SFB Bargaining power and the labor 
share – a structural break 
823 approach 
 
Kornelius Kraft, Alexander Lammers 
 
 
 
 
 
Nr. 12/2021 
 
 
 
 
 
 
 
Discussion Paper 
 
Bargaining Power and the Labor Share –
a Structural Break Approach
Kornelius Kraft† Alexander Lammers‡
May 2021
Abstract
In this paper we investigate the relevance of bargaining institutions in the decline in
labor share. Several explanations for the decline exist, which consider the relevance
of technology, globalization and markups. Surprisingly neglected so far, however, is
the influence of bargaining institutions, in particular with a focus on changes in the
outside option. We provide evidence of this issue, using the Hartz IV labor market
reform in Germany as an exogenous shock in the wage bargaining of employees,
and investigate its impact on the labor share. We begin by developing a theoretical
model in which we outline the effect of a decrease in the outside option within a
wage bargaining framework. Thereafter, the approach is twofold. Combining the
EU KLEMS and Penn World Table databases, we first endogenously identify the
Hartz IV reform as a significant structural break in the German labor share. Sec-
ond, we estimate the effect of the Hartz IV legislation on the aggregated labor share
using a synthetic control approach in which we construct a counterfactual Germany
doppelganger. Finally, we use rich firm-level panel data compiled by Bureau van
Dijk to support our results on the aggregated labor share. We find that the reform
decreases the labor share by 1.6 – 2.7 percentage points depending on method and
aggregation level. The synthetic control approach furthermore provides evidence
that this effect is persistent over time since the reform.
Keywords: Labor share, Hartz reform, change-point tests, inequality, synthetic
control method, GMM
JEL Codes: D04, E25, J51, L21, O43
Acknowledgments: We thank the German Research Foundation (DFG) for its
financial support of the Collaborative Research Center “Statistical modeling of
nonlinear dynamic processes” (SFB 823, Project A5). We received very helpful
comments and suggestions from the SFB 823 “Structural Break Day” in Bochum,
the annual meeting of the SFB 823 in Lüdenscheid, the internal colloquium of the
chair of Economic Policy and from the (virtual) 13th IAAEU Workshop on Labour
Economics. Any remaining mistakes are our own.
†TU Dortmund University, Faculty of Business and Economics, Vogelpothsweg 87, D-44227 Dortmund,
ZEW Mannheim, IZA Bonn and KU Leuven, Belgium. Email: Kornelius.Kraft@tu-dortmund.de.
‡Corresponding author: TU Dortmund University, Faculty of Business and Economics, Vogelpothsweg
87, D-44227 Dortmund. Email: Alexander.Lammers@tu-dortmund.de.
1 Introduction
There is intense debate on how economic outputs are divided between capital and labor
(Rodriguez & Jayadev 2013). This division is usually measured using the concept of the
labor share, i.e. the ratio of labor compensation to economic output. In macroeconomic
models, the stability of the labor share is often referred to as a stylized fact of growth
(e.g. Kaldor 1957). This stability, however, is challenged because of a decline in the
labor share in many countries over several decades (e.g. Barkai 2020; Cantore et al. 2020;
Karabarbounis & Neiman 2014).1 In Germany for example, the labor share declined by
roughly five percentage points from 70 % in the 1970s to 65 % in 2015 which also raises
distributional questions regarding inequality (e.g. Iñaki 2020; Card et al. 2020; Piketty &
Zucman 2014).
There is a wealth of theoretical and empirical literature on potential determinants
on the decline of labor share. One explanation named in this context is technological
progress such as the use of robots and algorithms as well as a decreasing price of capital
in relation to labor.2 Another line of research emphasized the role of so-called ‘superstar
firms’. These firms are based on capital-intensive production and exponential growth.3
Globalization combined with outsourcing of labor-intensive tasks is another explanation.4
In this paper we consider the decline of bargaining power as an so far overlooked reason
for the observed decrease in labor share, in particular with a focus on changes in the
outside option. We therefore utilize the unique exogenous reform shock of the Hartz
IV legislation, leading to a decrease in the threat point of unions within a bargaining
framework. For the investigation, our approach is twofold. We first show that the Hartz
legislation and, in particular, the Hartz IV reform in Germany contribute to a significant
1Figure A.1 in the Appendix provides an overview of labor share developments for different countries.
2See for example the literature by Acemoglu et al. (2020); Eden & Gaggl (2018); Acemoglu & Restrepo
(2018); Acemoglu (2003); Bentolila & Saint-Paul (2003). Results from these studies using firm-level data
from France suggests that the labor share declines by 4 to 6.3 percentage points for firms that adopt
robots (Acemoglu et al. 2020).
3This strand of the literature is in particular driven by work from Autor et al. (2020); De Loecker
et al. (2020); Kehrig & Vincent (2021).
4See for example Elsby et al. (2013) in the context of offshoring and Stockhammer (2017) for the
impact of financial globalization.
1
structural break in the time series of the aggregated labor share. We therefore apply
several endogenous tests drawn from the change point literature (e.g. Antoch et al. 2019;
Andrews 2003; Bai & Perron 2003) in which we identify the Hartz IV reform as a significant
structural break. In a second step, we estimate the reform effect on the labor share using
(i) data on the aggregated labor share and (ii) firm-level data (i.e. the ‘dafne’ dataset)
compiled by Bureau van Dijk. We apply ordinary least squares as well as a synthetic
control approach (e.g. Abadie et al. 2010, 2015; Abadie 2020) in which we construct
a Germany doppelganger as a counterfactual for what would have happened with the
German labor share in the absence of the Hartz IV reform. For this analysis we use
the EU KLEMS data combined with the Penn World Table database to investigate the
German labor share for the period 1970 to 2015. Regarding the firm-level data, we apply
fixed effects as well as System GMM estimation techniques. We provide evidence that
the exogenous shock of the Hartz IV reform reduces the German labor share by around
2 percentage points. The synthetic approach additionally suggests that this decline is
lasting, at least up to ten years after the reform was implemented.
Related literature also exists which examines the relationship between bargaining power
and the labor share, however with a different focus. For the aggregate labor share, Young
& Zuleta (2018); Blanchard & Giavazzi (2003) consider the direct bargaining power of
unions. In a similar vein, Fichtenbaum (2011) finds that the decline in union density
explains roughly one third of the decline in the share of labor. Bental & Demougin (2010)
develop a theoretical model which explain movements in the labor share which depend on
labor market institutions, and Brock & Dobbelaere (2006) develop a bargaining framework
for the effects of globalization on the labor share. More closely related are, for example,
Bazillier & Najman (2017), who investigate how crisis events affect the threat points of
workers and result in a decrease in the labor share. More recently, Stansbury & Summers
(2020) investigate the relevance of bargaining institutions for workers in the United States
and ? consider the impact of job protection deregulation. These authors in particular find
that the decline in workers’ bargaining power might be the main reason for changes in
the labor share. On the firm level, there are numerous studies examining the role of firm-
2
specific factors such as workforce or firm characteristics for the labor share (Harju et al.
2021; Siegenthaler & Stucki 2015). Although these studies focus on similar aspects of the
decline of labor share, no study focuses on changes in indirect measures for bargaining
power, such as the outside option.
The remainder of this paper proceeds as follows. In Section 2 we provide the insti-
tutional framework and background of the Hartz legislation in Germany. Moreover, we
provide a simple bargaining model in which we derive implications for the connection
between changes in the outside option in wage bargaining and the labor share. Section
3 then provides empirical evidence on the Hartz IV reform and identifies the reform as a
structural break in the German labor share. We apply several endogenous and exogenous
change point tests. Section 4 provides estimates of the magnitude of the reform on the
aggregated and firm level. Section 6 concludes and provides policy implications.
2 Institutional framework in Germany
2.1 The Hartz legislation
A persistent and high unemployment rate in Germany in the early years of the 21st cen-
tury led to the implementation of the so-called Hartz reforms, named after the chairman
of the commission, Peter Hartz.5 The reform consisted of four packages (Hartz I–Hartz
IV), implemented successively during the years 2003–2005 and were designed to increase
the flexibility of the labor market. Their main purpose was to reduce long-term unem-
ployment.
The reform package started with Hartz I and II, introduced on January 1st, 2003. Both
of these reforms led to increased labor market flexibility by deregulating temporary work,
dismissals and fixed-term contracts. Empirical evidence on these two reforms is provided,
for example, by Bradley & Kügler (2019) who find an increase in mini-job usage. The
Hartz III reform was aimed at increasing matching efficiency on the labor market by
5The unemployment rate in Germany was persistently high at roughly 10 percent and a peak was
reached at 11.1 percent in the year 2005 (Dustmann et al. 2014).
3
restructuring the Federal Employment Agency. It became effective on January 1st, 2004.
For empirical evidence from a macroeconomic point of view on effects of the reform on
matching efficiency see, for example, Launov & Wälde (2016) and Klinger & Weber (2016).
Finally, the Fourth Act for Modern Labour Market Services (commonly known as Hartz
IV) focused on the abolition of long-term wage-dependent support payments and a tran-
sition to fixed benefit levels equivalent to the socio-cultural subsistence level. This final
(and centerpiece) part of the reform became effective on January 1st, 2005. Before this re-
form, there had been a three-tier system consisting of short-term unemployment benefits
(Arbeitslosengeld ALG I ), unemployment assistance (Arbeitslosenhilfe) and social assis-
tance (Sozialhilfe). The short-term unemployment benefits amounted to roughly 60-67 %
of previous earnings and were usually paid for 12 months.
The Hartz IV reform transformed this system into a two-tier system, as depicted in
Figure 1. In particular, the reform comprised the following elements: merging of un-
employment assistance (Arbeitslosenhilfe) and social assistance (Sozialhilfe) into unem-
ployment benefit II (ALG II ); reduction of the period of entitlement to unemployment
benefit (ALG I) from a maximum of 32 to a maximum of 18 months; reduction of sup-
port for children and young people, extended means testing (crediting of own fortune
and income of partners against transfer payments) and new and stricter sanctions for
unfulfilled conditions in the search for employment. The reform therefore led to a dra-
matic cut in received benefits for the long-term unemployed, since they were no longer
eligible for long-term unemployment assistance (which was wage-dependent). As a result
of the reform (i) the probability of unemployment increased and (ii) the consequences of
unemployment in terms of wage cuts were more severe. Workers who rely on short-term
unemployment benefits, now lose their eligibility much sooner and thus experience a much
sharper reduction in benefits than before the reform.
In a similar vein, Hartung et al. (2018) also highlight, particularly for long-term em-
ployed workers with previously high wage payments, that the Hartz IV reform represents
a drastic reduction in benefits. This is also reported by Bradley & Kügler (2019), who find
4
Figure 1: Hartz IV reform: reduction in the outside option
Unemployment benefit Unemployment benefit
(ALG I): (ALG I):
60% 60%
Max. duration: 12-32 months Unemployment assistance Max. duration: 12-18 months
(until retirement)
53%
Unemployment benefit (ALG II):
Means tested
Social assistance:
Standard Rate in 2005: 
Means tested West 345€ / East 331 € 
Standard Rate in 2004: 279€
Unemployment Duration Unemployment Duration
Before Hartz IV Post Hartz IV
Notes: This figures shows the affects of the Hartz IV reform for a single household. The reform trans-
formed the three-tier system of unemployment benefits (‘Arbeitslosengeld’), unemployment assistance
(‘Arbeitslosenhilfe’) as well as social assistance (‘Sozialhilfe’) into a two-tier system of only unemploy-
ment benefits and social assistance (‘ALG II’). Slightly deviating illustration from Hochmuth et al. (2019).
that benefit payments were significantly reduced, especially for unskilled workers. This,
however, was intended and the reform was designed to shift the focus from unemployment
benefits as a form of insurance to incentives to take up work in such situations.
2.2 A simple bargaining model
In this section, we theoretically relate the exogenous reform shock to labor market institu-
tions such as unions. Drawing from the rent-sharing literature, we show a model of union
bargaining in which the threat point of unions is lowered because of the exogenous shock
on alternative income stemming from the Hartz IV legislation. In this literature, there are
direct and indirect factors affecting bargaining outcomes for workers in the labor market.
Whereas direct factors increase the power of workers in negotiations (e.g. Blanchard &
Giavazzi 2003), indirect factors change the threat point (or outside option) should the
negotiations break down. Our focus is on the latter, and there are in fact a few studies in
this context which investigate indirect effects stemming from welfare services in several
5
Benefit Level
Benefit Level
countries (e.g. Stockhammer 2017; Onaran 2009; Jayadev 2007).6
Explanations of the labor share based on bargaining power have to assume a rent-
sharing framework in which economic rents at either the organizational or the country
level have to be shared between capital and labor. Thus, a firm is not a price-taker and
possesses market power (De Loecker et al. 2020). In our model, however, the markup does
not arise because of markups stemming from product markets. Our markups arise from
the power of unions to shift the wage above its marginal product of labor. For a theoretical
foundation, we derive a simple model in which we assume a market with two duopolists
(firm 1 and firm 2) and a union which are involved in bargaining. The union’s utility
function is based on risk-neutral agents and is specified for the maximization of the rent
of its members. The rent that employee’s realize is the difference between the wage w and
an alternative wage wa. The monetary value of the alternative wage is determined either
by unemployment benefits alone, or by a weighted average of (i) the wage when employed
in another company and (ii) the unemployment benefit. The weights are the results of
the employees’ assessment of the probability of the two alternatives occurring. The value
of wa determines the lower limit of the negotiated wage w or the threat point during wage
negotiations in case negotiations fail. We focus in this paper on the relative change in
workers’ bargaining power. The introduction of the Hartz IV reform as outlined in Section
2.1, has led to a deterioration in financial support for large parts of the workforce. We
therefore assume that with the implementation of Hartz IV, wa has decreased for parts of
the workforce or at least is a very credible threat for lower wages when bargaining fails.
In the bargaining model, the rent per employee is multiplied by the number of employees
who are members of the union. The aim of the union is to maximize the difference between
the wage w and the alternative wage wa which is simultaneously the threat point of the
union. The term N̄ is considered as union membership in which not all employees from
the pool of employment N have to be union members (0 < N ≤ N̄). We consider the
6Although direct effects of bargaining power are not specifically considered in this paper, we include
union density as a measurement of direct bargaining power in our regressions to adjust for this channel.
6
following union’s objective function of a utilitarian form:
U(w) = N(w − wa) (1)
The function in Equation (1) is the well-known Stone-Geary utility function with risk-
neutral workers which, for example, is applied in other bargaining models (e.g. Blanch-
flower et al. 1996; Dobbelaere 2004). We also assume that, in an event of bargaining delay,
the firm earns zero profit because of the lack of workers, and employees receive the alterna-
tive wage wa since they are unemployed for the time-being. Because of the dual structure
of the industrial relations systems in Germany, unions at the industry-level usually bar-
gain with employers’ associations and determine wages but not employment. Thus, the
bargaining framework in this paper considers wage bargaining, since the determination of
employment levels is outside the scope of unions.7
Firm’s utility is symmetric for firm i, where i = 1, 2 in this model and equals its profits
πi which is the output qi times the price p. Output is produced using a Cobb-Douglas
production technology in which we assume no fixed costs F and labor as the only variable
input factor. Thus, the simple production function is qi = N in which the firm only has
to pay the input costs w. The profit function then reads as follows:
πi(w,N) = pqi − wqi (2)
For pricing, the following linear inverse demand function is assumed:
p = d− b(q1 + q2) (3)
As usual and shown in Equation (2), firms maximize the difference between sales and
7On the firm-level, however, wages are outside the field of application since they are determined on
the industry-level by unions. In this level, firm owners or managers bargaining with co-determination
institutions such as works council to determine employment. For a bargaining model on the company-
level see for example Kraft (1998). For the empirical wage determination depending on different contracts
between German unions and employer associations, see for example Fitzenberger et al. (2013).
7
costs which leads to the following profit function for firm 1:
π1 =(d− b(q1 + q2))q1 − wq1 (4)
=(d− b(q1 + q2)− w)q1
We consider the more realistic case of asymmetric generalized bargaining power (e.g.
Dobbelaere 2004; Blanchflower et al. 1996) in which the bargaining power of two players
is denoted by φ for the firm and 1 − φ for the union. The aims of the two parties are
combined by the well-known Nash bargaining solution with Equation (1) and (4):
Φ = ((d− b(q1 + q2)− w)N)φ(N(w − wa))1−φ (5)
For pure wage bargaining (and not efficient bargaining), N must be replaced by a func-
tion of w, respectively N(w), before maximizing this Nash bargaining function. For this
purpose, the profit function in Equation (4) is differentiated with respect to qi and solved
for output. Under the assumption of symmetric duopolists (with q1 = q2), this leads to:
d− w
q1 = (6)
3b
This function is inserted into the bargaining Equation (5) and after taking the logarithm,
this function reads:
( ) ( )
(d− w)2
lnΦ = φ ln + (1− (w − wa )(d− w)φ) ln (7)
9b 3b
From differentiation Equation (7) with respect to w (i.e. ∂lnΦ) follows:
∂w
1
w = (φ(wa − d) + wa + d) (8)
2
Unsurprisingly the negotiated wage w increases with wa. Inserting Equation (8) for w
8
into the expression for q1 which is Equation (6) gives the output and labor demand:
(1 + φ)(d− wa)
N = q1 = (9)
9b
Output and thus also the demand for labor decrease with higher wa. Then, in this Cournot
model profits are given by:
q2 (1 + φ)21 (d− w 2a)π1 = = (10)
b 36b
Therefore as shown in Equation (10), profits also fall with wa. We conclude from this
simple model that in the case of a lowered outside option resulting from the Hartz IV
legislation, wages will decrease, labor demand will increase and profits will rise. These
results are consistent with existing empirical research in which Grüner (2019) provides an
overview.
The less obvious question, however, is what happens with the labor share if wa falls.
The labor share here is defined as ls = wN/pq, and since in this simple model q = n, the
expression reduces to ls = w/p. By use of Equations (3) and (9) the following expression
for p can be derived:
1
p = d− (1 + φ) (d− wa) (11)
3
Then, the labor share ls is now:
1 (φ(wa − d) + wa + d)
ls = 2
d− 1
(12)
(1 + φ) (d− wa)3
As a final step, to show the effect of changes in the alternative wage wa, we take the
derivative with respect to this coefficient:
∂ls 3 (1 + φ) d
= > 0 (13)
∂wa 2 ((2− φ) d+ (1 + φ)wa)2
As evident from Equation (13) and outlined in the theoretical Section 2.1 in this paper,
the labor share ls falls with decreasing wa.
9
3 The Hartz reforms as a structural break in the la-
bor share
3.1 Data sources and measurement
We want to begin by identifying the Hartz IV reform, which was implemented on January
1st, 2005, as a significant break point in the time series of the German labor share. Tests
for structural breaks in an economic context actually have a long history, starting with
the early work Chow (1960) and Quandt (1960). More recent theoretical contributions
include Bai & Perron (1998); Han & Park (1989) as well as Hansen (2001), and nowadays
there are many applications of change point tests in different fields (e.g. Lunsford 2020;
Antoch et al. 2019; Link & van Hasselt 2019; Wiese 2014; Jayachandran et al. 2010).
The general idea is to check whether an economic reform or an intervention constitutes
a fundamental change in the data generating process and thus can be interpreted as a
change point. We apply different exogenous and endogenous tests to check whether the
introduction of Hartz IV in Germany in the year 2005 constitutes a significant impact
on the labor share. Whereas in exogenous tests we must explicitly define the year of the
break point, endogenous tests detect the break point year from within the data.
We use the data from the EU KLEMS8, revision 2019 dataset, which we combine with
data from the Penn World Tables and the OECD STAN database. Then, we calculate
the labor share for Germany for the years 1970 to 2015. The labor share LSt is defined
as
WtLt
LSt = (14)
Yt
where the expression WtLt denotes labor compensation and Yt gross value added at year t.
One additional advantage of the EU KLEMS dataset is the consideration of self-employed
workers who are often neglected when calculating the labor share (e.g. Cette et al. 2020).
In using this data, we therefore assume that the self-employed receive the same hourly
wage as employees in every industry and year and thus prevent measurement errors in
8For a comprehensive discussion of the dataset and methodology, see Stehrer et al. (2019).
10
the labor share calculation (Stehrer et al. 2019).
Figure 2: Trend in the German labor share
Hartz Reforms
1970 1980 1990 2000 2010 2020
Year
Notes: This figure shows the trend in the German labor share LSt over the years 1970 to 2015. The
German labor share is calculated as the ratio of labor compensation to gross value added for all industries
in year t as described in Equation (14). The data for the EU KLEMS release 2019 can be obtained on
https://euklems.eu/. For an overview of variable construction and methodology see Stehrer et al. 2019.
The blue shaded area indicates the implementation of the Hartz legislation in which Hartz I and II are
implemented in 2003, Hartz III in 2004 and finally Hartz IV in 2005.
As shown in Figure 2, the aggregated labor share for Germany is in line with several
other studies (e.g. Karabarbounis & Neiman 2014).) There are three main events in recent
decades which contribute to a change in the labor share in Germany. First, changes in
the 70s can be attributed to the two oil price shocks in which the labor share sharply
increases (Berthold et al. 2002). Second, the German reunification in 1990 also constitutes
a sharp increase in the labor share because of large monetary transfers from western
to eastern Germany in which the currency was not devalued.9 And, finally, the Hartz
reforms contribute to a significant decline in the labor share in which the share stays
rather constant hereafter. The only exception and sharp increase is due to the financial
crisis in the year 2009, which can be explained by sticky wages and labor hoarding, which
primarily affects capital incomes (Bazillier & Najman 2017). The literature suggests
9For an synthetic control analysis of the effects of the German reunification on GDP, see for example
Abadie et al. (2015).
11
Labor Share
0.64 0.66 0.68 0.70 0.72 0.74
that many firms use working-time arrangements such as ‘time accounts’ or other work-
sharing schemes (Teague & Roche 2014). Empirical studies indeed find that the labor
share increases in times of economic downturn, as for example the great financial crisis in
Germany of 2008–2009 (e.g. Bazillier & Najman 2017). Whether these changes, however,
are significant in a statistical manner is the question which obviously presents itself. In
the following we therefore test these hypotheses using structural break tests.
3.2 Supremum of a sequence of Wald tests
As it is apparent from Figure 2, there is a notable decline in the labor share around the
Hartz legislation between the years 2003 and 2005. Around this period, Figure 2 suggests
a change point in the mean of the labor share. Of course, we could apply a simple t-test for
pre- and post-reform mean differences using time dummy variables. However that would
require that the break occurs at a known point in time. This is easy in principle, since we
know the exact time of the implementation of the Hartz reforms and the potential break
points10 Choosing a fixed break date, however, might nevertheless be arbitrary since we
do not know whether there are any delay or anticipation effects of the reform (e.g. Wiese
2014; Piehl et al. 2003).
To solve this problem we apply endogenous tests for structural breaks in the mean for
unknown break dates (e.g. Lunsford 2020; Wiese 2014; Jayachandran et al. 2010; Hansen
2001). The endogenous approach is much more reliable than the one with, for example,
exogenously determined breakpoints because the endogenous test checks all possible al-
ternatives. As a first test, we therefore calculate Wald test statistics to determine whether
there is indeed a structural break for a variety of break dates and take the maximum as
the test statistic (Chow 1960; Quandt 1960). We test for a break in the mean of the labor
share (LSt) in year τ between t = 1, . . . , T where t = 1970 and T = 2015 estimating the
10In such cases, the Chow test might be a feasible alternative (Chow 1960).
12
following model several times11 for every possible break point,
LSt = α + δtDt(τ) + γtrend+ εt (15)
where Dt(τ) describes an indicator variable with Dt(τ) = 1 if t > τ and Dt(τ) = 0
otherwise. Thus, we test for all possible breaks in the mean for each year in the interval
1975 to 2009.12 Given our stationary time series, which we confirm using a Dickey-Fuller
test, we include a trend variable (e.g. Rodriguez & Jayadev 2013) and define the following
Wald test statistic in which there is no change before and after the Hartz IV reform in
the null hypothesis:
H0 : δt = δ0 ∀t,
δ1, t = 1, . . . , TπH1(π) : δt =  (16)δ2, t = Tπ + 1, . . . , T,
where the parameter π(0, 1) is the sample fraction before and after the break point and
Tπ corresponds to the year of the change point. Then, we test the null hypothesis that
there is no break point which is δt = 0.
The maximum value of the Wald statistic (sup Wald) over all possible breaks is used
to verify the break point and the significance of the break. Figure 3 shows the values for
every possible Wald test statistic for each year. The red line indicates the critical value
provided by Andrews (1993, 2003) for the assessment of significance.
As shown in Figure 3, the test statistic exceeds the critical value in the year of Ger-
man reunification in 1990. Hereafter, the test stays significant, indicating that German
reunification constitutes a rather lasting impact on the share of labor. The second break
is indicated in the year 2005, which is also the maximum of the Wald test statistic (sup
11We also estimated the model with successively added control variables in which we include the
number of strike days, the unemployment rate as well as the growth rate of GDP. Results can be found
in Table A.4 and Table A.5 of the Appendix.
12The test uses a slightly smaller sample size to ensure that the test has enough power. A common
approach therefore is to trim 15 percent from both ends of the sample (e.g. Jayachandran et al. 2010).
13
Figure 3: Wald test statistic for structural break
5 0 5 0 5 0
97 8 8 9 9 0 0
5 10
1 19 19 19 19 20 20 20
Year
Notes: The figure shows values of Wald test statistics as outlined in Equations (15) and (16). Test for
a change point in the mean of the labor share (LSt) in year τ between t = 1, . . . T where t = 1975 and
T = 2009. The labor share is calculated as outlined in Equation (14). The blue line shows the values of
the test statistics. The maximum value (sup Wald) of the Wald test statistic is 23.32, which occurred
in 2005, which is exactly in the middle of the Hartz legislation. The red line indicates the critical value
of the test statistics as provided by Andrews (1993, 2003). Values of the test statistics are provided in
Table 1. We trim 15 percent from both ends of the sample to ensure that the test has sufficient power.
Wald). It seems, therefore, that the Hartz IV reform is a profound structural break in the
mean of the German labor share. Table 1 presents results for the applied single structural
break tests. The p-values are calculated by the method provided by Hansen (1997) and
the test statistic are derived and tabulated by Andrews (1993, 2003). In addition to the
supremum Wald test we also apply an average Wald and exponential Wald test. These
tests tend to have more power compared to the supremum test (Andrews & Ploberger
1994). Our results, however, do not change.
3.3 Bai and Perron test for multiple breaks
The sequence of Wald tests are frequently applied in the empirical literature (e.g. Lunsford
2020; Link & van Hasselt 2019; Jayachandran et al. 2010; Piehl et al. 2003; Hansen 2001),
however these tests are limited to the occurrence of only one break point. A look at the
labor share time series in Figure 2 reveals, however, that there might in fact be more break
points. We therefore expand the analysis and additionally allow for unknown timings and
14
Wald Test Statistic
0 5 10 15 20
Table 1: Values for Wald test statistics
Value of test statistic Break year p-value
Test (1) (2) (3)
Supremum Wald 23.32 2005∗∗∗ .0002
Average Wald 12.10 .0005
Exponential Wald 8.99 .0003
Notes: This table reports values of the Wald test statistics as outlined in Equa-
tions (15) and (16). Test for a change point in the mean of the labor share (LSt)
in year τ between t = 1, . . . T where t = 1975 and T = 2009. The labor share
is calculated as outlined in Equation (14). Critical Values were obtained from
Andrews (1993, 2003).
different numbers of change points in the labor share time series using the Bai & Perron
(2003, 1998) test for multiple break points.13
The idea of the test is to create a step-by-step route through the adjusted labor share
time series LSt and create an optimal model with m breaks in m+1 regimes. Drawing on
a linear regression model (e.g. Casini & Perron 2019), we consider a model of the following
form. In addition to a common method in which only a constant term is included (Wiese
2014), we also include the trend in the following regression model.
LSt = δ1 + β1x+ ut, t = 1, 2, . . . T1 (17)
LSt = δ2 + β2x+ ut, t = T1 + 1, . . . T2
...
LSt = δm + βmx+ ut, t = Tm + 1, . . . T
in which the dependent variable is the labor share LSt and δm being a vector of estimated
constants of m+ 1 possible regimes. Thus, it is the mean of the different segments which
are divided into m breaks. The test then checks whether the change points are statistically
significant. The number of break points is selected according to the lowest overall residual
sum of square (RSS) for a given number of breaks and the Bayesian information criterion
(BIC) which are shown in Figure 4. Both criteria refer to the optimal number of m = 3
breakpoints, dividing the labor share time series in Figure 2 into m+ 1 = 4 regimes with
13See for example Wiese (2014); Benati (2007) for a similar application of the Bai & Perron test as
well as Casini & Perron (2019) for a general assessment of structural break tests in time series.
15
different intercepts.
Figure 4: Optimal number of break points
● B●IC
RSS
●
●
●
●
●
●
●
0 1 2 3 4
Optimal number of structural breaks
Notes: This figures shows the values of the selection criteria of the optimal number of unknown break
points m in the (Bai & Perron 1998, 2003) test. According to the lowest residual sum of square (RSS) and
Bayesian information criterion (BIC), the labor share times series in Figure 2 is divided into m + 1 = 4
regimes as shown in Figure 5.
The Bai & Perron (1998, 2003) test has different sequential stages, which will be briefly
outlined. First, a supF type test is carried out to determine whether there is no structural
break (m = 0) at all or a fixed number of breaks (m = k). In the next step, the null
hypothesis that no structural break is present is tested versus the alternative hypothesis
of an unknown number of structural breaks, with an upper limit being set. This test
is implemented with double maximum tests. The first of these tests is based on equal
weighting, while the second uses weights for the individual tests, which are calculated
in a way that the marginal p-values are equal across values of m. The weighting is
implemented because with an equal weighting the power of the test decreases when the
number of structural breaks increases.
The next step is to identify the optimal number of structural breaks. Bai & Perron
(1998, 2003) propose a test for a particular number of structural breaks l versus l + 1.
The corresponding test supFt (l + 1|l) then gives the maximum of the F-statistic, which
tests the null hypothesis that no additional structural break exists versus the existence of
16
−270 −265 −260 −255 −250
0.003 0.004 0.005 0.006 0.007 0.008 0.009
an additional structural break. This test is performed sequentially for all possible points
in time. The optimal number of structural breaks is then identified using residual sum of
square (RSS) and the Bayesian information criterion (BIC). The approach allows for non-
symmetric confidence intervals since the variance before and after a break does not have
to be constant. Furthermore, the variance covariance matrix is robust to serial correlation
and heteroscedasticity (Andrews 1991). The results of the described sequential testing
procedure are summarized in Figure 4. The number of breaks is plotted on the horizontal
axis, while the two vertical axes show the values of the BIC statistics and the residual
sum of squares. The BIC has its minimum at three breaks.
Figure 5: German labor share with identified break points
1970 1980 1990 2000 2010
Year
Notes: Own calculations using the EU KLEMS 2019 release. The German labor share over the year
1970–2015 is calculated as the ratio of labor compensation to gross value added for all industries as
shown in Equation (14). Dotted lines show endogenously identified change points using the Bai & Perron
(1998, 2003) test explained above. Red bars at the bottom indicate 95 % confidence intervals around the
estimated break point. The break points occur after the oil crisis in 1981, in 1990 during the period of
East and West German reunification as well as in the year 2004 during the implementation of the Hartz
reforms.
Figure 5 shows the exact times identified by the Bai & Perron (1998, 2003) test which
coincides exactly with the change points we earlier identified in our optical inspection
of the time series. Even more interesting, the first break occurs right after the second
oil price crisis in the year 1981 in which the oil prices rapidly fell (Autor et al. 2020).
17
Labor Share for Germany
0.64 0.66 0.68 0.70 0.72
Thus, the severe drop in oil prices might spur capital intensive production thus leading
to a decline in the labor share. The second break occurs shortly after East and West
German reunification in 1990 and the third break occurs at the time of the introduction
of the Hartz reforms in the year 2004. 95 % confidence intervals are shown in Figure 5
around the break points. Because of our rather short time series, since we use yearly data
compared to daily or monthly data, for example, the confidence intervals are quite broad.
Nevertheless, the breakpoints are consistent with the previous analysis of Wald statistics,
which is summarized in Table 1. Important to note in our analysis, however, is the fact
that these change points are endogenously identified within the labor share time series
and interestingly they also highlight the Hartz reforms as having a significant impact.
To summarize, we use an endogenous Wald test for a single break point as well as the BP
test for the identification of multiple endogenous break points. We can indeed verify that
the Hartz reforms in Germany constitute a significant shift in the mean of the labor share.
This result can be explained by the fact that the introduction of the Hartz IV reform has
reduced the outside option in our bargaining framework for employees and therefore had
a negative impact on the outcome in wage negotiations. The macroeconomic analysis has
the advantage that tests on structural breaks can be carried out without predetermined
break points and with several breaks. The disadvantages, however, are the small number
of observations and the lack of a cross-sectional dimension. It is quite likely that industries
and firms are affected differently, in particular when estimates are additionally adjusted
by control variables. For example, the decline in the degree of trade union organization or
the increasing decentralization of the negotiation process (e.g. Dustmann et al. 2014) may
explain the low wage increases, and in fact the often discussed real wage reductions in the
2000s. Since variables vary between sectors and firms, we carry out additional research
using different control variables to adjust for these channels in the following section. The
estimates are further supported by a synthetic control method on the aggregated labor
share as well as system GMM estimation for firm-level evidence.
18
4 Impact of the Hartz IV reform
4.1 First results using aggregated data
The structural break tests indeed indicate a significant break right before the Hartz IV
legislation in Germany became effective in the year 2005. In this section we therefore
inspect the effect of this exogenous shock of the Hartz IV reform on the aggregated labor
share. As outlined in Section 2.2, Equation (13), ), we expect that the exogenous negative
shock on the outside option in the bargaining equation subsequently results in lower wages
and, therefore, in a decrease in the labor share. To examine our hypothesis, we first apply
ordinary least squares (OLS) regressions of the following form14:
LSt = α + β1HartzIVt + β2Unemp+ β3Strike (18)
+ β4Union+ β5ExImRatio+ β6trend+ εt
Where LSt is the labor share in Germany ranging from t = 1970 to T = 2013. As
control variables we include the trade union density (Union), which is a measure for
the bargaining power of employees15. In fact, there is much literature about the impact
of labor unions on the distribution of incomes and factor shares by different channels.
First, there are direct positive effects stemming from bargaining in which labor unions
reduce within-group as well as between-group wage inequality (e.g. Kristal & Cohen 2017).
Furthermore, and more in line with our research, a strand of literature suggests that labor
unions affect the compensation of the management and also returns to capital (e.g. Lee
& Mas 2012). Second, a more recent paper suggests that labor unions do not affect the
wages of employees directly, but rather that positive distributional effects arise from more
generous fringe benefits (e.g. Knepper 2020). In this context, Card et al. (2020) provide
a very recent overview on labor unions and inequality.
In addition, we also include the unemployment rate of Germany (Unemp). A higher
14Results from a regressing the labor share on year dummies is provided in Figure A.6.
15Trade union density is measured as the members in the German federation of trade unions in the cor-
responding year (which can be found here: https://www.dgb.de/uber-uns/dgb-heute/mitgliederzahlen)
over the total employment as reported in the EU KLEMS dataset.
19
un- employment rate constitutes a higher risk for employees to go looking for a new
job and hence there is less bargaining power for employees. Unemployment in this view
constitutes a higher threat which restricts the demands and thus the power of employees
and unions within a bargaining framework. We also include lost workdays due to strike in
1,000 employees, strike as an additional measure for workers’ bargaining power. Finally,
the export-import ratio (ExImRatio) is included, which is a measure for trade openness
and globalization (e.g. Elsby et al. 2013). We expect this variable to carry a negative sign
since there is much evidence that the relationship between globalization and the labor
share is negative (Elsby et al. 2013).
Table 2 shows the descriptive statistics for the EU KLEMS data which is used for
estimating Equation (18).
Table 2: Descriptive statistics for German EU KLEMS sample (1970–2013)
Mean Std. dev. Min Max
Variables (1) (2) (3) (4)
Labor share 0.69 0.03 0.64 0.73
Unemployment rate 7.09 3.12 0.58 11.72
Trade union density 0.32 0.04 0.24 0.41
Export-import ratio 1.00 0.11 0.80 1.19
Lost workdays 24.05 60.01 0.40 278.60
Year 1970 2013
Observations 44
Notes: The table shows the descriptive statistics for the German
labor share sample ranging from 1970 to 2013. Data from the EU
KLEMS release 2019 dataset and trade union information from the
German federation of trade unions. Lost workdays due to strike from
the Hans Böckler Foundation, per 1,000 employees. The labor share is
calculated as LS = WtLtt Y as explained in Section 3. For an overviewt
of variable construction and methodology see Stehrer et al. (2019).
First results from estimating Equation (18) using OLS are presented in Table 3 with
additionally adding control variables in column (2). As expected and derived in the
theoretical model, the Hartz IV reform has a significantly negative impact on the labor
share in the magnitude of -2.7 percentage points when adjusting for control variables.
Regarding the control variable as shown in column (2) of Table 3, the unemployment rate
also carries a negative sign as described above. The results are also similar when we use
20
Table 3: Results for OLS regression for the German labor share
Labor Share
(OLS) (OLS)
(1) (2)
Hartz IV -.028*** -.016*
(.006) (.009)
Unemployment rate -.001
(.001)
Lost workdays -.016
(.018)
Trade union density .191**
(.090)
Export-import ratio -.061
(.037)
Linear trend -.001*** -.001*
(.000) (.000)
Constant .725*** .728***
(.004) (.043)
R2 .817 .838
Observations 44 44
Notes: This table show results from estimating Equation (18). Data
from the EU KLEMS release 2019 dataset and trade union information
from the German DGB trade union association. The labor share is
calculated as LS = WtLtt Y as explained in Section 3. For an overview oft
variable construction and methodology see Stehrer et al. (2019). Results
from regressing the labor share on year dummies is provided in Figure
A.6. Robust standard errors in parentheses. *, **, and *** denote
statistical significance at the .1, .05 and .01 level.
year dummy variables instead of a Hartz 4 indicator variable as shown in Figure A.6 in
the Appendix. The coefficient on trade union density has an expected positive sign and
measures the impact of an increase in bargaining power of employees on the labor share
(e.g. Brock & Dobbelaere 2006). Finally, the measure of globalization (export-import
ratio) also has a negative coefficient. As expected and shown in various studies, trade
openness and globalization lead to more offshoring of labor-intensive work and thus a
decrease in the labor share (e.g. Elsby et al. 2013).
21
4.2 Synthetic control method using a counterfactual Germany
By application of endogenous structural break models and simple OLS regressions as
shown in Table 3, our results presented so far support the hypothesis that the Hartz
reforms affected the labor share. In the next step we take possible selectivity effects into
account.
Considering causal models, there is the well-known fundamental problem of causal
inference which states that it is only possible to observe outcomes for entities (such as
countries or firms) which are either treated or untreated (e.g. Rubin 1974; Imbens &
Wooldridge 2009). A clearly defined control group with similar characteristics as the
treatment group is therefore needed to draw causal conclusions. In our specific case,
however, the Hartz reforms affected the whole economy in Germany and the labor share,
and there is no natural control group. In the next step we therefore apply what we
consider as a more advanced form of structural break analysis, which is known as the
synthetic control method to tackle the fundamental problem of causal inference (e.g.
Abadie et al. 2010, 2015; Abadie 2020). This method is not only more in line with recent
developments in econometrics (e.g. Imbens & Wooldridge 2009) but also referred to as
one of the most important innovation in the recent policy evaluation literature (Athey &
Imbens 2017). In fact, there is an ongoing further development of this method regarding
the implementation of covariates (e.g. Botosaru & Ferman 2019) as well as many empirical
applications in different fields of economics (Chen 2020; Peri & Yasenov 2019)
Data and sample construction. For the application of the synthetic control method
and the construction of a ‘synthetic twin of Germany’ the analysis requires additional
data on other countries. These countries are referred to as the donor pool to construct
the German doppelganger. We therefore need more information on industry particularities
of other countries and thus we combine the EU KLEMS dataset with the Penn World
Tables 9.0 database16 for information regarding GDP spending and the OECD STAN
16The Penn World Table database 9.0 covers information on relative levels of income, output, input
and productivity for 182 countries between 1950 and 2014. For an overview of the methodology as well
as variables see for example Feenstra et al. (2015). Missing data on the unemployment rate for various
countries were supplemented by World Bank data.
22
database for trade union density. Unfortunately, we do not have such rich information
for other countries that allow us to create such a long time series as we have for Germany
starting in the 1970s. Our analysis in this section therefore starts in the year 1995, for
which we have all information on control variables. Descriptive statistics are provided in
Table 4.
Table 4: Descriptive statistics for EU / World sample
Mean Std. dev. Min Max
Variables (1) (2) (3) (4)
Labor share 0.62 0.06 0.49 0.86
Trade union density 32.35 21.20 5.50 95.80
Unemployment rate 8.27 4.05 2.25 27.48
Human capital index 3.21 0.27 2.55 3.73
Share of gross capital formation 0.25 0.05 0.10 0.47
Share of government consumption 0.19 0.05 0.09 0.42
Share of exports 0.48 0.27 0.08 1.39
Share of import -0.51 0.28 -1.47 -0.11
Year 1995 2015
Observations 412
Notes: The table shows the descriptive statistics for the shorter but more comprehen-
sive country panel dataset. Data from the EU KLEMS release 2019, Penn World Table
9.0, OECD STAN as well as World Bank. The labor share is calculated as LS = WtLtt Yt
as explained in Section 3 for each country. Figure A.1 on the Appendix provides the
labor share trends for each country. Data sets are merged using country names and
the corresponding year. For an overview of the EU KLEMS data see Stehrer et al.
(2019) and for Penn World tables see Feenstra et al. (2015). More information re-
garding the human capital index is provided in Table A.1. The sample comprises the
countries: Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France,
Greece, Hungary, Ireland, Italy, Japan, Latvia, Lithuania, Luxembourg, Netherlands,
Poland, Slovenia, Spain, Sweden, United Kingdom and the United States.
Methodology. Following the notation of Abadie et al. (2010), we apply the synthetic
control method for the case that a single unit (Germany) is exposed to some treatment
(the Hartz IV legislation) and there is no natural control group. The other (J+1) countries
remain unexposed to the reform and are referred to as the donor pool. This pool is then
used to construct the Germany doppelganger as a counterfactual Germany without the
Hartz legislation. Basically, the idea of this approach is to build a counterfactual Germany
without the Hartz IV reform from the donor pool of the other N = 22 countries17.
17The countries that comprise the donor pool are in alphabetical order: Austria, Belgium, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, Latvia,
23
We observe the labor share for T periods in which the intervention starts in some
period T0 + 1 which is in our case the year 2005. Furthermore, we define the outcomes
Yjt which are the observed outcomes for the treated as well as the control countries. The
fundamental problem in such a causal analysis is that we do not observe the labor share Y1t
for a counterfactual Germany, without the Hartz IV reform, after period T0. Fortunately,
the synthetic control method offers a solution for the estimation of Y1t, by creating a
‘synthetic control Germany’ as a weighted combination of other countries (wjYjt) which
best approximate relevant pre-intervention variables. The weighting vector is defined as
W = (w2, . . . , w(J+1)) in which wj is the contribution of each of the N = 22 donor pool
countries.18 The counterfactual Germany is constructed as a convex combination of the
observed outcomes of the other countries and there should be no difference in the real
and the synthetic Germany prior to the intervention:
∑J+1
Y1t = wjYjt, t = 1, . . . , T0 (19)
j=2
The effect of the intervention for the aggregated time period after T0 is then obtained
by the difference of Equation (19) for the time∑period after the intervention compared to
prior to the intervention which is δ = Y − J+1jt 1t j=2 wjYjt. This can be estimated using
a difference-in-differences (DiD) framework in which we regress the difference between
the real and the synthetic Germany on a Hartz IV variable which takes unit value for all
years after 2004 and zero otherwise. This synthetic control method derives the well-known
average treatment effect on the treated (ATT) (Abadie 2020).
Country Weights and Counterfactual Germany. As shown in Table 5 there are
four states which in particularly resemble the German trend in the labor share quite
well. These countries receive the corresponding weight which is shown in Table 5 for
the construction of the counterfactual Germany as shown in Equation (19). Thus, using
Lithuania, Luxembourg, Netherlands, Poland, Slovenia, Spain, Sweden, United Kingdom and the United
States.
18Since Germany is the treatment state it is not part of the weighting vector. Moreover, the weights
are constrained in that wj ≥ 0 and they sum up to one (w2 + . . .+ w(J+1) = 1).
24
the synthetic control method with covariates (e.g. Botosaru & Ferman 2019) as provided
in Table 4 for the construction of the Germany doppelganger, the Netherlands, Spain,
Slovenia as well as the United Kingdom in particular are used as weighted aggregated
comparisons.
Table 5: Country weights from donor pool
Country Weight Country Weight
Austria < 0.01 Japan < 0.01
Belgium < 0.01 Latvia < 0.01
Czech Republic < 0.01 Lithuania < 0.01
Denmark < 0.01 Luxembourg < 0.01
Estonia < 0.01 Netherlands 0.276
Finland < 0.01 Poland < 0.01
France < 0.01 Spain 0.273
Greece < 0.01 Slovenia 0.226
Hungary < 0.01 Sweden < 0.01
Ireland < 0.01 United Kingdom 0.225
Italy < 0.01 United States < 0.01
Notes: This table shows how the weighting vector in Equation (19) is resembled and
which weights (i.e. W = (w2, . . . , w(J+1))) each donor pool country receives for the
construction of the counterfactual Germany. Within the synthetic control method,
variables are averaged for the pre-intervention period 1995 – 2004 (the share of capital
formation, government spending, export as well as imports are averaged 1995 – 1999).
Own calculations using the parametric synthetic control approach (e.g. Abadie et al.
2010, 2015; Abadie 2020).
Balancing of covariates. Similar to other matching algorithms that depend for ex-
ample on the propensity score (e.g. Caliendo & Kopeinig 2008), the credibility of the
synthetic control method also relies on the balancing of covariates. The balancing of the
pre-intervention variable means should be checked, which is done in Table 6 by compar-
ing the means between the weighted control group and treated Germany. In our case, we
construct the synthetic Germany as a convex combination of the 22 donor pool states that
resemble Germany as closely as possible in terms of pre-intervention variables. According
to the literature, we use quite common variables to construct the Germany doppelganger.
First, trade union density and the unemployment rate are included as a measure of
bargaining power (Blanchard & Giavazzi 2003; Bental & Demougin 2010). Also, the share
25
of capital formation (as % of GDP) is included as a measure of capital accumulation in
the economy, which is relevant to account for production capacities (Piketty & Zucman
2014). The share of government consumption is also included as a proxy for the welfare
state (i.e. a proxy for social protection) which is, for example, also applied by Bazillier
& Najman (2017). As a measure for globalization, we include the share of exports and
imports (as % of GDP) (Elsby et al. 2013). And, finally, we account for the stock and
quality of human capital in the economy by using the ‘human capital index’ provided by
the Penn World Tables dataset. For example, firms need human capital to innovate and
improve existing technologies which, in turn, affects capital and the production process.
Thus, recent lines of research suggest accounting for this measurement in labor share
regressions (e.g. Arif 2021).
Table 6: Labor share predictor means before intervention
Germany
Real Synthetic
Covariates (1) (2)
Labor share .684 .684
Trade union density 25.22 28.06
Unemployment rate 8.81 8.44
Human capital index 3.55 3.10
Share of capital formation .251 .252
Share of government consumption .137 .160
Share of exports .356 .356
Share of imports -.355 -.390
Notes: This table shows the mean comparisons of used covariates for the calculation of the
counterfactual labor share which is shown in Figure 6 and the real German labor share.
Means for the synthetic Germany are calculated using the weights provided in Table 5. For
the construction of the weights, all variables are averaged for the pre-intervention period
1995–2004 (the share of capital formation, government spending, export as well as imports
are averaged 1995–1999).
Results of the synthetic control method. Results from the synthetic control ap-
proach in addition to the trends among the synthetic and real Germany, are presented in
Figure 6. Depicted in Table 6, the pre-intervention differences are balanced and trends
between both labor shares are quite similar prior to the Hartz IV treatment. The Hartz
26
IV reform was enacted at the beginning of the year 2005 in which we see a sharp decline
in the German labor share; however, not in the counterfactual trend. Interestingly, both
trends capture the effects of the financial crisis in the year 2009 very well, however the
real German increase is much more pronounced. What is additionally important besides
the strong decline in the real Germany, is the fact that the differences among the labor
share are persistent after the Hartz IV legislation.
Figure 6: Trends in labor shares: real vs. synthetic Germany
Hartz IV
95 96 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
19 19 19
9 99 99 00 00 00 00 00 00 0 0 0 0 1 1 1 1 1 11 1 2 2 2 2 2 2 20 20 20 20 20 20 20 20 20 20
Year
Germany synthetic Germany
Notes: The figure shows the trends in the real and the synthetic labor share of Germany. The labor
share is calculated as outlined in Equation (14). Trends for the synthetic Germany are calculated using
the Netherlands, Spain, Slovenia and the United Kingdom with the corresponding weights as shown in
Table 5, calculation according to Equation (19). All variables are averaged for the pre-intervention period
1995–2004 period (the share of capital formation, government spending, export as well as imports are
averaged 1995–1999). Data from the EU KLEMS, Penn World Tables, OECD STAN as well as World
bank.
Using the synthetic control approach, we are able to compare the real Germany where
the Hartz IV legislation was enacted, with our synthetic control Germany doppelganger
which never experienced the Hartz IV reform. Our graphical results in Figure 6 show the
significant negative impact of the Hartz IV reforms for the aggregated real labor share
27
Trend in the labor share
.6 .62 .64 .66 .68 .7 .72 .74
in Germany compared to the synthetic labor share. Regression results using a Hartz
IV dummy variable which takes unit value after the year 2005 and zero otherwise, yield
similar results as before. The negative reform effect is significant and in the magnitude
of 2.7 percentage points.
Compared to the estimates using the longer time series for Germany only, as presented
in Table 3, the effect of the synthetic method is slightly smaller, but also highly significant.
The decline in the labor share is roughly 1.6 percentage points after the Hartz IV reform
was implemented at the beginning of 2005. The comparison of Germany with the synthetic
control group shows that both follow the same downward trend in labor share over some
time, but in contrast to the control observation this trend became stronger for Germany
after the Hartz reforms. Moreover, the impact of the reform is strongest in the early years
before the great financial crisis (2009), although the difference remains, albeit slightly
smaller in terms of magnitude.
5 Robustness using firm-level evidence
5.1 Benchmark results
In this section we provide evidence on labor share changes stemming from the firm level
(e.g. Harju et al. 2021). The use of firm-level data has two main advantages. First, we
are able to take changing sector and industry composition into account that may affect
the labor share (Siegenthaler & Stucki 2015). Second, as mentioned by Gollin (2002);
Karabarbounis & Neiman (2014), aggregate labor share measures may be confounded by
capital incomes earned by entrepreneurs and sole proprietors. We use firm-level data
stemming from the ‘dafne’ dataset compiled by Bureau van Dijk which allows us to
measure the impact of a change in the outside option more precisely. We use information
for the years 2000–2011.
Dependent variable For the dependent variable, we use the same variables as ex-
plained earlier in Equation (14). Thus, we measure the labor share as the share of labor
28
compensation to value added of the firm. We measure value added as the gross output
minus intermediate inputs, depreciation as well as interest expenses. See Figure A.7 for
a histogram of the labor share and Figure A.8 for the development of the labor share.
Comparing the firm-level labor share with the aggregated German labor share, we see a
quite similar development; a sharp decline around the Hartz legislation as well as a spike
during the financial crisis.
Control variables With respect to control variables, we implement variables which are
common in the literature as determinants of the labor share. First, in neoclassical growth
models, the labor share is a function of the capital-output ratio (Bentolila & Saint-Paul
2003; Siegenthaler & Stucki 2015). Thus, we implement the logarithm of the capital-to-
output ratio as an explanatory variable. The sign of the capital-to-output ratio depends
on the elasticity of substitutions between capital and labor (Siegenthaler & Stucki 2015).
In the case where labor and capital are complements, the capital-output-ratio increases
the labor share. In the case of a substitutive relationship between capital and labor,
the capital-output ratio decreases the labor share. The empirical literature usually finds
controversial signs in different studies.
To account for unobserved demand shocks within the regression framework, we also
add the logarithm of the ratio of intermediate inputs to firms’ value added and its square
to the regression equation. The idea is to take changes in the input factors into account
when firms are hit by various demand shocks (e.g. Levinsohn & Petrin 2003; Siegenthaler
& Stucki 2015). The labor share also depends on the degree of organization of the work-
force or unions. In line with the literature, we expect a negative sign of this variable.
However, the relevance of collective bargaining agreements as well as the trend of declin-
ing unionization (Oberfichtner & Schnabel 2019) we therefore expect lower wages (e.g.
Akyol et al. 2013).
In the case of a rather inelastic demand curve this also implies a reduction of the labor
share. With respect to the sign of the coefficient, we therefore expect a positive sign of our
union measure. With respect to the union measure we calculated a unique measure for
29
union density on the industry level. See Section A.3 in the Appendix for the construction
of the index. We also include detailed NACE (rev. 2.0) two-digit industry-fixed effects
as well as year-fixed effects in the regression model. Finally, we include further control
variables subsumed in Xit. The vector includes an indicator variable whether the firm is
a stock company or a Societas Europaea (SE) and whether the firm is located in Western
Germany. Descriptive statistics are provided in Table 7.
Table 7: Descriptive statistics for firm-level data
Mean Std. dev. Min Max
Variables (1) (2) (3) (4)
Laborshare .456 .173 .001 .998
ln (Capital-output ratio) .139 .271 -5.22 4.17
ln (Intermediate inputs) .689 .546 -.559 6.95
ln (Intermediate inputs squared) .769 1.55 .001 48.42
Trade union density .194 .095 .008 .960
No stock company .736 .440 0 1
Stock company .261 .439 0 1
Societas Europaea (SE) .002 .048 0 1
Western Germany .762 .425 0 1
Year 2000 2011
Observations 38,808
Notes: The data is based on the “dafne” dataset compiled by Bureau van Dijk; years
2000 – 2011. The labor share is calculated as LS = WtLtt Y as explained in Section 3.t
Trade union density is measured at the industry level as outlined in Section A.3.
Regression framework We apply a quite common regression framework for labor share
regressions by using the logarithm of the defined labor share as the dependent variable
ln(LSit) for firm i in year t as follows:
ln(LSit) = β0 + β1ln(kit) + β2HartzIV + β3Orgit + β4Zit
+ β5Xit + µi + θt + εit (20)
In this specification the labor share depends on the capital-output ratio (kit), a set of
firm specific control variables (Xit) such as being located in Western Germany or being
a limited liability company. We estimate this specification using ordinary least squares
(OLS), random effects (RE) as well as fixed effects (FE) models shown in Table 8.
30
As a final robustness check and to take potential endogeneity into account, we estimate
System-GMM models (Blundell & Bond 1998). Therefore, we estimate dynamic models
of the labor share with lagged levels of the labor share in the dynamic setting.19 Gen-
erated instruments are stacked into one vector to limit the number of instruments and
prevent weak instruments. Tests support our choice of instruments. To test the validity
of our instrumental variables, we apply the standard Hansen test to check over-identifying
restrictions (Hansen 1982). In addition, the system GMM estimator requires that there is
no significant second-order auto-correlation in the residuals series. We therefore also test
for first AR(1) and second-order AR(2) auto-correlation (Arellano & Bond 1991). With
respect to standard errors, we use the quite standard two-step clustering approach and
apply the Windmeijer (2005) finite sample correction.
Results Similar to our initial results for Germany, as well as the more sophisticated
synthetic control approach, we also find a reduction of the labor share on the firm level
stemming from the Hartz IV legislation. The size of reduction is very similar to the
magnitude found in the regressions on the aggregated labor share series earlier. These
firm-level results are consistent among pooled OLS, random and fixed effects as well as
system GMM estimation.20 With respect to the latter estimation results, the test statistics
also support our results. After adjusting for time specific shocks in the labor share series
using year-fixed effects, the Hartz IV dummy variable points to a significant negative
relationship in the magnitude of around two percentage points. The point estimates
are consistent among specifications and similar to the findings on the aggregated labor
share. In line with the literature (e.g. Arif 2021; Siegenthaler & Stucki 2015), we also
find that labor and capital in our data are complements (measured by the positive impact
of capital-output ratio). With respect to our measure of trade union density, we find
a positive association between bargaining power and the labor share as, for example,
also found in Stansbury & Summers (2020). Regarding the measurement of intermediate
inputs, our results are also in line with the findings by (Siegenthaler & Stucki 2015) in
19For a similar approach, see Böckerman & Maliranta (2012); Yang & Tsou (2021).
20We also applied different specifications in which the results are very consistent among specifications.
31
Table 8: Results for firm-level regressions
Labor Share
OLS Random Fixed System-
effects effects GMM
Variables (1) (2) (3) (4)
Lag labor share 0.789∗∗∗
(0.101)
Hartz IV -0.016∗ -0.018∗∗∗ -0.020∗∗∗ -0.028∗∗
(0.009) (0.006) (0.006) (0.012)
Capital-output ratio 0.040∗∗∗ 0.065∗∗∗ 0.075∗∗∗ 0.061
(0.006) (0.007) (0.009) (0.132)
Trade union density 0.010∗∗ 0.008∗∗ 0.007∗∗ 0.039
(0.005) (0.003) (0.003) (0.095)
Intermediate inputs 0.009 0.072∗∗∗ 0.106∗∗∗ 0.526∗∗∗
(0.006) (0.009) (0.011) (0.155)
Intermediate inputs squared -0.010∗∗∗ -0.008∗∗ -0.007∗ -0.192∗∗∗
(0.002) (0.003) (0.004) (0.056)
Western Germany 0.016∗∗∗ 0.016∗∗∗ -0.011∗
(0.003) (0.003) (0.006)
Constant 0.352∗∗∗ 0.269∗∗∗ 0.319∗∗∗ -0.183
(0.016) (0.013) (0.012) (0.267)
Industry fixed effects X X X X
Time fixed effects X X X X
Limited liability controls X X X X
R2 .159 .128 .136
No. of instruments 105
AR1 (p-value) .000
AR2 (p-value) .602
Hansen-J (p-value) .422
Observations. 38,808 38,808 38,808 29,501
Notes: This table shows results from estimating Equation (20). The data is based on
the “dafne” dataset compiled by Bureau van Dijk; years 2000 – 2011. The labor share
is calculated as LS = WtLtt Y as explained in Section 3. (Hansen 1982) test is applied tot
check for over-identifying restrictions, and tests for first AR(1) and second-order AR(2)
auto-correlation are provided (Arellano & Bond 1991). Firm-level clustered standard
errors in combination with Windmeijer (2005) finite sample correction in parentheses.
*, **, and *** denote statistical significance at the .1, .05 and .01 level respectively.
which we also see an inverted u-shaped relationship.
Summarizing, our robustness test by application of microeconomic data and quite dif-
ferent econometric methods supports our earlier results based on macroeconomic data.
Our results are well in line with the empirical literature as, for example, Karabarbounis
& Neiman (2014) found very similar estimates for the firm level labor share.
32
5.2 Testing the ‘superstar’ hypothesis
The narrative of the applied literature on the labor share is that the decline is primarily
driven by large so-called ‘superstar’ firms (e.g. Autor et al. 2020; Kehrig & Vincent 2021).
This interpretation is also consistent with the findings by De Loecker et al. (2020) in which
large firms tend to have more power due to less competition and rising markups. We test
this hypothesis by choosing a value of 2,000 employees as cutoff point, which marks the
change from one-third to quasi-parity employee representation in corporate boards (e.g.
Jäger et al. 2019; Gorton & Schmid 2004). Thus, we perform a sample split and estimate
the specification for large firms (above 2, 000 employees) and small firms (below or equal
2, 000 employees) according to our definition. Results for large firms are presented in the
following Table 9 and for small firms in Table 10.
Table 9: Results for ‘large firms’ > 2, 000 employees
Labor share
OLS Random Fixed System-
effects effects GMM
Variables (1) (2) (3) (4)
Lag labor share .423*
(.230)
Hartz IV -.025** -.023*** -.026*** -.053**
(.013) (.009) (.009) (.024)
Industry fixed effects X X X X
Time fixed effects X X X X
R2 .173 .148 .111
No. of instruments 107
AR1 (p-value) .006
AR2 (p-value) .304
Hansen-J (p-value) .154
Observations 11,940 11,940 11,940 5,709
Notes: This table shows results from estimating Equation (20) for ‘large firms’
> 2, 000 employees. The data is based on the “dafne” dataset compiled by Bureau
van Dijk; years 2000 – 2011. The labor share is calculated as LS = WtLtt Y ast
explained in Section 3. (Hansen 1982) test is applied to check for over-identifying
restrictions, and tests for first AR(1) and second-order AR(2) auto-correlation
are provided (Arellano & Bond 1991). Firm-level clustered standard errors in
combination with Windmeijer (2005) finite sample correction in parentheses. *,
**, and *** denote statistical significance at the .1, .05 and .01 level respectively.
As shown in both tables, there is indeed evidence according to the ‘superstar’ hypothesis
33
Table 10: Results for ‘small firms’ ≤ 2, 000 employees
Labor share
OLS Random Fixed System-
effects effects GMM
Variables (1) (2) (3) (4)
Lag labor share .573*
(.332)
Hartz IV .004 -.002 -.005 -.023
(.013) (.009) (.009) (.016)
Industry fixed effects X X X X
Time fixed effects X X X X
R2 .163 .148 .099
No. of instruments 103
AR1 (p-value) .019
AR2 (p-value) .973
Hansen-J (p-value) .443
Observations 26,868 26,868 26,868 18,564
Notes: This table shows results from estimating Equation (20) for ‘small firms’
≤ 2, 000 employees. The data is based on the “dafne” dataset compiled by Bureau
van Dijk; years 2000 – 2011. The labor share is calculated as LS = WtLtt Y ast
explained in Section 3. (Hansen 1982) test is applied to check for over-identifying
restrictions, and tests for first AR(1) and second-order AR(2) auto-correlation
are provided (Arellano & Bond 1991). Firm-level clustered standard errors in
combination with Windmeijer (2005) finite sample correction in parentheses. *,
**, and *** denote statistical significance at the .1, .05 and .01 level respectively.
as outlined in De Loecker et al. (2020); Autor et al. (2020), that the decline in the labor
share is mostly driven by large firms. We find more pronounced effects in Table 9 for
large firms compared to the point estimates in Table 8. Moreover, our results show that
the decline in the labor share is indeed not driven by small firms since there is no effect
discernible. Point estimates within each table, however, are quite consistent among the
estimated OLS, fixed effects as well as System GMM specifications.
6 Conclusion
In this paper we investigate the relevance of bargaining institutions for the decline in
the German labor share. The Hartz IV reform, enacted in Germany in the year 2005
provides a unique exogenous reform shock which allows us to estimate the impact of a
reduction in the outside option in wage bargaining. Since the reform reduces long-term
34
unemployment benefits for all workers in Germany, the threat point in bargaining between
unions and employers is reduced and the threat of unemployment is more severe. We first
present a simple bargaining model in which we analyze the relevance of the reduction in
the outside option for the decline of the labor share. The model implies that rents are
generated within a firm duopoly in which a union is the bargaining partner. Furthermore,
the model connects the wage which is bargained for and the alternative wage which is
exogenously reduced because of the Hartz IV reform.
The empirical part consists of three parts. We first combine the EU KLEMS, Penn
World Tables and OECD STAN databases to identify the Hartz reforms as a significant
structural break in the time series of the labor share. We therefore apply a variety of
endogenous change point tests for single as well as multiple breakpoints, in which the
tests reveal the Hartz reforms as a significant structural break in the labor share. They
additionally point to the fact that, besides the Hartz IV reform, the reunification of East
and West German is also an interesting factor worth considering with respect to the labor
share. Second, estimates on the aggregated labor share imply that the Hartz IV reform
shock reduces the labor share by around two percentage points, in particular after the
first five years after the reform was implemented. Using a synthetic control approach
to construct a counterfactual Germany doppelganger for drawing causal conclusions, we
provide evidence that the effect is persistent. In a final robustness section, we additionally
use rich firm-level panel data compiled by Bureau van Dijk in combination with fixed
effects and System GMM estimation techniques to support the previous findings on the
aggregated labor share. We therefore contribute to the burgeoning literature regarding the
labor share in the context of technological progress, globalization and mark-ups stemming
from increasing market concentration. In this context, using a unique exogenous reform
shock we therefore provide novel evidence of the effects of a reduction in bargaining power
and the share of labor.
Besides the endogenously identified Hartz reforms in the labor share series and the
application of recent econometric methods in the area of program evaluation, our study is
not without limitations. First, there is a debate regarding the measurement of the labor
35
share in which the income of self-employed and real estate income is often neglected (e.g.
Cette et al. 2020). With respect to the database, our data includes income of the self-
employed but does not take revenues from real estate into account. Second, because of
data limitations, our time series for the construction of the synthetic Germany is slightly
shorter compared to the time series which only considers Germany.
With respect to policy implications, we provide a missing link for the effects on the labor
share. Whereas studies as, for example, De Loecker et al. (2020) investigate the relevance
of decreasing competition and thus an increase in power and mark-ups for the decrease in
labor share, we provide evidence from a different direction. Our results show that also the
decrease in unionization and thus bargaining power to increase the wage over its marginal
product is reduced. Further studies in this context (e.g. Stansbury & Summers 2020)
even argue that the decline in worker power is the major aspect of structural changes in
the labor share. For Germany, the decline in unionization and representation of workers
by co-determination rights on the establishment level, as mentioned, for example, by
Addison et al. (2017), should therefore be in the focus of research on developments of
the labor share. In summary, our study adds knowledge to the burgeoning literature on
determinants of the labor share. Besides technological progress, globalization and mark-
ups, we show within a bargaining framework the relevance of changes in the threat point
or outside option, which has been neglected so far.
To this end, additional research might be helpful to investigate the reform effect on
different kinds of employment such as temporary or marginal employment. Furthermore,
future work should address the question of how to estimate the labor share more precisely
and consistently within and between countries. Since the relevance and interest in tech-
nological progress and union power seems likely to increase in the future, more studies
are to be expected on this topic.
36
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42
A Appendix
A.1 Figures
Figure A.1: Labor share for different countries
Austria Belgium Bulgaria
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Cyprus Czech Republic Germany
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Denmark Estonia Greece
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Notes: The figure plots the labor share for different countries between 1995 and 2015. The labor share
is calculated as LS = WtLtt Y which is the total compensation of employees in the economy in relation tot
gross valued added. Data from the EU KLEMS release 2019. For an overview of variable construction
and methodology see Stehrer et al. (2019).
43
0.65 0.67 0.69 0.60 0.64 0.68 0.64 0.68
0.56 0.60 0.64 0.51 0.53 0.55 0.610 0.625 0.640
0.57 0.60 0.63 0.63 0.65 0.67 0.69 0.45 0.55 0.65
Figure A.2: Labor share for different countries: continued
Spain Finland France
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Hungary Ireland Italy
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Lithuania Luxembourg Latvia
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Notes: The figure plots the labor share for different countries between 1995 and 2015. The labor share
is calculated as LS = WtLtt Y which is the total compensation of employees in the economy in relation tot
gross valued added. Data from the EU KLEMS release 2019. For an overview of variable construction
and methodology see Stehrer et al. (2019).
44
0.50 0.54 0.58 0.54 0.58 0.62 0.63 0.65 0.67
0.55 0.57 0.59 0.61 0.40 0.50 0.60 0.63 0.65 0.67 0.69
0.50 0.54 0.58 0.62 0.64 0.66 0.660 0.675 0.690
Figure A.3: Labor share for different countries: continued
Malta Netherlands Portugal
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Romania Sweden Slovenia
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Slovakia United Kingdom United States
1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015
Year Year Year
Notes: The figure plots the labor share for different countries between 1995 and 2015. The labor share
is calculated as LS = WtLtt Y which is the total compensation of employees in the economy in relation tot
gross valued added. Data from the EU KLEMS release 2019. For an overview of variable construction
and methodology see Stehrer et al. (2019).
45
0.49 0.51 0.53 0.50 0.60 0.70 0.80 0.57 0.59 0.61
0.60 0.64 0.54 0.56 0.66 0.68 0.70
0.56 0.58 0.60 0.70 0.75 0.80 0.85 0.60 0.64 0.68
Figure A.4: Wald test robustness I
75 80 85 09 9 9 99 99
5 00 05 10
1 1 1 1 1 20 20 20
Year
Notes: The figure shows values of the Wald test statistics as outlined in Equations (15) and (16). Regres-
sion includes the number of strike days as well as the unemployment rate as additional control variables.
Test for a change point in the mean of the labor share (LSt) in year τ between t = 1, . . . T where t = 1977
and T = 2009. The labor share is calculated as outlined in Equation (14). The blue line shows the values
of the test statistics. The maximum value (sup Wald) of the Wald test statistic is 13.63 which occurred
in 2005, which is exactly the mid-point of the Hartz legislation. The red line indicates the critical value
of the test statistics as provided by Andrews (1993, 2003). Values of the test statistics are provided in
Table 1. We trim 15 percent from both ends of the sample to ensure that the test has sufficient power.
Figure A.5: Wald test robustness II
75 80 85 909 9 9
5 00 05 10
1 1 19 19 19 20 20 20
Year
Notes: The figure shows values of the Wald test statistics as outlined in Equations (15) and (16). Regres-
sion includes the number of strike days, unemployment rate as well as GDP growth as additional control
variables. Test for a change point in the mean of the labor share (LSt) in year τ between t = 1, . . . T
where t = 1977 and T = 2009. The labor share is calculated as outlined in Equation (14). The blue line
shows the values of the test statistics. The maximum value (sup Wald) of the Wald test statistic is 27.48
which occurred in 2004, which is exactly the mid-point of the Hartz legislation. The red line indicates
the critical value of the test statistics as provided by Andrews (1993, 2003). Values of the test statistics
are provided in Table 1. We trim 15 percent from both ends of the sample to ensure that the test has
sufficient power.
46
Wald Test Statistic Wald Test Statistic
0 5 10 15 20 0 5 10 15 20
Figure A.6: Hartz IV Dummy variable point estimates
Point estimates year dummies
2001 2002 2003 2004 2005 2006 2007 2008
Year
Notes: The figure plots the point estimates from regressing the labor share on all control variables and
year dummies as outlined in Equation (18).
Figure A.7: Distribution of the firm-level labor share
0 .2 .4 .6 .8 1
Labor Share
Notes: The figure plots the firm-level labor share. The data is based on the “dafne” dataset compiled by
Bureau van Dijk; years 2000 – 2011.
47
Percentage of firms Change in labor share
0 200 400 600 800 1000 -.04 -.02 0 .02 .04
Figure A.8: Development of the firm-level labor share
00
0 01 02 03 04 05 06 7 80 0 0 0 0 0
9 10 11
2 2 2 2 20 20 20 20 20 20 20 20
Year
Notes: The figure plots the development of the firm level labor share. The data is based on the “dafne”
dataset compiled by Bureau van Dijk; years 2000 – 2011.
48
Labor share (in %)
.44 .45 .46 .47 .48
A.2 Tables
Table A.1: Description, Explanation and Source of Variables
Variable Description and Explanation
Dependent Variable
Labor share Source: EU KLEMS; Bureau van Dijk
WtLt
LSt =
Yt
Which is labor compensation WtLt in relation to
gross value added Yt at year t in the corresponding
country.
Control Variables
Share of gross capital formation Source: Penn World Tables 9.0. The share in re-
lation to GDP measures the stock in real capital
within a country.
Share of government consumption Source: Penn World Tables 9.0. The share in re-
lation to GDP measures the government consump-
tion within a country.
Share of exports Source: Penn World Tables 9.0. The share in rela-
tion to GDP measures the exports within a coun-
try.
Share of import Source: Penn World Tables 9.0. The share in rela-
tion to GDP measures the imports within a coun-
try.
Human capital index Source: Penn World Tables 9.0. The human cap-
ital index is based on average years of schooling
as calculated in Barro & Lee (2013) in combina-
tion with an assumed rate of return to education
stemming from a Mincer equation as defined in
Psacharopoulos (1994). See also the more compre-
hensive and detailed definition In the PWT Defi-
nition File.
Unemployment rate Source: The World Bank. Unemployment is the
share of the labor force that is without work but
available for work and seeking employment.
Trade union density Source: OECD STAN. Members of trade unions
compared to total employment within in defined
industry.
Other variables are drawn from the ‘dafne’ dataset compiled by Bureau van Dijk. Description
as outlined in Section 5. See Section A.3 for the construction of the union density.
49
A.3 Construction of the industry union density measure
Data For the construction of the union density measure on the industry level we use
the number of trade union members as provided by the German trade union association
as well as the EU KLEMS data set for information regarding the number of employees in
every industry.
Calculation For the calculation we performed the following steps.
ˆ Trade unions must be assigned to the sectors in order to obtain a specific degree of
organization. The constitutions (Satzungen) of the DGB trade unions were reviewed
and the organizational areas listed were assigned to the respective sectors.
ˆ The degree of organization is recorded as a ratio. This involves dividing the number
of union members in a specific union in a year by the number of employees in all
industries in a year in which the union is active. A major problem here is that some
industries have more than one union. In such cases, the employees in an industry
are divided by the number of relevant unions.
ˆ This calculation results in what is known as the gross degree of organization, since
union members also include those who have left the labor force.
ˆ The degree of organization calculated for a union as an average across all sectors
(relevant for the respective union) is assigned to the sectors in the next step. For
example, if the union IG Metall is relevant in some sectors for examples 1 and
2, the same degree of organization is found in both sectors. If several unions are
represented in these industries, the unweighted average of the n unions is used.
ˆ The gross degree of organization for industry j at time t and union i is then calcu-
lated as:
Orggrossjt = [∑ Mit ] (21)K ( )1
j=1 Bn jt
where M is the number of union members in a given trade union, B the number of
employees in an industry and K the number of industries which are represented by
trade union i and finally n is the number of trade unions in a given industry j.
50