# Long-Term Employment Effects of the Minimum Wage in Germany: New Data and
Estimators

Marco Caliendo
University of Potsdam, CEPA, IZA, BSE, DIW, IAB
Nico Pestel
Maastricht University, IZA, CESifo
Rebecca Olthaus
University of Potsdam, CEPA, BSE, DIW e-mail<EMAIL_ADDRESS>Corresponding address: University of Potsdam, Chair of Empirical Economics,
August-Bebel-Str. 89, 14482 Potsdam, Germany. Tel: +49 331 977 3225. Fax: +49
331 977 3210.e-mail<EMAIL_ADDRESS>olthaus@uni-
potsdam.de.
The authors thank the Federal Statistical Office and the Statistical Offices
of the Federal States for their help in supplying the data. Financial support
of the German Minimum Wage Commission for part of this research is gratefully
acknowledged.

(Working Paper
)

###### Abstract

We study the long-term effects of the 2015 German minimum wage introduction
and its subsequent increases on regional employment. Using data from two waves
of the Structure of Earnings Survey allows us to estimate models that account
for changes in the minimum wage bite over time. While the introduction mainly
affected the labour market in East Germany, the raises are also increasingly
affecting low-wage regions in West Germany, such that around one third of
regions have changed their (binary) treatment status over time. We apply
different specifications and extensions of the classic difference-in-
differences approach as well as a set of new estimators that enables for
unbiased effect estimation with a staggered treatment adoption and
heterogeneous treatment effects. Our results indicate a small negative effect
on dependent employment of 0.5 percent, no significant effect on employment
subject to social security contributions, and a significant negative effect of
about 2.4 percent on marginal employment until the first quarter of 2022. The
extended specifications suggest additional effects of the minimum wage
increases, as well as stronger negative effects on total dependent and
marginal employment for those regions that were strongly affected by the
minimum wage in 2015 and 2019.

Keywords: Minimum Wage, Employment, Regional Bite
JEL codes: J23, J31, J38

##  1 Introduction

The introduction of a statutory minimum wage in Germany in 2015 was one of the
largest labour market policy reforms in many years, and it had been
controversially debated in both academia and politics. Against the background
of the minimum wage debate in the literature since the early-1990s (Card and
Krueger, 1994, 2000; Neumark and Wascher, 2000) and the controversy about the
direction of employment effects of minimum wages (Neumark et al., 2014;
Allegretto et al., 2017), the contemporary discussion at the time focused on
the question of whether the German minimum wage of initially €8.50 per hour
would cause substantial employment losses.111Upon introduction, the minimum
wage equalled about 49.8% (57.6%) of the mean (median) wage in Germany and
about 11.4% of workers were affected by it (Structure of Earnings Survey,
2014).

In the meantime, the short- to medium-term employment effects of the German
minimum wage introduction have been extensively studied in the literature (for
summaries see Caliendo et al., 2018, 2019; Bruttel, 2019; Bossler and Gerner,
2020; Mindestlohnkommission, 2020).222There also exist older studies about the
previously introduced sector-specific minimum wages, mostly not finding
significant employment effects (see Bosch and Weinkopf, 2012 and Möller, 2012
for a detailed overview and Fitzenberger and Doerr, 2016 for a critical
assessment of the applied methods). Nonetheless, there were some signs of a
tendency towards negative labour market effects in East Germany, where the
impact intensity of the minimum wage is substantially higher than in West
Germany due to the overall lower wage level. Overall, most studies find no or
only small negative effects of the minimum wage introduction on total
employment (Mindestlohnkommission, 2018; Bonin et al., 2018; Caliendo et al.,
2019; Bruttel et al., 2019; Pestel et al., 2020). Hereby, the effect is
predominantly due to marginal employment, while employment subject to social
security contributions remained stable (Caliendo et al., 2018; Bonin et al.,
2018; Ahlfeldt et al., 2018; Garloff, 2019; Holtemöller and Pohle, 2020;
Schmitz, 2019; Pestel et al., 2020).333Friedrich (2020) even identifies
positive effects of the minimum wage on employment subject to social security
contributions until the first increase in 2017. Pestel et al. (2020) find that
the effects can be mainly attributed to the introduction of the minimum wage,
while the first increase had no considerable additional effect, and
regions/sectors with a below-average growth dynamic experienced stronger
negative employment effects. Bossler (2016, 2017) and Bossler and Gerner
(2020) show that the minimum wage had an impact on the employment dynamic by
reducing the number of new hires. While focusing mainly on effects on wage
inequality induced by the minimum wage, Bossler and Schank (2023) show that
their finding of a significantly reduced inequality in monthly earnings is not
driven by employment effects as they find no significant effects on
employment. Biewen et al. (2023) also identify a significant increase in wages
and a reduction in wage inequality due to the minimum wage introduction, but
no significant effect on the distribution of weekly working hours. Dustmann et
al. (2022) find that instead of the feared employment effects, a reallocation
of the employees subject to the minimum wage into more productive firms took
place. Hereby, they identify substantial wage gains in the lower part of the
wage distribution, of which one quarter can be explained by changes from
smaller (relatively low paying) to larger (relatively high paying) firms. This
“upgrade” only occurs for low-wage workers and not for higher-earning workers.

The existing literature mostly focuses on the short-term effects two to three
years following the minimum wage introduction, while much less is known about
the medium- and especially long-term effects. This is relevant for different
reasons. First, employment adjustments may unfold over a longer period than
simply a few years, especially in the setting of the German labour market
where firing is rather difficult. Second, the minimum wage has been increased
multiple times and may have caused additional employment effects after the
initial adjustment phase of the introduction. In 2017 and 2019, the minimum
wage was raised to €8.84 and €9.19, respectively, and since then it has been
increased several more times to a current level of €12.444See Table A.1 in the
Appendix for an overview of the development of the minimum wage level over
time. Additionally, previous studies are mainly based on data from the 2014
(pre-introduction) Structure of Earnings Survey (SES) to determine the
treatment status across labour market regions in Germany. However, the
composition of regions mainly affected by the introduction may differ from
that of subsequent major increases of the minimum wage.

This paper studies the longer-run employment effects of the minimum wage
introduction in Germany. The analysis is based on aggregate administrative
data on employment at the level of regional labour markets over the period
from 2013 to 2022. Regions were differently affected by the minimum wage
introduction due to regional differences in wage levels and the distribution
of wages. Thus, there is a strong variation in the regional minimum wage bite.
We exploit this variation to apply a difference-in-differences (DiD) approach
to estimate the causal effects of the minimum wage on employment. We
operationalise the regional minimum wage bite using the regional wage gap
based on the SES 2014. Given that the SES is conducted every four years, we
can measure the regional wage gap again in 2018 with respect to the minimum
wage level after it had been substantially raised. Thus, we have a measure of
the degree of regional exposure to the minimum wage at two different points in
time. Overall, the wage gap substantially decreased between 2014 and 2018,
while the fraction of affected workers declined to a much lesser extent. We
observe that a substantial share of German labour market regions changed
between treatment and control status between 2014 and 2018. To the best of our
knowledge, we are the first to use two waves of the SES to study the
employment effects of the minimum wage in Germany.

In our main specification, we estimate the effects of the minimum wage
introduction alone using a treatment indicator based on the SES 2014. In a
second step, we account for the increases of the minimum wage and the
substantial change in strongly affected regions over time in multiple ways.
First, we add interaction terms for the minimum wage increases to the basic
specification to check for additional effects of the raises. Second, we apply
a specification with three treatment groups that are defined by having a
relatively high minimum wage bite in 2014, 2018 or both years. Regions with a
relatively low minimum wage bite in both years form the control group.
Finally, we treat the minimum wage introduction and the increase in 2019 as
one treatment that was introduced in a staggered manner, where some regions
start treatment in 2014 and others in 2019. In this setting, the classic TWFE
estimator may be biased if treatment effects are heterogeneous across
groups/units or time. This bias can be caused by so-called “forbidden
comparisons” (Borusyak and Jaravel, 2017) between the outcomes of later- and
earlier-treated units.

Several different new estimators have recently been developed to obtain
unbiased DiD estimates despite a setting deviating from the canonical one with
two groups and two periods. We compare the estimates of the classic TWFE with
those of new estimators for the longer-term effects of the German minimum wage
on employment if treatment adoption is considered to be staggered. We apply
the estimators developed by Sun and Abraham (2021), Callaway and Sant’Anna
(2021), Borusyak et al. (2021), and De Chaisemartin and d’Haultfoeuille
(2022a).

Our main findings confirm the negative but moderate employment effects of the
minimum wage introduction, which is mainly driven by significant reductions in
marginal employment. While the effect on total dependent employment has
decreased in magnitude over time, the effect has amplified over time for
marginal employment. The negative employment effect on marginal employment is
also substantially stronger for regions with a relatively low GDP growth rate
prior to the introduction of the minimum wage. We find that the regional
minimum wage bite decreased in all regions, albeit not at the same rate,
whereby the ranks of the regional bite substantially changed between 2014 and
2018. One consequence is that while the initial minimum wage introduction
mainly affected the labour market in East Germany, the recent minimum wage
hikes are also increasingly affecting lower-wage regions in West Germany. This
results in the finding that the minimum wage increases – especially the one in
2019 – have resulted in additional employment effects on top of the longer-
term effects of the minimum wage introduction of 2015. Regions with a
relatively high wage gap in 2014 and 2018 experience substantially stronger
negative employment effects than those that only have a high wage gap in one
of the two years. Finally, we document that the alternative DiD estimators
overall support our main findings.

The remainder of the paper is structured as follows. Section 2 describes the
data and provides descriptive results. In Sections 3 and 4, we explain the
empirical approach and present our regression results. Section 5 concludes.

##  2 Data and Descriptive Results

###  2.1 Data Sources

We use the SES of 2014 and 2018 to measure the regional minimum wage
bite.555Source: RDC of the Federal Statistical Office and Statistical Offices
of the Federal States, Structure of Earnings Survey, 2014
(DOI:10.21242/62111.2014.00.00.1.1.1) and 2018
(DOI:10.21242/62111.2018.00.00.1.1.0). The SES is conducted every four years
and the data is provided by the Federal Statistical Office of Germany. It
includes information on earnings of employees in Germany as well as other
detailed information about employment, such as the hours worked, industry, and
personal characteristics of the employees. The data covers the month of April
of the respective year and thus stems from a point in time directly prior to
the introduction of the minimum wage, which was announced in July 2014. Firms
are obligated to provide information and for a high level of
representativeness, firms are chosen stratified for states, industry and firm
size category (FDZ, 2019). The SES 2014 (2018) contains information about
approximately one million employment relationships from about 71,000 (60,000)
companies with at least one employee subject to social security contributions.
The SES 2014 has previously been used for evaluating the minimum wage’s
employment effects (Bruttel et al., 2018; Bonin et al., 2018; Caliendo et al.,
2018; Pestel et al., 2020) although – to our knowledge – we are the first to
use the SES 2018.

The SES has two major advantages compared to other data sources that are firm-
based: first, it allows a precise estimation of hourly wages on the individual
level, which in turn allows determining the bite on different dimensions; and
second, the large number of observations enables an analysis at the level of
the 257 labour market regions, as in our analysis. However, results below the
regional level of the federal state are not representative per se (FDZ, 2019).
Another caveat is that the SES does not include regional information for civil
servants below the level of the federal states, and thus we have to exclude
them from our analysis. Since the SES 2014 and 2018 share the same
characteristics, the SES 2018 allows smoothly continuing with the minimum wage
evaluation and showing developments between the year prior to the minimum wage
introduction and the year prior to the second increase in 2019. The 257 labour
market regions are divided into a control and treatment group based on the
wage gap calculated using the SES 2014. We also divide the labour market
regions into a treatment and control group based on the SES 2018, which
documents the development of the degree of exposure over time and which we
will use in additional analyses.

The data for our outcome measures come from the statistical department of the
Federal Employment Agency, which publishes the number of employed people on a
quarterly basis at a regional level. The statistics are based on process data
of the Federal Employment Agency as well as the statutory pension insurance
and can be considered as very reliable. In our analysis, we use data from the
first quarter of 2013 until the first quarter of 2022. The Federal Statistical
Office differentiates between marginal employment and employment subject to
social security contributions, and further between exclusive marginal
employment and marginal employment as a side job. We calculate the total
number of persons in dependent employment as the sum of employment subject to
social security contributions and exclusive marginal employment. Further, we
use data for regional economic and demographic indicators such as GDP and
population from the regional statistics of the Federal Statistical Office.
Moreover, we include regional information about the settlement structure
(classification in urban and rural areas) from the Federal Institute for
Research on Building, Urban Affairs and Spatial Development.

###  2.2 Treatment Indicator

In order to identify a causal effect of the minimum wage on employment
outcomes in Germany, we use a DiD approach (see Section 3). However, due to
the universal nature of the minimum wage in Germany, there is no suitable
control group that is not subject to the minimum wage.666There were a few
exceptions from the minimum wage upon its implementation in 2015, yet the
number of excepted employees is quite low, and these groups cannot be
adequately compared to regular employees as they are mostly apprentices,
interns, and teenagers below the age of 18. Further, sectors with their own
minimum wages above the general minimum wage are also not an appropriate
control group, because they represent a very selective sample of the labour
market. Therefore, we divide regions into a control and a treatment group
based on the degree to which they are affected by the minimum wage. To measure
the degree to which a region is affected, we use the wage gap, describing the
average absolute difference between the hourly wage and the minimum wage of
€8.50 for the SES 2014 (€9.19 for the SES 2018) for hourly wages below the
minimum wage, while the difference is equal to zero for wages of at least
€8.50 (€9.19):

$WageGap_{it}=\frac{\sum_{w=1}^{N_{it}}max[MW_{t}-Wage_{wit},0]}{N_{it}},$

with $i$ representing the region, $t$ the year (2014 or 2018), $w$ the
individual worker, and $N$ the number of workers. The concept of the wage gap
that we use is based on the population of all employees not exempt from the
minimum wage and quantifies the minimum wage exposure in respect to the number
of employees as well as considering the level of the minimum wage relative to
the base level of wages. We focus on the wage gap, because – in contrast to
other measures (i.e. Kaitz- or Fraction-Bite) – it quantifies the size of the
adaption of wages that is necessary to raise the hourly wage from April 2014
(April 2018) to the level of the minimum wage of €8.50 (€9.19). The final
division between the treatment and control group is contingent on the median
of the regional wage gaps (weighted by the regional population in 2013).
Regions with a minimum wage gap above (below) the weighted median are part of
the treatment (control) group.

###  2.3 Descriptive Statistics

#### Minimum Wage Bite Over Time

The map on the left-hand side of Figure 1 shows the wage gap for all labour
market regions in 2014. The wage gap is especially large in East Germany and
lowest in the south, especially in the federal state of Bavaria. The size of
the wage gap varies between 0.021 and 0.652. The right-hand side panel of
Figure 1 shows the wage gap for all labour market regions in 2018. While the
wage gap has declined in all regions, the geographical distribution is no
longer as clear. Especially, East Germany does not stand out any longer and
there are substantially more regions in West Germany with an above-median wage
gap. This change also becomes clear when looking at the correlations of the
wage gaps in 2014 and 2018. The Pearson’s correlation coefficient with 0.295
and the Spearman rank correlation coefficient of 0.4082 show that the two wage
gaps are only weakly correlated.777For illustrative purposes, Figure A.1 in
the Appendix shows scatter plots for the wage gap ranks 2014 (8.50€) / 2018
(9.19€), 2014 (8.50€) / 2014 (9.19€), and 2014 (9.19€) / 2018 (9.19€). The
wage gap ranks of 2014 and 2018 show no strong relationship (irrespective of
whether the wage gap in 2014 is relative to 8.50€ or 9.19€) while the two wage
gaps in 2014 are very closely and positively related. This suggests that the
change in wage gap ranks between 2014 and 2018 is not due to differences in
the wage distribution in an interval between €8.50 and €9.19 that already
existed in 2014.

Table A.2 in the Appendix takes a closer look at characteristics of the labour
market regions in 2014 and 2018 for the whole group as well as those with a
relatively low and high wage gap separately. In 2014, 144 labour market
regions belonged to the treatment group and 113 regions to the control group.
The average overall wage gap was 0.203, while it was 0.281 in the treatment
group and 0.104 in the control group. In 2018, the number of regions in the
treatment group increased to 153, while the number in the control group
decreased to 104. With 0.034, the average wage gap was substantially lower in
2018 than in 2014. Hereby, the average was 0.043 in the treatment and 0.019 in
the control group. The settlement structure of regions in the two groups only
slightly varied between 2014 and 2018. In both years, there are more urban
regions in the control group and more rural areas in the treatment group.
Further, there are no large differences between the treatment and control
group or across years regarding the employment structure by sectors and in
terms of the population share between the ages of 18 and 64 in 2013. In both
years, the labour market regions in the treatment group experience a lower GDP
growth between 2010 and 2013 and between 2015 and 2018. The share of regions
with a GDP growth rate between 2010 and 2013 in the bottom quartile is higher
in the control group than the treatment group in 2014. However, in 2018, the
share is almost equal. The share of regions with a GDP growth rate between
2015 and 2018 in the bottom quartile is substantially higher in the treatment
groups in 2014 and 2018.

Figure 1: Regional wage gap to €8.50 in 2014 (left) and to €9.19 in 2018
(right) Source: SES 2014, 2018; own calculations. Note: The map on the left
shows the regional wage gap to €8.50 in 2014. The map on the right shows the
regional wage gap to €9.19 in 2018. The respective wage gaps are grouped into
five categories (separately for 2014 and 2018) with a different shade of blue
(2014) or red (2018) for each of them. For the definition of the wage gap, see
Section 2.2. Figure 2: Treatment groups based on the wage gaps in 2014 and
2018 Source: SES 2014, 2018; own calculations. Note: The map shows the labour
market regions sorted into four groups based on their wage gaps in 2014 and
2018. “low” describes a wage gap below the weighted median of all regions in
2014 or 2018 and “high” describes a wage gap at or above that median. For the
definition of the wage gap, see Section 2.2.

#### Switching Treatment Status

The majority of labour market regions do not change their binary treatment
status between 2014 and 2018. Sixty-eight regions have a relatively low wage
gap in both years and 108 regions a relatively high wage gap. However, a
substantial share of about 31.5 percent of the regions that change between a
low and high wage gap in that period. Forty-five regions switched from a
relatively low to a relatively high wage gap and 36 regions did the opposite.
Based on this observation, we categorise the labour market regions into four
different groups: “low/low group” (relatively low wage gap both in 2014 and
2018), “low/high group” (a low wage gap in 2014 and a high wage gap in 2018),
“high/low group” (a high wage gap in 2014 and a low wage gap in 2018), and
“high/high group” (a high wage gap in both years). We will use these four
groups in one of our DiD specifications described in Section 3, where we
estimate separate treatment effects for each group.

Figure 2 is a map showing the regional distribution of these four groups.
While most East German regions are in the high/high group and many southern
regions belong to the low/low group, there are especially (but not
exclusively) many regions in the state of Lower Saxony in north-western
Germany that switched between a relatively high and low wage gap. Table A.3 in
the Appendix shows descriptive statistics similar to Table A.2 for the four
groups. By definition, the average wage gap in 2014 (2018) is larger in the
high/low and high/high (low/high and high/high) groups. Of special interest
are the switchers. The regions in the low/high group decrease their minimum
wage exposure in 2018 on average by almost 63 percent compared to 2014. At the
same time, the regions in the high/low group reduced their exposure between
2014 and 2018 by about 91 percent. All groups reduced the fraction of
employees directly affected by the minimum wage, but again there is large
variation between the groups. The fraction in the low/high group only
decreased by about 6 percent, while the high/low group experienced a large
decrease in affected employees of approximately 62 percent. The average hourly
wage was significantly lower for the high/low group than for the low/high
group in 2014, although in 2018 the averages are virtually the same across
both groups. Accordingly, the hourly wages increased at more than twice the
rate in the high/low group compared with the low/high group (17.8 to 8.0
percent). These numbers suggest that the development of wages following the
introduction of the minimum wage varied between groups and different regional
developments between 2014 and 2018 led to changes in the exposure to the
minimum wage increase relative to its introduction.

#### Development of Outcomes Over Time

Figure A.2 in the Appendix shows the development of total employment over time
separately for labour market regions with a high and a low wage gap upon its
introduction. During the observation period, the dependent employment
generally increases (with small seasonal cycles). It increased slightly more
strongly in regions with a low wage gap and has been at the same level in both
groups since the end of 2018. The employment subject to social security
contributions makes up the large majority of the dependent employment and
hence moves very similarly over time.

Marginal employment remained stable until the end of 2019 in regions with a
low wage gap, while it decreased in regions in the treatment group after the
introduction of the minimum wage. This already hints towards a reduction in
marginal employment in the treatment group through the introduction of the
minimum wage. The difference between the two groups increased over time and
has remained constant from 2019 onwards. Throughout the Covid-19 pandemic,
marginal employment strongly decreased in both groups, but the difference
between them remained almost unchanged.

##  3 Empirical Approach

Our baseline DiD regression equation for estimating the cumulative effect of
the German minimum wage on employment outcomes over the observation period
reads as follows:

$Log(Y_{it})=\beta(WageGap_{i,2014}^{high}\times
I_{t>Q2/2014})+X_{it}\gamma+\theta_{i}+\theta_{t}+\epsilon_{it},$ (1)

where $Log(Y_{it})$ is the log of the dependent variable in labour market
region $i$ in quarter $t$. $\theta_{i}$ represents regional fixed effects that
control for all time-invariant characteristics such as geographic location.
$\theta_{t}$ adds quarter fixed effects that capture time-specific effects
such as the overall economic development. The treatment variable in our DiD
analysis $WageGap_{i,2014}^{high}\times I_{t>Q2/2014}$ is the interaction
between a binary indicator for regions with a wage gap at or above the median
and a binary indicator for post-treatment quarters. The treatment period in
our specification starts after the second quarter of 2014 to account for
potential anticipation effects since the law introducing the minimum wage was
passed in July 2014. Consequently, $\beta$ is the coefficient of interest that
measures the average treatment effect of a relatively high minimum wage bite
on the respective outcome. $X_{it}$ is a vector of control variables that can
vary between labour market regions and over time such as differing trends for
urban and rural regions.888The control variables included are interactions of:
time, east, and population share between 18 and 64 years in 2013; time, east,
and type of labour market region; time, east, and employment share in
different sectors; and time and GDP per capita in 2013. We cluster the
standard errors at the level of the labour market regions to allow for
correlation of unobservable characteristics of a labour market region over
time. Further, observations are weighted with the number of employees in April
2014, such that the results are not driven by relatively small labour market
regions.

To analyse the dynamic development of the minimum wage effects over time, we
apply an event-study approach. The corresponding estimation equation reads as
follows:

$Log(Y_{it})=\sum_{\tau=Q1/2013,\tau\neq
Q2/2014}^{Q3/2021}\beta_{\tau}(WageGap_{i,2014}^{high}\times
I_{t=\tau})+X_{it}\gamma+\theta_{i}+\theta_{t}+\epsilon_{it},$ (2)

where $WageGap_{i,2014}^{high}$ is interacted with indicators for all quarters
except for the baseline period (the second quarter of 2014). Thus, the
coefficient vector $\beta_{\tau}$ contains the estimated treatment effect for
every quarter before and after the minimum wage was announced relative to the
baseline quarter. Insignificant estimates for pre-treatment periods support
the identifying assumption of parallel trends between treated and control
regions.

We also estimate Equations (1) and (2) with an additional interaction of the
treatment indicator with a binary indicator for a relatively low GDP growth
between 2010 and 2013 to test whether the treatment effect varies with the
regional growth dynamic prior to the introduction of the minimum wage. Hereby,
“low” is defined as a regional GDP growth rate in the bottom quartile of all
regions.

We also extend Equation (1) to study additional effects of the minimum wage
raises on January 1 of 2017 and 2019 to 2022:

$\begin{split}Log(Y_{it})=\beta(WageGap_{i,2014}^{high}\times
I_{t>Q2/2014})+\sum_{\tau=2016,\tau\neq
2017}^{2021}\delta_{\tau}(WageGap_{i,2014}^{high}\times I_{t>Q4/\tau})\\\
+X_{it}\gamma+\theta_{i}+\theta_{t}+\epsilon_{it},\end{split}$ (3)

where the coefficients $\delta_{\tau}$ indicate the additional effects of
minimum wage raises beyond the initial introduction in 2015. Additionally, we
also apply a shortened version only including the first two increases.

We exploit variation in the minimum wage bite between 2014 and 2018 by
estimating an additional regression model using the four groups of regions
that we introduced in Section 2.3. These groups are based on the regional wage
gaps relative to the respective population-weighted median in 2014 and 2018:
low/low, low/high, high/low, and high/high. We include treatment indicators
for the last three groups, which makes the first group the control group. The
corresponding estimation equation is:

$\begin{split}Log(Y_{it})=\beta(WageGap_{i,2014,2018}^{low,high}\times
I_{t>Q2/2014})+\gamma(WageGap_{i,2014,2018}^{high,low}\times I_{t>Q2/2014})\\\
+\delta(WageGap_{i,2014,2018}^{high,high}\times
I_{t>Q2/2014})+X_{it}\lambda+\theta_{i}+\theta_{t}+\epsilon_{it}.\end{split}$
(4)

We also add a placebo term in the form of
$\alpha(WageGap_{i,2014}^{high}\times I_{t<Q2/2014})$ to Equations (1) and
(3). Equation (4) contains one placebo term of this kind for each of the three
treatment groups. These placebo terms show whether the trends of the treatment
and control group prior to the treatment were significantly different from
each other. If this is not the case, it supports the common trend assumption
necessary to identify a causal effect.

Finally, we also use an alternative estimation based on a staggered treatment
adoption. Here, treatment starts in the third quarter of 2014 for those
regions with a relatively high wage gap in 2014 (as is the case in the
baseline setting) and in 2019 for regions that had a relatively low wage gap
in 2014 and a high wage gap in 2018. Regions with a relatively low wage gap in
both periods are never treated in this setting. The estimation equation reads
as follows:

$\begin{split}Log(Y_{it})=\beta(WageGap_{i,year}^{high}\times I_{t\geq
F})+X_{it}\gamma+\theta_{i}+\theta_{t}+\epsilon_{it},\end{split}$ (5)

with $F$ referring to the time when a region starts treatment for the first
time (Q3 2014 or Q1 2019). The corresponding year of the binary minimum wage
bite is either 2014 or 2018. Once a region is treated, it remains treated for
the whole observation period. Recent advances in the econometrics literature
have shown that in settings with a staggered treatment adoption, TWFE
estimates can be biased if treatment effects are heterogeneous across
groups/units or time (see, for example, Sun and Abraham, 2021). If units are
treated at different points in time, estimates of a classic TWFE model can
include “forbidden comparisons” (Borusyak and Jaravel, 2017) between two
treated groups or units (one earlier treated and one later treated). In case
of heterogeneous treatment effects, this can cause the TWFE estimates to be
biased. We see potential sources for such a treatment heterogeneity; for
example, the treatment effect could differ between regions starting treatment
in 2014 and 2019 or because the treatment intensity (the continuous wage gap)
even differs within the treatment groups. Another possible reason is varying
economic growth across regions that could affect the size of the treatment
effect.

Several different new estimators have recently been developed to obtain
unbiased DiD estimates despite a treatment that is adopted in a staggered
manner. Usually, the idea behind the newly developed estimators is to only
include “clean” comparisons between observations that are treated and those
that have not (yet) been treated. These comparisons are then aggregated using
different weights (that are to be chosen).999See De Chaisemartin and
d’Haultfoeuille (2022b) and Roth et al. (2023) for comprehensive overviews of
the recent advances in the DiD literature. We compare the estimates of the
classic TWFE with those of some of the newly developed estimators. The
estimator developed by Sun and Abraham (2021) generalises the event-study
approach to settings with a staggered treatment adoption and is based on
cohort- and period- specific effect estimates. Treatment start is defined as
the time when a unit’s treatment status changes for the first time and the
control group is either the never-treated or the last-treated group(s). By
contrast, the estimator by Callaway and Sant’Anna (2021) can use the not-yet-
treated or never-treated groups as controls. The basis of their approach is
the estimation of group-time-average treatment effects. For example, these can
be aggregated over groups (a group is defined by a common time of treatment
start), by time relative to treatment start, or over all groups and periods to
obtain an overall average treatment effect on the treated. The estimator
proposed by De Chaisemartin and d’Haultfoeuille (2022a) generalises “the
event-study approach to such designs, by defining the event as the period
where a group’s treatment changes for the first time” (De Chaisemartin and
d’Haultfoeuille, 2022b, p.20). Borusyak et al. (2021) apply a different
approach than the previously described estimators, developing an imputation
estimator (others like Gardner (2022) use similar approaches). First, the
counterfactual outcome for the treated observations is predicted by regressing
the outcome on group and time fixed effects for the sample of not-treated
observations. In a second step, the counterfactual outcome is subtracted from
the observed outcome for the treated observations to obtain the treatment
effect (Borusyak et al., 2021; De Chaisemartin and d’Haultfoeuille, 2022b).

##  4 Results

In this section, we present our regression results. We start in Section 4.1 by
showing the estimates for the employment effects of the minimum wage
introduction based on Equations (1) and (2). Additionally, we also estimate
the treatment effects if the binary treatment is interacted with regional
economic growth prior to the introduction of the minimum wage. In Section 4.2,
we present results for the incremental changes of the minimum wage according
to Equation (3). This is followed by estimations with three different
treatment groups (Equation (4)) in Section 4.3 and results for a staggered
treatment adoption in Section 4.4 (Equation (5)).

###  4.1 Long-Term Effects of the Minimum Wage Introduction

#### Baseline results.

We present our baseline findings for the long-term effects of the minimum wage
introduction on employment outcomes in Table 1. Panel A shows the treatment
estimates according to Equation (1) for dependent employment, employment
subject to social security contributions, and marginal employment including
all of the covariates described in Section 3.

Column (1) of Panel A in Table 1 shows that the minimum wage introduction had
a significant negative impact on the total dependent employment. The effect
size is about $-0.5$ percent and statistically significant at the 10 percent
level. The coefficient for the employment subject to social security
contributions in column (2) is positive but very small and not statistically
significant. Column (3) of Table 1 shows the results for marginal employment.
The introduction of the minimum wage had a negative and statistically
significant effect (at the 1 percent level) on the marginal employment of
about $–2.4$ percent. The placebo terms are insignificant for all three
outcomes, thereby supporting the assumption of common pre-trends.

Table 1: Effects of the minimum wage introduction on regional employment VARIABLES | Dependent | Employment | Marginal
---|---|---|---
employment | subject to SSC | employment
Panel A: Binary treatment (wage gap)
Treatment | -0.00511* | 0.000456 | -0.0239***
| (0.00260) | (0.00286) | (0.00763)
Placebo | 0.000569 | 0.00142 | -0.00140
| (0.00111) | (0.00107) | (0.00246)
R2 | 0.597 | 0.584 | 0.472
Panel B: Binary treatment (wage gap) interacted with growth
Treatment | -0.00434 | 0.000229 | -0.0192**
| (0.00332) | (0.00357) | (0.00888)
Placebo (Treatment) | 0.000593 | 0.00172 | -0.00222
| (0.00124) | (0.00119) | (0.00281)
Treatment x Low growth 2010-2013 | -0.00571 | -0.00159 | -0.0232*
| (0.00549) | (0.00661) | (0.0121)
Placebo (Treatment x Low growth | 0.00152 | 0.000757 | 0.00417
2010-2013) | (0.00228) | (0.00223) | (0.00473)
R2 | 0.605 | 0.590 | 0.484
Observations | 9,509 | 9,509 | 9,509
Labour market region FE | X | X | X
Quarter FE | X | X | X
Controls | X | X | X
Source: Regional Statistic of the Federal Employment Agency; SES 2014; Federal
Statistical Office; Federal Institute for Research on Building, Urban Affairs
and Spatial Development; own calculations. Note: The treatment effect refers
to the coefficient $\beta$ in Equation (1), estimated with TWFE. The binary
treatment equals 1 if the regional wage gap is equal to or above the
population-weighted median. The control variables included are interactions
of: time, east, and population share between 18 and 64 years in 2013; time,
east, and type of labour market region; time, east, and employment share in
different sectors; time and GDP per capita in 2013. The specification in Panel
B additionally includes the interactions of time and the indicator for a low
GDP between 2010 and 2013. Standard errors (in parentheses) are clustered at
the level of the labour market regions. Confidence level: ***p$<$0.01,
**p$<$0.05, *p$<$0.1.

Figure 3 depicts the results of the extended DiD approach of Equation (2). In
addition to the point estimator for each quarter, it also shows the 95-percent
confidence intervals as well as vertical lines that mark the announcement of
the minimum wage and its introduction. Again, the specifications include all
of the time-variant control variables. The assumption of parallel pre-trends
seems to hold for all three outcomes, since the point estimates prior to the
second quarter of 2014 are not significantly different from zero. Similar to
the simple DiD model, the results show a continuously negative effect on the
total dependent employment.

Figure 3: Effect of the minimum wage on employment

(a) Dependent employment

(b) Employment subject to SSC

(c) Marginal employment

Source: Regional Statistic of the Federal Employment Agency, SES 2014, Federal
Statistical Office, Federal Institute for Research on Building, Urban Affairs
and Spatial Development (FBUS); own calculations. Note: The vertical lines
show the points of time when the minimum wage law was passed (August 2014) and
introduced (January 1, 2015). The point estimates and confidence intervals
refer to the vector $\beta$ in equation 2. The control variables included are
interactions of: time, east, and population share between 18 and 64 years in
2013; time, east, and type of labour market region; time, east, and employment
share in different sectors; time and GDP per capita in 2013. Standard errors
(in parentheses) are clustered at the level of the labour market regions.

The coefficients switch between significance at the 5 and 10 percent level
throughout the observation period. This negative effect is hereby fully
attributable to the marginal employment for which the effect strongly
increased over time in absolute terms. There is no statistically significant
effect on the employment subject to social security contributions, although
there appears to be a positive (albeit not significant) trend over the last
few quarters during the observation period.

#### Interaction with Economic Growth

In order to ascertain whether regions are affected differently by the
treatment based on their economic growth prior to the introduction of the
minimum wage, we interact the binary treatment with an indicator for low
growth between 2010 and 2013. Hereby, low growth is defined as a growth rate
in the bottom quartile among all labour market regions.

The results for the total effect are presented in Panel B of Table 1. The main
treatment coefficient for dependent employment remains negative but is no
longer significant. The estimate for the interaction with a low growth rate is
negative but also insignificant. For employment subject to social security
contributions, the main treatment indicator is again positive and
insignificant, while the interaction term with economic growth is also
negative and insignificant. The main treatment effect for marginal employment
is statistically significant at the 5-percent level and negative, but has
decreased in magnitude to about $-1.9$ percent. The interaction with a low
growth rate prior to treatment start is significant at the 10-percent level at
$-2.3$ percent. While the marginal employment decreases in all treated regions
on average, it does so more than twice as much in regions with a low growth
dynamic between 2010 and 2013.

Figure 4 shows the event-study results separate for the treatment interacted
with a relatively low growth rate and the main treatment indicator (which
shows the treatment effect for regions with a relatively high growth rate). In
Panels (a) and (b), it becomes clear that the treatment effects on dependent
employment and employment subject to social security contributions for regions
with a relatively high growth rate are insignificant throughout the
observation period. By contrast, the effect on dependent employment among
regions with a relatively low GDP growth is significantly negative (at the 5
percent level) in the majority of periods. For marginal employment, the main
treatment effects turn significantly negative at the end of 2018, while they
are negative and significant right from the start for regions with a low
economic dynamic.

Figure 4: Effect of the minimum wage on employment interacted with the
regional economic growth

(a) Dependent employment

(b) Employment subject to SSC

(c) Marginal employment

Source: Regional Statistic of the Federal Employment Agency, SES 2014, Federal
Statistical Office, Federal Institute for Research on Building, Urban Affairs
and Spatial Development (FBUS); own calculations. Note: The vertical lines
show the points of time when the minimum wage law was passed (August 2014) and
introduced (January 1, 2015). The point estimates and confidence intervals
refer to coefficients of Equation (2) augmented by an interaction of the
binary treatment and a binary indicator for having a regional GDP growth in
the lower 25% of all regions and an interaction of time and low growth between
2010 and 2013. The black markers show the point estimates for the main
treatment indicator and the red markers those for the interaction of treatment
and low growth between 2010 and 2013. The control variables included are
interactions of: time, east, and population share between 18 and 64 years in
2013; time, east, and type of labour market region; time, east, and employment
share in different sectors; time and GDP per capita in 2013. Standard errors
(in parentheses) are clustered at the level at the labour market regions.

###  4.2 Effects of the Minimum Wage Increases

Thus far, we have presented estimates of the longer-term effects of the first-
time introduction of the German minimum wage in 2015. In the next step, we
explicitly consider the subsequent increases in the level of the minimum wage
after its introduction. For this purpose, we apply Equation (3), which
includes interaction terms of the treatment and indicators for the post-
increase periods. We include the minimum wage increases from January 1 of each
year between 2017 and 2022 (except 2018). We do not consider the increase from
July 1, 2021, due to its small magnitude. We also consider a shorter version
that only includes the increases in 2017 and 2019. The results are presented
in Table 2, whereby Panel A presents the results for the short estimation with
only two increases and Panel B those for the entire Equation (3).

The estimate for the treatment effect of the minimum wage introduction for
dependent employment in column (1) shows a significant effect (at the 5
percent level) of $-0.3$ percent in both Panels A and B, while the placebo
terms are insignificant. The effect size is smaller in magnitude compared to
the results for the introduction alone in Table 1. The coefficients for the
increases between 2017 and 2020 are negative and turn positive for the
subsequent increases. However, they are all very small and insignificant,
suggesting that the minimum wage increases had no additional significant
effects on the overall dependent employment. The main treatment effect on
employment subject to social security contributions in column (2) is
insignificant in both specifications, as was the case in the main results in
Table 1. The coefficients for all raises are insignificant and with the
exception of the estimate for the increase in 2019 in Panel B, they are all
positive, yet very small. Finally, the main treatment coefficient for marginal
employment is similar and significant at the 10 percent level in both panels
with $-1.1$ percent. Thus, it is smaller in magnitude compared to Table 1. In
addition to the introduction, it appears that all increases had significant
additional negative effects between 0.4 and 1.6 percent. Overall, these
results suggest significant additional effects of the increases of the minimum
wage, especially for the first two in 2017 and 2019 and on marginal
employment.

Table 2: Effects of the minimum wage introduction and its raises on regional employment | (1) | (2) | (3)
---|---|---|---
VARIABLES | Dependent | Employment | Marginal
| employment | subject to SSC | employment
Panel A: Minimum Wage increases in 2017 and 2019
Treatment 2014 | -0.00294** | -0.000116 | -0.0113*
| (0.00144) | (0.00151) | (0.00590)
Placebo | 0.000595 | 0.00141 | -0.00124
| (0.00112) | (0.00107) | (0.00246)
Treatment 2014 x (Time $>$ 2016) | -0.00197 | 0.000380 | -0.0101***
| (0.00188) | (0.00194) | (0.00357)
Treatment 2014 x (Time $>$ 2018) | -0.00233 | 0.000845 | -0.0160***
| (0.00188) | (0.00188) | (0.00395)
R2 (within) | 0.598 | 0.585 | 0.487
Panel B: Minimum Wage increases in 2017, 2019, 2020, 2021, and 2022
Treatment 2014 | -0.00294** | -0.000111 | -0.0113*
| (0.00144) | (0.00151) | (0.00590)
Placebo | 0.000595 | 0.00141 | -0.00123
| (0.00112) | (0.00107) | (0.00246)
Treatment 2014 x (Time $>$ 2016) | -0.00197 | 0.000388 | -0.0101***
| (0.00188) | (0.00194) | (0.00357)
Treatment 2014 x (Time $>$ 2018) | -0.00219 | -0.000423 | -0.00925***
| (0.00133) | (0.00130) | (0.00310)
Treatment 2014 x (Time $>$ 2019) | -0.000443 | 0.00122 | -0.00678***
| (0.00114) | (0.00119) | (0.00239)
Treatment 2014 x (Time $>$ 2020) | 0.000305 | 0.000907 | -0.00466**
| (0.000976) | (0.00105) | (0.00230)
Treatment 2014 x (Time $>$ 2021) | 0.000650 | 0.00111 | -0.00389**
| (0.000727) | (0.000747) | (0.00174)
R2 (within) | 0.598 | 0.585 | 0.488
Observations | 9,509 | 9,509 | 9,509
Labour market region FE | X | X | X
Quarter FE | X | X | X
Controls | X | X | X
Source: Regional Statistic of the Federal Employment Agency; SES 2014; Federal
Statistical Office; Federal Institute for Research on Building, Urban Affairs
and Spatial Development; own calculations. Note: The treatment effects refer
to the coefficients $\delta_{\tau}$ in Equation (3), estimated with TWFE. The
binary treatment equals 1 if the regional wage gap is equal to or above the
population-weighted median. The control variables included are interactions
of: time, east, and population share between 18 and 64 years in 2013; time,
east, and type of labour market region; time, east, and employment share in
different sectors; time and GDP per capita in 2013. Standard errors (in
parentheses) are clustered at the level of the labour market regions.
Confidence level: ***p$<$0.01, **p$<$0.05, *p$<$0.1.

###  4.3 Effects of the Minimum Wage for Switching Treatment Groups

In Section 2, we have documented that the regional wage gap substantially
changed between 2014 and 2018, as well as the regional ranking by size of the
wage gap. We take these changing wage gaps into account by estimating effects
for three distinct treatment groups that are defined based on the relative
size of the regional wage gap with respect to the median in 2014 and 2018. As
already described in Section 2, these groups are as follows: low wage gap in
2014, high wage gap in 2018 (low/high group); high wage gap in 2014, low wage
gap in 2018 (high/low group); high wage gap in 2014 and 2018 (high/high
group). The group of regions with a relatively low wage gap in both years form
the control group for this analysis (low/low group). This specification
accounts for the whole treatment path combined instead of single treatments at
different points in time. In addition to the three treatment indicators, we
also add a placebo term for each of them.

Table 3: Effects of the minimum wage introduction on regional employment with multiple treatment groups  | (1) | (2) | (3)
---|---|---|---
VARIABLES | Dependent | Employment | Marginal
| employment | subject to SSC | employment
Group low/low: Reference group |  |  |
Group low/high | -0.00710 | -0.00511 | -0.0208***
| (0.00439) | (0.00448) | (0.00676)
Group high/low | -0.00372 | 0.00165 | -0.0207*
| (0.00364) | (0.00411) | (0.0117)
Group high/high | -0.0108*** | -0.00378 | -0.0401***
| (0.00286) | (0.00335) | (0.00956)
Placebo Group low/high | 0.00181 | 0.00259 | -0.000553
| (0.00177) | (0.00166) | (0.00351)
Placebo Group high/low | 0.00167 | 0.00288** | -0.000956
| (0.00128) | (0.00134) | (0.00340)
Placebo Group high/high | 0.00108 | 0.00222 | -0.00204
| (0.00144) | (0.00142) | (0.00290)
Observations | 9,509 | 9,509 | 9,509
R2 (within) | 0.601 | 0.587 | 0.480
Labour market region FE | X | X | X
Quarter FE | X | X | X
Controls | X | X | X
Source: Regional Statistic of the Federal Employment Agency; SES 2014; Federal
Statistical Office; Federal Institute for Research on Building, Urban Affairs
and Spatial Development; own calculations. Note: The treatment effects refer
to the coefficients $\beta$, $\gamma$, and $\delta$ in Equation (4), estimated
with TWFE. Group low/low is the reference group and includes regions with a
wage gap below the weighted median in 2014 and 2018. Group low/high includes
regions with a wage gap below (at or above) the median in 2014 (2018). Group
high/low includes regions with a wage gap at or above (below) the median in
2014 (2018). Group high/high includes regions with a wage gap at or above the
median in 2014 and 2018. The control variables included are interactions of:
time, east, and population share between 18 and 64 years in 2013; time, east,
and type of labour market region; time, east, and employment share in
different sectors; time and GDP per capita in 2013. Standard errors (in
parentheses) are clustered at the level of the labour market regions.
Confidence level: ***p$<$0.01, **p$<$0.05, *p$<$0.1.

The results are presented in Table 3. The effect on dependent employment is
negative for all three treatment groups and the placebo terms are all
insignificant. The estimate is insignificant for both the low/high and
high/low groups. The effect is largest and statistically significant at the 1
percent level for the high/high group with $-1.1$ percent. Thus, the effect
for the group that is strongly affected by the minimum wage in 2014 and 2018
is about twice as large as the overall effect in Panel A of Table 1. For the
employment subject to social security contributions, all three coefficients
are insignificant and the placebo term for the high/low group is significant.
By contrast, all of the placebo terms are insignificant for the estimation of
effects on marginal employment. The coefficients for the low/high and high/low
groups are about the same size with almost $-2.1$ percent, respectively. The
former is significant at the 1 percent level and the latter at the 10 percent
level. With $-4.0$ percent, the effect on marginal employment for the
high/high group is almost twice as strong and significant at the 1 percent
level.

###  4.4 Staggered Treatment Adoption

Another way to exploit both the wage gaps of 2014 and 2018 for treatment
estimation is to combine both into a treatment that is adopted in a staggered
manner at two points, namely 2014 and 2019. Hereby, we assume that treatment
is absorbing, thus a region that is treated once remains treated until the end
of the observation period. First, we estimate the effect of this staggered
treatment via the TWFE model applied in the previous sections and apply the
decomposition of the treatment coefficient introduced by Goodman-Bacon (2021).
As described in Section 3, effect estimates of a staggered treatment can be
biased if treatment effects are heterogeneous across time and/or regions.
Therefore, we test the robustness of the TWFE estimates against using
alternative new estimators by Callaway and Sant’Anna (2021), Sun and Abraham
(2021), De Chaisemartin and d’Haultfoeuille (2022a), and Borusyak et al.
(2021).

Table A.4 in the Appendix shows the estimates for the staggered treatment
using the same TWFE model as before (see Equation (5)). The coefficient for
the total dependent employment is identical in direction and significance
level and very similar in magnitude to that from Table 1. The estimate for the
employment subject to social security contributions changes its sign and is
now negative, but it remains small and insignificant. While the estimate for
the marginal employment is negative and significant – as was the case in Table
1 – its magnitude has substantially decreased from 2.4 to 1.4 percent.

We decompose our TWFE estimations according to Goodman-Bacon (2021) (using the
user written Stata command “bacondecomp” (Goodman-Bacon et al., 2019)) to
identify the different components of the overall DiD estimates and their
respective weights.101010The detailed decomposition results are provided by
the authors upon request. These components include 2x2 DiDs comparing the two
treatment groups to the never-treated group. Further components are
comparisons between the earlier- and later-treated group and a within
component that is caused by differences in covariates within groups. The
overall DiD estimate is the weighted sum of these terms. The decomposition
results show that the effect estimates for the 2x2 DiD between the later-
treated and never-treated groups are smaller in absolute terms than the 2x2
DiD estimate for the earlier-treated and never-treated groups. The DiD
estimates comparing the two treatment groups with each other are positive in
all cases and they have a weight of about one-third. The fact that there is
substantial weight on these estimates and they include “forbidden” comparisons
between earlier- and later-treated units supports the notion of testing the
robustness of the results using the aforementioned newly developed estimators.

Figure 5: Effect of the minimum wage on employment with staggered treatment
adoption and different estimators Source: Regional Statistic of the Federal
Employment Agency; SES 2014, 2018; Federal Statistical Office; Federal
Institute for Research on Building, Urban Affairs and Spatial Development; own
calculations. Note: The treatment effect refers to the coefficient $\beta$ in
Equation (5). The binary treatment equals 1 if the regional wage gap is equal
to or above the population-weighted median. The exact choice of control
variables varies between estimators due to their varying ability to
accommodate covariates. TWFE and Sun and Abraham (2021): interactions of:
time, east, and population share between 18 and 64 years in 2013; time, east,
and type of labour market region; time, east, and employment share in
different sectors; time and GDP per capita in 2013. Callaway and Sant’Anna
(2021): type of labour market region, the GDP per capita in 2013, the
population share between 18 and 64 years in 2013, and the employment shares of
different sectors in 2013 as constant controls (it can only accommodate
invariant controls). Borusyak et al. (2021): the same variables as for
Callaway and Sant’Anna (2021), but interacted with time. De Chaisemartin and
d’Haultfoeuille (2022a): reduced number of controls without “east/west” in the
interactions.

Figure 5 compares the estimates for the staggered treatment based on the TWFE
model with those of the aforementioned estimators by De Chaisemartin and
d’Haultfoeuille (2022a), Callaway and Sant’Anna (2021) (with the never-treated
regions and with the not-yet-treated regions as control group), Sun and
Abraham (2021), and Borusyak et al. (2021).111111The results were estimated
using the Stata packages “did_multiplegt” (de Chaisemartin and
d’Haultfoeuille, n.d.), “csdid” (Rios-Avila et al., n.d.),
“eventstudyinteract” (Sun, 2021), and “did_imputation” (Borusyak,
n.d.).,121212The exact choice of control variables varies between estimators
due to their varying ability to accommodate covariates. The estimator by Sun
and Abraham (2021) allows for the same set of time varying controls as the
TWFE estimator described in Section 3. The estimator by Callaway and Sant’Anna
(2021) can only accommodate invariant controls and thus we add the type of
labour market region, the GDP per capita in 2013, the population share between
18 and 64 years in 2013, and the employment shares of different sectors in
2013 as constant controls. For the estimator by Borusyak et al. (2021), we
include the same variables, but interacted with time. We cannot add
“east/west” in the set of interactions because the estimator does not allow
controls that perfectly predict treatment status. As all eastern regions start
treatment in 2014, this would be the case here. Finally, the estimator by De
Chaisemartin and d’Haultfoeuille (2022a) appears to have problems with
estimation upon adding the large number of interactions included in the TWFE
estimation. Thus, we add a reduced number of controls where we leave
“east/west” out of the interactions. All estimates for all three outcomes are
negative and thus the direction of the effects is the same, irrespective of
using a TWFE or any of the new estimators. The TWFE coefficient for dependent
employment is smaller in absolute terms than any of the other estimators,
although the difference is only moderate. With the exception of the estimator
by Sun and Abraham (2021), all of the other coefficients have wider confidence
intervals, so that their coefficients are not statistically significant. The
TWFE estimate is significant at the 10-percent level and the estimate of Sun
and Abraham (2021) at the 5-percent level. For the employment subject to
social security contributions, the effect sizes are even closer to each other,
so that no systematic difference exists. None of the coefficients reach any
conventional level of significance. The difference between the TWFE and all
other coefficients are largest for marginal employment. While all estimates
are negative and statistically significant, the effect magnitude is stronger
with any of the newly developed estimators compared to the TWFE model. While
most of the new estimators yield similar results between $-4.4$ and $-5.2$
percent, the coefficient for Sun and Abraham (2021) of $-2.9$ percent lies
between them and the TWFE estimate with $-1.4$ percent.

There appear to be two main explanations for the apparent downward bias in the
magnitude of the TWFE estimates. First, the treatment effect (compared to the
never-treated group) seems to be different for regions starting treatment in
2014 and 2019. As the coefficient is a combination of the treatment effect of
regions starting in 2014 and those starting in 2019, this affects the size of
the overall estimate. Second, the late-treated group is compared to the early
treated group and vice versa. As the early treated regions already experience
a treatment effect before the late-treated regions start treatment, this
biases the estimated effect on the late-treated regions.

##  5 Conclusion

Our analysis has shown that the introduction of the statutory minimum wage in
Germany in 2015 had had significant negative effects on dependent employment
during the period until the first quarter of 2022. However, the effect is
rather small with -0.5 percent less dependent employment in regions with a
relatively high wage gap compared to those with a relatively low wage gap.
Moreover, compared to prior studies (Pestel et al., 2020) that analysed the
period until the first quarter of 2019, the magnitude of the effect decreased.
The results further show that the effect is completely attributable to
marginal employment, for which the trend of an increasingly negative effect
over time became even stronger. We cannot detect a significant effect on
employment subject to social security contributions. Interestingly, the
overall effect as well as the estimates during the last quarters of the
observation period are positive, but very small and insignificant. Our results
suggest that the increases of the minimum wage (especially the first two
increases in 2017 and 2019) had additional negative effects, particularly on
the marginal employment.

We have been able to extend the existing literature studying the German
minimum wage by using measurements of the regional exposure to the minimum
wage at two points in time. Based on this data, we found variation in the
minimum wage bite over time, whereby about 32 percent of regions changed their
treatment status over time. Eighteen (14) percent of these switching labour
market regions were weakly (strongly) affected by the minimum wage in 2014
before its introduction and then strongly (weakly) affected in 2018, prior to
the second increase. When accounting for these treatment changes over time, we
find that employment effects are strongest for the group of regions that was
strongly affected at both points in time. Even early on, these regions
experienced a larger decline in marginal employment than the regions that were
also strongly affected in 2014, but later changed their treatment status.

Overall, the results are in line with previous studies and they show that even
after up to seven years the minimum wage does not seem to have the large
negative employment effects that some had predicted prior to its introduction.
However, the negative employment effects are stronger for regions with a
relatively low GDP growth rate prior to the introduction of the minimum wage,
especially for marginal employment. The analysis based on the multiple
treatment groups suggests that the regional labour markets developed quite
differently even within treatment and control group of 2014. While all regions
saw a strong decline in the average wage gap with regard to the current
minimum wage between 2014 and 2018, the size of the decrease (in absolute and
relative terms) was rather heterogeneous, whereby many regions switched
between the treatment and control group. Finally, defining treatment as
staggered and applying newly developed estimators alongside the classic TWFE
approach reveals that the latter appears to underestimate the effect of the
minimum wage on the regional employment, especially on marginal employment.
The coefficient of the TWFE estimator suggests an effect of -1.4 percent,
while the new estimators mostly suggest a decrease of more than 4 percent.

There is a need for further research regarding the longer-term effects of the
introduction as well as the short- to medium-term effects of the already
implemented and upcoming increases on employment and unemployment. The German
minimum wage was substantially increased to €12 from October 1, 2022, onwards,
which raises the question of non-linearities in the effects of minimum wages.
Similar to the introduction of the minimum wage of €8.50 in 2015, the ad-hoc
increase to €12 is also a profound cut in the wage structure for many
companies and employees. Since it cannot be ruled out that the effects of the
statutory minimum wage are characterised by non-linearities, there could be a
tipping point from which a further increase has stronger negative employment
effects. Similarly, large increases in the minimum wage could have different
effects than a sequence of moderate adjustments (see Ahlfeldt et al., 2022).
Such non-linearities have not yet been sufficiently explored. The experience
with relatively high minimum wages at the local level in the US (for example,
$15 in Seattle) is not representative, as wage levels in the affected cities
are higher and thus the depth of intervention of the minimum wage is lower
than compared to the nationwide wage level (see Dube, 2019).

It also holds interest to study the mechanism(s) that drive the differential
development of the labour market regions after the introduction of the minimum
wage. The open questions concern the causes of the substantial changes to the
order of the regional wage gaps between 2014 and 2018 and the reasons why some
regions with a high wage gap experience a substantially larger negative
employment effect than others.

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## Appendix

Figure A.1: Wage gap ranks of labour market regions in 2014 and 2018

(a) Wage gap ranks 2014 (to 8.50 Euro) and 2018 (to 9.19 Euro)

(b) Wage gap ranks 2014 (to 8.50 Euro and to 9.19 Euro)

(c) Wage gap ranks 2014 (to 9.19 Euro) and 2018 (to 9.19 Euro)

Source: SES 2014, 2018; own calculations. Note: Scatter plots of labour market
region ranks in terms of the wage gaps in 2014 and 2018. Scatter plot a) plots
the ranks of the labour market regions in terms of their wage gap to €8.50
against the rank according to their wage gap to €9.19 in 2018. Scatter plot b)
plots the ranks of the labour market regions in terms of their wage gap to
€8.50 against the rank according to their wage gap to €9.19 in 2014. Scatter
plot c) plots the ranks of the labour market regions in terms of their wage
gap to €9.19 against the rank according to their wage gap to €9.19 in 2018.

Figure A.2: Outcome evolution over time by treatment status Source: Regional Statistic of the Federal Employment Agency; SES 2014; own calculations. Note: The graph shows the development of dependent employment, employment subject to social security contributions, and marginal employment between 2013 and 2022 separate for labour market regions with a wage gap at or above and below the population-weighted median. Table A.1: Development of the minimum wage level in Germany Date | MW level | $\Delta$
---|---|---
| (in €) | (in %)
01.01.2015 | 8.50 |
01.01.2017 | 8.84 | 4.00
01.01.2019 | 9.19 | 3.96
01.01.2020 | 9.35 | 1.74
01.01.2021 | 9.50 | 1.60
01.07.2021 | 9.60 | 1.05
01.01.2022 | 9.82 | 2.29
01.07.2022 | 10.45 | 6.42
01.10.2022 | 12.00 | 14.83

Source: Federal Statistical Office; own calculations. Note: The first column shows the date on which the respective increase of the minimum wage was implemented. The second column shows the new level of the minimum wage after it was increased. The third column displays the percentage change of the minimum wage due to the respective increase with respect to the previous level of the minimum wage. Table A.2: Descriptive statistics for labour market regions prior to the introduction and the increase of the minimum wage | SES 2014 | SES 2018
---|---|---
Minimum wage exposure | All | Low | High | All | Low | High
(relative to the median wage gap)
Average wage gap 2014 (in Euro) | 0.203 | 0.104 | 0.281 |  |  |
Average wage gap 2018 (in Euro) |  |  |  | 0.034 | 0.019 | 0.043
Regions in East Germany in %) | 21 | 0 | 37.5 | 21 | 7.7 | 30.1
Settlement structure (in %) |  |  |  |  |  |
Urban | 44.7 | 52.2 | 38.9 | 44.7 | 51.9 | 39.9
Rural with tendencies to densification | 24.9 | 22.1 | 27.1 | 24.9 | 25 | 24.8
Sparsely populated, rural | 30.4 | 25.7 | 34 | 30.4 | 23.1 | 35.3
Empl. structure by sector 2013 (in %) |  |  |  |  |  |
Empl. in agriculture, forestry and fishing | 2.4 | 2.3 | 2.5 | 2.4 | 2.1 | 2.6
Empl. in services | 13.7 | 13.7 | 13.7 | 13.7 | 13.9 | 13.5
Empl. in manufacturing | 29.2 | 31 | 27.8 | 29.2 | 30.5 | 28.3
Empl. in the public sector | 30.5 | 28.9 | 31.7 | 30.5 | 29.3 | 31.2
Empl. in trade, transport and hospitality | 24.2 | 24.1 | 24.3 | 24.2 | 24.2 | 24.3
Popul. share 18-64 years (2013, in %) | 62.4 | 62.6 | 62.2 | 62.4 | 62.6 | 62.2
Economic growth |  |  |  |  |  |
GDP growth rate 2010-2013 (in %) | 9.8 | 10.2 | 9.5 | 9.8 | 10.4 | 9.4
Low GDP growth 2010-2013 (share in %) | 25.7 | 30.1 | 22.2 | 25.7 | 25 | 26.1
GDP growth rate 2015-2018 (in %) | 10.1 | 11.2 | 9.3 | 10.1 | 10.8 | 9.7
Low GDP growth 2015-2018 (share in %) | 29.2 | 20.4 | 36.1 | 29.2 | 22.1 | 34
Number of labour market regions | 257 | 113 | 144 | 257 | 104 | 153

Source: SES 2014, 2018; Federal Institute for Research on Building, Urban Affairs and Spatial Development (FBUS), Federal Statistical Office; own calculations. Note: The table presents mean values for all regions and separately by relative size of the regional wage gap for 2014 and 2018. A high (low) minimum wage gap means that the wage gap is above (below or equal to) the median. The division of the labour market regions in types of settlement structure is based on information from the FBUS. The employment by sector, the gross domestic product, and the population shares are taken from the regional statistic from the Federal Statistical Office. Services: Financial, insurance, and business services, real estate and housing. Public services: public and other services, education and health. Trade, transport and hospitality includes information and communication services. Table A.3: Descriptive statistics for labour market regions grouped according to their treatment status in 2014 and 2018 | (1) | (2) | (3) | (4)
---|---|---|---|---
Minimum wage exposure in 2014/2018 | Low/ | Low/ | High/ | High/
(relative to the median wage gap) | Low | High | Low | High
Minimum wage bite |  |  |  |
Average wage gap 2014 (in Euro) | 0.098 | 0.113 | 0.234 | 0.296
Average wage gap 2018 (in Euro) | 0.019 | 0.042 | 0.021 | 0.044
Absolute difference (in Euro) | -0.079 | -0.071 | -0.214 | -0.252
Percentage difference | -80.6 | -62.8 | -91.5 | -85.1
Fraction with hourly wage below | 8.86 | 10.35 | 16.58 | 19.49
8.50€ 2014 (in %)
Fraction with hourly wage below | 5.73 | 9.74 | 6.22 | 10.98
9.19€ 2018 (in %)
Difference in percentage points | -3.13 | -0.61 | -10.36 | -8.51
Percentage difference | -35.3 | -5.9 | -62.5 | -43.7
Regions in East Germany in %) | 0 | 0 | 22.2 | 42.6
Settlement structure (in %) |  |  |  |
Urban | 51.5 | 53.3 | 52.8 | 34.3
Rural with tendencies to densification | 26.5 | 15.6 | 22.2 | 28.7
Sparsely populated, rural | 22.1 | 31.1 | 25 | 37
Empl. structure by sector 2013 (in %) |  |  |  |
Empl. in agriculture, forestry and fishing | 2.2 | 2.6 | 2 | 2.7
Empl. in services | 13.9 | 13.4 | 14.1 | 13.6
Empl. in manufacturing | 31.8 | 29.8 | 28 | 27.7
Empl. in the public sector | 28.2 | 30 | 31.5 | 31.8
Empl. in trade, transport and hospitality | 24 | 24.3 | 24.5 | 24.3
Popul. share 18-64 years (2013, in %) | 62.7 | 62.3 | 62.4 | 62.2
Economic growth |  |  |  |
GDP growth rate 2010-2013 (in %) | 10.7 | 9.4 | 9.8 | 9.5
Low GDP growth 2010-2013 (share in %) | 26.5 | 35.6 | 22.2 | 22.2
GDP growth rate 2015-2018 (in %) | 11.5 | 10.7 | 9.5 | 9.2
Low GDP growth 2015-2018 (share in %) | 19.1 | 22.2 | 27.8 | 38.9
Hourly wage |  |  |  |
Average hourly wage 2014 (in Euro) | 16.92 | 16.03 | 14.87 | 14.20
Average hourly wage 2018 (in Euro) | 18.67 | 17.32 | 17.50 | 16.02
Absolute difference (in Euro) | 1.75 | 1.29 | 2.64 | 1.81
Percentage difference 2014-2018 | 10.3 | 8.0 | 17.8 | 12.7
Number of labour market regions | 68 | 45 | 36 | 108

Source: SES 2014, 2018; Federal Institute for Research on Building, Urban Affairs and Spatial Development (FBUS), Federal Statistical Office; own calculations. Note: The table presents mean values for four different groups of regions that are defined by the relative size of their wage gaps in 2014 and 2018. A high (low) minimum wage gap means that the wage gap is above (below or equal to) the median. The division of the labour market regions in types of settlement structure is based on information from the FBUS. The employment by sector, the gross domestic product, and the population shares are taken from the regional statistic from the Federal Statistical Office. Services: Financial, insurance, and business services, real estate and housing. Public services: public and other services, education and health. Trade, transport and hospitality includes information and communication services. Table A.4: Effects of the minimum wage introduction on regional employment with a staggered treatment | (1) | (2) | (3)
---|---|---|---
VARIABLES | Dependent | Employment | Marginal
| employment | subject to SSC | employment
Treatment (staggered) | -0.00475* | -0.00315 | -0.0139**
| (0.00251) | (0.00239) | (0.00596)
Observations | 9,509 | 9,509 | 9,509
R2 (within) | 0.598 | 0.586 | 0.469
Labour market region FE | X | X | X
Quarter FE | X | X | X
Controls | X | X | X
Source: Regional Statistic of the Federal Employment Agency; SES 2014; Federal
Statistical Office; Federal Institute for Research on Building, Urban Affairs
and Spatial Development; own calculations. Note: The treatment effect refers
to the coefficient $\beta$ in Equation (5), estimated with TWFE. The treatment
is binary, staggered, and absorbing. Regions with a wage gap equal to or above
the population-weighted median in 2014 start treatment in Q3 2014 and regions
with a wage gap below (equal to or above) the population-weighted median in
2014 (2018) start treatment in Q1 2019. The control variables included are
interactions of: time, east, and population share between 18 and 64 years in
2013; time, east, and type of labour market region; time, east, and employment
share in different sectors; time and GDP per capita in 2013. Standard errors
(in parentheses) are clustered at the level of the labour market regions.
Confidence level: ***p$<$0.01, **p$<$0.05, *p$<$0.1.

## Supplementary Appendix

Table B.1: Results for the Goodman-Bacon decomposition of the TWFE results with a staggered treatment VARIABLES | Dependent | Employment | Marginal
---|---|---|---
employment | subject to SSC | employment
Overall DiD estimate | -0.004784 | -0.003177 | -0.013888
Overall DiD variance | 0.000006 | 0.000006 | 0.000036
DiD estimate between treatment groups | 0.001759 | 0.002070 | 0.009555
DiD estimate between early treated and never treated groups | -0.032767 | -0.022127 | -0.104456
DiD estimate between late treated and never treated groups | -0.012759 | -0.007378 | -0.031371
DiD estimate within | 0.020987 | 0.011631 | 0.056897
Weight on DiD estimate between treatment groups | 0.354919 | 0.354919 | 0.354919
Weight on DiD estimate between early treated and never treated groups | 0.213239 | 0.213239 | 0.213239
Weight on DiD estimate between late treated and never treated groups | 0.221776 | 0.221776 | 0.221776
Weight on DiD within estimate | 0.210065 | 0.210065 | 0.210065
Source: Regional Statistic of the Federal Employment Agency; SES 2014, 2018;
Federal Statistical Office; Federal Institute for Research on Building, Urban
Affairs and Spatial Development; own calculations. Note: The table shows the
results for a decomposition of the TWFE estimate with a staggered treatment
(coefficient $\beta$ of Equation (5)) according to Goodman-Bacon (2021). The
coefficients for the overall DiD estimate are negligibly different from those
in Table A.4 in the Appendix, because of slight differences in the underlying
estimation between the commands “bacondecomp” and “reghdfe” (the former is
used for the decomposition and the latter is used for the TWFE estimations
throughout the paper). The regressions underlying the decomposition include
all control variables that are also included in all the TWFE estimations
throughout the paper. These control variables are interactions of: time, east,
and population share between 18 and 64 years in 2013; time, east, and type of
labour market region; time, east, and employment share in different sectors;
time and GDP per capita in 2013. “Between treatment groups” refers to 2x2 DiDs
between the later and the earlier treated groups. This includes valid
estimates for the treatment effect on the earlier treated group with the later
treated group as control group as well as “forbidden” comparisons with the
earlier treated group as the control group for the later treated group.
“Between early (late) treated and never treated groups” refers to 2x2 DiDs
between the earlier (later) and the never treated groups. “within estimate”
refers to the component of the overall DiD estimate that is caused by
differences in covariates within groups.