts for all of the non-concentration based software intensity—>labor share co-movement.

This accounting leaves my story in a similar place to Stansbury and Summers — declining worker power is the primum movens. Compared to Stansbury and Summers, I orient attention to the post-2001 period, and I place greater emphasis on the interaction of informal norms with the rise of software and the existence of super-cycles. Unionization rates are still partially explanatory but must be supplemented with less tangible factors. One thing I haven’t examined is how much the level of the real minimum wage plays a role: some of the independent labor-rents channel is surely due to the gap between real minimum wage levels in the US and EU.

More generally, if you buy the Gutiérrez and Piton results46 — that (among major OECD countries) the labor share decline is a US-specific development — either a worker power hypothesis or a market power hypothesis is forced upon you. All of the other major explanations I can think of would fail to account for the singularity of the US’s labor share trend. As should be clear, I think Acemoglu and Restrepo are right that automation plays a role in the labor share decline; but unless Gutiérrez and Piton are wrong, I don’t see how automation can be the fundamental cause. I would also mention — as Stansbury and Summers point out47 — that insisting on automation as primary runs up against the fact of lower unemployment in the last 20 years. Many of Acemoglu and Restrepo’s papers stress the job-displacement automation induces: good luck squaring that circle with unemployment rates.

One side hypothesis related to automation that I haven’t seen mentioned elsewhere: I wonder if the interaction between automation caused job displacement and the US’s geography contributes (at all) to the labor share trend? The hypothesis being that mid-western manufacturing workers displaced from their jobs in the US would have had farther to travel for a good job in a big city than similarly displaced workers in Europe, making them less likely to make such a move, and more likely to settle for a middling job in their smaller town or nearby smaller city. I’m totally prepared to reject this idea but haven’t been able to find any academic literature on it, so I figured I’d toss it out.

Anyway.

The “story” I have offered here is just that: a story. Many of the individual pieces lack empirical corroboration. The whole ship would be capsized if one major measurement issue is off — firm market power could, in fact, be more important than worker power; or the US labor share might not even be declining! I’ve presented what I think is the best available account based on the existing evidence; by no means have I read every paper in this literature abstract through appendix. I may be placing too much weight on a few particular regressions using particular data sets that, if biased in some way, could jeopardize my entire reasoning. Any and all feedback would be appreciated.

Significance and policy responses

Everything outlined here fits within standard fare about the hollowing out of the middle class, escalating income inequality, and the swelling of a fissured labor force who, dependent on performative service jobs, cannot organize for a more equal distribution of corporate winnings.

Stansbury and Summers point out that from a policy perspective, the worker power framing of the labor share decline is dispiriting, relative to a market power perspective. If firms have too much market power, tried-and-true anti-trust legislation will make workers and consumers better off; but if the underlying situation is an imbalance between capital and labor power, one of the two parties must be made worse off, and no consumer boost comes with it on the side. Redistributing from capital to labor might still be a net good, and inequality telescoping, but it is not as glaringly beneficial as solutions to market power problems (and is likely to face wider political opposition).

To make matters worse, my version of things’ attention to more informal, cultural wage-setting norms, as well as “real” economic shocks like SBTC and Cowen’s productivity monitoring, are less policy-lever fixable than just encouraging unionization. The cultural norms, indeed, are not something you can take to the tailor for a quick hem. Changing them requires long-term activism, idea mongering, and the use of art and marketing to sway people towards a different vision of society. Responding to the “real” shocks that have hurt the average worker necessitates a deeper rethinking of how taxes and transfers and business regulations should work in a service-driven economy.

If there truly has been a ~6% decline in the US labor share in the last 20 years, that is a significant change to the balance of compensation in the American economy. A change that inevitably has had political implications; and a change that deserves consideration when crafting 21st-century policy.

Thanks to Tyler Cowen for feedback on this post.

References

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1

Stansbury and Summers (2020), p.1 [Page numbers refer to the version of the paper I link to, which is not necessarily the published version]

7

See, for an example of a discussion of these type of issues, Stansbury (2021)

8

See p.1 and figure 2 on p.36 of the linked working paper PDF.

9

Note that Cette, Koehl, and Phillipon (2020) offers a very similar analysis.

10

Self-employment income is ambiguous as to whether it should count as “labor” or “capital” — it really should depend on the type of self-employment — but in the absence of more detailed data, what is important is to standardize the way it is treated across countries. Gutiérrez and Piton do this in a way that includes self-employment in the labor share, but still have to rely on various estimation techniques of self-employment wages. If you believe that self-employment income should not be part of the labor share, that restores a global downward trend in labor shares, but still leaves the US looking unique, and therefore demanding its own explanation.

Adjusting for housing (corporate dwellings) is in line with Rognlie (2015), which documents how important housing is to the rise of the economy-wide capital share (see figure 3 if you follow the link). More and more value has gone to housing the past ~70 years, taking away from labor’s share of income. That pattern is critical for understanding how something like wealth inequality has evolved over time. But most people interested in the labor share are more concerned with how private sector firms allot their resources between labor and capital: thus, it is the corporate labor share that is the object of study, and Gutiérrez and Piton’s point is that some housing sneaks its way in to non-US accounts of the corporate share. This seems like a highly defensible adjustment to me, and I have not come across any response to their paper which disputes it.

11

What about Canada!? I’m not going to discuss Canada in the rest of this post. According to Williams (2021), when data sources that include “supplementary labor income” are used, the Canadian labor share has not in fact declined. I’m not in a position to adjudicate Williams versus Gutiérrez and Piton, but see the discussion on p.8/9 of Williams and his table 3 for more on this.

12

How much should we believe this modification? Their methodology is twofold: 1) to look at how much a firm’s labor share decreases in the year after switching from C-Corp to S-Corp status and correspondingly adjust the C-Corp labor share series to a counterfactual world where that labor share decline does not occur 2) to treat partnerships as C-Corps. Both fixes are entirely reasonable, and helpful, but do remain “just an estimate.” Table 2 and Table A4 in the appendix of their paper present a variety of different estimates, under alternative methods; they range from accounting for 20.6% to 40.4% of the labor share decline since 1978 — their preferred estimate is 32%. To be conservative, we could call it 15-45%.

13

In the period of declining labor share, the BEA series goes from .645—>.579, while the adjusted series moves from .655—>.595 (.595 picked to ensure the 1.6% gap). Which means that the BEA series declines .066 and the adjusted declines .060. The difference between them is .006, and 0.06/.066 gives us 9.09%. Alternatively, if you take their preferred estimate of how much of the labor share trend is accounted for by passthrough income — 32% — and multiply it by 0.6/1.6 (the amount of gap that opens post-2001), you get that they account for 12% of the post-2001 decline.

14

The exact details here are a bit confusing — see p. 7-9 of Eisfeldt et al. for more. The basic idea is that existing measures only count “non-qualified stock options” as labor income, when 1/3-1/2 of equity distribution are “qualified stock options” that are taxed as capital gains, and therefore included in capital income. Further, non-qualified stock options are only included in labor’s share when they are sold. Since the distribution rate of non-qualified stock options has continued to rise in recent years, that means there is now a larger chunk of as-yet-unexercised non-qualified stock options out there in the economy than there were five years ago, and the same is true of five years ago relative to ten, and onwards back in time; meaning that existing labor share measures underestimate the “true” labor share.

15

In 1980, both series are at ~.635. By 2001, equity=0.65, no-equity=0.575; by 2019, equity=0.51, no-equity=0.44 — all of the movement is between 1980 and 2001.

16

Koh et al. (2020) claim a very significant effect for miscounted “intellectual property products capital,” but they note within that their “preferred interpretation” of this mismeasurement “is the portion of IPP rents paid to workers in the form of equity.” (p.19 in just linked PDF) But this means that more direct measures of equity miscounting, like Eisfeldt et al., will tell us more about the true mismeasurement problem.

17

See figure 1 in Bridgman (2014) or figure G1 in the online appendix of Gutiérrez and Piton

18

I will discuss their paper more soon, but I want to credit Aum and Shin (2020) for emphasizing the post-2001 nature of the labor share decline.

19

I could come up with a more precise estimate here of how much higher, but any attempt to do so would likely be overfitting on what are already a series of uncertain estimates. Somewhere in the range of 2-3% higher seems likely based on the fact that there is a 1% gap between the passthrough included/excluded series, and that equity-comp explains 20-32% of overall behavior — 20-32% of a 6% decline being 1.2-2% undercounting. And then 1+1.2=2.2 (low end), 1+2=3 (high end), so 2.2-3% is a ballpark estimate.

20

One potential confounder is if states/industries that saw simultaneous declines in rents and labor share experienced those declines because of “rents” that got re-allocated to equity compensation. But for states like West Virginia and Indiana (on the left-side of the above graph), a rise in equity compensation does not fit my (admittedly armchair) impression of the types of businesses and industries that operate in those locales — providing support for a correspondence between labor rent and labor share declines.

22

See appendix Table A-1 of Acemoglu and Restrepo (2021)

23

Again see appendix Table A-1 in Acemoglu and Restrepo (2021)

24

One alarm bell to snooze here, albeit not turn off, is equity compensation. The worry is that software intensive industries are more equity-intensive, accounting for the software intensity—>labor share connection. But given our previous finding that equity compensation mismeasurement is concentrated in the pre-2001 period, this shouldn’t be too concerning. There is certainly some chance that equity compensation continues to be mismeasured in the post-2001 period and Eisfeldt et al. don’t catch it, but more likely is that there is a real effect of software intensity on the labor share.

25

Hsieh and Ross-Hansberg (2019) and Rossi-Hansberg et al. (2021) both find rising national concentration alongside decreasing local concentration.

Lanier, Yurukoglu, and Zhang (2021) also find decreasing local concentration, but run against the grain of the larger literature by finding decreasing national concentration as well.

26

See Figure 1 Panel A in Covarrubias et al. (2019) or Figure 4 in Autor et al. (2020)

28

Also see Ganapati (2021) for “superstar” evidence.

29

Bivens et al. (2018) also effectively demonstrate that labor market monopsony power on the part of firms is not a significant cause of the labor share trend.

30

Barkai (2020) finds greater significance of concentration in his regressions (unclear to me why/how), but controls for none of the other variables of interest.

33

This is not dependent on choosing top-20 sales concentration as the relevant measure. See footnote 58 of Stansbury and Summers (2020).

34

Quoted from their abstract.

35

See the trends in output and prices on p.29 figure 6 and p.35 figure 6.

36

More supporting evidence comes from looking at figure 2 in Acemoglu and Restrepo (2020), which shows that mining has had only a very small increase in robot usage — suggesting that worker power is primary when it comes to the mining sector labor share fall.

37

See footnote 28 on p.21 of the McKinsey report and Beyond the supercycle: How technology is reshaping resources, McKinsey Global Institute, February 2017.

38

I’m getting that estimate by taking the McKinsey 33% attribution as an upper-bound and simply adding in a good deal of downward uncertainty.

39

Some evidence that could be argued for here is that if you look at figure 2 in Acemoglu and Restrepo (2020), you will see that mining and construction both have experienced high IT-capital growth. But IT-capital does not equal software, and as Aum and Shin (2020)’s regressions showed, it is software intensity, not computer exposure, which has a significant relationship with the labor share.

40

Schmitt and Mitukiewicz’s numbers for the US union membership decline are slightly smaller than Stansbury and Summers’, but even if we use Stansbury and Summers’ private sector only measure for the 1980-2007 period, eight countries had larger declines than the US.

41

Someone might (reasonably) protest that this difference does not apply as much to the US versus Japan. This well may be true, but given the adverse economic circumstances in Japan in the last ~30 years, explaining why their labor share has not declined is an easier task: business have not grown enough to generate negative pressure against worker power (if true, this does indicate how linked worker power and market power are).

43

In Acemoglu and Restrepo (2021), they try and show that SBTC is not as powerful an explanation as automation by using fixed effects for different education levels and wage levels in 1980. Within that setup, they establish that automation is the dominant explanation. But I’m not convinced that setup is sufficient validation; it excludes the possibility that skill-variation within educational buckets has been the leading driver of SBTC (wage in 1980 is not a good enough measure of this).

44

For examples, see, among others, figure 6 in Stansbury and Summers (2020), table 5 of Acemoglu and Restrepo (2021), or the discussion on p.34 of Autor et al. (2020)

45

Why the service-sector labor share was rising 1980-2000 is something I would like to investigate in more detail.

47

Consult section IV of Stansbury and Summers (2020)