Review of literature

The existing literature on monopsonies has mainly referred to two related topics. The first is the estimation of employers’ labour market power, and the second analyses the impact of minimum wages on the employment of low-wage workers. The vast majority of studies that deal with the identification of monopsony power rely on the empirical framework of a dynamic monopsony model introduced by Reference ManningManning (2003). ^{Footnote 1} The modern view of monopsony power is based on the ability of employers to push wages below those in competitive labour markets. As the classical definition relies on a limited number of firms in (regional) labour markets, this is sometimes called a quasi-monopsony. Unlike competitive markets, some labour market frictions allow employers to determine the number of applicants by setting wages at a certain level. This also means that wages and employment are set at the same time. The labour market frictions are then identified by the estimation of finite labour supply elasticities.

In a competitive market, labour supply elasticities should be infinitely elastic. This model is applied to different issues (cf. Reference ManningManning, 2011). Among others, Reference WebberWebber (2016) identifies lower supply elasticities for women. Therefore, they argue that at least a part of the gender wage gap is generated by employers’ monopsony power. Similar results occur for supply elasticities and monopsony structures to explain discrimination against immigrants (eg. Reference Hirsch and JahnHirsch and Jahn, 2015). Alongside other studies, Reference Méndez and SepúlvedaMéndez and Sepúlveda (2019), Reference FalchFalch (2017), and Reference Dube, Jacobs and NaiduDube et al. (2018) find relevant positive labour supply elasticities for some occupational groups. Reference Depew and SoerensenDepew and Soerensen (2013) and Reference Hirsch, Jahn and SchnabelHirsch et al. (2018) show that supply elasticities are not constant over time and reflect changes in labour market power during a business cycle.

Another approach to calculating monopsony power is to estimate markdowns using production functions. Reference Hershbein, Macaluso and YehHershbein et al. (2019) find an average difference between market wage and marginal product of 78% for the United States (US). Other studies use concentration measures and thus show the market power of companies on the labour market. (cf. Reference Azar, Marinescu and SteinbaumAzar et al., 2020; Reference Berger, Herkenhoff and MongeyBerger et al., 2019; Reference Jarosch, Nimczik and SorkinJarosch et al., 2019).

Further analyses have used various methods of the difference-in-differences or regression discontinuity models to examine the employment effects of minimum wages. Since the preliminary work of Reference Card and KruegerCard and Krueger (1994, Reference Card and Krueger1995), a large number of studies have contributed to the still-controversial discussion about the impact of minimum wages on employment. Recent surveys by Reference de Linde Leonard, Stanley and Doucouliagosde Linde Leonard et al. (2014), Reference Hafner, Taylor and PankowskaHafner et al. (2017), Reference Belman and WolfsonBelman and Wolfson (2014), Reference Lukiyanova and VishnevskayaLukiyanova and Vishnevskaya (2016) and Reference Chletsos and GiotisChletsos and Giotis (2015) for several international studies including in the US, United Kingdom (UK) and other countries are not able to identify large employment effects. Only Reference Hafner, Taylor and PankowskaHafner et al. (2017) find some negative employment effects for part-time workers in the UK. In addition, Reference Neumark, Salas and WascherNeumark et al. (2014) state that there are still some problems with methodological issues and some reduction in labour demand for particular groups like teenagers. Reference Jung, McFarlane and DasJung et al. (2020) show a positive influence of rising minimum wages on retail trade sales in Canada and, therefore, higher welfare of the recipients of minimum wages.

In 2015, the German government introduced a new statutory minimum wage of EUR 8.50 per hour. Since then, the minimum wage has been raised three times to an hourly wage of EUR 9.35 in 2020. Most studies find little or no evidence for an overall reduction of employment (eg. Reference Bonin, Isphording and AnnabelleBonin et al. 2019; Reference Bossler and GernerBossler and Gerner, 2020; Reference BruttelBruttel, 2019; Reference Caliendo, Fedorets and PreussCaliendo et al. 2018; Reference GarloffGarloff, 2019; Reference Heise and PuschHeise and Pusch, 2020; Reference Herr, Herzog-Stein and KromphardtHerr et al. 2017; Reference Herzog-Stein, Lübker and PuschHerzog-Stein et al. 2020). Among these, Reference Bossler and GernerBossler and Gerner (2020) is the only study that explicitly estimates labour demand elasticities using the German minimum wage as an instrument. If negative effects do occur, they belong to the marginally employed, but the loss for these workers is partly balanced by a rise of regular employment (Reference Bonin, Isphording and AnnabelleBonin et al. 2019; Reference BruttelBruttel, 2019; Reference Caliendo, Fedorets and PreussCaliendo et al. 2018; Reference GarloffGarloff, 2019). Nevertheless, some ex-ante studies and projections that have predicted strong job losses of up to 900,000 workers due to the introduction of the minimum wages in Germany – outcomes that have not occurred since 2015 (eg. Reference Knabe and SchöbKnabe et al. 2014). These analyses are based on the estimation of neoclassical labour demand models and rely heavily on the assumption of constant own-wage elasticities on the labour market. Since the quality of the empirical results is rather low, the neoclassical model of labour demand is often rejected, especially by heterodox economists (eg. Reference HeiseHeise, 2020). Possibly, the poor quality of the projections can also be derived from a misapplication of the model. Low-skilled workers are more likely to face labour non-competitive market conditions with a high probability of wage setting power for the employer, because of a small share of jobs for low-skilled workers, limitations in mobility and a higher unemployment rate for these workers. Following the notions of Reference Boal and RansomBoal and Ransom (1997) and Reference Neumark and WascherNeumark and Wascher (1994), I will argue, that there are structural breaks in the demand for low-skilled workers. Having reviewed the existing literature, I now turn to some theoretical aspects in the next section and derive some hypotheses for the empirical research.

Theory and hypotheses

In the following, I apply a neoclassical model of labour demand. This is usually derived from profit maximising or cost minimising behaviour by firms. Normally, own-wage elasticities η _ii have been calculated from the outcome of these strategies. A commonly used method is to minimise a cost function according to all its inputs (Reference HamermeshHamermesh, 1993: 34). It is quite obvious that in a monopsony labour, demand is also determined by the supply side of the market, and the employment outcome does not reflect the labour demand curve (Reference ManningManning, 2003) and will be a source of endogeneity in the empirical part of the study. Hence, we observe labour supply elasticities $\epsilon$ _Lw on a monopsonistic labour market. The supplement contains the derived elasticities. These elasticities are defined as:

(1) $\frac{b_{ii}}{s_i}+\hspace{0.17em}{s}_i-1\hspace{0.17em}=\{\begin{array}{c}{\eta }_{ii}\hspace{0.17em}\mathrm{for a competitive labour market}\\ {\epsilon }_{Lw}\hspace{0.17em}\mathrm{for a monopsony labour market}\end{array}$

With b_ii as parameter of wages for qualification level i on the employment of qualification level i in the cost function and si as wage share of qualification level i of total costs (see supplement for derivation). The η_ii are defined as negative values and the ε_Lw are larger than zero, and the estimation of labour demand functions that do not take into account these breaks is probably misleading if only the own-wage elasticities η_ii are the focus of the analysis. On the other hand, if a monopsony determines significant parts of the market, the estimations of the η_ii for the competitive part of the market will be downwards biased if we attempt to calculate a singular η_ii for the whole market. In case of a monopsony, employment is determined by the labour supply curve if wages are below the level of a competitive market. If payments increase beyond that level, employment is set according to the labour demand curve. In addition, the empirical literature suggests elasticities for low-wage workers that are rather small compared to the expected outcomes and other calculations of labour demand elasticities (cf. Reference Addison, Bellmann and SchankAddison et al. 2008). Moreover, the idea of a completely monopsonistic market (as well as a completely competitive market) is clearly unrealistic. Like oligopolies and monopolistic competition on the goods markets, we can argue that labour markets are most likely described as oligopsonies or with a kind of monopsonistic competition (Reference ManningManning, 2021). The previous analysis leads to the following hypotheses:

Empirical model and data

From equation (1), it is obvious that the parameter b_ii is needed to calculate the elasticities of interest. As the endogenous variable is a share, it is not useful to estimate a linear model. One way to estimate the model using panel data is the fractional panel probit regression (Reference Papke and WooldridgePapke and Wooldridge, 2008). The Mundlak/Chamberlain device (Reference MundlakMundlak, 1978; Reference ChamberlainChamberlain, 1982) is used to control for the unobserved heterogeneity as a normally distributed variable conditional on the averages of the time-varying exogenous regressors. Reference WooldridgeWooldridge (2019) proposes a linear function of the time averages with different coefficients for each number of observations for an entity if unbalanced data is used ² . The empirical model is the given by:

(2) $\hspace{0.17em}\left(s_{it}|ln{w}_{it},\hspace{0.17em}ln{w}_{jt},\hspace{0.17em}ln{Y}_t,\hspace{0.17em}{z}_{it}\right)=\Phi \left(b_{ii}·ln{w}_{it}+\sum _{i\ne j}{b}_{ij}·ln{w}_{jt}+d_i·ln{Y}_{it}+\delta i\cdot zit+\hspace{0.17em}{\sum }_r\left({\psi }_r+\hspace{0.17em}{\overline{z}}_i{\xi }_r\right)+a_i\right)$

with Φ as the standard normal cumulative distribution function (cdf), z_it as additional exogenous variables of the model that are introduced later, ${\overline{z}}_i$ as averages of all time-varying z_it including lnw_i, lnw_j and lnY_i, δ and ξ as additional parameters, r as the number of observations for each firm in the data and ψ_r becomes 1 if r observations are available for an establishment and zero otherwise.

Although Reference ManningManning (2006) argues that dynamic labour demand models probably indicate employers’ monopsony power, the labour demand model used here is a static model and does not contain lagged variables. Moreover, the data subsequently used in the analysis consist of yearly data, ie. the gap between two employment figures is 12 months. Therefore, it is not possible to observe the job turnover that occurs within that year. Some points justify the static approach. First, from theory we can identify labour supply elasticities with a static model. Second, we know from other studies that most of the adjustment process takes place within a few months (Reference Brenzel, Czepek and KubisBrenzel et al. 2016). Due to the short time span associated with filling vacancies, it is rather unlikely that the data will allow for the monitoring of adjustment processes. Thus, in the vast majority of cases the observed employment level corresponds to the desired level and deviations from it are probably random. Then, annual data is over-aggregated, and it is impossible to identify dynamic labour demand behaviour (Reference HamermeshHamermesh, 1993: 253). Finally, the use of lagged dependent variables to model labour demand dynamics is caused by a specific quadratic adjustment of the cost function. This is very restrictive and questionable, as empirical studies with other cost functions, like lumpy or linear costs, illustrate results with at least the same efficiency (Reference HamermeshHamermesh, 1993).

The representative data used in the investigations comes from the Institute of Employment Research (IAB) Establishment Panel and consists of observations of German establishments from 1996 to 2018 (Reference Fischer, Janik and MüllerFischer et al. 2008, Reference Fischer, Janik and Müller2009). This data is augmented with information from the Establishment History Panel, which is official data from the social security system that provides detailed information about different qualifications and their respective daily remuneration in the observed firms (Reference Eberle and SchmuckerEberle and Schmucker, 2017). Please see the Supplemental file for further details about the sample.

I follow the strategy of most extant empirical work in this field and replace the total cost by the firm’s turnover Y in the share of labour costs (cf. Reference HamermeshHamermesh, 1993: 92, Reference Lichter, Peichl and SieglochLichter et al., 2015). This implies the assumption of competitive markets. Therefore, the estimates include the Herfindahl–Hirschman Index (HHI) as an additional exogenous variable to control for market concentration and imperfect competition. Moreover, I focus on the demand for low-skilled labour in the subsequent regressions, where low-skilled employees are defined as individuals with a lower secondary, intermediate secondary or upper secondary school completion certificate but no vocational qualifications. Therefore, w_i and L_i are the remuneration and the employment of low-skilled workers. I assume that this group receives the lowest wages and experiences the most difficult labour market conditions, which means they are the most likely to face employers’ wage-setting power. This information is taken from the Establishment History Panel, while turnover is observed in the IAB Establishment Panel. Establishments without low-skilled employees are excluded from the analysis.

The Establishment History Panel contains the number for each qualification level with full- or part-time contracts. We know the number of part-time workers for each skill level, but, unfortunately, the data does not provide the exact number of working hours. Therefore, in order to calculate the amount of full-time low-skilled employees, part-time workers are assigned a value of 0.5. Table 1 contains the average shares of different skill levels in the surveyed sample.

Table 1. Average share of different qualifications in firms’ employment.

Note: IAB-Establishment Panel 1996–2018; 234,642 observations.

The majority of the workforce consists of medium-skilled workers, with more than 70% belonging to this group. The shares of low-skilled and high-skilled workers are much lower. The share of highly skilled is larger than the value of low-skilled (15.4% vs. 13.1%). The remaining workers have an unknown qualification. Therefore, I analyse a rather small share of the workforce. Please note that the difference between low- and medium-skilled workers is not about school completion, but about vocational qualification. This indicates the high influence of the domestic vocational training system on the labour market in Germany.

The Establishment History Panel also offers information about the mean and the median daily remuneration of full-time employees for each observed qualification level. Additionally, the regressions contain the wage information for other qualification levels, as I have to take into account complementary or substitutionary relationships between skill levels, ie. the cross-wage elasticities. For this analysis, the median of wages is used as it is less affected by coincidental inferences and censoring. The variable includes special payments, such as holiday pay or 13th monthly salary, but only contains values up to the upper earnings limit for statutory pension insurance contributions. This means that about 10% of the data is censored and the earnings means are biased. To remedy this censoring problem, the data provider regularly imputed the information on daily wages according to the procedure of Reference Card, Heining and KlineCard et al. (2015) before the medians were calculated. This inaccuracy of the data is probably a negligible problem for wages of low-skilled workers.

The empirical model is expanded with additional variables z_i. The IAB Establishment Panel contains information about firms’ value added in the year prior to the interview. Establishments that do not report value added, including banks, insurance companies, and public administrations, are excluded from the database. Other variables used from the IAB Establishment Panel are shares of part-time workers, female workers, temporary employees, employees subject to the social insurance scheme, and dummies for coverage by a collective bargaining agreement; Western Germany; establishment size; the firms’ profitability, the firms’ state of machinery; industries; and years. Profitability and state of machinery are based on a self-rating of the establishments on a range from 1 (very low response up to date) to 3 (very high response outdated). Moreover, the Establishment History Panel contains information about employees’ age and nationality. Therefore, the regressions also include the shares of workers that are younger than 25 and older than 50. I also use the shares of foreign workers from within the European Union (EU) countries and from beyond the EU.

The inclusion of a variable for the costs of capital on the micro level is problematic. For example, there are no observations of the firms’ interest rates they are required to pay for credits. On the other hand, one can assume that the firms’ capital costs depend on market conditions and firm-specific indicators (Reference KöllingKölling, 2012). Market conditions are regularly expressed through interbank rates, like the Euro Interbank Offered Rate (Euribor). Firm-specific indicators that influence credit worthiness include variables like firm size, profitability and industry that are already included in the regressions. The variable indicating market concentration, HHI, is calculated as a weighted sum of market shares based on the stratifications of the random sample of the IAB Establishment Panel.

To control for structural changes due to the new minimum wage law, I defined a dummy variable that becomes one for observations from 2015 on. In addition, the estimations use interaction variables between this dummy and the wage variables for all qualifications to identify changes in the calculated elasticities. As already mentioned, the firms’ monopsony power is probably the source of endogeneity that prevents to observe the downward sloping labour demand curve and therefore, I apply a two-step ‘control function’ or 2RSI approach (Reference WooldridgeWooldridge, 2015). The intuition to control for endogeneity is to analyse whether the positive wage elasticities are related to monopsonies or not. After applying such a model, the labour demand curve should be estimated with negative wage elasticities and it is probably possible to conclude that the original results are due to monopsonistic structures. On the first step, I estimate three models with the particular wage levels as endogenous variables. Then, I calculate the residual of each regression and add them to the model in equation (3). This requires the use of additional variables that explain the wage levels and fulfil the exclusion restriction. A strong instrument requires (partial) correlation with the potentially endogenous variable and must not be correlated with the error term of the main regression. This means that the instrument should be correlated with the median wages of workers, but not with the firm wage share of low-skilled workers, in order to control for the potential endogeneity of the wage level. No further causal relationship between the instrument and the potentially endogenous variable is required. A possible instrument is the regional unemployment rate that indicates the conditions on the local labour market. Although the unemployment rate results from the interaction of labour supply and demand, and would therefore possibly continue to be endogenous in the regression model. However, the influence of a firm’s labour demand on the unemployment rate should be negligible. According to the Federal Statistical Office, there are currently more than 41 million people in employment in the German labour market. Across the 401 districts, this results in an average labour market of more than 100,000 employees. In addition, more than 97% of the companies employ less than 50 employees. The local unemployment rate information is available since 1998 and therefore, used as additional instrument in the subsequent wage regressions of the first step of the control function approach.

Equation (1) indicates a probable structural break because of a change from a competitive labour market to a monopsony and vice versa. I identify this break, through a dummy indicator variable to conduct switching regressions. Then, the empirical model in equation (2) becomes,

(3) $\begin{array}{c}\left(s_{it}|ln{w}_{it},\hspace{0.17em}ln{w}_{jt},\hspace{0.17em}ln{Y}_t,\hspace{0.17em}{z}_{it}\right)=\\ \{\begin{array}{c}\Phi \left(b_{ii}·ln{w}_{it}+\sum _{i\ne j}{b}_{ij}·ln{w}_{jt}+d_i·ln{Y}_{it}+{\delta }_i\cdot z_{it}+{\sum }_r\left({\psi }_r+\hspace{0.17em}{\overline{z}}_i{\xi }_r\right)+a_i\hspace{0.17em}\right)\hspace{0.17em}if\hspace{0.17em}{w}^{\text{res}}\le w\ast \\ \Phi \left(b{\text{'}}_{ii}·ln{w}_{it}+\sum _{i\ne j}b{\text{'}}_{ij}·ln{w}_{jt}+d{\text{'}}_i·ln{Y}_{it}+\delta {\text{'}}_i\cdot z_{it}+{\sum }_r\left(\psi {\text{'}}_r+\hspace{0.17em}{\overline{z}}_i\xi {\text{'}}_r\right)+a{\text{'}}_i\right)\hspace{0.17em}if\hspace{0.17em}{w}^{\text{res}}>w\ast \end{array}\end{array}$

with w^res as residual wages and w* as threshold value. The ’ indicates the different parameter estimates in the two regimes. Technically, all covariates are multiplied with this indicator to create additional exogenous variables.

Empirical research implies that the wage level is correlated with firms’ labour market power (Reference Hershbein, Macaluso and YehHershbein et al. 2019; Reference Azar, Marinescu and SteinbaumAzar et al. 2020; Reference Benmelech, Bergman and KimBenmelech et al., 2018). It is obvious that labour markets are not simply defined by wages and salaries, and could vary over regions, industries and other variables. On the other hand, the observed workers in the analysis do not have vocational training and therefore job opportunities are very restricted. Hence, I apply a two-stage procedure, controlling for firm-specific differences in payments for low-skilled workers. The wage regression for the low-skilled workers is also used to calculate the residual for each entity. The lower the estimated residual, the lower is cp. the remuneration compared to similar firms and, thus, the larger is the probable markdown of wages. The residual wages are used to find the threshold indicator identifying the model of highest validity.

Moreover, according to the Mundlak/Chamberlain device and Reference WooldridgeWooldridge (2019), the regressions contain the means of all time-varying exogenous variables multiplied by a dummy, indicating the number of observations of each establishment in the unbalanced panel. Finally, all variables that are nominal values are discounted by the producer price index. Moreover, the data set is checked for outliers. The Supplemental file contains the descriptive statistics for the principal variables. The following section presents the estimation outcomes of the regressions and the calculations of the particular marginal effects and elasticities.

Econometric results

The econometric work starts with identifying a threshold to detect firms with competitive and monopsonistic labour market conditions. A detailed description of the procedure can be found in the Supplemental file. From the regressions, the model with the threshold at the 82nd percentile of residual wage distribution shows the lowest values for the Akaike and Bayesian information criterion (AIC, BIC) respectively the highest pseudo maximum likelihood. Moreover, I found a higher explanatory power of the threshold model compared to a base model without the interaction variables. An LR-test of the interaction variables indicates a joint significance on the 1% level [χ²(107) = 868.35**]. This outcome is in line with hypothesis I and confirms the need to consider a structural break in the regressions. After determining the optimal threshold value, I turn to the estimation of the main model. Table 2 contains the marginal effects of the parameters in the base model and the switching regression:

Table 2. Average partial effects of labour demand regressions for low-skilled workers (fractional panel probit, dependent variable: Share of labour costs to total revenue).

Source: IAB Establishment Panel 1996–2018.

Note: Second column of (b) and (c) indicate the average partial effects of the interaction variables, ie. the differences to the first column. The model also includes the following dichotomous and auxiliary variables: establishment size (7 dummies), firm profitability (2), state of machinery (2), industry (42), year of observation (21) and a constant. The Chamberlain/Mundlak approach requires inclusion of the means of the time-varying covariates and an indicator that identifies the number of observations of each unit respectively of the interactions of both in the regression. Robust standard errors adjusted for clustering on establishments in parentheses. ** and * denote significance at the .01 and .05 levels, respectively. Grey shaded boxes indicate significant differences for both samples in the switching regression on a .05 level.

The first column contains the results for the base model without a threshold. The estimate for the wages of low-skilled workers is significant but close to zero. This does not mean that the calculated own-wage elasticity is also zero. Then, from equation (2), the elasticities are negative and near to (s_i – 1). Subsequently, these results will be presented in Table 3. The outcome for the wages of medium-skilled workers is positive and significant at a 1%-level. This indicates a substitutional relationship among low- and medium-skilled workers (Reference HamermeshHamermesh, 1993: 41). The variables indicating the introduction of the statutory minimum wage have no significant influence on the low-skilled wage share. Probably, the number of low-skilled workers had reduced to compensate for the larger remuneration. At least, I cannot find a significant positive or negative effect on the wage share and therefore support for hypothesis III. Also, I cannot find significant positive partial effects for capital costs. The negative partial effect value for the log of value added seems odd in the beginning. But, as I used the observable turnover instead of the unobservable total costs, and value added is defined as turnover reduced by intermediate materials, the specific elasticity calculations contain analogues to the calculation of the demand elasticities, the addition of 1, and I will receive a positive influence of firms’ production on the demand for low-skilled labour ^{Footnote 3} . The share of workers covered by the German social insurance scheme have a significant positive influence on labour demand for low-skilled work. This also applies to, both shares indicating foreign workers, the share of younger workers and the dummy for Western Germany. When interpreting these outcomes, we have to take into account that the shares belong to total employment instead of shares of low-skilled. Unfortunately, the data does not provide this specific information. The results in the two columns under (b) contain the results of the switching regression with the threshold at the 82^nd percentile of wage distribution. As said before, an LR-Test of joint significance of all interacting variables shows a highly significant value indicating that the switching regression has a higher validity compared to the base model. While the first column on the left side of (b) contains the average partial effects of the variables without interaction, the second column indicates the values including the effect from the interaction variable. The grey shaded boxes indicate significant differences between both regimes at a 5% level. The dummy indicating a constant effect of low-wage firms on the wage share is statistically different from zero, indicating a 4.8%-point larger wage share of low-skilled for those firms with low wages for these workers and showing the importance of low-skilled workers in low-wage firms. Additionally, there are also some remarkable outcomes of the switching regression. The marginal effect of the wages for low-skilled workers is significantly negative for establishments paying wages above the threshold, while the opposite occurs for the other establishments. This could be an indicator for differences in the own-wage elasticities as this parameter is used to calculate the values. Moreover, medium- and low-skilled workers are substitutes in the sample with payments above the threshold, but, independently from the introduction of the minimum wage, the relation becomes insignificant for firms with low remuneration. Other significant differences according to the threshold are given for value added, the shares of temporary workers and for establishments in Western Germany. The other results are comparable to parameters of the base model. The results in (c) show the average partial effects when I control for the probable endogeneity of the wage variables. The outcome of the wage regressions on the first step of the control function approach are presented in the Supplemental file. The residuals of the low-skilled wage regression are significant for both parts of the regression. Because of this, it is not possible to reject the hypothesis of endogeneity of wages of low-skilled. Probably, as the parameters have opposite signs, there are different sources of endogeneity. From the partial effects in Table 2, I now calculate the average elasticities as in equation (1):

Table 3. Average labour demand elasticities η for low-skilled workers.

Table 3 contains the calculated observed elasticities for the demand of low-skilled workers in the estimated models. The first three rows belong to the base model. The outcome in this model is quite homogenous. The overall mean is −0.640, indicating that a 1% increase in wages leads to a 0.64% decrease in low-skilled employment. If I distinguish between firms that pay more or less than the wages at the threshold, I find only small differences to the overall outcome.

This picture changes completely if we look at the switching regression model. The mean elasticity for establishments that pay less than threshold is positive, indicating an increase in low-skilled employment of about 1.12% if wages increase 1%. This outcome supports the assumption of monopsonistic structures in low-wage firms on the labour market. The average elasticities for firms paying wages to low-skilled that are larger than the 82^nd percentile is negative of about −1.627, indicating a reduction of more than 1.5% of low-skilled employment if the wages for these workers rise by 1%. The results before and after the introduction of the statutory minimum wage hardly differ from the overall results. This indicates that the minimum wage has little influence on the structure of the labour market.

From the empirical model, I identified the influence of monopsonies on labour demand as a kind of endogeneity. Hence, I applied a control function method and use the residuals of wage regressions as additional covariates in the switching regression model. This has some effects on the calculated elasticities in the last three rows of Table 3. Now, both results are negative and quite elastic. It seems that the predominant source of endogeneity is the wage level and the method used controls for this bias in the own-wage labour demand elasticities. Hence, the outcomes support the proposition of hypothesis II.

The result for the parameters concerning the observations since the introduction of a statutory minimum wage in Germany in 2015 are mainly insignificant for both regimes. This is in line with Reference KöllingKölling's (2020) results that the introduction of the statutory minimum wage did not change the own-wage elasticities and that monopsonistic structures on the labour market for low-skilled have continued since 2015. This means that I cannot confirm Hypothesis III, directly.

Hence, from the empirical outcomes, I identified two different areas of the labour market. When employers have some wage-setting power, the labour demand elasticity is dominated by monopsonistic structures and shows positive values. If the firms pay wages that are larger than the median, the labour market becomes (im)perfectly competitive and increasing payments lead to lower employment. This means that the majority of, but not all, low-skilled workers faced a monopsonistic labour market and the introduction of a statutory minimum wage in Germany did not change this situation.

Summary

The study at hand investigates labour demand elasticities for low-skilled workers in Germany. I assume that this group has a high probability of experiencing a markdown of wages according to monopsony wage setting of firms. Applying a theoretical model with a flexible translog cost function, I can show that the observed elasticities are the particular labour supply elasticities if monopsonistic market structures occur. This finding is confirmed with a review of the existing literature as the introduction of minimum wages do not lead to large losses in employment and empirical studies show that labour supply is not infinitely elastic as it should be in competitive markets. Coming from this, I derive three hypotheses for further analysis. Firstly, following Reference Neumark and WascherNeumark and Wascher (1994) and Reference Boal and RansomBoal and Ransom (1997), if monopsony power is relevant, there should be some structural breaks in the observed labour demand curve. Secondly, if labour supply determines a part of the labour demand curve, then the calculated elasticities should be positive.

I use large panel data of German establishments from 1996 to 2018 to validate the hypotheses. A switching regression fractional panel probit estimation is applied to identify a break between competitive and monopsonistic labour market structures. The specific effects of the introduction of a statutory minimum wage in Germany are measured through additional interaction variables. From the regressions, I calculate the particular wage elasticities of interest. Moreover, a two-step instrument variable procedure was used to correct for endogeneity of wages and the particular wage elasticities of interest from the regression outcomes were calculated.

As a main outcome, the regressions indicate that the demand for low-skilled labour differs with the compensation level, taking into account firm-specific differences in payments. I calculate positive average elasticities for firms paying lower wages compared to similar firms. The effect on total employment is positive at an observed demand elasticity of about +1.117, which is similar to comparable studies for the total employment (eg. Reference ManningManning, 2011; Reference Hirsch, Jahn and SchnabelHirsch et al., 2018). This reflects the higher probability of monopsonistic market structures for this group and questions the use of neoclassical models of the labour market at least for low-skilled workers. Also, I find that the majority of, but not all, low-skilled workers are affected by monopsonistic structures. Some share of low-skilled workers that receive a relatively high remuneration participate in competitive labour markets, with a negative influence of wages on employment for these workers, similarly to competitive labour markets. Further, if we control for endogeneity of the remuneration, the differences between the firms below and above the threshold diminish. The calculated elasticities become negative for all low-skilled workers. This probably indicates the influence of monopsonistic structures on the labour market.

The variables that reflect the influence of the newly introduced statutory minimum wage in Germany are insignificant in most cases. This means that minimum wages do not increase the particular wage share even if I observe monopsonistic market structures with positive wage elasticities. Furthermore, the minimum wage changes the measured elasticities only slightly. Therefore, I conclude that there are probably some other adjustment processes like less working hours, substitution with other qualifications or the retention of the minimum wage that prevent the increase of the wage share and a more just distribution of income. Nevertheless, the study illustrates the low employment effects of the introduction of a statutory minimum wage in Germany. Since the results are consistent with most of the findings of international studies, it is likely that the results can be generalised to other countries.

Moreover, I can identify several implications for further research and practice from the investigations. It seems that it could be important for research to take into account the workforce heterogeneity. It is also possible that the labour market for other qualifications have partly monopsonistic structures. On the other hand, this leads to some limitations that arise from the available data. Firstly, I observe qualifications instead of occupation or operations in the data. The first relies on formal education that was probably acquired a long time ago, while the latter describes the present situation and is therefore a better instrument for the workers labour market situation. Secondly, I simply use the residual wage level as an indicator for structural breaks. This is possibly too elementary, as the markdown of wages is determined by other variables (cf. Reference Hershbein, Macaluso and YehHershbein et al. 2019). Hence, the threshold of the switching regression should be determined endogenously with an elaborated model. Moreover, the use of linked employer-employee data can help to overcome these problems. These issues should be addressed in future research. Despite these caveats, I can show in the analysis that labour markets structures are not homogenous for comparable workers as it is possible that some face monopsonistic structures while others are paid according to competitive markets.