What Does the German Minimum Wage Do? The Impact of the Introduction of the Statutory Minimum Wage on the Composition of Low-and Minimum-Wage Labour

: In this article, we examine structural changes in minimum wage and low wage labor following the introduction and ﬁ rst increase of the German minimum wage. Changes in the impact that workers face earning gross hourly wages below the minimum-wage or low-wage thresholds are identi ﬁ ed by comparing individual, company and sectoral characteristics based on the Structure of Earnings Surveys (SESs) 2014 and 2018. The SES is a mandatory survey of companies that provides information on wages and working hours for approximately 1 million jobs and nearly 70,000 companies across all industries. Using these rich data, we present the ﬁ rst systematic analysis of how structural changes in individual-, company, and industry-level determinants a ﬀ ect minimum-and low-wage workers. Using descriptive analysis, we ﬁ rst summarize the changing pattern in jobs, companies, and industries after the introduction of minimum wage. Second, we use random intercept-only models to estimate the explanatory power at the individual, company, and industry levels in 2014 and 2018. Third, we perform logistic and linear regression estimations to assess the changing trends in having a minimum-or low-wage job and the distance between a worker ’ s actual earnings and the minimum-and low-wage


Introduction
Labor markets are composed of various segments that vary regarding their working conditions.With a view of the national wage distribution, the bottom endalso denoted as the low-wage segmentis often the main focus.Low-paid employees are generally perceived as having comparatively little power to act and negotiate (Bruttel et al. 2017;Dütsch and Bruttel 2021).Therefore, the low-wage segment is regarded as risk-generating and sociopolitically problematic (Gautié and Schmitt 2010;Kalleberg 2011), with the size of the low-wage sector providing an indication of the opportunity and risk structures in national labor markets.From a sociopolitical perspective, measures to reduce the low-wage sector as a whole and prevent low wages overall are widely discussed (Bosch 2018).In this context, minimum wages are considered a key instrument of labor market policy for intervening in the low-wage sector (Kalleberg 2011).
In the empirical literature, several qualitative and quantitative descriptions of minimum wage or low-wage employees exist thus far (Dütsch and Himmelreicher 2020;Gallie 2007;Kalina and Weinkopf 2015, 2017, 2018;Kalleberg 2011).However, to our knowledge, there is no systematic analysis of the determinants of convergence in wages or of structural changes in minimum-wage or low-wage employment after the introduction or increase in a minimum wage.From a conceptual point of view, various individual and company response patterns affect low-wage labor, which can lead to similar or even contradictory developments.Convergence can occur due to wage increases for employees affected by the minimum wage (Burauel et al. 2020;Cengiz et al. 2019;Phelan 2019).Noncompliance, by contrast, reduces such wage increases and, thus, convergence (Low Pay Commission 2021;Mindestlohnkommission 2018).Compositional changes can be the consequence of employment effects and can be both negative and positive (Borjas 2015;Manning 2003), affecting low-wage labor and consequently its sociodemographic composition.Furthermore, regarding compositional effects, institutionalist and behavioral theories predict changes in work intensity and productivity or reductions in special payments and nonwage benefits (Hirsch et al. 2015;Lester 1960Lester , 1964;;Schmitt 2015).This can result in the replacement of (lower-skilled) minimum wage employees by higher-wage (and better-skilled) employees, as well as in movement of employees between companies (Dustmann et al. 2022).Thus, structural shifts in the low-wage sector are likely to depend on individual determinants but also, in line with Coleman (1990) and Esser (1996), on companies and industries as relevant contextual factors.
Against this backdrop, we examine structural changes associated with the German statutory minimum wage and raise the following question: Did the introduction and first uprating of the minimum wage in Germany lead to convergence or compositional changes in low-wage employment?In an international comparison, the introduction of the minimum wage represented a strong intervention in the lower range of the wage distribution (Bruttel et al. 2018;Mindestlohnkommission 2016): Approximately 4 million jobs or 11.3 percent of all jobs were previously paid below 8.50 euros.We aim to explore individual and structural determinants that had an impact on the incidence of earning wages below the minimum wage and low wage thresholds in 2014, the year prior to the introduction of the statutory minimum wage, and 2018, the year after the first increase in the minimum wage, which constitutes a medium-term period.For a valid measurement of composition changes, we use rich and representative datasets from 2014 to 2018, each containing information on approximately 1 million jobs and approximately 70,000 companies from all industries.These data allow us to assess the significance of not only individual determinants but also company-level and industry-level determinants, which we present here in detail for the first time.In the empirical part, we describe in the first step the respective determinants and the frequency of employment in the minimum-wage and low-wage sectors in 2014 and 2018.In the second step, random intercept-only models are estimated to assess the explanatory power of the individual, company, and industry levels in 2014 and 2018 regarding minimum-wage and low-wage labor.Third, changing correlations between the determinants at those three levels and the affectedness of being employed in the minimum-wage and low-wage sectors between the two years are determined in regression analyses.
In the next section, we provide a comprehensive review of the current state of research on this topic, present theoretical assumptions, and derive two hypotheses.Data and the estimation strategy are described in Section 3. Section 4 contains the empirical results, and Section 5 presents the findings and conclusion.

State of Research and Theoretical Assumptions
To understand minimum-and low-wage employment and its implications for individual careers, recent research has focused on 4 topics.The first addresses the determinants of being in a low-wage job or the individual characteristics that are typical for low-wage employment (Bosch and Kalina 2008;Bruttel et al. 2017;Kalina andWeinkopf 2015, 2017).The second topic addresses the question of how long employees remain in low-wage positions and whether they successfully transition into regular employment (through the steppingstone effect) or become unemployed and end up in the 'low-pay, no-pay cycle' (Fok et al. 2015;Knabe and Plum 2013;Mosthaf et al. 2011;Schnabel 2016).The third topic is the body of studies examining the consequences of low-wage employment for employees' well-being, labor intensity and health (Appelbaum 2010;Fedorets and Himmelreicher 2021;Gallie 2007;Kalleberg 2011).The fourth topic is possible alternatives to taking up a low-wage job or remaining in the low-wage sector through strategies such as searching longer and more intensely for better paid employment or participating in further training (Schnabel 2016).Our paper contributes to the first strand of research and extends it with an analysis of structural changes following the introduction of a minimum wage.Such changes are often described as a general shift in the working population or are traced back to individuals and their characteristics.However, structuralist theories of action incorporate contextual factors and show that they influence individual opportunities and risks (Coleman 1990;Esser 1996).Consequently, theoretical explanations should account for actors and corresponding framework conditions.
A minimum wage is a labor market institution that raises the wages of employees having earned less than the new minimum.Since the minimum wage segment represents a substantial part of the low wage segment, the low wage segment and, thus, the probability of low wages occurring can potentially be decreased by a minimum wage introduction or hike.Beyond the effect on minimum wage earners, a reducing effect on the low wage probability is likely to be stronger the more pronounced the compression effects of the minimum wage are (Burauel et al. 2020;Cengiz et al. 2019;Phelan 2019).This is because the low-wage threshold is a relative measure that refers to the median wage.The higher the minimum wage is in relation to the median wage and the stronger the compression effects are, the more pronounced the reduction in the low-wage sector due to the minimum wage.In Germany, the introduction of the minimum wage in 2015 led to a significant wage compression (Mindestlohnkommission 2016), while spillover effects could not be found (Burauel et al. 2020).Both findings indicate a convergence at the bottom of the income distribution; this implies a concentration of wages at and just above the minimum wage, also called the ripple effect of a minimum wage (Phelan 2019).As a result, the minimum wage became the going rate for many low-paid employees (Brown 1999).Therefore, the function of minimum wages is primarily to raise wages at the bottom of the wage distribution.Overall, this development is likely to lead to a convergence of individual-, company-and industry-specific incidences of earning low wages and, in particular, minimum wages.This means that groups of employees, companies and sectors that had the highest incidence of earning below 8.50 euros prior to the introduction of the minimum wage in Germany, such as women, those younger than 35 years old and older than 55 years old, foreigners, low-skilled workers, temporary and fixed-term employees, mini-jobbers, those working in small companies, those without collective bargaining obligations or those in the service sector (Dütsch and Himmelreicher 2020;Kalina and Weinkopf 2015), are assumed to continue to exhibit a similar risk but at an even lower level.Thus, regarding the groups mentioned above, the share of employees with low or minimum wages and their likelihood of receiving such wages should decrease in the sense of convergence.Additionally, it is important to consider that a minimum wage can be effective only if organizations comply with it.Noncompliance reduces the positive wage effects (Low Pay Commission 2021; Mindestlohnkommission 2018).Nevertheless, convergence should be evident, albeit to a lesser extent than with full compliance.
Hypothesis 1: Individual, company-specific and sectoral risks of being paid in the minimum-wage and low-wage segments declined between 2014 and 2018, leading to convergence.
In the discussion on the impact of minimum wages, compositional effects are a further issue.They first refer to the composition of the workforce regarding characteristics such as gender, age or education.Changes in such characteristics of low-wage labor can occur in the case of disemployment (Borjas 2015;Manning 2003).Thus, workers who receive a minimum wage that is higher than their marginal productivity are laid off according to the approach of a perfectly competitive labor market.This impacts the composition of the low-wage workforce.After the introduction of the German minimum wage, there were negative employment effects among marginal employees, which are still observable in the medium term (Caliendo et al. 2018;2022, Isphording et al. 2022)).Concurrently, findings indicate that some of the formerly marginal employment was converted into part-time employment subject to social security contributions (Bonin et al. 2018;Pestel et al. 2020).Accordingly, compositional changes should be evident in terms of the form of employment.Furthermore, gender-specific changes are to be expected, as marginal employment was characterized by female workers in particular.Moreover, institutionalist and behavioral theories predict restructuring in low-wage employment as companies seek to compensate for higher wage costs due to a minimum wage.Changes in work intensity and productivity measures (Hirsch et al. 2015;Lester 1960Lester , 1964;;Schmitt 2015) can result in the replacement of (lower-skilled) minimum-wage employees by higher-wage (and better-skilled) employees.Reductions in special payments and fringe benefits, by contrast, can lead to voluntary withdrawals from companies (ibid.).Second, compositional effects are assumed to stem from changing framework conditions within which individuals act and operate.Differences in company structure result from the type of production and corresponding productivity (Card et al. 2018), the size of the company (Struck 2006) and the collective bargaining agreement of companies (Fitzenberger and Seidlitz 2020).In this regard, Dustmann et al. (2022) found that the German minimum wage increased the company wage premium, suggesting a compositional shift toward more productive and higher-paying companies.Furthermore, small companies are generally considered less able to adapt to changing market conditions than their larger counterparts.Large companies, for example, are better able to cope with profit losses than small companies because they can compensate for revenue shortfalls or higher expenses (Struck 2006).Indeed, studies have shown a decrease in the number of small businesses due to the minimum wage in Germany (De Monte et al. 2022;Dustmann et al. 2022;Isphording et al. 2022).Third, the industries in which jobs are performed are significant contextual factors.The industry to which a company belongs is strongly associated with its employees' wages.This correlation is confirmed by several studies focusing on Germany (Bispinck 2017;Mindestlohnkommission 2018).While the creation of value and thus the scope of profit distribution is comparatively high in the manufacturing industry, this is less the case in the service sector.Accordingly, the average wage level is higher in the manufacturing industry than in other sectors, especially the service sector (Dütsch and Himmelreicher 2020).Consequently, the extents to which sectors are affected by the minimum wage are likely to lead to a shift in the size and composition of industries in the low-wage sector.For example, in the hospitality industry, there were collective agreements with earnings groups below 8.50 euros prior to the introduction of the minimum wage.The range of wages between the highest and lowest collectively agreed wages fell most sharply there between December 2014 and June 2017, at 7.2 percent (Statistisches Bundesamt 2017).Against this background, a second hypothesis can be derived.
Hypothesis 2: Between 2014 and 2018, the introduction of the minimum wage involved a shift in the composition of the minimum-wage and low-wage sectors in terms of individual and company characteristics and sectors.
For our empirical analysis, we use the last two survey waves in 2014 and 2018 of the Structure of Earnings Survey (SES).The SES is a mandatory cross-sectional survey of companies in Germany, which is collected every 4 years (Statistisches Bundesamt 2020).The use of the earnings surveys (VE) conducted in 2015, 2016 and 2017, whose participation was not mandatory but voluntary in contrast to the SES, is waived.This is partly because of the potential selection problem and partly because the significantly smaller number of cases does not promise any additional insight (Caliendo et al. 2022).Although it is companies that are surveyed, the statistical unit of the survey is employment relationships, encompassing individual-, company-and sector-level information; this provides a unique opportunity to examine our hypotheses.The primary source of the SES data is the payroll accountings of the surveyed companies, which are subject to internal and external audits (Statistisches Bundesamt 2016).Thus, the information on wages is highly accurate.This is not always the case for information regarding working hours, which are partially estimated by the reporting companies.Nevertheless, all information is extensively checked by the statistical offices of the federal states, improving reliability (Statistisches Bundesamt 2016).Starting with 2014, the SES was broadened to include companies with fewer than 10 employees, and its sampling scheme was altered to increase overall representativeness.With these improvements, the SES covers nearly all sectors except private households and exterritorial organizations and corporations, fulfilling the prerequisites for evaluating the minimum-and low-wage segments.Moreover, the changes in the 2014 SES were exactly preserved in the 2018 SES, allowing us to directly compare the two surveys, which was only partially possible for previous waves of the SES.Additionally, the data on earnings refer only to the month of April in the respective survey years.Thus, SES 2014 and 2018 let us compare the situation just before the introduction of the minimum wage and 4 years thereafter.We use the SES 2014 because it is not expected to be influenced by any anticipatory effects.This is important, as it allows the state of the employment structure to be analyzed when it has not yet been influenced by the minimum wage.
We restricted our sample to employees older than 18 years of age and excluded those who were partially retired as well as apprentices, trainees, and interns.This left us with a sample of 978,817 jobs in 70,303 companies in 2014 and 969,477 jobs in 70,512 companies in 2018.Our main dependent variable is gross hourly wages.It was computed by taking gross monthly earnings and subtracting any overtime earnings as well as allowances for shift, night, Sunday and holiday work.We then divided wages by monthly paid working hours (without overtime).In addition, we use two indicator variables for minimum wage and low wage jobs throughout our analysis, What Does the German Minimum Wage Do? which rely on the computed gross hourly wages.For 2014, the minimum wage threshold was set at the level of 8.50 euros, equal to the rate introduced in 2015.The low-wage threshold, which is defined as two-thirds of the median wage, amounted to 10.33 euros in 2014.Similarly, for 2018, we used 8.89 euros as the minimum wage threshold, which is 5 cents higher than the minimum wage applicable at the time to account for measurement errors.This procedure has been frequently adopted in other studies on the minimum wage (Bachmann et al. 2022;Bruckmeier and Schwarz 2022;Mindestlohnkommission 2020). 1 The low-wage threshold in that year was 11.05 euros.This procedure left us with a total of 4 dummy variables indicating whether or not a job was paid below or above the minimum-and low-wage threshold at both observation dates.Additionally, in some of the analyses, we use distance variables, which were calculated by subtracting the gross hourly wage a job is paid from the respective minimum-wage and low-wage thresholds.
The central explanatory variables are various individual and company characteristics as well as information on the industrial sector.Individual characteristics include sex, age, the highest educational degree obtained, tenure, employment status (full-time, part-time, or marginal employment), 2 type of contract (fixed-term or permanent), and whether employment is temporary.Company-level characteristics include information on whether the company is bound by sectoral collective or company collective agreements, the size of the company (<5, 5-49, 50-249, and 250 or more employees), gender distribution, and the region where the company is located (northwest including Berlin, northeast, west and south).Industrial sectors are classified according to the sections of the Statistical Classification of Economic Activities (NACE, Rev. 2), excluding the categories 'Activities of households as employers; undifferentiated goods-and services-producing activities of households for own use' and 'Activities of extraterritorial organizations and bodies' because they are not part of the sample.
Regarding the empirical procedure, first, descriptive analyses give an overview of low-paid workers and low-wage companies as well as minimum-wage workers and minimum-wage companies in 2014 and 2018.In a second step, random intercept-only models are estimated to assess the explanatory power of the individual, company, and industry levels in 2014 and 2018 regarding minimum-wage and low-wage labor.Third, logistic and linear regressions are performed considering individual, company-and industry-specific characteristics for pooled data of the survey years 2014 and 2018.Specifically, we assess compositional changes between the two years by introducing interaction terms for the four-year comparison and the explanatory variables.
The multivariate analyses are based on three-level data.These data structure is an important aspect when choosing an estimation procedure.Moulton (1986Moulton ( , 1990) ) noted that the inclusion of meso-and macrolevel variables in a standard regression analysis in which observations are assumed to be independent leads to inefficient coefficients and biased standard errors.Therefore, in the first step, multilevel models are estimated because they allow a grouping of jobs i within companies j nested in industries k by considering residuals at the company and industry levels.These residuals represent unobserved characteristics that cause correlations between outcomes for jobs from the same company and industry.The empirical analyses are performed with the following three-level random intercept-only model (Rabe-Hesketh and Skrondal 2008): where β 0 represents the regression constant and C ( 2) jk and C ( 3) k denote the random effects that are assumed to be independent not only of each other but also across clusters.C ( 2)  jk is also assumed to be independent across units.ε ijk is the error term.In the third and fourth steps, we estimate logit models for binary variables and linear OLS models with cluster-robust standard errors (Wooldridge 2012).

Descriptive Statistics
In Germany in 2018, after the introduction and the first increase of the national minimum wage to 8.84 euros, approximately 4 percent of jobs were paid at or below the minimum wage threshold of 8.89 euros, and approximately 22 percent were paid What Does the German Minimum Wage Do? below the low wage threshold of 11.05 euros. 3Compared with the situation in 2014, before the introduction of the minimum wage in Germany, the minimum wage incidence decreased by 7 percentage points, and the low wage incidence rose by approximately 1 percentage point (Table 1).The average gross hourly wage amounted to 18.97 euros in 2018.In the minimum-wage and low-wage ranges, the mean wages were 8.55 euros and 9.68 euros, respectively.In both wage brackets, the average hourly wages increased by approximately 1.5 euros between 2014 and 2018.These developments, although merely descriptive, point to a convergence of earnings in the minimum-wage sector but to a still widespread and even slightly increasing low-wage sector.Overall, in 2018, approximately 49 percent of workers were female; approximately 5 percent of women earned less than 8.89 euros, and approximately 28 percent earned less than 11.05 euros.The share of women and men in minimum wage jobs was similar, while the low wage incidence was 10 percentage points higher for women.Compared with 2014, in 2018, the minimum wage incidence of women decreased by 9 percentage points, and the low wage incidence rose by approximately 1 percentage point.Thus, after the introduction of the minimum wage in Germany, more women than men left the minimum wage segment.Regarding age, higher risks of earning low or minimum wages could be observed for younger workers aged 18 to 24 and those 65 years and older.Approximately one in ten of the younger and older employees were in the minimum-wage segment, and nearly half were in the low-wage segment.Over time, the share of younger and older minimum wage earners strongly declined by approximately 15 percentage points; their share in the low-wage segment rose by 5 percentage points.Approximately 8 percent of employees did not complete vocational training; in comparison with other education groups, they showed the largest shares in the minimum-wage (8 percent) and low-wage segments (41 percent).The minimum wage incidence of unskilled workers fell by more than 11 percentage points by 2018 compared with 2014, while the low wage incidence increased by 5 percentage points.Nevertheless, approximately 16 percent of employees with a vocational qualification received low pay.Regarding the type of employment, approximately 58 percent of jobs were full time, 27 percent were part time, and 15 percent were marginal in 2018.Among the workers with marginal employment, 14 percent were paid below the minimum wage and 71 percent below the low-wage threshold.They earned significantly lower average hourly wages (11.06 euros) than part-time (17.06 euros) or full-time workers (21.86 euros).Furthermore, the average wages of the marginally employed who were paid in the minimum-wage or low-wage segments amounted to only 8.68 euros and 9.58 euros, respectively.The introduction of the minimum wage led to a shrinking share of marginal jobs paid below the minimum wage threshold by 23 percentage points but a 7 percentage point increase in the share of marginal jobs paid below the low wage threshold.The marginally employed often earned less than the minimum wage, even in companies with higher sectoral or company collective bargaining agreements (see Table A1).This can be traced back to the fact that marginal part-time workers, who are composed above average of low-skilled, foreign and female workers, often have comparatively little market power.In addition, companies often use this form of employment to increase the internal flexibility of their workforce (Dütsch and Struck 2011).Both of these factors have considerable disadvantages for the income of the employees concerned.Additionally, numerous labor law provisions, such as continued payment of wages in the event of illness or time off, are observed much less frequently in marginal employment relationships than in employment relationships subject to social insurance contributions (Bachmann et al. 2017).
Six percent of workers with fixed-term contracts were in minimum-wage employment and 34 percent in low-paid employment in 2018 (Table 1).These were significantly higher shares than those for permanent employees.Approximately 37 percent of temporary work was low paid, while the share among regular work was 22 percent.However, the proportion of temporary jobs below the minimum wage threshold amounted to 3 percent and was thus remarkably similar to regular employment.Compared to 2014, the share of temporary workers earning less than minimum or low wages disproportionately declined by 9 and 4 percentage points after the introduction of the minimum wage.This may be due to sectoral collective agreements negotiated for this industrial sector (Personaldienstleiter 2019).Additionally, job tenure seems to be an important factor regarding minimum-and low-wage employment: The share of minimum-wage jobs (7 percent) and low-wage jobs (36 percent) among employees working at most four years in their jobs clearly exceeded the percentage of employees with a longer employment history.
With regard to individual-level determinants, the descriptive results show two different trends.First, the relative share of individual characteristics regarding minimum wage work decreased.This especially applies to female, marginally employed, unskilled, or fixed-term employees and employees with a short period of employment.Second, the relative share of individual characteristics regarding low wage work increased slightly, especially for unskilled employees and those in marginal employment.Accordingly, there seems to be an elevator effect, since at the bottom of the income distribution, the shares of exceptionally low wages decreased.Concurrently, there was obviously a selective redistribution of minimum wage employees into only slightly higher wage ranges and, thus, a shift in the composition of minimum wage and low wage labor after the introduction of the minimum wage.
In Table 2, company-level characteristics of jobs in Germany are described.This shows that the larger the company is, the smaller the proportion of jobs below the minimum-wage and low-wage thresholds.Small companies with fewer than 5 employees had the highest shares of minimum-wage (8 percent) or low-wage employment (46 percent).After the introduction of the minimum wage, the share of small companies paying wages below the minimum wage threshold shrank by 15 percentage points, and the share of low-wage workers grew by 4 percentage points.Approximately 42 percent of all jobs were in companies not bound by a collective agreement.Of these jobs, 31 percent were paid below the low-wage threshold, and 6 percent were paid even below the minimum-wage threshold.Compared to 2014, the share of minimum wage workers declined by 12 percentage points, and the share of low wage workers remained almost the same.In comparison, employees in companies bound by sectoral or company collective bargaining agreements were better protected against wages below the low-wage or minimum-wage thresholds.This becomes also evident in Pen's Parades in Figure 1, which depicts the distribution of hourly wages according to collective bargaining coverage in 2014 and 2018.by collective bargaining agreements.However, in total, sectoral and company collective bargaining agreements lead to higher wages in the entire wage distribution. 4egarding the internal gender distribution (see Table 2), low-wage jobs were observed more often in female-dominated companies (28 percent) than in maledominated companies (17 percent).Thus, obviously, there is an interaction between the gender composition of the workforce and the wage structure in the company as a whole.Furthermore, companies in the northeastern part of Germany had the greatest shares of minimum-wage (6 percent) and low-wage employment (31 percent); they also paid below-average wages.Between 2014 and 2018, a convergence in regional differences can be observed because the share of employees paid below the minimum wage threshold levelled off considerably.However, there is still a strong south-north divide in terms of low wages, with significantly lower shares of low-wage employment in southern Germany.Overall, descriptive results of company-level characteristics mostly point to decreased frequencies of companies paying minimum or low wages due to a compression of wages on the lower end of the wage scale: The frequency decreased, especially among small, nonbounded companies in northeastern Germany.
Minimum wage and low wage incidences differed in distribution across industrial sectors (Table 3).Jobs that paid below the low-wage threshold could rarely be found in the sectors 'Public administration and defense as well as compulsory social security', 'Mining and quarrying', 'Electricity, gas, steam and water supply', 'Financial and insurance activities', and 'Education'.However, there are comparatively large proportions of low-wage and minimum-wage jobs in the sectors 'Transportation and storage', 'Administrative and support service activities', 'Agriculture, Forestry and Fishing', 'Arts, entertainment and recreation', and 'Accommodation and food service activities'.In the last sector, the share of employees with wages below the low-wage threshold amounted to over 70 percent in 2018, but the proportion of employees earning minimum wages decreased by 30 percentage points to 14 percent between 2014 and 2018.
Thus, the industry-specific allocation of minimum wage employment fell by more than 7 percentage points after the introduction of the minimum wage, but the risks of receiving low wages increased somewhat overall, especially in retail trade, accommodations, and food services.One additional and notable point is that in the sectors with large proportions of low-wage or minimum-wage workers, the share of marginally employed workers was also high (see Table A1).Generally, there was great heterogeneity among industrial sectors regarding the incidence of low pay.In summary, the factors that were associated with a high share of employees with wages below the minimum wage threshold in 2014 were associated with high shares of employees in the low-wage segment in 2018, with the gross hourly wage increasing by approximately 2-3 euros.We referred to this increase as the elevator effect, which, however, brought hardly any compositional changes for low-wage companies or employees.In the next section, the significance of the individual, company, sectoral and regional levels regarding their power to explain low-wage and minimum-wage employment in 2018 are assessed.

Examination of the Variance Components
We use estimates for 3-level logistic random intercept models to analyze the probability of being employed in the low-wage or minimum-wage sector and to assess the distance to both thresholds.In models without explanatory variables (intercept-only models), the variance in the outcome variable can be decomposed into proportions associated with the individual level, the company level, and the industry level.For this purpose, the random part of the 3-level models is explored by considering the estimated residual intraclass correlation ρ of the latent responses.It is assumed that in models of the risk of earning a minimum wage or low wages, the level-1 error variance is equal to π 2 /3 for the logistic link function, while ψ ( 2) is the variance between companies and ψ ( 3) is the variance between industrial sectors (Rabe-Hesketh and Skrondal 2008).We thus obtain for the similarity of employees i within the same industrial sector k: Within the same company j (and the same industrial sector k), we obtain: In the linear intercept-only models on the distance between a worker's actual earnings and the minimum-and low-wage thresholds, the level-1 error variance is θ.Thus, the similarity of employees i within the same industrial sector k is: Within the same company j (and the same industrial sector k), we obtain: Figure 2 shows random-intercept models without explanatory variables. 5The values of the random part denote that in 2018, 46.70 percent of the differences in the employment situation regarding being employed in a low-wage job or not are explained by the company level, 27.62 percent are explained by the industrial sector level, and 25.68 percent are explained by the individual level.Regarding the employment situation of being employed in a minimum wage job, 54.39 percent and 14.52 percent of the differences can be attributed to the company level and industrial sector level, respectively; 31.09percent relate to the individual level.Regarding the differences in the distance between earnings and the low-wage threshold, 40.05 percent can be traced back to the company level, 3.58 percent to the industrial sector level, and 56.38 percent to the individual level.The company level and the industrial sector level account for 71.86 percent and 7.05 percent, respectively, of the differences in the distance to the minimum wage threshold, and the individual level accounts for the remaining 21.08 percent.
A comparison of the relative explanatory power between 2014 and 2018 highlights that the explanatory power of the levels for the probability of earning low wages remained approximately the same.In contrast, regarding the probability of earning minimum wages, the explanatory power of the individual level in particular increased, while the power of the sectoral level decreased.However, structural conditions still explain more than two-thirds of both probabilities.The relative explanatory power of the individual level is more pronounced, especially considering the distance to the low-wage threshold.It increased even more during the observation period.The formerly high explanatory power of the individual level for the distance to the minimum wage threshold had decreased very strongly by 2018.Then, the relative proportion decreased to less than half, while the company level especially gained importance.These results indicatein line with findings from Card et al. ( 2013)strong explanatory power of the company level regarding the risk of being employed in the minimum-wage or low-wage segment of the workforce and regarding the distance to both thresholds in the German labor market.Industrial sectors impact the risk of earning low or minimum wages, but they impact the distance to low-and minimumwage thresholds to a lesser extent.Individual characteristics explain more variance in the wage gap than in the probability of earning more or less than a low wage or minimum wage, with a considerable drop regarding the latter between 2014 and 2018.We discuss the drivers of the change in the significance of the individual-, company-, and industry-level characteristics for being employed in the low-wage and minimum-wage ranges in the next section.Additionally, the two hypotheses derived in Section 2 are tested.

Estimating Compositional Changes Between 2014 and 2018
To assess changes in the correlation of individual, company and sectoral determinants over time, we perform multivariate regressions.To this end, the explanatory factors shown in Tables 1-3 are interacted with a dummy variable for the year.Since we are particularly interested in changes, Figures 3-5 display only the interaction effects. 6The corresponding coefficients indicate whether and how the relationship between minimum-or low-wage employment and an explanatory variable changed in 2018 compared with 2014.In the left parts of Figures 3-5, the average marginal effects of logit estimates on the probability of earning below the low-wage threshold (blue dots) and the minimum-wage threshold (red diamonds) are depicted.The right parts of the figures display coefficients from linear OLS regressions indicating the distance between the gross hourly wage and the low-wage threshold (blue dots) and the minimum-wage threshold (red diamonds).Although the results are presented in three figures, they come from one estimation that includes variables at the individual, company, and industry levels.
Figure 3 shows that the risk of being employed in low-wage and minimum-wage jobs significantly decreased for women in 2018 compared to 2014.In addition, the distance to the low-wage threshold narrowed.Regarding the highest educational degree, the findings are ambiguous.While the risk of earning below the low-wage threshold slightly increased in 2018 for unskilled employees, the likelihood of earning below the minimum-wage threshold remained almost unchanged.However, the distance to the minimum wage and the low wage declined.Employees with a polytechnic or university degree had a higher probability of working low-or minimum-wage labor in 2018 than they had four years before.Furthermore, the distance to both thresholds rose.In regard to age and tenure, there were no changes over time.Distinct shifts between 2014 and 2018 can be found regarding employment status.While the probability of earning below the minimum-and low-wage thresholds increased for part-time workers in 2018, it decreased for marginal workers.However, both forms of employment saw a reduction in the distance to the minimum-wage and low-wage thresholds.This change was particularly pronounced in the case of marginal employment.A slight decline in the risk of working minimumor low-wage work occurred regarding fixed-term employment; no change between 2014 and 2018 could be observed regarding temporary work.However, the distance to the low-wage threshold in temporary employment fell.The dependent variable 'probability' is coded as a dummy variable.The value 1 represents a job paying less than 10.33 euros (low-wage threshold) or 8.50 euros (minimum-wage threshold); the dependent variable 'distance' is a metric and denotes the gap between the hourly wage and the low or minimum wage.In the case of binary logit estimates, the average marginal effects are shown.Although the results are presented in Figures 3-5, they come from one estimation that included individual-, company-, and industry-level variables.Spikes are drawn for 99.9 %, 99 %, and 95 % confidence intervals.Source: Research data centers of the statistical offices of the Federation and the Länder, SES 2018; own calculations.
In the case of company-level determinants, the probability of employment in the minimum-wage and low-wage ranges significantly diminished between 2014 and 2018 for smaller companies with fewer than 5 or between 5 and 49 employees.However, there are no effects on the distance to either threshold.Regarding the region where a company is located, a significantly decreased risk of earning below the low-wage and especially the minimum-wage level in the northeast of Germany is observed.In this region, the distance between employees' wages and the minimumwage and low-wage thresholds also fell significantly.The risk of being employed in the minimum-wage or low-wage segment increased in companies that were not bound by a collective wage agreement.At the same time, however, the wage gap to the minimum wage and low-wage threshold decreased.Finally, for individuals working in companies with a higher share of female employees, the low-wage risk increased significantly in 2018, while the minimum-wage risk did not change.
Regarding industrial sectors, there were generally only small changes in the relationship with low-or minimum-wage labor between 2014 and 2018.The strongest reductions in low-wage or minimum-wage risks occurred in the sectors 'accommodation and food service activities', 'administrative and support service activities', 'public administration and defense; compulsory social security', 'arts, entertainment, and recreation', and 'other service activities'.With respect to the 'financial and insurance activities' and 'education' industries, the low-wage risk significantly increased.Except for 'public administration and defense; compulsory social security', 'real estate activities', and 'human health and social work activities', most industries showed that the distance to both thresholds also dropped significantly.This was true for the 'transportation and storage' industry.In contrast, the distance to the minimum-wage and low-wage thresholds increased in the 'mining and quarrying' sector.
The multivariate results point to different implications regarding the two hypotheses derived for the three levels of individuals, companies, and economic sectors.With respect to Hypothesis 2, there seems in fact to be a shift in composition within the minimum wage and low-wage sectors at the individual level due to increases in minimum-wage and low-wage risks with respect to the highest level of education attained and part-time employment.This also applies to the company level because employees' minimum-wage and low-wage risks grew depending on the presence of collective agreements and the gender distribution within a company.In contrast to Hypothesis 2, but in line with Hypothesis 1, a convergence appears to have taken place between 2014 and 2018 regarding the risk of being paid in the minimum-wage and low-wage ranges as far as the sectoral level is concerned.In typical minimum-wage industries, such as accommodations or food services, low-wage or minimum-wage risks decreased between 2014 and 2018.

Discussion of Results and Conclusions
Minimum wages are considered key instruments of labor market policy for preventing low wages (Kalleberg 2011).Thus, the increase or introduction of a new minimum wage makes it reasonable to assume that it causes changes not only in the size but also in the composition of the minimum-wage or low-wage labor segment.Empirically, to our knowledge, there are no studies offering a systematic characterization of structural changes in minimum-wage or low-wage employment after the introduction or increase of a minimum wage but only cross-sectional studies for a specific year (Dütsch and Himmelreicher 2020;Gallie 2007, Kalina and Weinkopf 2015, 2017, 2018;Kalleberg 2011).
Against this backdrop, we used the introduction of the statutory minimum wage in Germany, which represented a strong intervention in the lower range of the wage distribution (Bruttel et al. 2017(Bruttel et al. , 2018;;Mindestlohnkommission 2016), as an analytic framework and compared minimum-wage and low-wage labor in 2014 and 2018.The research question was whether the introduction and first uprating of the minimum wage in Germany led to convergence or compositional changes in minimum and low-wage employment.The year 2014 represented the situation immediately before the introduction of the minimum wage, and the year 2018 represented the situation after the introduction and first increase of the minimum wage.
What Does the German Minimum Wage Do?
Empirically, we first showed that between 2014 and 2018, the incidence of minimum wage employment fell by 7 percentage points to approximately 4 percent, while the low wage incidence rose by approximately 1 percentage point to approximately 22 percent.In the minimum-wage and low-wage sectors, mean wages amounted to 8.55 euros and 9.68 euros, respectively, in 2018-an increase of approximately 1.5 euros in both wage groups.Thus, earnings in the minimum wage range converged due to wage compression at the lower end of the wage distributiondespite the existence of noncompliance (Mindestlohnkommission 2020).This is consistent with the results of causal analyses that found wage compression due to the introduction of the German minimum wage (Mindestlohnkommission 2016).However, wage compression was limited to the minimum wage range and failed to spill over to the low wage range.
Second, concerning the specific determinants of minimum wage and low-wage labor, the significance of individual characteristics for the receipt of a minimum wage decreased, especially for women, marginally employed and fixed-term employees.These were the groups of employees that had an above-average probability of earning below the minimum wage threshold in 2014 (Dütsch and Himmelreicher 2020;Kalina and Weinkopf 2015).The low-wage risk, however, declined only for women.Additionally, the distance to the minimum wage and low-wage threshold decreased among marginal and part-time employees.Those employees were obviously able to benefit from the introduction of the minimum wage.In contrast, the probability of earning low wages slightly increased, especially for part-time workers (see also Beckmannshagen and Schröder 2022).At the company level, the minimum wage and low-wage risk for smaller companies and those in northeastern Germany decreased because of convergence; consequently, there was also an elevator effect for the companies most affected prior to the introduction of the minimum wage.However, importantly, as shown descriptively, there is still a strong north-south divide in low wages, with significantly higher shares of minimum wage and low-wage earners in the northeast (see also Caliendo et al. 2022).Since minimum-wage and low-wage risks increased for companies not bound by collective bargaining agreements, the introduction of minimum wages seems to have raised the pressure on these companies to provide certain wage levels.These findings indicate compositional changes at the individual and company levels.At the sectoral level, the sharpest decline in low or minimum wages was observed in numerous service sectors that were characterized by low wage levels before the introduction of the minimum wage, such as 'accommodations and food service activities' and 'other service activities' (Kalina and Weinkopf 2015).In these sectors, which are often not covered by collective bargaining agreements (Kohaut and Ellguth 2022), there appears to have been an elevator effect.This led to the convergence of the economic sectors.In the intercept-only models, all  industries contained in the dataset were used.Source: Research data centers of the statistical offices of the Federation and the Länder, SES ; own calculations.
Table A: Changes in the relationship between low-wage and minimum-wage labor and selected individual-, company-, and industry-specific characteristics between  and .

Figure 1 :
Figure 1: Distribution of hourly wages differentiated by collective bargaining coverage (Pen's Parade).The red line denotes the minimum wage threshold, and the blue line denotes the low wage threshold.Source: Research data centers of the statistical offices of the Federation and the Länder, SES 2014, SES 2018; all indications are population weighted; own calculations.

Figure 2 :
Figure 2: Probabilities and distances earning low and minimum wages 2014 versus 2018.Estimation results for intercept-only models (3-level random intercept models without explanatory variables).In the intercept-only models, all 44 industries contained in the dataset are used.Source: Research data centers of the statistical offices of the Federation and the Länder, SES 2014, SES 2018; own calculations.

Figure 3 :
Figure 3: Changes in the relationship between low-wage and minimum-wage labor and individual characteristics between 2014 and 2018.Standard errors are clustered at the company level.The dependent variable 'probability' is coded as a dummy variable.The value 1 represents a job paying less than 10.33 euros (low-wage threshold) or 8.50 euros (minimum-wage threshold); the dependent variable 'distance' is a metric and denotes the gap between the hourly wage and the low or minimum wage.In the case of binary logit estimates, the average marginal effects are shown.Although the results are presented in Figures3-5, they come from one estimation that included individual-, company-, and industry-level variables.Spikes are drawn for 99.9 %, 99 %, and 95 % confidence intervals.Source: Research data centers of the statistical offices of the Federation and the Länder, SES 2018; own calculations.

Figure 4 :
Figure 4: Changes in the relationship between low-wage and minimum-wage labor and companyspecific characteristics between 2014 and 2018.Standard errors are clustered at the company level.The dependent variable 'probability' is coded as a dummy variable.The value 1 represents a job paying less than 10.33 euros (low-wage threshold) or 8.50 euros (minimum-wage threshold); the dependent variable 'distance' is a metric and denotes the gap between the hourly wage and the low or minimum wage.In the case of binary logit estimates, the average marginal effects are shown.Although the results are presented in Figures 3-5, they are derived from an estimation including individual-, company-, and industry-level variables.Spikes are drawn for 99.9 %, 99 %, and 95 % confidence intervals.Source: Research data centers of the statistical offices of the Federation and the Länder, SES 2018; own calculations.

Figure 5 :
Figure5: Changes in the relationship between low-wage and minimum-wage labor and industryspecific characteristics between 2014 and 2018.Standard errors are clustered at the company level.The dependent variable 'probability' is coded as a dummy variable.The value 1 represents a job paying less than 10.33 euros (low-wage threshold) or 8.50 euros (minimum-wage threshold); the dependent variable 'distance' is a metric that denotes the gap between the hourly wage and the low or minimum wage.In the case of binary logit estimates, the average marginal effects are shown.Although the results are presented in Figures3-5, they are derived from an estimation including individual-, company-, and industry-level variables.Spikes are drawn for 99.9 %, 99 %, and 95 % confidence intervals.Source: Research data centers of the statistical offices of the Federation and the Länder, SES 2018; own calculations.

Table  :
Description of the individual-level characteristics of jobs in Germany in  with comparison to .

Table  :
Description of company-level characteristics of jobs in Germany in  with comparison to .

Table  :
(continued) imum wage is the going rate for the lower third of employees in companies not bound

Table  :
Description of the sectoral characteristics of jobs in Germany in  with comparison to .

Table  :
(continued) Source: Research data centers of the statistical offices of the Federation and the Länder, SES , SES ; all indications are population weighted; own calculations.

Table A :
Estimation results for intercept-only models  (-level random intercept models without explanatory variables).
In the intercept-only models, all  industries contained in the dataset were used.Source: Research data centers of the Statistical Offices of the Federation and the Länder, SES, ; own calculations.

Table A :
(continued)All figures are population weighted, which correct for sex, region, type of employment and company size.Source: Research data centers of the statistical offices of the Federation and the Länder, SES ; own calculations.

Table A :
Estimation results for intercept-only models  (-level random intercept models without explanatory variables).