The Relative Skill Demand of Superstar Firms andAggregate Implications∗

Anders Akerman†

July 31, 2018

Abstract: This paper proposes a new reason for why the relative demand for skilledworkers has increased over past decades. I suggest that increases in market concentrationand the rise of superstar firms may be important causes for the rise in demand for skill. I usedetailed employer-employee data for the Swedish manufacturing sector between 1997 and2014 to validate my hypothesis. My analysis demonstrates a strong correlation betweenfirm size and the skilled share of a firm’s worker mix. The slope of this relationship is atits steepest in the right tail of the size distribution. I also, as Autor et al. (2017b), find asubstantial rise in market concentration in Swedish manufacturing, both in the aggregateand across sub-sectors. The rise in market concentration is strongly correlated with a risein the relative usage of skilled workers. Furthermore, a majority of the change in skillusage is due to between-firm variation, a reallocation of production across firms. Thissupports the notion that market concentration, rather than a general skill upgrading acrossall firms, has caused the rise in skill demand. Finally, the reallocation of production wasmost pronounced in industries characterized by large increases in market concentration. Iestimate that about a tenth of the rise in the usage of skilled labor in Swedish manufacturingis due to the increasing importance of the largest firms.

Keywords: Relative Skill Demand; Skill Premium; Market Concentration; SuperstarFirmsJEL codes: D22; D33; D43; J24; J31; L13; L40

∗I gratefully acknowledge valuable comments David von Below and Nanna Fukushima, and researchfunding from the Torsten Söderberg’s Research Foundation.†Stockholm University, Department of Economics. Email: anders.akerman@ne.su.se.

1 Introduction

On August 1, 2018, the electronics producer Apple became the first publicly tradedcompany to ever attain a market capitalization exceeding 1 trillion US dollars. The rise of“superstar firms” has generated a recent literature and policy debate which focus on a risein market concentration over the past three or four decades. Autor et al. (2017a; 2017b)document that markets are increasingly concentrated in most US industries, and in manyother countries too. On a similar note, De Loecker and Eeckhout (2018) find that globalmarkups have increased over recent decades. This development may pose challenges forpolicy-makers and economists. Autor et al. (2017b) show, for example, that the share ofGDP that is paid to workers, the labor share, has dropped in industries and countries wheremarket concentration has increased. Market concentration thus appears to increase incomeinequality between labor and other production factors. Market concentration has beenargued to raise inequality between workers too, which is what my paper is about. Moreexplicitly I study how the relative demand for college-educated (henceforth “skilled”)workers changes when markets become more concentrated. I use data for the Swedishmanufacturing sector during 1997–2014, and find that market concentration is stronglyassociated with a rise in the relative employment of skilled workers and the share of thetotal wage bill that is paid to these workers. Sectors where markets are more concentrated,be it that the leading four firms have become more important in total sales or employment,or that the Herfindahl-Hirschman index (henceforth “Herfindahl index”) has increased,increase their use of skilled workers relatively more than other sectors. The share ofworkers in Swedish manufacturing that hold a college degree has, like in other countries,increased dramatically during recent decades – in my sample it has more than doubledfrom 9% to 22%. I estimate that around a tenth of this increase is due to increases inmarket concentration.

I therefore propose a new explanation for why the relative demand for college-educatedworkers has increased over recent decades (Katz and Murphy, 1992). I argue that increasesin market concentration, and the reallocation of production from smaller to larger firms thatthis means, raise relative skill demand since large firms systematically employ relativelymore skilled workers than smaller firms.1 The relationship in Swedish manufacturingbetween firm size and the share of skilled workers in employment is remarkably strongacross the entire support of firm size. If anything, the slope is steepest among firmsin the right tail of the size distribution. Therefore, if a rise in market concentrationreallocates market share from small to large firms in an industry, it should follow thatthe relative demand for skill in that industry rises. I observe this chain of events in the

1This is similar in spirit to the recent literature on market concentration and labor shares.

1

Swedish manufacturing sector. Between-firm changes are more important for changesin the aggregate demand for skill than for example within-firm changes or changes dueto entry and exit of firms. In other words, the increase in the share of skilled workersin employment has been mainly due to a reallocation of production across firms. Andthis has been a more important source of change than, for example, a rise in the averageemployment of skilled workers across all firms or from entry and exit of firms in a waythat is systematically linked with the relative employment of skilled workers. 2 Moreover,the between-firm component is strongly correlated with changes in market concentration.Reallocation of production away from firms using relatively fewer skilled workers to firmsusing relatively more of them is therefore especially high in industries where superstarfirms have become more powerful and concentration has increased the most. My analysisis based on linked employer-employee level data which is collected by the Swedish TaxAuthority annually, and which is generally considered to be of very high quality. I focusespecially on the manufacturing sector given the attention to this sector in the existingliterature and because of the strong global rise in market concentration in this sector asdemonstrated by Autor et al. (2017b).

Recent decades have seen rises in income inequality in wages in most countries.3 Fewwould question the importance of understanding why inequality has been increasing and ifit will continue. In the vast literature on this issue the two most important drivers of risingincome inequality typically mentioned are skill-biased technological change (that recenttechnologies are complementary to skill)4 and globalization (that increasing trade with oroutsourcing to relatively low-skill abundant countries will increase the relative demand forskill at home)5 or complementarities between these two effects such as in Bustos (2011).

2See for example Song et al. (2015) for more evidence on the importance of firms in determining thewage distribution. For analyses of this phenomenon in a Swedish setting, see for example Nordström Skanset al. (2009) or Akerman et al. (2013).

3See for example Atkinson (2015), Goldin and Katz (2001), Katz and Autor (1999), Piketty and Saez(2003) and Piketty (2014) for overviews and discussions). Attanasio and Pistaferri (2016) discuss howincome inequality translates into consumption inequality. Autor and Dorn (2013) demonstrate that labormarkets also become more polarized in addition to more unequal. See Fredriksson and Topel (2010), Roineand Waldenström (2015) and Nordström Skans et al. (2009) for descriptions of the Swedish labor marketand its institutions as well as the evolution of income inequality over time in Sweden.

4See Acemoglu (1998; 2002) and Hornstein et al. (2005) for a theoretical background and overviews onskill-biased technological change, and Goldin and Katz (1998) for a history covering a longer time period.Akerman et al. (2015), Autor et al. (1998) and Beaudry et al. (2010) provide specific examples of the effectsof broadband internet and the personal computer.

5See Krugman (2008) and Helpman (2018) for a summary of the subject and a literature overview. Autoret al. (2013) and Feenstra and Hanson (1999) provide specific estimates of effects of import exposure to Chinaand outsourcing, respectively. Helpman et al. (2017) show how the interaction between firm heterogeneityand trade participation creates a link between unemployment and globalization under more realistic labormarket assumptions than in original trade models on the topic. Michaels (2008) uses variation in trade accessfor rural counties due to exogenous components in how the US interstate highway system was expanded andanalyzes the effect on relative skill demand.

2

Other factors, such as changes in the minimum wage, the decline in unionization rates, orderegulation of labor markets, have generally not been found to contribute much to therising college wage premium.6 My finding that the rise in market concentration explainspart of the rise in the relative demand for skill provides a new explanation for why incomeinequality has increased in recent decades. Moreover, it appears likely that this explanationis quantitatively important. My contribution therefore suggests a new source for one of themost important economic developments in the past 40 years: increasing income inequalityand specifically the rise of the college premium.

The fact that market concentration has increased across markets and countries inrecent decades seems to be well-established by now. For example, Kahle and Stulz(2017) find that from 1975 to 2015, the number of top firms earning 50 percent of thetotal earnings of public firms in the US has decreased from 109 to just 30. Autor et al.(2017b) document a rise in several measures of market concentration across most U.S.industries and several other countries as well. They also find that the sectors experiencingthe fastest rise in concentration are those with fast technological progress. Grullon et al.(2018) document a rise in market concentration in 75% of U.S. industries over the last twodecades. They attribute it to, somewhat similar to what Autor et al. (2017b) find, largertechnological barriers of entry, but also to less aggressive antitrust enforcement. Moreover,this concentration appears to lead to higher markups. De Loecker and Eeckhout (2018)analyze more than 70,000 firms in 134 countries and find an increase in the average globalmarkup ratio from 1.1 in 1980 to 1.6 to 2016. Evidence also suggests that the increasein concentration is associated with a reduction in the labor share (Autor et al., 2017b,and Barkai, 2016). Given the body of evidence, I take as given that the rise of marketconcentration is a fact and, without analyzing why it occurs, instead focus on studying itsimpact on the relative demand for skill.

My paper’s methodology is close to that in Autor et al. (2017b) and intentionally so.While their paper documents a rise in market concentration across a multitude of industriesand countries and demonstrate that the inequality between labor and other productionfactors increases, my paper focuses on the inequality within labor, i.e. between workerswith and without a college degree. Using a similar methodology facilitates qualitativeand quantitative comparisons between the two phenomena. Section 2 discusses the datasources used and presents summary statistics. It also shows the evolution of aggregateskill demand and market concentration over time in Sweden. Section 3 shows the strongcorrelation between firm size and the share of employment of skilled workers. Section 4analyzes whether the changes in skill shares are systematically linked to changes in marketconcentration. Section 5 decomposes the change in aggregate skill demand and analyzes

6See Bourguignon (2015) for a review of evidence concerning these factors.

3

which components vary systematically with market concentration. Section 6 concludes.Appendices A and B contain additional tables and figures, respectively.

2 Data

2.1 Sources and summary statistics

The paper is based on registry data, collected by the Swedish Tax Authority, on the balancesheets of the universe of private firms in Sweden. I use data for the period 1997–2014.The main focus will be on the manufacturing sector although results for other sectors arereported in an appendix. I include only firms which employ at least five workers, since Iam interested in variation in the share of skilled workers in the number of employees andwages of firms. In the smallest firms there will naturally be less variation.

To calculate the share of workers in a firm that are skilled, I link the firm level data toindividual level data which contains information on both the education as well as annualincome for all workers employed by private firms during the sample period. In line withmost of the previous literature on the rise of the skill premium or the market for skill,I count workers as skilled if they have completed college education. My data thereforecovers the universe of firms and individuals in the private sector of Sweden. Its reliabilityand quality are regarded as very high since misreporting is punishable by law.

In addition, I use data from UN Comtrade on merchandise imports to Sweden. I usecross-walks from Autor et al. (2013) that link six-digit Harmonized System product codes(HS) to four-digit 1987 Standard Industrial Classification System sector codes (SIC87).I also use cross-walks from Eurostat’s Ramon server which link SIC87 to the EuropeanNACE rev 1 system (with four digits), which corresponds to the sectoral codes for Swedishfirms. I therefore observe sector-level imports in all sectors in Sweden, from all foreigncountries, during these years. I divide exporting countries into twelve broader groups, aswill be specified later, and aggregate the import volumes to these groups.

Table 1 provides descriptive data for the manufacturing industry in Sweden and showsthat it consists of 237 four-digit industries and 11,101 firms. The wages to sales ratiois remarkably similar to that reported by Autor et al. (2017b), 15.21 in my sample and15.24 in their sample for US manufacturing firms. Another similarity is that the wagesto sales ratio (the labor share) decreases throughout the sample period. Regarding theimportance of college educated workers in employment, I see that about a quarter of wagesof a representative firm are paid to skilled workers, and that almost a fifth of the workers areskilled. The difference reflects the skill premium: skilled workers are paid more than lessskilled workers. Moreover, skilled workers increase in importance throughout the sample,both in their share of wages and employment. Swedish manufacturing seems somewhat

4

Table 1. Descriptive statistics.

Mean Std. dev. Min Max

Manufacturing (237 industries, 4,080 observations)

Number of firms 11,101 546 9,967 11,732

Wages to Sales Ratio 15.21 5.62 1.03 97.85Change in Wages to Sales Ratio -0.01 1.95 -76.39 53.96

Share of Skilled Wages 23.39 16.42 0.00 80.55Change in Share of Skilled Wages 0.81 2.94 -50.05 60.23

Share of Skilled Workers 18.72 14.59 0.00 72.20Change in Share of Skilled Workers 0.80 2.69 -38.46 45.08

CN4 57.78 28.17 5.09 100.00Change in CN4 0.11 5.88 -60.11 67.42

CN20 84.18 19.91 19.09 100.00Change in CN20 0.07 2.74 -29.08 27.63

Herfindahl Index 24.83 25.07 0.39 100.00Change in Herfindahl Index 0.37 6.60 -73.71 75.06Note: Detailed descriptions of the variables are given in Appendix Table A.1. All numbers show weighted averages over four-digitsectors for the years 1997–2014, where the weights are 1997 levels of value added at the four-digit sector level. Appendix Table A.2.shows the corresponding values for two-digit manufacturing sectors. Appendix Table A.3. shows the corresponding values for othersectors than manufacturing.

more concentrated than its US equivalent. For example, the mean market share of the top4 firms is 58 percent in Sweden and 41 percent in the US. All three measures, the shares ofthe top 4 and 20 largest firms (CN4 and CN20) as well as the Herfindahl index indicatethat concentration rises throughout the sample. Appendix Tables A.2 and A.3 show theequivalent numbers for two-digit manufacturing sub-sectors and for non-manufacturingindustries, respectively.

2.2 Evolution of aggregate skill composition and market concentration over time

I display the evolution of market concentration in the manufacturing sector in Figure 1.The values I show are weighted averages across all four-digit manufacturing sectors wherethe weights are levels of value added in the first year of the sample. I plot the share ofsales and employment, respectively, that is accounted for by the four largest firms (CN4)and also the Herfindahl index based on sales and employment, respectively. When I usesales as a measure of concentration, I observe a steady increase throughout the sample.

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Figure 1. Evolution of market concentration in the manufacturing sector.Note: The sample consists of firms in the manufacturing sector during 1997–2014. For each year, I calculate for each four-digit sectorthe share of the four largest firms as well as the Herfindahl index and then calculate the overall weighted mean where the weights arethe 1997 levels of value added for each four-digit sector. I calculate values based on both sales (solid lines) and employment (dashedlines).

This is regardless of which concentration measure I use. I find an increasing slope forthe Herfindahl index also when I look at concentration of employment, but not for theimportance of the four largest firms. This difference between patterns for concentrationmeasures based on sales and employment is in line with the mechanisms I have in mind. Itis also similar to what Autor et al. (2017b) find for the United States. Appendix FigureB.1 conducts the same exercise at a more disaggregated level and plots the sales-basedconcentration measures for each two-digit manufacturing sector. I find that 10 out of14 two-digit manufacturing sectors experienced increasing concentration regardless ofmeasure used. Finally, Appendix Figure B.2 reports concentration measures also fornon-manufacturing sectors. While the retail sector, like manufacturing, experiences strongincreases in market concentration, patterns in the other sectors are less clear.

Figure 2 shows how the skill composition of workers in the manufacturing sectorevolves during the sample period. The increase is dramatic: the share of workers that havea college degree has more than doubled from 9% in 1997 to 22% in 2014. The share ofwages paid to skilled workers has also roughly doubled. Appendix Figure B.3 shows theincrease in two-digit manufacturing sectors and that the share has increased in all sectors.The same is true also for non-manufacturing sectors which can be seen in Appendix Figure

6

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Figure 2. Evolution of worker skill composition in the manufacturing sector.Note: The sample consists of workers for firms in the manufacturing sector during 1997–2014. For each year, I calculate the share ofworkers that have a college degree and the share of total wages that is paid to these workers.

B.4. The manufacturing sector has, however, seen the largest increase in proportionalterms, which is interesting given its large increase in market concentration.

3 Do larger firms employ more skilled workers?

The hypothesis of the paper is that market concentration affects the aggregate relativedemand for skill by reallocation production from firms using fewer skilled workers to firmsusing more. A requirement for this hypothesis is that larger firms systematically differfrom smaller firms in the skill composition of their workers. I illustrate the relationshipbetween size and skill intensity in worker composition in Figure 3. I divide all 199,824firm-year observations into twenty quantiles based on sales, and plot the mean share ofskilled workers in employment for each quantile in panel a). I observe a remarkably strongcorrelation between size and the skill intensity in employment. Only about 6 percent of theworkforce of the smallest firms has a college degree versus 17 percent for workers in thefirms in the highest size quantile. In panel b) I weight each observation by its value addedbut the pattern is the same. In panel c) I plot the weighted residuals after taking out sectorand year fixed effects and, if anything, the slope of the line seems to become steeper. Thisis true especially for the largest firms.

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Figure 3. Firm size and the share of skilled workers in employment.Note: I divide the manufacturing sample consisting of 199,824 firm-year observations into 20 quantiles based on annual sales andplot the mean share of skilled workers in employment for each quantile. In panels b), c) and d) I weight each firm by its value added.In panel c) I do not use raw numbers but instead residuals after taking out four-digit sector and year fixed effects. In panel d) I useresiduals after taking out firm and year fixed effects. Appendix Figure B.5 shows the same figures but uses the wage share of skilledworkers rather than the employment share. Appendix Figure B.6 shows that these patterns for the entire private economy.

A way to see if these differences across firms are stable across time or if firms insteadadjust the skill composition among their workers when the firms grow or shrink, is to look atresiduals after taking out also firm fixed effects. I show the results from doing this in paneld) and note that the differences are very small (although the slope is positive). Differencesacross firms therefore indeed seem to be the main cause for the patterns I observe in theprevious figures: variation in skill composition is mainly due to time-invariant differencesacross firms rather than firms changing their technologies when they change size. In fact,84 percent of the variation in the skill composition across observations is between-firmobservation and only 16 percent is within-firm variation. Finally, Appendix Figure B.5shows that these patterns hold also when I look at the wage share of skilled workers ratherthan the employment share. Appendix Figure B.6 shows that the patterns hold for theentire private economy and is not a unique characteristic of the manufacturing sector.

To see if there is a significant change over time in the relationship between size and the

8

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Figure 4. Firm size and the skill share over time.Note: For the first, middle and last year of the firm sample (1997, 2005 and 2014) I divide the observations into 20 quantiles basedon annual sales and plot the mean share of skilled workers in employment for each quantile, separately by year. All observations areweighted by value added and are the residuals after taking out fixed effects for four-digit sectors.

skill intensity of the workforce, I plot how this relationship evolves over time in Figure 4.All three series use residuals after taking out fixed effects for four-digit sector and year.The slopes do not differ dramatically, except perhaps towards the right tail where the slopeis steeper in more recent years. But since a correlation between size and skill intensity hasprevailed throughout the sample, a reallocation of production from the smaller to the largerfirms must mean that the aggregate utilization of skilled workers increases.

4 Skill composition and market concentration

I now investigate whether an increase in market concentration has increased the usage ofskill in production. I first plot a scatter diagram where I link overall changes during thesample period in the share of workers that have a college degree to the change in marketconcentration. I do this for two-digit and four-digit sectors, respectively, and look at thechange in the concentration among the four largest firms and the change in the Herfindahlindex. Figure 5 shows that there appears to be a positive correlation, regardless of whetherone looks at two-digit industries in panel a) or four-digit industries in panel b) or whetherone looks at the share of the four largest firms or the Herfindahl index. The industries

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Figure 5. Change in the share of workers with a college degree and change in marketconcentration.

Note: I calculate for each manufacturing industry the share of workers that have a college degree and the market concentration for thefirst and last year of the sample: 1997 and 2014. I then plot the changes in the figures where the size of the circles is determined bythe baseline value added of each industry. In panel (a) I use two-digit industries and in (b) I use four-digit industries. The straight lineshows a linear relationship between the two variables. This line is weighted by the baseline value added in each industry.

which experienced an increase in concentration relative to other industries therefore alsoincreased their employment of college-educated workers relatively more.7

The main specification for my regressions follows that in Autor et al. (2017b) and isthe following:

∆Yit = β∆Cit +dt + εit (1)

where Yit is one of my measures of the share of skilled workers in production in industryi and year t, Cit is the market concentration and dt are year fixed effects. I use yearlychanges in my baseline specification but also look at 2-year changes. The errors εit areclustered by industry which allows for correlation over time.

7Appendix Figure B.7 shows that an almost identical pattern applies when one looks at changes in theshare of the wage bill that is paid to college-educated workers instead.

10

Row 1 in Table 2 reports the results for the the baseline specification, both for the1-year and 2-year changes. I start by looking at the manufacturing sector. For each case,I report the share of the top four firms, the top twenty firms and the Herfindahl index. Iobserve for all cases positive and statistically significant estimates of the coefficient ofinterest. Industries that experience a relatively larger rise in market concentration thanother industries also experience a relatively stronger rise in the share of workers thathave a college degree. An increase in the rate of change in the concentration index byone standard deviation results in an increase of 13%, 10% and 15%, respectively, of astandard deviation in the rate of change of the share of workers with a college degreedepending on whether one uses the share of the top four firms in sales, top twenty firmsand the Herfindahl index, respectively, as the measure for market concentration. LaterI will also calculate the counterfactual share of college-educated workers based on themodel in 1 and under the scenario that concentration measures remain constant throughoutthe sample. I will then be able to compare the counterfactual levels with actual outcomesto quantify the importance of my estimates. In row 2 I add industry fixed effects, whichmeans that I use only changes in the rate of change, or, put differently, accelerations anddecelerations in the rate of change within four-digit industries. The coefficients are of verysimilar magnitudes, however, although the errors are slightly larger. In rows 3 and 4 Isplit the sample into two time periods to examine whether the patterns hold throughout thesample. The coefficients are largely similar, except for the effect of the Herfindahl indexwhich is more pronounced in the early period although the estimates are significant andreasonably large also in the second period. In row 5 I use concentration measures based onemployment instead of sales and find somewhat larger coefficients. Finally, I account alsofor imports since the Swedish market is served not only by domestic firms but also by firmsfrom abroad. Ignoring foreign supply may therefore lead to an exaggeration of the truelevels of concentration. I include imports from twelve blocks of countries and treat theseblocks as individual firms.8 Note that the imports therefore enter also the denominatorin the construction of the concentration measures since the total market is larger when Iinclude also the sales of foreign firms in Sweden. Row 6 reports these estimates and I notethat the estimates do not change substantially.

In Table 3 I report the estimates from equation (1) for the entire economy as well as forlarger sectors. I note that, although the magnitudes vary, the coefficients are positive for allsectors and specifications and in most cases also statistically significant. Precision is poorin the Utilities and Transportation sector but the magnitudes are not that different fromthose of the overall economy. The estimates are smaller in the service, retail and wholesale

8The blocks of countries are the following: Denmark; Norway; Finland; Germany; the United Kingdom;the rest of Western Europe; Eastern Europe including Russia; China; NAFTA; East and South-East Asia;South and Central America; and the rest of the world.

11

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rsto

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sth

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attr

ibut

edto

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larg

estf

our

(tw

enty

)fir

ms

ina

four

-dig

itin

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fers

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erfin

dahl

inde

xfo

ra

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ific

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cts.

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ow6

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udes

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rts

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uctio

nof

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less

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nd**

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ssth

an1%

.

12

sectors but the estimates are nevertheless mostly statistically significant.In Figure 6 I show the quantitative importance of the change in market concentration

in explaining the evolution of the skill composition among manufacturing firms. I add tothe baseline share of college-educated workers in the workforce the coefficients on thetime dummies in equation (1). I do this both with and without controlling for the changein market concentration. The values for the case when I control for the change in marketconcentration therefore give me a counterfactual level of the skill composition, in otherwords what share of workers would have had a college degree had market concentrationstayed constant. The values for the case when I do not control for the change in marketconcentration give me the actual outcomes instead. I see that the size of the differenceis somewhat sensitive to what measure of market concentration I use. The Herfindahlindex appears to be the most important concentration measure – in 2014 I see that theshare of college-educated workers would have been 24.2% instead of the actual 25.8% hadthe Herfindahl index remained at its 1997 levels among manufacturing industries. Thisaccounts for about 11% of the total increase in the share of college-educated workers overthis time period.

5 Decomposing aggregate changes into within and between firm changes

I have now seen that a rise in market concentration is associated with an increase in theshare of a sector’s college-educated workers. However, to see if this relationship is dueto a reallocation of production across firms, i.e. from smaller firms with less educatedworkers towards larger firms with more educated workers, I decompose the changes in theaggregate skill composition into within and between firm changes as well as changes dueto the entry and exit of firms. Between-firm changes must be quantitatively important ifreallocation across firms is an important mechanism.

I follow Autor et al. (2017b) to use the model in Olley and Pakes (1996) to divide thechange in the aggregate skill composition into, on one hand, changes in the unweightedmean across firms and, on the other hand, changes in the allocation of production acrossfirms. I also follow the extension by Melitz and Polanec (2015) to account for changes dueto entry and exit as well.

In line with Olley and Pakes (1996) I decompose the aggregate share of skilled workers,Y , in the following way:

Y = ∑i

siYi = Y +∑i(si− s)(Yi− Y ) (2)

where si denotes the share of firm i in an industry’s value added; Yi denotes the firm-level

13

Tabl

e3.

Reg

ress

ion

resu

ltsfo

rall

sect

ors.

Skill

edsh

are

ofem

ploy

men

tSk

illed

shar

eof

wag

ebi

ll

CN

4C

N20

HH

IC

N4

CN

20H

HI

(1)

(2)

(3)

(4)

(5)

(6)

N

1.A

llse

ctor

s0.

08**

*0.

09**

*0.

15**

0.10

***

0.12

***

0.17

**6,

058

(0.0

3)(0

.02)

(0.0

7)(0

.03)

(0.0

3)(0

.07)

2.M

anuf

actu

ring

0.11

***

0.12

**0.

18**

0.14

***

0.16

***

0.20

**3,

766

(0.0

4)(0

.04)

(0.0

9)(0

.05)

(0.0

5)(0

.08)

3.Se

rvic

es0.

050.

07**

0.11

**0.

040.

07*

0.10

*68

6(0

.03)

(0.0

3)(0

.05)

(0.0

4)(0

.03)

(0.0

6)4.

Util

ities

and

Tran

spor

tatio

n0.

130.

370.

200.

140.

330.

2140

6(0

.09)

(0.3

2)(0

.21)

(0.0

8)(0

.24)

(0.2

2)5.

Ret

ailT

rade

0.03

*0.

06**

*0.

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04*

0.09

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0.01

1,11

5(0

.02)

(0.0

2)(0

.03)

(0.0

2)(0

.03)

(0.0

3)6.

Who

lesa

leTr

ade

0.04

***

0.04

***

0.06

***

0.04

**0.

05**

0.08

***

85(0

.01)

(0.0

1)(0

.01)

(0.0

1)(0

.01)

(0.0

2)

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e:T

hesa

mpl

eco

nsis

tsof

allf

our-

digi

tind

ustr

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ng19

97–2

014.

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umns

(1)

to(3

)us

eas

depe

nden

tvar

iabl

eth

esh

are

ofw

orke

rsth

atha

vea

colle

gede

gree

whi

le(4

)to

(6)

use

the

shar

eof

the

wag

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llth

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paid

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llege

-edu

cate

dw

orke

rs.E

ach

cell

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rts

estim

ates

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oeffi

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tβin

equa

tion

(1).

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coef

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ore

repr

esen

tsth

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erag

eco

rrel

atio

nbe

twee

nth

ean

nual

chan

gein

the

sale

s-ba

sed

conc

entr

atio

nm

easu

rean

dth

esh

are

ofw

orke

rsth

atha

veco

llege

degr

ees.

The

unit

ofob

serv

atio

nis

afo

ur-d

igit

indu

stry

and

each

indu

stry

isw

eigh

ted

byits

base

line

leve

lof

valu

ead

ded.

Eac

hre

gres

sion

incl

udes

year

fixed

effe

cts

and

the

erro

rsar

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uste

red

atth

efo

ur-d

igit

indu

stry

.C

N4

(CN

20)

refe

rsto

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attr

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larg

est4

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firm

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HI

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rsto

the

Her

finda

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dex

fora

four

-dig

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dust

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ote

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the

sum

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enu

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bser

vatio

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row

1ex

ceed

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thos

ein

row

s2–

6.T

here

ason

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atth

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2–6

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lude

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,and

***

less

than

1%.

14

.1.1

5.2

.25

share

skill

ed w

ork

ers

1997 2002 2007 2012year

unconditional conditional

(a) Share of sales by top 2 firms.

.1.1

5.2

.25

share

skill

ed w

ork

ers

1997 2002 2007 2012year

unconditional conditional

(b) Share of sales by top 4 firms.

.1.1

5.2

.25

share

skill

ed w

ork

ers

1997 2002 2007 2012year

unconditional conditional

(c) Share of sales by top 20 firms.

.1.1

5.2

.25

share

skill

ed w

ork

ers

1997 2002 2007 2012year

unconditional conditional

(d) Herfindahl index.

Figure 6. The importance of market concentration for the change in the skill compositionin manufacturing.

Note: The sample consists of all four-digit manufacturing industries during 1997–2014. The number of (industry-year) observationsis 3,766. I estimate the regression in equation (1) with and without controlling for the change in market concentration. The values arethe cumulative coefficients from adding the baseline (year 1997) value of the skill share to the cumulative value of the coefficients onthe time dummies in equation (1). The red solid line calculates these values without including the change in market concentration inthe regression while the blue dashed line reports values when including the the change in market concentration. The red line thereforerepresents the actual shares of college-educated workers while the blue line represents a counterfactual of how high these shares wouldhave been if market concentration were to have stayed constant throughout the sample.

15

skill share; and s and Y denote unweighted means of the share of value added and the skillshare, respectively. The first term, Y , captures the mean skill share across firms, whichis independent of allocation of production. The second term, ∑i (si− s)(Yi− Y ), captureshow the allocation of production across firms with varying skill shares affects the aggregateskill share.

When I analyze the change in the aggregate skill share, ∆Y ≡ Y2−Y1 where thesubscripts indicate time, and attribute this change to changes in its various components, itis useful to account also for the effect of entry and exit. Melitz and Polanec (2015) expandsthe model in equation (2) in the following way:

∆Y = ∆YS +∆

(∑

i(si− s)(Yi− Y )

)S

+ sE2 (YE2−YS2)+ sX1 (YS1−YX1) (3)

where subscript S, E and X indicate firms that survive, enter and exit, respectively. sE2

therefore denotes the share of value added in period 2 of firms that enter, while sX1 denotesthe share of value added in period 1 of firms that exit. The first component in equation(3) is therefore the change in the unweighted mean skill share. The second componentcontains the change in the covariance between size and skill shares. The third componentshows the effect from entry: the share of value added of these firms in the second periodmultiplied with how their skill composition of workers differ from that of existing firms.Similarly, the fourth component captures the effect from exit by multiplying the share ofvalue added of exiting firms with how their skill composition differs from surviving firms.

Figure 7 shows the contribution of the four components to the change in the share ofcollege-educated workers in employment. I compute annual changes and panel a) showsthe cumulative contributions for the entire sample period. I notice that the single mostimportant source from a quantitative aspect is the between-firm change. This is quiteremarkable given the wide-spread belief that the share of skilled workers has increasedacross most firms in the industry and given that the aggregate change is so large. Exit offirms has also had a non-negligible positive impact, which means that exiting firms havehad a less educated workforce compared with the average firm. In panel b) I divide thesample into two time periods. While within-firm changes have been more or less equallyimportant in the two time periods, between-firm changes were most important in the earlyhalf of the sample. From Figure 1 I know that the rise in market concentration largely takesplace in the first half of the sample and much less in the second half, which may explainthe difference I observe here. Appendix Figure B.8 uses the college-educated share of thewage bill instead of employment and corroborates the conclusions from Figure 7. In Table4I also report five-year changes and note that the contributions from between-firm changesare larger than or as large as within-firm changes in all five-year periods. Similarly, exit

16

has a positive impact also here.The final part of my hypothesis that I wish to establish whether there is a direct link

between the rise in concentration and the reallocation of production from firms with a lessskilled workforce to those with more skilled workforce. A way to analyze this is to examinewhether the between-firm component is correlated with changes in market concentration,and if it is more strongly correlated than the other components of aggregate change are.Figure 8 plots the cumulative effects of each component for each four-digit industry versusthe change in market concentration based on the share in industry sales by the largest fourfirms. It is evident from this exercise that changes in market concentration are most stronglycorrelated with the between-firm component. Appendix Figures B.9 and B.10 show thatthis pattern holds also when I use the share in industry sales by the top twenty firms andthe Herfindahl index of sales, respectively, as measures of market concentration instead.9

Table 5 provides results from regressing annual levels in the four different componentsthat Melitz and Polanec (2015) emphasize on the change in market concentration at thefour-digit manufacturing industry level. The regressions contain year fixed effects andindustries are weighted by baseline levels of value added. Panel A shows the results for thedifferent regressions when using the entire sample period, both when using the skill shareof employment (columns 1–4) and the skill share of the wage bill (columns 5–8) as theaggregate measure of the skill share. I note that the between component seems by far themost strongly correlated with changes in market concentration, regardless of concentrationmeasure used or whether I calculate skill shares based on employment or wage bills. InPanels B and C I split the sample in two and perform separate regressions. The pattern Ihighlight holds in both time periods. It is statistically weaker in the second half, which isperhaps not surprising given that the change in market concentration is less pronounced inthis period.

I conclude that the between-firm component is quantitatively the most importantsource of change in the aggregate share of college-educated workers in employment. Ialso conclude that the between-firm component is the component that is most stronglycorrelated with changes in market concentration. This means that the main mechanismby which a rise in market concentration raises the skill utilization in an industry is byreallocating production across firms in a way that is systematically linked to how firmsdiffer in their use of skilled workers.

9The patterns are virtually the same when I use the share of the wage bill instead. These graphs areavailable upon request.

17

0.09

−0.01

0.03

0.07

−.0

30

.03

.06

.09

Co

ntr

ibu

tio

n t

o c

ha

ng

e in

skill

ed

la

bo

r sh

are

1997−2014

between entry

exit within

(a) One time period.

0.07

−0.00

0.01

0.04

0.02

−0.01

0.02

0.03

−.0

30

.03

.06

.09

Co

ntr

ibu

tio

n t

o c

ha

ng

e in

skill

ed

la

bo

r sh

are

1997−2006 2007−2014

between entry

exit within

(b) Two time periods.

Figure 7. Decomposition of the aggregate change in the skilled share of employment intoentry, exit, and within and between firm components.

Note: The sample consists of all 199,824 firm-year observations in the manufacturing sector during 1997–2014. For each year Idecompose the change in the aggregate share of college-educated workers in employment into within firm change, between firmchange as well as entry and exit according to Melitz and Polanec (2015) as outlined in equation (3). In panel (a) I report cumulativecontributions to the aggregate change for the entire sample period, while in panel (b) I divide the sample into two time periods.Appendix Figure B.8 reports the same estimates but uses the share of college-educated workers in the wage bill instead of employment.

18

Tabl

e4.

Dec

ompo

sitio

nof

aggr

egat

ech

ange

insk

illco

mpo

sitio

nin

toen

try,

exit,

and

with

inan

dbe

twee

nfir

mco

mpo

nent

s.

Shar

eof

colle

ge-e

duca

ted

inem

ploy

men

tSh

are

ofco

llege

-edu

cate

din

wag

ebi

ll

Tota

lB

etw

een

With

inE

xit

Ent

ryTo

tal

Bet

wee

nW

ithin

Exi

tE

ntry

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Pane

lA.F

ive-

year

chan

ges

1997

–200

20.

040.

020.

010.

010.

000.

040.

020.

010.

010.

0020

02–2

007

0.08

0.04

0.03

0.01

0.00

0.08

0.05

0.03

0.01

0.00

2007

–201

20.

050.

020.

020.

01-0

.01

0.04

0.01

0.02

0.02

-0.0

1

Pane

lB.T

wo

time

peri

ods

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–200

60.

110.

070.

040.

010.

000.

120.

070.

040.

02-0

.01

2007

–201

40.

060.

020.

030.

02-0

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0.05

0.01

0.03

0.02

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1

Pane

lC.O

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ll19

97–2

014

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19

Tabl

e5.

The

com

pone

nts

ofch

ange

sin

aggr

egat

esk

illsh

ares

inem

ploy

men

tand

thei

rrel

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arke

tcon

cent

ratio

n.

Skill

edsh

are

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ploy

men

tSk

illed

shar

eof

wag

ebi

ll

Bet

wee

nW

ithin

Ent

ryE

xit

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ryE

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(1)

(2)

(3)

(4)

(5)

(6)

(7)

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0.41

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0.07

***

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0.53

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CN

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0.05

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0.05

0.05

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Figure 8. The components of changes in aggregate skill shares in employment and changein market concentration (share in sales to top four firms) across four-digit industries.

Note: The sample consists of all four-digit industries in the manufacturing sector during 1997–2014. For each year I have decomposedthe change in the aggregate share of college-educated workers in employment into between firm change, within firm change as wellas entry and exit according to Melitz and Polanec (2015) as outlined in equation (3). The vertical axis in the scatter diagram containsthe cumulative effect of a specific component and the horizontal axis contains the change in market concentration as measured by theshare of the top four firms in total industry sales. The straight line shows a linear relationship between the two variables. This line isweighted by the baseline value added in each industry. Appendix Figures B.9 and B.10 show the same graphs using the share of thetop twenty firms in sales and the Herfindahl index of sales, respectively, instead.

6 Conclusion

This paper aims to analyze the role of the increase in market concentration and the riseof “superstar firms” in explaining the increased demand for skilled and college-educatedworkers. Using detailed linked employer-employee data for the Swedish manufacturingsector during 1997–2014, I observe a sharp rise in the usage of skilled workers throughoutthe sample. I also show how market concentration has risen considerably. The risein market concentration can potentially explain some of the rise in demand for skill ifsuperstar firms systematically use skilled workers relatively more than other firms. I findthat they do. There is a strong correlation between size and the share of employees thathave a college degree as well as the share of the wage bill that is paid to college-educated

21

workers.My analysis shows that the changes in the share of skilled workers in employment

across manufacturing sectors are systematically linked to changes in market concentration.Regardless of concentration measure, be it the share of the top four or twenty firms insales or the Herfindahl index, sectors where superstar firms become more important alsoincrease their usage of skilled workers. I find that this link is robust to several specificationchecks and also holds for different sample periods and also outside the manufacturingsector. The link is of quantitative importance: when using for example the sales-basedHerfindahl index as a measure of concentration I find that the rise in concentration accountsfor a tenth of the increase in the share of skilled workers in production.

I subsequently decompose the change in aggregate skill demand. I analyze whetherthe rise in skill demand primarily comes from a rise across all firms (the within-firmcomponent), from a reallocation of production across firms such that more production isperformed by firms that use skilled workers more intensively (the between-firm component),from entry of new firms that systematically demand more educated workers than existingfirms (the entry component) or from exiting firms that use fewer educated workers thansurvivors (the exit component). I find that the between-firm component has been mostimportant for the evolution of the aggregate skill utilization. This means that the risein skill demand primarily comes from a reallocation of production from firms usingrelatively fewer skilled workers to firms using more skilled workers. And the between-firmcomponent is the component that is by far most strongly correlated with changes in marketconcentration. This shows that sectors with rising concentration have also had a higherreallocation of production from less skill-intensive to more skill-intensive firms than othersectors. This means that what has happened is not that some unobserved factor has causedboth a rise in concentration and a rise in the demand for skill. Rather, I observe that therise in concentration has increased reallocation of production across firms in a way thathas systematically raised the aggregate demand for skill.

This paper points at a new reason for the rise in the demand for skill and potentiallyalso income inequality, namely that the structure of markets has changed in a way thathas benefited firms using skilled workers more intensively. If superstar firms are moreskill-intensive than other firms, any policy or technology that causes these firms to expandmore than other firms will raise the aggregate demand for skilled workers. Of course, itmay also be the case that an increase in the supply of skilled workers benefits firms thatuse them intensively (similar to how the Rybczynski Theorem in neoclassical models ofinternational trade dictates that the increase in the supply of a production factor under fixedrelative goods prices changes the allocation of production rather than relative factor prices).If this were the case, however, I would also see downward pressure on, or no change in, the

22

relative wages of skilled workers. This is not in line with the rise in the college premiumobserved in most countries in recent decades. Autor et al. (2017b) demonstrate for manycountries and sectors that market concentration may lower the share of labor in income. Iinstead make the point that market concentration may not only lead to inequality betweenworkers and others, but also among workers as well.

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25

Appendix A: Data and expansion

Table A.1. Variable definitions

Variable Description

Firm accounts Source: The Account Statistics.Revenues Total sales by a firm in year t.Value added Total value added by a firm in year t.Industry 4-digit code classifying a firm’s main activity in year t according to the Nomenclature

of Economic Activities (SNI2002/NACE Rev. 1) system.

Individualcharacteristics

Source: National Education Database and Central Population Register.

Education level Years of schooling.Annual income Labor income of an individual in year t in Swedish kronor.

International Trade Source: UN Comtrade.Imports Imports in a year t by country grouping at the four-digit sectoral level.

26

Table A.2. Summary statistics for two-digit manufacturing sectors

Mean Std. dev. Min MaxFood products, beverages and tobacco (34 industries, 575 observations)Number of firms 972 38 909 1,026Share of Skilled Wages 15.51 7.42 0.00 43.85Change in Share of Skilled Wages 0.54 2.21 -30.63 23.16Share of Skilled Workers 11.54 5.57 0.00 39.47Change in Share of Skilled Workers 0.51 1.58 -37.50 20.00CR4 72.66 23.56 29.97 100.00Change in CR4 -0.25 3.87 -18.79 30.69Herfindahl Index 37.70 29.79 4.46 100.00Change in Herfindahl Index -0.43 7.93 -64.65 62.07

Textiles and textile products (17 industries, 273 observations)Number of firms 212 26 173 249Share of Skilled Wages 12.04 4.19 0.00 31.03Change in Share of Skilled Wages 0.50 1.68 -9.38 10.12Share of Skilled Workers 9.46 3.72 0.00 26.90Change in Share of Skilled Workers 0.50 1.42 -10.71 12.50CR4 58.22 28.51 12.75 100.00Change in CR4 0.15 4.06 -15.00 16.03Herfindahl Index 24.29 26.23 2.06 100.00Change in Herfindahl Index 0.62 5.73 -35.77 46.78

Leather and leather products ( 9 industries, 162 observations)Number of firms 99 30 68 164Share of Skilled Wages 12.61 7.00 0.00 33.87Change in Share of Skilled Wages 0.94 2.10 -19.42 15.41Share of Skilled Workers 10.70 6.33 0.00 30.77Change in Share of Skilled Workers 0.88 1.80 -15.50 18.27CR4 71.81 18.54 28.50 100.00Change in CR4 0.90 5.85 -19.98 30.40Herfindahl Index 33.65 22.66 5.77 100.00Change in Herfindahl Index 0.71 7.38 -49.59 48.03

Wood and wood products (6 industries, 108 observations)Number of firms 943 72 788 1,029Share of Skilled Wages 8.34 1.78 0.00 11.60Change in Share of Skilled Wages 0.31 0.62 -4.76 9.38Share of Skilled Workers 6.45 1.59 0.00 11.11Change in Share of Skilled Workers 0.28 0.39 -7.78 11.11CR4 23.88 9.47 13.48 100.00Change in CR4 -0.15 2.73 -25.74 13.11Herfindahl Index 3.42 3.52 1.42 100.00Change in Herfindahl Index 0.02 0.92 -32.94 25.93

27

Mean Std. dev. Min MaxPulp and paper; publishing and printing (20 industries, 360 observations)Number of firms 1,346 226 976 1,685Share of Skilled Wages 19.68 12.91 0.00 62.55Change in Share of Skilled Wages 0.73 1.17 -29.07 26.52Share of Skilled Workers 16.58 12.61 0.00 60.46Change in Share of Skilled Workers 0.77 1.09 -23.78 25.81CR4 39.79 20.86 10.77 100.00Change in CR4 0.14 3.05 -28.74 33.65Herfindahl Index 10.68 11.60 0.95 100.00Change in Herfindahl Index 0.16 2.54 -60.54 44.97

Coke, refined petroleum products and nuclear fuel (3 industries, 40 observations)Number of firms 16 1 13 18Share of Skilled Wages 37.38 13.85 0.00 61.29Change in Share of Skilled Wages 1.24 1.75 -2.02 7.74Share of Skilled Workers 31.28 11.98 0.00 51.79Change in Share of Skilled Workers 1.18 1.45 -3.57 4.83CR4 86.75 11.06 69.19 100.00Change in CR4 0.16 4.32 -8.57 10.12Herfindahl Index 58.25 25.95 21.59 100.00Change in Herfindahl Index 0.91 8.85 -22.59 23.00

Chemicals and man-made fibres (20 industries, 333 observations)Number of firms 270 10 251 285Share of Skilled Wages 43.95 16.71 0.00 76.90Change in Share of Skilled Wages 0.70 2.29 -30.35 29.64Share of Skilled Workers 36.15 14.82 0.00 72.20Change in Share of Skilled Workers 0.76 2.28 -25.00 25.00CR4 80.87 18.53 27.03 100.00Change in CR4 -0.15 3.30 -19.15 20.53Herfindahl Index 42.39 20.94 5.74 100.00Change in Herfindahl Index 0.31 4.55 -47.05 52.54

Rubber and plastic (7 industries, 126 observations)Number of firms 552 29 487 585Share of Skilled Wages 11.81 3.07 3.21 19.73Change in Share of Skilled Wages 0.36 1.08 -7.41 5.63Share of Skilled Workers 8.69 2.30 2.69 14.09Change in Share of Skilled Workers 0.33 0.81 -4.52 6.05CR4 33.00 24.52 11.60 100.00Change in CR4 -0.12 3.91 -24.57 29.48Herfindahl Index 9.74 15.36 1.34 100.00Change in Herfindahl Index -0.03 5.28 -45.75 43.74

28

Mean Std. dev. Min MaxOther non-metallic products (24 industries, 417 observations)Number of firms 273 11 249 298Share of Skilled Wages 12.34 5.32 0.00 80.55Change in Share of Skilled Wages 0.34 2.38 -50.05 60.23Share of Skilled Workers 9.24 3.99 0.00 66.67Change in Share of Skilled Workers 0.34 1.91 -38.46 45.08CR4 76.42 22.72 17.59 100.00Change in CR4 0.18 4.15 -39.24 15.80Herfindahl Index 37.82 28.55 2.98 100.00Change in Herfindahl Index 0.43 6.82 -58.07 54.43

Basic metals and fabricated metal products (33 industries, 582 observations)Number of firms 2,908 98 2,741 3,123Share of Skilled Wages 10.41 4.64 0.00 41.00Change in Share of Skilled Wages 0.43 1.21 -10.92 17.14Share of Skilled Workers 7.68 3.18 0.00 35.09Change in Share of Skilled Workers 0.38 0.70 -5.34 9.88CR4 42.84 29.24 5.09 100.00Change in CR4 -0.06 5.33 -36.04 28.61Herfindahl Index 13.68 16.63 0.39 100.00Change in Herfindahl Index -0.23 5.45 -37.88 48.91

Machinery and equipment nec (23 industries, 384 observations)Number of firms 1,429 76 1,307 1,528Share of Skilled Wages 20.12 8.69 3.55 46.20Change in Share of Skilled Wages 0.78 2.93 -21.35 29.24Share of Skilled Workers 15.08 7.24 2.00 38.63Change in Share of Skilled Workers 0.69 1.79 -11.24 17.56CR4 54.07 21.53 16.25 99.70Change in CR4 -0.14 9.05 -60.11 67.42Herfindahl Index 18.44 14.15 1.95 95.07Change in Herfindahl Index 0.00 8.11 -73.71 75.06

Electrical and optical equipment (17 industries, 306 observations)Number of firms 1,008 49 922 1,092Share of Skilled Wages 41.31 16.67 5.47 67.23Change in Share of Skilled Wages 1.39 5.95 -15.64 25.92Share of Skilled Workers 34.05 16.60 3.64 62.51Change in Share of Skilled Workers 1.54 5.79 -13.57 26.83CR4 71.54 24.66 25.00 100.00Change in CR4 0.13 6.65 -52.89 29.74Herfindahl Index 43.24 33.92 4.11 93.27Change in Herfindahl Index 1.81 8.91 -56.58 35.36

29

Mean Std. dev. Min MaxTransport equipment (11 industries, 198 observations)Number of firms 515 20 469 541Share of Skilled Wages 23.91 9.51 0.44 54.68Change in Share of Skilled Wages 1.17 0.96 -7.90 8.83Share of Skilled Workers 18.76 8.28 0.70 47.54Change in Share of Skilled Workers 1.06 0.78 -3.97 7.06CR4 67.91 22.53 20.12 100.00Change in CR4 0.99 6.42 -22.85 25.67Herfindahl Index 22.59 11.43 2.76 95.90Change in Herfindahl Index 0.52 6.43 -18.92 37.02

Manufacturing nec (13 industries, 216 observations)Number of firms 559 46 481 624Share of Skilled Wages 9.53 5.18 0.00 43.07Change in Share of Skilled Wages 0.56 1.30 -7.78 12.32Share of Skilled Workers 7.66 4.67 0.00 42.41Change in Share of Skilled Workers 0.51 1.08 -7.84 11.53CR4 42.34 18.98 16.68 100.00Change in CR4 0.06 11.61 -49.25 45.28Herfindahl Index 12.92 12.33 2.16 100.00Change in Herfindahl Index -0.12 9.17 -41.83 49.48

Note: Detailed descriptions of the variables are given in Appendix Table A.1. All numbers show weighted averages over four-digit sectors for the years 1997-2014, where the weights are 1997 levels of value added at the four-digit sector level. These sectorscover all two-digit sectors in manufacturing.

30

Table A.3. Summary statistics for all sectors

Mean Std. dev. Min MaxManufacturing (237 industries, 4,080 observations)Number of firms 11,101 546 9,967 11,732Wages to Sales Ratio 15.21 5.62 1.03 97.85Change in Wages to Sales Ratio -0.01 1.95 -76.39 53.96Share of Skilled Wages 23.39 16.42 0.00 80.55Change in Share of Skilled Wages 0.81 2.94 -50.05 60.23Share of Skilled Workers 18.72 14.59 0.00 72.20Change in Share of Skilled Workers 0.80 2.69 -38.46 45.08CR4 57.78 28.17 5.09 100.00Change in CR4 0.11 5.88 -60.11 67.42CR20 84.18 19.91 19.09 100.00Change in CR20 0.07 2.74 -29.08 27.63

Services (52 industries, 821 observations)Number of firms 16,036 3,120 11,337 21,566Wages to Sales Ratio 21.95 12.07 4.24 61.96Change in Wages to Sales Ratio 0.19 3.49 -40.39 32.69Share of Skilled Wages 33.92 19.97 0.00 88.78Change in Share of Skilled Wages 0.75 1.79 -39.56 25.94Share of Skilled Workers 28.15 18.70 0.00 78.83Change in Share of Skilled Workers 0.88 1.88 -25.00 26.45CR4 21.96 17.68 6.04 100.00Change in CR4 -0.28 5.06 -57.73 57.86CR20 44.99 21.54 15.43 100.00Change in CR20 -0.25 3.69 -29.57 24.14

Utilities and Transportation (35 industries, 522 observations)Number of firms 5,535 377 4,895 6,000Wages to Sales Ratio 17.44 9.86 1.92 49.30Change in Wages to Sales Ratio -0.16 1.76 -14.62 10.95Share of Skilled Wages 27.36 22.51 0.00 100.00Change in Share of Skilled Wages 1.28 13.68 -92.84 100.00Share of Skilled Workers 23.44 22.47 0.00 100.00Change in Share of Skilled Workers 1.25 14.84 -92.98 100.00CR4 55.10 30.06 3.49 100.00Change in CR4 -0.37 4.35 -30.28 26.37CR20 77.99 27.36 14.72 100.00Change in CR20 0.05 2.24 -28.99 13.34

31

Mean Std. dev. Min MaxRetail Trade (82 industries, 1311 observations)Number of firms 12,860 196 12,622 13,256Wages to Sales Ratio 27.95 7.69 1.84 64.34Change in Wages to Sales Ratio -0.02 2.11 -25.25 32.54Share of Skilled Wages 19.27 16.17 0.00 73.69Change in Share of Skilled Wages 0.56 1.44 -35.12 17.04Share of Skilled Workers 16.01 13.82 0.00 66.25Change in Share of Skilled Workers 0.59 1.18 -18.62 20.00CR4 37.00 24.53 5.44 100.00Change in CR4 0.18 5.07 -41.85 44.62CR20 59.64 22.57 19.15 100.00Change in CR20 0.27 3.21 -28.79 31.57

Wholesale Trade (5 industries, 90 observations)Number of firms 2,771 204 2,458 3,024Wages to Sales Ratio 29.09 3.55 18.19 36.78Change in Wages to Sales Ratio -0.11 2.08 -8.90 4.47Share of Skilled Wages 7.53 3.65 2.10 20.77Change in Share of Skilled Wages 0.26 0.48 -1.51 2.92Share of Skilled Workers 5.92 2.71 1.75 15.75Change in Share of Skilled Workers 0.27 0.46 -1.63 2.33CR4 20.61 13.83 7.46 59.95Change in CR4 0.11 4.18 -21.41 32.09CR20 41.25 12.96 22.86 85.81Change in CR20 0.09 3.74 -22.53 17.72

Note: Detailed descriptions of the variables are given in Appendix Table A.1. All numbers show weighted averages over four-digit sectors for the years 1997-2014, where the weights are 1997 levels of value added at the four-digit sector level.

32

Appendix B: Figures

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1.1

2.1

3h

erf

inda

hl in

dex

.3.3

2.3

4.3

6to

p 4

co

nce

ntr

atio

n

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(h) Rubber and plastic.

.36

.38

.4.4

2.4

4herf

inda

hl in

dex

.75

.76

.77

.78

top 4

concentr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(i) Other non-metallicproducts.

.12

.14

.16

.18

.2herf

ind

ahl in

de

x

.4.4

2.4

4.4

6.4

8to

p 4

concentr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(j) Basic metals and fabricatedmetal products.

.15

.16

.17

.18

.19

.2herf

indahl in

dex

.48

.5.5

2.5

4.5

6.5

8to

p 4

concentr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(k) Machinery and equipmentnec.

.2.3

.4.5

.6herf

inda

hl in

dex

.68

.7.7

2.7

4.7

6to

p 4

concentr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(l) Electrical and opticalequipment.

.15

.2.2

5.3

.35

herf

indahl in

dex

.55

.6.6

5.7

.75

.8to

p 4

concentr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(m) Transport equipment.

.1.1

5.2

.25

herf

ind

ahl in

de

x

.35

.4.4

5.5

top 4

concentr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(n) Manufacturing nec.

Figure B.1. Evolution of market concentration in two-digit manufacturing sectors.Note: The sample consists of firms in the manufacturing sector during 1997–2014. For each year and two-digit sector, I calculate foreach four-digit sector the share of sales of the four largest firms as well as the Herfindahl index for sales and then calculate the overallweighted mean where the weights are the 1997 levels of value added for each four-digit sector. The dashed lines show linear trendsfor the two variables of interest.

33

.2.2

2.2

4.2

6.2

8h

erf

ind

ah

l in

de

x

.55

.56

.57

.58

.59

.6to

p 4

co

nce

ntr

atio

n

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(a) Manufacturing.

.03

5.0

4.0

45

.05

.055

he

rfin

da

hl in

de

x

.2.2

1.2

2.2

3.2

4to

p 4

co

nce

ntr

atio

n

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(b) Services.

.22

.24

.26

.28

.3.3

2h

erf

inda

hl in

de

x

.52

.54

.56

.58

top

4 c

on

ce

ntr

atio

n

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(c) Utilities and Transportation.

.1.1

2.1

4.1

6.1

8h

erf

inda

hl in

de

x

.32

.34

.36

.38

.4to

p 4

co

nce

ntr

ation

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(d) Retail Trade.

.02

.03

.04

.05

.06

he

rfin

da

hl in

de

x

.18

.2.2

2.2

4to

p 4

co

nce

ntr

atio

n

1995 2000 2005 2010 2015year

top 4 concentration herfindahl index

(e) Wholesale Trade.

Figure B.2. Evolution of market concentration in entire private sector.Note: The sample consists of firms in the manufacturing sector during 1997–2014. For each year and sector, I calculate for eachfour-digit sector the share of sales of the four largest firms as well as the Herfindahl index for sales and then calculate the overallweighted mean where the weights are the 1997 levels of value added for each four-digit sector.

34

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(a) Food products, beveragesand tobacco.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(b) Textiles and textileproducts.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(c) Leather and leatherproducts.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(d) Wood and wood products.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(e) Pulp and paper.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(f) Coke and refinedpetroleum products.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(g) Chemicals and man-madefibres.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(h) Rubber and plastic.

0.1

.2.3

.4.5

share

of skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(i) Other non-metallicproducts.

0.1

.2.3

.4.5

share

of skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(j) Basic metals and fabricatedmetal products.

0.1

.2.3

.4.5

share

of skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(k) Machinery and equipmentnec.

0.1

.2.3

.4.5

share

of skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(l) Electrical and opticalequipment.

0.1

.2.3

.4.5

share

of skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(m) Transport equipment.

0.1

.2.3

.4.5

share

of skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(n) Manufacturing nec.

Figure B.3. Evolution of worker skill composition in two-digit manufacturing sectors.Note: The sample consists of workers for firms in the manufacturing sector during 1997–2014. For each year, I calculate for eachtwo-digit manufacturing sector the share of workers that have a college degree and the share of total wages that is paid to these workers.

35

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(a) Manufacturing.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(b) Services.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(c) Utilities and Transportation.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(d) Retail Trade.

0.1

.2.3

.4.5

sh

are

of

skill

ed

1995 2000 2005 2010 2015year

share of workers share of wages

(e) Wholesale Trade.

Figure B.4. Evolution of worker skill composition in in entire private sector.Note: The sample consists of workers for firms during 1997–2014. For each year, I calculate for each sector the share of workers thathave a college degree and the share of total wages that is paid to these workers.

36

.05

.1.1

5.2

skill

ed

sh

are

of

wa

ge

s

14 16 18 20 22log sales

(a) Unweighted.

.1.2

.3.4

.5.6

skill

ed

sh

are

of

wa

ge

s

16 18 20 22 24 26log sales

(b) Weighted by value added.

0.1

.2.3

.4re

sid

ua

l skill

ed

sh

are

of

wa

ge

s

−2 0 2 4 6 8residual log sales

(c) Four-digit sector and year fixed effects.

−.0

01

0.0

01

.00

2re

sid

ua

l skill

ed

sh

are

of

wa

ge

s

−.5 0 .5 1residual log sales

(d) Firm fixed effects.

Figure B.5. Firm size and the share of skilled workers in the wage bill.Note: I divide the manufacturing sample consisting of 199,824 firm-year observations into 20 quantiles based on annual sales and plotthe mean share of skilled workers in the wages paid by firms for each quantile. In panels b), c) and d) I weight each firm by its valueadded. In panel c) I do not use raw numbers but instead residuals after taking out four-digit sector and year fixed effects. In panel d) Iuse residuals after taking out firm and year fixed effects.

37

.12

.14

.16

.18

.2.2

2skill

ed

sh

are

of

wo

rke

rs

14 16 18 20log sales

(a) Unweighted.

.15

.2.2

5.3

.35

.4skill

ed

sh

are

of w

ork

ers

15 20 25log sales

(b) Weighted by value added.

0.0

5.1

.15

.2re

sid

ua

l skill

ed

sh

are

of

wo

rke

rs

−2 0 2 4 6 8residual log sales

(c) Four-digit sector and year fixed effects.

−.0

04

−.0

02

0.0

02

resid

ua

l skill

ed

sh

are

of

wo

rke

rs

−1 −.5 0 .5 1residual log sales

(d) Firm fixed effects.

Figure B.6. Firm size and the share of skilled workers in employment. Entire privatesector.

Note: I divide the sample consisting of 1,145,210 firm-year observations into 20 quantiles based on annual sales and plot the meanshare of skilled workers in employment for each quantile. In panels b), c) and d) I weight each firm by its value added. In panel c) Ido not use raw numbers but instead residuals after taking out four-digit sector and year fixed effects. In panel d) I use residuals aftertaking out firm and year fixed effects.

38

0.1

.2.3

.4change in s

hare

of w

age b

ill to c

olle

ge−

educate

d w

ork

ers

−.1 0 .1 .2 .3 .4change in share of sales by top 4 firms

0.1

.2.3

.4change in s

hare

of w

age b

ill to c

olle

ge−

educate

d w

ork

ers

−.4 −.2 0 .2 .4 .6change in herfindahl index

(a) Two-digit industries.

−.4

−.2

0.2

.4change in s

hare

of w

age b

ill to c

olle

ge−

educate

d w

ork

ers

−.4 −.2 0 .2 .4change in share of sales by top 4 firms

−.4

−.2

0.2

.4change in s

hare

of w

age b

ill to c

olle

ge−

educate

d w

ork

ers

−1 −.5 0 .5 1change in herfindahl index

(b) Four-digit industries.

Figure B.7. Change in the share of the wage bill that is paid to workers with a collegedegree and change in market concentration.

Note: I calculate for each manufacturing industry the share of the wage bill that is paid to workers that have a college degree and themarket concentration for the first and last year of the sample: 1997 and 2014. I then plot the changes in the figures where the size ofthe circles is determined by the baseline value added of each industry. In panel (a) I use two-digit industries and in (b) I use four-digitindustries. The straight line shows a linear relationship between the two variables. This line is weighted by the baseline value addedin each industry.

39

0.08

−0.02

0.04

0.07

−.0

30

.03

.06

.09

Co

ntr

ibu

tio

n t

o c

ha

ng

e in

skill

ed

la

bo

r sh

are

1997−2014

between entry

exit within

(a) One time period.

0.07

−0.01

0.02

0.04

0.01

−0.01

0.02

0.03

−.0

30

.03

.06

.09

Co

ntr

ibu

tio

n t

o c

ha

ng

e in

skill

ed

la

bo

r sh

are

1997−2006 2007−2014

between entry

exit within

(b) Two time periods.

Figure B.8. Decomposition of the aggregate change in the skilled share of the wage billinto entry, exit, and within and between firm components.

Note: The sample consists of all 199,824 firm-year observations in the manufacturing sector during 1997–2014. For each year Idecompose the change in the aggregate share of college-educated workers in the wage bill into within firm change, between firmchange as well as entry and exit according to Melitz and Polanec (2015) as outlined in equation (3). In panel (a) I report cumulativecontributions to the aggregate change for the entire sample period, while in panel (b) I divide the sample into two time periods.

40

−.4

−.2

0.2

.4siz

e o

f th

e b

etw

een c

om

ponent

−.2 0 .2 .4 .6change in share of sales by top 20 firms

(a) Between firm component.

−.4

−.2

0.2

.4siz

e o

f th

e w

ithin

com

ponent

−.2 0 .2 .4 .6change in share of sales by top 20 firms

(b) Within firm component.

−.4

−.2

0.2

.4siz

e o

f th

e e

ntr

y c

om

ponent

−.2 0 .2 .4 .6change in share of sales by top 20 firms

(c) Entry component.

−.4

−.2

0.2

.4siz

e o

f th

e e

xit c

om

ponent

−.2 0 .2 .4 .6change in share of sales by top 20 firms

(d) Exit component.

Figure B.9. The components of changes in aggregate skill shares in employment andchange in market concentration (share in sales to top twenty firms) across four-digit

industries.Note: The sample consists of all four-digit industries in the manufacturing sector during 1997–2014. For each year I have decomposedthe change in the aggregate share of college-educated workers in employment into between firm change, within firm change as wellas entry and exit according to Melitz and Polanec (2015) as outlined in equation (3). The vertical axis in the scatter diagram containsthe cumulative effect of a specific component and the horizontal axis contains the change in market concentration as measured by theshare of the top twenty firms in total industry sales. The straight line shows a linear relationship between the two variables. This lineis weighted by the baseline value added in each industry.

41

−.4

−.2

0.2

.4siz

e o

f th

e b

etw

een c

om

ponent

−1 −.5 0 .5 1change in herfindahl index

(a) Between firm component.

−.4

−.2

0.2

.4siz

e o

f th

e w

ithin

com

ponent

−1 −.5 0 .5 1change in herfindahl index

(b) Within firm component.

−.4

−.2

0.2

.4siz

e o

f th

e e

ntr

y c

om

ponent

−1 −.5 0 .5 1change in herfindahl index

(c) Entry component.

−.4

−.2

0.2

.4siz

e o

f th

e e

xit c

om

ponent

−1 −.5 0 .5 1change in herfindahl index

(d) Exit component.

Figure B.10. The components of changes in aggregate skill shares in employment andchange in market concentration (Herfindahl index) across four-digit industries.

Note: The sample consists of all four-digit industries in the manufacturing sector during 1997–2014. For each year I have decomposedthe change in the aggregate share of college-educated workers in employment into between firm change, within firm change as wellas entry and exit according to Melitz and Polanec (2015) as outlined in equation (3). The vertical axis in the scatter diagram containsthe cumulative effect of a specific component and the horizontal axis contains the change in market concentration as measured by theHerfindahl index of industry sales. The straight line shows a linear relationship between the two variables. This line is weighted bythe baseline value added in each industry.

42