The Levelling Effect of Product Market Competition on Gender Wage Discrimination

Using linked employer-employee panel data for West Germany that include direct information on the competition faced by plants, we investigate the effect of product market competition on the gender pay gap. Controlling for match fixed effects we find that intensified competition significantly lowers the unexplained gap in plants with neither collective agreements nor a works council. Conversely, there is no effect in plants with these types of worker codetermination, which are unlikely to have enough discretion to adjust wages in the short run. We also document a larger competition effect in plants with few females in their workforces. Our findings are in line with Beckerian taste-based employer wage discrimination that is limited by competitive forces.


Introduction
Studies documenting a significant, persistent gender pay gap are legion, as are studies relating this gap to wage discrimination in the labour market 1 .The usual theoretical approach to wage discrimination originates in the pathbreaking work by Becker (1971).According to Becker, discrimination stems from personal prejudices among employers, co-workers, or consumers that constitute discriminatory preferences among these groups.As a case in point, discriminatory employers may suffer a disutility from employing women.To be compensated for the loss in utility following from employing women, these employers pay lower wages to women than to men, ceteris paribus.In the non-segregating equilibrium, all female workers receive a lower wage than men, no matter whether they work for an employer with or without discriminatory preferences.
Yet, as pointed out by Arrow (1973), in equilibrium, non-discriminatory employers employ more women at below-productivity wages than their discriminatory counterparts and therefore gain a competitive advantage over their competitors.Put differently, indulging discriminatory preferences comes at a cost in this framework.Indeed, empirical studies have documented that discriminatory employers make lower profits (Hellerstein et al. 2002;Kawaguchi 2007) and are more likely to exit the market (Weber and Zulehner 2014).Employers actually seem to pay for discrimination.
For discrimination to prevail, discriminatory employers must possess some market power on their product markets, enabling them to indulge their costly preferences.Otherwise, discrimination would simply be competed away.And thus, the strength of product market competition should put limits on the viability of discrimination, with gender pay gaps being lower in more competitive environments.Following this line of reasoning, we investigate whether strong product market competition reduces gender wage discrimination in West Germany and whether this effect is more pronounced in the so-called codetermination-free sector, i.e., in plants with neither collective agreements nor a works council.In contrast with previous studies, we use linked employeremployee panel data that include a plant-level assessment of the strength of product market competition.
Almost exclusively, extant studies have used aggregate or indirect measures of competition such as the intensity of international trade (Black and Brainerd 2004;Juhn et al. 2014), the extent of market regulation (Black and Strahan 2001), market structure (Winter-Ebmer 1995;Heyman et al. 2013), or combinations of these (Jirjahn and Stephan 2006;Weichselbaumer and Winter-Ebmer 2007;Zweimüller et al. 2008;Heinze and Wolf 2010).Such measures, however, suffer from at least two severe shortcomings: First, although these proxies may be informative on the average intensity of product market competition within a product market, they do not provide information on changes in competitive pressure at the level of the individual firm where decisionmaking takes place.Even worse, using these measures requires the researcher to implicitly define plants' relevant product and geographical markets, which turns out to be far from trivial.Notably, the inevitable problems in doing so in a convincing and unambiguous way drove the German Monopolies Commission to cease reporting classic concentration measures, like the Herfindahl index or the concentration ratio, altogether (Monopolies Commission 2012, p. 12).Second, through the lens of the structure-conduct-performance paradigm, utilising these measures also claims that the market structure uniquely determines market participants' behaviour, thereby abstracting from different ways of competition on different product markets that may add further ambiguity to the proxy at hand.As a case in point, Sutton (1991) shows that fierce competition on a market with substantial entry costs may lead to high concentration in an industry (the limiting case being two incumbents competing à la Bertrand).To sidestep these problems related to aggregate or indirect proxies of product market competition, we will use a direct plant-level measure of competitive pressure based on a self-assessment by plants' managers.Therefore, we do not have to define plants' relevant market ex ante, and basing our measure on the beliefs of plants' managers about competition guarantees that it is relevant for managements' decision-making.
To the best of our knowledge, Belfield and Heywood (2006) and Hirsch et al. (2012) are the only scholars in this strand of the literature to base their evidence on direct information on the competition faced by individual firms.While Hirsch et al. (2012) find a negative correlation between firms' self-assessment on product market competition and the unexplained gender pay gap in West Germany, Belfield and Heywood (2006) document a negative link for the U.K. that is more pronounced in the non-unionised sector.Both studies, however, rely on cross-sectional data onlywith Hirsch et al. (2012) utilising the 2008 cross section of the data set used in this study.They thus cannot rule out that differences in pay gaps, reflecting unobserved heterogeneity among firms facing different levels of product market competition and/or self-selection of workers into firms with different competitive pressure rather than a genuine competition effect.
Against this background, our study contributes to the literature in three ways: First, our panel data permit us to investigate the impact of plant-level product market competition on the unexplained gender pay gap, controlling for match fixed effects, i.e., time-invariant unobserved heterogeneity for every plant-worker pair.We thus base our investigation on direct information on the competition faced by plants, with identification relying on the differential impact of within-plant variation in competitive pressure on within-plant wage growth of men and women.As a consequence, estimated effects are neither contaminated by unobserved time-invariant plant heterogeneity nor by self-selection of workers.
Second, apart from identification, we add to the literature by investigating heterogeneities in the competition effect on gender wage discrimination by plants' industrial relations regime.German industrial relations are characterised by a dual system of worker representation through (sectoral) trade unions and works councils that can be elected by the workforce in plants with at least five employees (for details, see Keller 2004or Addison 2009).As plants' discretion to alter wages in response to changes in competitive pressure should be more limited if they are bound by a collective agreement or if they have a works council, we analyse whether the competition effect is stronger in the sector with none of these types of worker representation (which in Germany is usually referred to as the codetermination-free sector).
Third, we investigate whether the effect is larger in plants with a below-average share of females in their workforces.Since theory suggests that these plants have more pronounced discriminatory preferences, a stronger competition effect in these plants would further substantiate that fierce competition limits taste-based employer discrimination.
The remainder of this paper is organised as follows: Section 2 describes our data set and Section 3 our econometric approach.Section 4 presents and discusses our results, and Section 5 concludes.

Data
The data used in this paper consist of three waves of the cross-sectional model of the linked employer-employee data set of the Institute for Employment Research (LIAB) for the years 2008-2010 (for details, see Alda et al. 2005 andHeining et al. 2013).The data set links the IAB Establishment Panel, a representative survey of German plants (not companies), to the administrative data on all those individuals who work for these plants and contribute to the social insurance system.
The administrative data are based on the notification procedure for the German health, pension, and unemployment insurances.This requires all employers to report the necessary information on their workers if covered by the system, where misreporting is legally prohibited.Thus, among others, civil servants, self-employed, and individuals in marginal employment are not included.All in all, about 80 per cent of all people employed in Germany are covered by the social security system.Inter alia, the data include information for every worker on the daily gross wage, age, education, sex, nationality, tenure, occupation, and industry at the 30th of June of each year.
The employer side of our data comes from the IAB Establishment Panel (for details, see Kölling 2000), a stratified random sample of all plants that employ at least one worker covered by the social security system at the 30th June of each year.Starting in 1993, the IAB Establishment Panel has surveyed plants from all industries in West Germany.Response rates of units that have been interviewed repeatedly exceed 80 per cent.Questions deal, among other things, with the number of workers, the composition of the workforce, the plant's commitment to collective agreements at the sector or plant level, the existence of a works council, the plant's exporting activity, and its production technology.
From 2008 onwards, the data additionally include a plant-level self-assessment of product market competition on a four-point Likert scale that enables us to distinguish plants facing strong competition from other plants 2 .Using this information, we set up a panel data set for West Germany in the years 2008-2010 to investigate the effect of product market competition on the gender pay gap in profit-oriented plants 3 .
Whereas the wage information included in the LIAB is highly reliable, there are two shortcomings of the data crucial to our investigation: Firstly, the data set includes daily wages only and no detailed information on working hours.As a consequence, we have to exclude part-time workers.Secondly, wages are top-coded at the social security contribution ceiling, which affects 16.2 per cent of our male and 6.0 per cent of our female observations.To deal with this second issue, we apply the standard single imputation procedure proposed by Gartner (2005) and impute top-coded wages.In a first step, we estimate yearly Tobit models for each combination of sex and competition (e.g., females working for plants facing strong competition), where the regressand is the log daily gross wage and the regressors are those included in the subsequent analysis.In a second step, for every observation with a top-coded wage, a random value is drawn from a normal distribution left-truncated at the respective social security contribution ceiling, with the predicted log wage as mean and the standard deviation as estimated from the Tobit models 4 .
All in all, we end up with a sample of 1,239,911 observations of 627,076 male workers and 305,876 observations of 166,759 female workers employed by 6,114 plants.As can be seen from Table 1, 66 per cent of male and 61 per cent of female observations belong to plants facing strong product market competition.Furthermore, 6 per cent of male and 10 per cent of female observations are in the codetermination-free sector, i.e., work in plants that are neither bound by collective agreements nor have a works council.Turning to wages, women earn about 21 per cent lower wages than men on average.This number hardly changes when considering the subgroups of workers working for plants facing strong or weak competition, though workers' wages are generally higher in plants with strong competitive pressure 5 .(For more descriptive statistics, see Table 2.) As the transition matrix in Table 3 makes clear, plants' self-assessment on product market competition is extensively varied over time.During our period of observation, 1,715 transitions between strong and weak competition take place compared to 5,077 instances where competition stays constant.As a consequence, 23 per cent, or 171,369 out of 751,952 workers, are employed in plants with changing product market competition, thereby enabling us to rest identification on within-plant variation in competition.Notably, the number of transitions is not only reasonably large but is also roughly symmetrical with increases in competitive pressure being of similar magnitude as decreases.This renders it unlikely that plants with changing product market competition are a selective sample 6 .

Econometric Approach
To test the hypothesis that product market competition lowers the gender pay gap, we will run augmented Mincerian wage regressions.Our baseline specification is a fully interacted model where ln w ijt is the log gross daily wage of worker i working for plant j in period t; fem i is a female dummy, and comp jt is a dummy indicating strong product market competition.comp jt × fem i is the interaction of these two, and π 1 , π 2 , and π 3 are the corresponding coefficients.Furthermore, x it denotes a vector of worker characteristics, z jt a vector of plant characteristics, ε ijt the idiosyncratic error component, and α, β, γ, and δ are the corresponding coefficient vectors.In using a fully interacted model, we allow each worker and plant characteristic to affect men's and women's wages differently and thus exploit a more flexible framework than the earlier contributions by Belfield and Heywood (2006) and Hirsch et al. (2012), which also utilise plant-level measures of product market competition.
Worker controls comprise potential experience and tenure (both linearly and squared), dummy variables for joining the plant before 1975 (i.e.censored job tenure), five levels of education, non-German nationality, year of observation, and three-digit occupation.Plant controls include log plant size and its square, the shares of female and low-skilled workers in the plant's workforce, dummies for works council existence, a collective agreement at either firm level or sector level, exporting activity, new production technology, plant location in a rural area, and one-digit industry.
To ease interpretation, all regressors are centred around their sample averages, so that π 1 can be interpreted as the average unexplained gender pay gap in the full sample.The coefficients of main interest are π 2 and π 3 , where π 2 gives the effect of strong product market competition on males' wages, and π 3 is the difference in the competition effect across the sexes.We expect strong competition to depress the overall rents accruing and thus workers' wages in general.Moreover, strong competition should also confine employers' ability to discriminate against women by sharing rents disproportionately with male workers (cf.Black and Strahan 2001).Hence, we expect π 2 to have a negative sign and π 3 to have a positive sign, the latter indicating that strong competition reduces the gender pay gap by inducing a smaller adverse effect on females' compared to males' wages.
In this baseline specification, identification rests on both inter-plant and within-plant variation in competition.It is therefore unclear whether the results are driven by unobserved plant heterogeneity correlated with plants' competitive pressure or by a genuine competition effect.To come closer to the true competition effect, we next add plant-sex fixed effects to the model, i.e., we control for permanent differences in plants' sex-specific wage policies.As discussed in Section 2, this is viable in our data because we have a sufficient number of plants with varying product market competition over time.Our second specification thus is where the plant fixed effect for men and women is v j and v j + ζ j , respectively 7 .In this second specification, identification of π 2 and π 3 relies on within-plant variation in competition and the accompanying changes in male and female workers' wages.Hence, π 2 tells us how males' wages and π 3 how the unexplained gender pay gap responds to intensified competition.That said, changes in workers' wages due to varying competition may stem from two different sources: Either varying competition triggers wage changes for on-going jobs, i.e., for given worker-plant pairs, or wages change due to altering worker composition.And workers with different unobserved characteristics, like motivation, career outlook, or mobility, may self-select themselves into plants with different competitive pressure.As women and men have been found to differ considerably in both career aspirations and job mobility (e.g., Chevalier 2007 andHirsch andSchnabel 2012), self-selection of workers may contaminate within-plant comparisons of unexplained gender pay gaps.In order to address self-selection of workers, we next include match fixed effects to our model, i.e., we control for the permanent wage component of every worker-plant pair.Hence, our third specification is given by with match fixed effect ϕ ij .In this final specification, identification of π 2 and π 3 rests solely on changes in workers' within-plant wage growth, which is occurring simultaneously with within-plant variation in competition, i.e., wage changes within a given worker-plant pair.Estimated competition effects are thus free from biases stemming from unobserved heterogeneity in plants' permanent sex-specific wage policies and self-selection of workers with different unobserved time-invariant characteristics.A fall in workers' within-plant real wage growth may stem from various channels, such as decreased bonus payments, below-inflation nominal wage increases, or a reduction in the wage cushion between contract wages and effective wages.We should make clear, though, that both specifications (2) and (3) just identify shortrun effects of product market competition on workers' wages, i.e., changes in wages occurring simultaneously with within-plant variation in competition.However, long-run effects, which we cannot identify given the short time horizon of our data, may be larger as it may take some time for employers to alter wages.Furthermore, plants' discretion to adjust wages in the short run is likely to differ depending on their industrial relations regime.Arguably, plants bound by legally binding collective agreements may find it harder to cut wages in response to intensified competitive pressure.In a similar vein, works councils are likely to protect workers' rents and lower plants' discretion to reduce wages in such an event 8 .We thus expect to find marked competition effects only in plants belonging to the codetermination-free sector.

Results
Running the three wage regressions ( 1)-( 3) on our full sample yields the results summarised in Table 4.In the OLS specification, we find a highly significant average unexplained gender pay gap of 14.6 log points, which is similar in magnitude to previous studies for West Germany, such as Gartner and Hinz (2009) and Hirsch (2013).As can be seen from the estimated coefficient of the competition dummy, male workers' wages are 1.1 log points lower in plants facing strong product market competition, which is statistically insignificant at conventional levels.The interaction effect of the female and the competition dummy indicates that the competition effect is almost zero and statistically insignificant.Note that the estimated coefficients of other regressors (which we do not report in Table 4 for the sake of brevity) show no surprises and are in line with the previous literature.
The picture hardly changes when resting identification on within-plant variation in competition in specifications ( 2) and (3).Intensified competition lowers male workers' wages by 0.8 (0.9) log points in the specification with plant-sex (match) fixed effects, where the coefficient is statistically significant at the 5 (10) per cent level.Yet, the interaction effect of the female and the competition dummy is still very small and statistically insignificant throughout.So in the full sample, there is no indication of a differential short-run effect of intensified product market competition on female and male workers' wages and thus no evidence of a (levelling) competition effect on gender wage discrimination.
However, as discussed in Section 3, short-run effects are expected to be only visible in plants that possess enough discretion to adjust wages in the short run.We therefore think that effects are more likely to be visible in plants not subject to worker codetermination.
To check this, we split our sample in two subsamples: plants bound by a collective In Model 1, additional regressors are potential experience and tenure (linearly and squared), dummy variables for joining a plant before 1975, five levels of education, non-German nationality, the shares of female and low-skilled workers in the plant's workforce, log plant size and its square, dummies for works council existence, a collective agreement at either firm level or sector level, exporting activity, new production technology, plant location in a rural area, one-digit industry, three-digit occupation, and year of observation.Model 2 additionally includes plant-sex fixed effects, whereas Model 3 includes match fixed effects.All regressors are centred around their sample averages and also interacted with the female dummy.
agreement and/or having a works council and codetermination-free plants.The results of running wage regressions on both subsamples are summarised in Table 5.
In line with earlier contributions, like Jirjahn and Stephan (2006) or Heinze and Wolf (2010), the unexplained gender pay gap is lower if some sort of worker codetermination is present.In the OLS specification (1), the gap amounts to 22.3 log points in codetermination-free plants but just 14.7 log points in plants with worker codetermination.As expected, in codetermined plants workers' wages do not respond much to intensified competition.In the specifications with plant-sex or match fixed effects, an increase in competition causes male workers' wages to fall by 0.7-0.8log points, where the effect is statistically insignificant in the specification including match fixed effects.Furthermore, as the interaction effect is almost zero, there is clearly no differential effect across the sexes.
Results are different for the codetermination-free sector in which workers' wages are responding to intensified competition.This is in line with an earlier finding by Belfield and Heywood (2006) for the U.K. that the cross-sectional link between competition and the gap is driven by the non-unionised sector.Depending on specification, males' wages decrease by 1.5-3.2log points if competition gets fierce, where all effects are statistically significant at least at the 5 per cent level.As the interaction effect indicates that women's wages are considerably less depressed than men's, the unexplained gender pay gap is significantly reduced by 1.2-2.1 log points.In our preferred specification including match fixed effects and thus addressing unobserved plant heterogeneity and worker self-selection, intensified product market competition reduces males' wages by 1.9 log points 9 , while females' wages are almost unaffected as the interaction effect also accounts to 1.8 log points 10 .This is in line with our expectation that intensified competitive pressure reduces the rents accruing and thus restricts employers' ability to share rents disproportionately with male workers.Consequently, the unexplained gender pay gap falls by 1.8 log points if competition gets fierce.As the average gap in codetermination-free plants accounts to 22.3 log points, this means that it drops by about 8 per cent.Since this fall in the gap represents a short-run effect, and the long-run effect is arguably larger, we regard the competition effect on the gender pay gap as non-trivial from an economic point of view 11 .
To further scrutinise our results, we next split our sample by the share of females in plants' workforces.In Becker's (1971) model with taste-based employer discrimination, plants employing fewer women are not only more discriminatory employers but also less profitable.Therefore, we may expect the competition effect on the gender pay gap to be more pronounced in plants with a below-average share of female workers, which should be hit disproportionately by intensified product market competition.
To be precise, this notion is not literally true in Becker's (1971) original model where the gender pay gap is the same for all women, no matter whether they work for discriminatory or non-discriminatory employers.However, this latter conclusion of the model hinges on the assumption that workers can instantaneously and costlessly switch employers.Once one builds in some forces restricting worker mobility, it does not hold anymore.For instance, Bowlus and Eckstein (2002) incorporate discriminatory employer preferences into Mortensen's (1990) equilibrium search model with on-the-job search.They show that employers with more pronounced discriminatory preferences offer lower wages to women than employers with less pronounced tastes for discrimination and also end up with lower profits.Since intensified competition puts additional pressure on firm profitability, it restricts discriminatory employers' ability to pay for discrimination, and it does more so for more discriminatory employers who already make lower profits than their competitors.Hence, we expect the unexplained gender pay gap to fall to a larger extent in plants with a lower share of females in their workforces 12 .
To check whether the effect of competition on the unexplained gender pay gap is more pronounced in plants employing fewer women, we run wage regressions separately for workers employed by plants with below-average and plants with above-average shares of female workers (in the respective two-digit industry) 13 .Table 6 presents the estimated competition effects from our preferred specification with match fixed effects.When not distinguishing plants depending on worker codetermination, intensified competition lowers the gender pay gap by 0.5 log points in plants with a below-average female share, which is not statistically significant.This levelling effect of product market competition is somewhat smaller (0.3 log points) in plants with some worker codetermination and much larger (2.0 log points) and statistically significant at the 5 per cent level in codetermination-free plants.Remarkably, competition has no effect on the gender pay gap in plants with an above-average female share.Since, according to theory, plants with a below-average female share are more discriminatory employers, these findings are suggestive that intensified product market competition indeed reduces gender discrimination stemming from employer prejudices against women.

Conclusions
Using linked employer-employee panel data for West Germany for the years 2008-2010 that include a plant-level self-assessment on product market competition, we have investigated the effect of competition on the gender pay gap.In our preferred specification, we control for match fixed effects, thereby resting identification on the differential impact of within-plant variation in competitive pressure on within-plant wage growth of men and women.We thus address both unobserved time-invariant plant heterogeneity and worker self-selection into plants facing different levels of competition.
In line with Becker's (1971) model of taste-based employer discrimination where competition limits employers' ability to discriminate against women, we find that intensified competition significantly lowers the unexplained gender pay gap in plants without any worker codetermination by 1.8 percentage points.On the other hand, there is no levelling effect of competition in plants bound by collective agreements and/or that have a works council.There are three explanations for this latter finding that seem to be consistent with our evidence: First, institutions of codetermination may yield sluggish wage reactions, and longer-term estimates might show a response that mimics those without codetermination.Second, institutions of codetermination may resist any rent reduction (even if rents largely accrue to male workers).And third, institutions of codetermination may reduce the gender pay gap sufficiently on their own such that there is no added reduction associated with product market competition.While we do not have a strong preference for any of these explanations, we are also not aware of a convincing way how to discriminate among these in our data.
We also document that there is a more pronounced competition effect on the gender pay gap in plants with a below-average share of females in their workforces and that such an effect is generally absent in plants with an above-average female share.Since, according to theory, employers employing fewer women are more discriminatory, these findings are suggestive that competition indeed restricts gender wage discrimination, thus, reeling in employer prejudices against women.
Although we were able to improve on earlier contributions, particularly in terms of identification, the brief time horizon of our panel data only permited us to identify the short-run effect of product market competition on gender wage discrimination.While this short-run effect turned out to be non-trivial in magnitude, the long-run effect is likely to be larger, and we therefore regard our estimates as a lower bound of the competition effect.Investigating the long-run effect of product market competition on the gender pay gap seems to be a promising avenue for future research.

Table 2
Descriptive statistics Notes: LIAB cross-sectional model, West Germany, 2008-2010.Tenure is left-censored if the worker's job with the plant started before 1975.

Table 1
Wages by sex and product market competition Notes: LIAB cross-sectional model, West Germany, 2008-2010.Wages are deflated by the consumer price index.Strong product market competition refers to the highest category on a four-point Likert scale of a plant-level self-assessment of competition.

Table 3
Transitions between strong and weak product market competition

Table 4
Wage regressions (full sample) LIAB cross-sectional model, West Germany, 2008-2010.The regressand is the log gross daily wage.Standard errors in parentheses are clustered at the plant level.

Table 5
Wage regressions by worker codetermination LIAB cross-sectional model, West Germany, 2008-2010.The regressand is the log gross daily wage.Standard errors in parentheses are clustered at the plant level.***/**/*denotesstatistical significance at the 1/5/10 per cent level.Regressors are those listed in Table4. Notes:

Table 6
Wage regressions with match fixed effects by worker codetermination and the share of females in plants' workforces Notes: LIAB cross-sectional model, West Germany, 2008-2010.The regressand is the log gross daily wage.The coefficient shown is the interaction effect of the competition and the female dummy.Standard errors in parentheses are clustered at the plant level.***/**/*denotesstatistical significance at the 1/5/10 per cent level.Regressors are those listed in Table4.