American Economic Review: Papers & Proceedings 2017, 107(5): 180–185 https://doi.org/10.1257/aer.p20171102 Concentrating on the Fall of the Labor Share† By David Autor, David Dorn, Lawrence F. Katz, Christina Patterson, and John Van Reenen* There has been an upswing of interest in eco- sectors such as wholesale, retail, and utilities, a nomics and the media over the decline in the pattern not readily explained by rising trade. share of GDP going to labor. The stability of Karabarbounis and Neiman (2014) instead the labor share of GDP was one of the famous emphasize that the cost of capital has fallen rel- Kaldor (1961) “stylized facts” of growth. The ative to the cost of labor, driven especially by macro stability of labor’s share was always, as rapid declines in quality-adjusted equipment Keynes remarked, “something of a miracle” and prices of information and communication tech- disguised instability at the industry level (Elsby, nologies. A decline in the relative price of capi- Hobijn, and Sahin 2013). Karabarbounis and tal will lead to a decline in the labor share under Neiman (2014) emphasize that the decline in the CES production functions if the capital-labor labor share is not confined to the United States elasticity of substitution is greater than unity. and occurs primarily within rather than between Although Karabarbounis and Neiman present industries. Although there is controversy over evidence that the elasticity exceeds unity, the the degree to which the fall in the labor share is bulk of the empirical literature suggests a much due to measurement issues such as the treatment lower elasticity (e.g., Lawrence 2015). Since of housing (Rognlie 2015) and intangible capi- changes in relative factor prices tend to be simi- tal (Koh, Santaeulàlia-Llopis, and Zheng 2016), lar across firms, lower elasticity, i.e. below unity, there is consensus that there has been a decline lower relative equipment prices should lead to in the US labor share since the 1980s, particu- greater capital adoption and falling labor shares larly in the 2000s. in all firms. In Autor et al. (2017) we find the Nevertheless, little consensus exists on the opposite: the unweighted mean labor share causes of the decline in the labor share. Elsby, across firms has not decreased much since 1982. Hobijn, and Sahin (2013) argue for the impor- Thus, the average firm shows little decline in its tance of international trade and find that the labor labor share. To explain the decline in the aggre- share declines the most in US industries strongly gate labor share, one must study the reallocation affected by import shocks. However, labor of activity among heterogeneous firms toward shares have also declined in most nontraded firms with low and declining labor shares. In Autor et al. (2017) we propose a new * Autor: MIT Department of Economics, Cambridge, superstar firm model that emphasizes the role of MA 02142 (e-mail:dautor@mit.edu); Dorn: Department of firm heterogeneity in the dynamics of the aggre- Economics, University of Zürich, 8001 Zürich, Switzerland gate labor share. We hypothesize that industries (e-mail: david.dorn@econ.uzh.ch); Katz: Department of are increasingly characterized by a “winner Economics, Harvard University, Cambridge, MA 02138 (e-mail: lkatz@harvard.edu); Patterson: MIT Department take most” feature where one firm (or a small of Economics, Cambridge, MA 02142 (e-mail:cpatt@mit. number of firms) can gain a very large share edu); Van Reenen: MIT Department of Economics and of the market. Large firms have lower labor Sloan School, Cambridge, MA 02142 (e-mail:vanreene@ shares if production requires a fixed amount mit.edu). This is a companion paper to Autor et al. (2017). of overhead labor in addition to a size-depen- We thank Daron Acemoglu and Jason Furman for help- ful discussions. This research was funded by the National dent variable labor input, or if markups in the Science Foundation, the European Research Council, the product market correlate positively with firm Economic and Social Research Council, the MIT Initiative size. Possible explanations for the growth of on the Digital Economy, and the Swiss National Science winner take most include the diffusion of new Foundation. † Go to https://doi.org/10.1257/aer.p20171102 to visit the competitive platforms (e.g., easier price/quality article page for additional materials and author disclosure comparisons on the Internet), the proliferation statement(s). of information-intensive goods that have high 180 VOL. 107 NO. 5 ConCentrating on the Fall oF the labor Share 181 fixed and low marginal costs (e.g., software imperfect competition, firms with larger market platforms and online services), or increasing shares will be able to set higher markups (e.g., competition due to the rising international inte- Cournot competition), also leading to a negative gration of product markets. New technologies relationship between firm size and labor shares. may also have strengthened network effects and In either case, when there is an exogenous favored firms that are more adept at adopting change that allocates more market share to a and exploiting new modes of production. small number of large superstar firms, the aggre- This paper exposits and evaluates two core gate labor share will fall as the economy shifts claims of the superstar firm explanation: (i) toward these low labor share firms. Autor et al. the concentration of sales among firms within (2017) formalize this idea in a simple superstar an industry should rise across much of the US firm model for a monopolistically competitive private economy; and (ii) industries with larger setting. Distinct from the prior literature, the increases in concentration should experience a superstar firm model emphasizes the heteroge- larger decline in labor’s share. neity of firms within industries as being critical for understanding the fall in the labor share. We I. Model next show that, in line with the model’s mech- anism, the concentration of sales across firms To see the intuition for a link between the within industries has grown in most US sectors. rise of superstar firms and a decline in the labor share, consider a production function II. Data and Empirical Findings Y = A V αL K 1−α L where Y is value-added, V is variable labor, K is capital, and A is Hicks-neutral We use data from the US economic census, efficiency ( TFPQ), which we assume is hetero- conducted every five years to enumerate all geneous across firms. There is a fixed amount establishments in select sectors on current eco- of overhead labor F  needed for production, so nomic activity. We focus on the economic census total labor is L = V + F. We assume that factor from 1982 to 2012 for six large sectors: manu- markets are competitive with wage w and cost of facturing, retail trade, wholesale trade, services, capital r being equal to the input factors’ mar- finance, and utilities and transportation. The cov- ginal revenue products, while there is imper- ered establishments in these six sectors account fect competition in the product market. From for four-fifths of total private sector employment. the static first-order condition for labor, we can For the six sectors, the census reports each write the share of labor costs (w L) in nominal establishment’s annual payroll, output, employ- value-added ( PY ) as ment, and an identifier for the firm to which the establishment belongs. To measure the con- (1) S = _w_L_ = _ α_L _ + _ _w_F_ _ , centration of sales within an industry, we use i (PY) μi i ( PY)i an output measure capturing total sales by the establishment during the survey year. To mea- where μ is the markup, the ratio of product sure sales at the firm level, we aggregate the sales price (P ) to marginal cost ( c ), and F is fixed of all establishments that belong to the same firm overhead labor costs. The firm subscripts i indi- and the same industry. If a firm operates estab- cate that for given economy-wide values of lishments in several industries, each combina- (α L , w, F ), a firm will have a lower labor share tion of firm and industry is counted as a separate if (i) its share of fixed costs in total revenues firm, capturing the firm’s separate contributions is lower or (ii) its markup is higher. Superstar to sales concentration in several industries. firms (firms with high A i ) will be larger because To implement our industry-level analysis, we they produce more efficiently and capture a assign each establishment in a given year to a higher share of industry output. Superstar firms 1987 SIC-based time-consistent industry code therefore will have a lower share of fixed costs as described in Autor et al. (2017). Our meth- in total revenues, and thus a lower labor share. odology yields 676 industries, 388 of which In monopolistically competitive models, the are in manufacturing. All of our measures use markup is the same across firms in an indus- these time-consistent industry definitions lead- try: μ = ρ /( ρ − 1) , where ρ is the price elas- ing to measures of industry concentration that ticity of demand. However, in other models of differ slightly from published statistics. The 182 AEA PAPERS AND PROCEEDINGS MAY 2017 Panel A. Manufacturing Panel B. Finance 44 75 35 60 42 40 70 30 55 38 65 25 50 36 34 60 20 45 1980 1990 2000 2010 1990 1995 2000 2005 2010 Panel C. Services Panel D. Utilities and transportation 16 28 40 64 14 26 62 24 35 12 60 22 30 10 20 58 8 18 25 56 1980 1990 2000 2010 1990 1995 2000 2005 2010 Panel E. Retail trade Panel F. Wholesale trade 30 6045 30 25 40 25 50 20 35 20 40 15 30 15 30 10 25 10 20 1980 1990 2000 2010 1980 1990 2000 2010 CR4 with sales CR4 with employment CR20 with sales CR20 with employment Figure 1. Average Top 4 Industry Concentration by Major Industry Group Notes: This figure plots the average concentration ratio in six major sectors of the US economy. Industry concentration is calculated for each time-consistent four-digit industry code as described in Autor et al. (2017), and then averaged across all industries within each of the six sectors. The solid line with circles, plotted on the left axis, shows the average fraction of total industry sales that is accounted for by the largest four firms in that industry, and the solid line with triangles, also plotted on the left axis, shows the average fraction of industry employment utilized in the four largest firms in the industry. Similarly, the dashed line with circles, plotted on the right axis, shows the average fraction of total industry sales that is accounted for by the largest 20 firms in that industry, and the dashed line with triangles, also plotted on the right axis, shows the average fraction of industry employment utilized in the 20 largest firms in the industry. Data for the financial sector in panel B and for utilities and transportation in panel D are available only since 1992. correlation between our calculated measures or the fraction of sales accruing to its 20 largest and those based on the published data is close firms (denoted CR20). Figure 1 plots the aver- to one, however, for periods without changes in age CR4 and CR20 across four-digit industries industry definitions. for our six sectors from 1982 to 2012. The level We measure the concentration of sales within of sales concentration varies considerably across an industry as either the fraction of total sales sectors. In each year, the top four firms in an accruing to its four largest firms (denoted CR4) average manufacturing industry capture more Top 4 concentration Top 4 concentration Top 4 concentration Top 4 concentration Top 4 concentration Top 4 concentration Top 20 concentration Top 20 concentration Top 20 concentration Top 20 concentration Top 20 concentration Top 20 concentration VOL. 107 NO. 5 ConCentrating on the Fall oF the labor Share 183 than one-third of the industry’s total sales, while Panel A. Top 4 concentration the top four firms in the average service industry 45 combine for less than one-sixth of total sales. There is a remarkably consistent upward trend 40 in concentration in each sector. In manufactur- ing, the sales concentration ratio among the top four increases from 38 percent to 43 percent; in 35 finance, it rises from 24 percent to 35 percent; in services from 11 percent to 15 percent; in utili- 30 ties from 29 percent to 37 percent; in retail trade 1990 1995 2000 2005 2010 from 15 percent to 30 percent; and in whole- Survey year sale trade from 22 percent to 28 percent. Over the same period, there were similar or larger Panel B. Top 20 concentration increases in CR20 for sales. To further characterize the emergence of 75 superstar firms, Figure 1 also plots CR4 and CR20 concentration measures based on firm 70 employment rather than sales. Again, we observe 65 a rise in concentration in all six sectors for 1982 to 2012, although employment concentration 60 has grown notably more slowly than sales con- 55 centration in finance, services, and especially in 1990 1995 2000 2005 2010 manufacturing. The pattern suggests that firms Survey year may attain large market shares with a relatively small workforce, as exemplified by Facebook Sales by domestic firms Including imports and Google. In Autor et al. (2017) we show that the two Figure 2. Industry Concentration Adding Imports main qualitative findings of Figure 1 are robust to the use of an industry’s Herfindahl-Hirschman Notes: This figure plots the average sales concentration in ( ) US four-digit manufacturing industries from 1992 to 2012. index HHI . Sales have become more concen- The line with triangular markers the average fraction of total trated in each of the six broad sectors of the US sales by domestic firms that is accounted for by an indus- economy. try’s four largest firms (corresponding to the CR4 Sales data A measurement challenge for our finding series in the top left panel of Figure 1). The line with squares of rising concentration for broad US sectors is markers the fraction of the total US market, defined as sales by domestic firms plus industry imports, which is produced that our concentration measures are calculated by an industry’s four largest “firms”, where each group of exclusively using US-based establishments. exporting countries is counted as an individual firm. Imports Thus, our measures include production by for- are based on UN Comtrade data as described in Autor et al. eign multinationals operating in the United (2017), and the six country groups are: Canada, Mexico/ CAFTA, China, low-income countries except China, States, but they exclude imports. A measure eight developed countries (Australia, Denmark, Finland, that includes only the market shares of US Germany, Japan, New Zealand, Spain, and Switzerland), producers may mischaracterize concentration and rest of the world. On average, 0.94 country groups are trends given rising import shares, particularly among the top four firms in panel A, and 2.7 country groups for manufacturing. are among the top 20 firms in panel B. We assess the importance of trade in the com- petitive structure of manufacturing by calcu- lating import-adjusted concentration ratios that concentration. The slightly higher level of the treat imports from major country groups as if adjusted concentration ratios implies that for- they belong to a single firm. Figure 2 plots the eign producers (such as China) account for a import-adjusted CR4 and CR20 measures along sizable fraction of sales in some manufactur- with the original measures only for US-based ing industries. Imports in such industries likely establishments. The series with and with- originate from a small number of major foreign out trade adjustment track each other closely, firms, but our data do not permit a firm-level reaffirming our main finding of rising sales breakdown of imports. 184 AEA PAPERS AND PROCEEDINGS MAY 2017 A further implication of our superstar firm 0.6 model is that the labor share should fall differ- 0.4 entially in industries that are experiencing larger 0.2 increases in concentration. Intuitively, the causal 0.124 force in our model is the shift in competitive 0 −0.14 conditions, which reallocates market share to −0.2 −0.238 −0.265 larger and more productive firms. Indeed, Autor −0.4 −0.366 −0.404 et al. (2017) document a strong negative rela- −0.6 tionship in the cross section between a firm’s −0.8 market share and its labor share. Thus, rising 87 92 97 02 07 12 19 19 19 20 20 20 concentration and falling labor shares should 2– 7– – – – –98 8 92 97 02 071 19 19 19 20 20 move in tandem, both in aggregate and between industries. Figure 3. Correlation between Changes in Labor Autor et al. (2017) test this implication by Share and Changes in Industry Concentration in the estimating bivariate regressions of five-year US Manufacturing Sector at Five-Year Intervals, 1982–1987 through 2007–2012 changes in the payroll share of value-added on the contemporaneous change in concentration Notes: This figure plots point estimates and 95 percent con- for the 388 manufacturing industries for the fidence intervals from Autor et al. (2017) for ordinary least years 1987–2012. Figure 3 (sourced from Autor squares bivariate regressions of the change in the payroll to et al. 2017) summarizes these regressions. In value-added share on the change in the CR20 index and a constant, estimated at the level of four-digit US manufac- the initial five years of our sample, we detect no turing industries and separately for each of the indicated significant cross-industry relationship between five-year intervals. Regressions are weighted by industries’ rising concentration and falling labor share. But shares of v alue-added in 1982. the cross-industry relationship between rising concentration and falling labor share becomes negative and significant in the next five-year interval, and grows in absolute magnitude across each subsequent interval. In the final period from barriers would enable incumbents to have higher 2007 to 2012, we estimate that each percentage monopolistic rents and therefore lower the labor point rise in an industry’s CR20 concentration share. index predicts a 0.4 percentage point fall in its In the first set of explanations, the industries labor share. We also observe a similar negative becoming increasingly concentrated will tend to relationship between changes in the share of be more dynamic with higher productivity and labor in sales and concentration in all six sectors. technical change. By contrast, in the second set Why has industry sales concentration of explanations, the concentrating industries are increased? One set of explanations involves likely to be dominated by less productive and a technological change that has made markets less dynamic incumbents. increasingly “winner take most” so that super- To shed light on these alternatives, we explored star firms with higher productivity increasingly the relationship between changes in concentra- capture a larger slice of the market. Or if incum- tion and changes in other industry character- bents are more likely to innovate and the per- istics. Data limitations restrict this analysis to sistence of incumbent’s innovative advantage manufacturing. We find that the industries that has risen (Acemoglu and Hildebrand 2017), became more concentrated over our sample the incumbent advantage would increase and so period were also the industries in which produc- would incumbents’ market shares. tivity—measured by either output per worker, An alternative set of explanations posits that value-added per worker, TFP, or patents per higher concentration could arise from anticom- worker—increased the most. Interestingly, there petitive forces whereby dominant firms are is no strong relationship between the change in increasingly able to prevent actual and poten- concentration and the change in average wages. tial rivals from entering and expanding (Barkai The findings suggest that a positive productiv- 2016). For instance, firms may lobby for regu- ity-concentration relationship will most likely latory barriers that complicate market entry/ feature in any plausible explanation of rising expansion for new and small firms. Higher entry industry concentration. Coefcient estimates VOL. 107 NO. 5 ConCentrating on the Fall oF the labor Share 185 III. Conclusions of Innovation: Facts and Theory.” http:// economics.mit.edu/faculty/acemoglu/paper. We have considered a superstar firm expla- Autor, David, David Dorn, Lawrence F. Katz, nation for the much-discussed fall in labor share Christina Patterson, and John Van Reenen. of GDP. Our hypothesis is that technology or 2017. “The Fall of the Labor Share and the market conditions—or their interaction—have Rise of Superstar Firms.” http://economics.mit. evolved to increasingly concentrate sales among edu/faculty/dautor/policy. firms with superior products or higher productiv- Barkai, Simcha. 2016. “Declining Labor and Capital ity, thereby enabling the most successful firms Shares.” http://home.uchicago.edu/%7Ebarkai/ to control a larger market share. Because these doc/BarkaiDecliningLaborCapital.pdf. superstar firms are more profitable, they will have Elsby, Michael W. L., Bart Hobijn, and Aysegul a smaller share of labor income in total sales or Sahin. 2013. “The Decline of the U.S. Labor value-added. Consequently, the aggregate share Share.” Brookings Papers on Economic Activ- of labor falls as the weight of superstar firms in ity (Fall): 1–42. the economy grows. The model yields many pre- Kaldor, Nicholas. 1961. “Capital Accumulation dictions that are elaborated and tested in Autor et and Economic Growth.” In The Theory of Cap- al. (2017). A key underpinning of the superstar ital, edited by F. A. Lutz and D. C. Hague, firm explanation for declining labor share is that 177–222. New York: Stockton Press. sales should become increasingly concentrated Karabarbounis, Loukas, and Brent Neiman. 2014. in a small number of firms across a wide range “The Global Decline of the Labor Share.” of industries. Consistent with the model, we find Quarterly Journal of Economics 129 (1): that the concentration of sales (and of employ- 61–103. ment) has indeed risen from 1982 to 2012 in each Koh, Dongya, Raül Santaeulàlia-Llopis, and Yu of the six major sectors covered by the US eco- Zheng. 2016. “Labor Share Decline and Intel- nomic census. In Autor et al. (2017), we further lectual Property Products Capital.” Barce- show that those industries where concentration lona Graduate School of Economics Working rises the most have the sharpest falls in the labor Papers 927. share, and that the fall in the labor share is mainly Lawrence, Robert Z. 2015. “Recent Declines due to a reallocation of labor toward firms with in Labor’s Share in US Income: A Prelimi- lower (and declining) labor shares, rather than nary Neoclassical Account.” National Bureau due to declining labor shares within most firms. of Economic Research Working Paper 21296. 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