Skip to main content

Main menu

  • Home
  • Content
    • Current
    • Ahead of print
    • Archive
    • Supplementary Material
  • Info for
    • Authors
    • Subscribers
    • Institutions
    • Advertisers
  • About Us
    • About Us
    • Editorial Board
  • Connect
    • Feedback
    • Help
    • Request JHR at your library
  • Alerts
  • Free Issue
  • Special Issue
  • Other Publications
    • UWP

User menu

  • Register
  • Subscribe
  • My alerts
  • Log in
  • My Cart

Search

  • Advanced search
Journal of Human Resources
  • Other Publications
    • UWP
  • Register
  • Subscribe
  • My alerts
  • Log in
  • My Cart
Journal of Human Resources

Advanced Search

  • Home
  • Content
    • Current
    • Ahead of print
    • Archive
    • Supplementary Material
  • Info for
    • Authors
    • Subscribers
    • Institutions
    • Advertisers
  • About Us
    • About Us
    • Editorial Board
  • Connect
    • Feedback
    • Help
    • Request JHR at your library
  • Alerts
  • Free Issue
  • Special Issue
  • Follow uwp on Twitter
  • Follow JHR on Bluesky
Research ArticleArticles

Gender Wage Gaps Reconsidered

A Structural Approach Using Matched Employer-Employee Data

Cristian Bartolucci
Journal of Human Resources, October 2013, 48 (4) 998-1034; DOI: https://doi.org/10.3368/jhr.48.4.998
Cristian Bartolucci
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • Article
  • Figures & Data
  • Supplemental
  • Info & Metrics
  • References
  • PDF
Loading

Abstract

In this paper, we study the extent to which wage differentials between men and women can be explained by differences in productivity, disparities in friction patterns, segregation, and wage discrimination. For this purpose, we propose an equilibrium search model that features rent-splitting, on-the-job search, and two-sided heterogeneity in productivity. The model is estimated using German matched employer-employee data. Overall, the results reveal that female workers are less productive and more mobile than males. In addition, female workers have on average slightly lower bargaining power than their male counterparts.

I. Introduction

In this paper, we estimate an equilibrium search model to study the extent to which wage differentials between men and women can be explained by differences in productivity, disparities in friction patterns, segregation, and direct wage discrimination. The model features on-the-job search, rent-splitting, and productivity heterogeneity in firms and workers. The structural estimation combines group-specific productivity measures and the empirical distribution of firms’ productivity estimated from firm-level data, group-specific friction patterns estimated from individual duration data, and individual wages. The model implies a structural wage equation, which illustrate the precise relationship between wages, worker ability, firm productivity, friction patterns, and bargaining power. The wage equation estimated in this paper may be best understood as the structural counterpart of a standard Mincer equation, including only wage determinants that are relevant from a theoretical point of view. The model allows for counterfactual analysis, such as the decomposition of the observed wage gaps in terms of the differences in productivity and frictions, or segregation and discrimination, taking into account equilibrium effects.

Understanding wage gaps across different demographic groups always has been a central concern in labor economics. Many studies have focused on explaining how much of the unconditional mean wage differential between groups may be understood as wage discrimination.1 The standard strategy involves estimating Mincer-type equations for both groups and then decomposing the difference in mean wages into “explained” and “unexplained” components. The fraction of the gap that cannot be explained by differences in observable characteristics is considered discrimination. This kind of analysis is very informative from a descriptive perspective but the causal interpretation and the nature of discrimination are not clear. The reason is that most of the observable characteristics included in the standard reduced-form wage equations, such as education or experience may be understood as proxies of the true wage determinants, such as productivity, outside options, and the rent-splitting rule. Whenever there is a residual difference between groups in some of these wage determinants, the measure of discrimination may be biased. The primary candidate to generate these biases is a between-group difference in productivity that may persist after controlling for education, occupation, age, and tenure.

To deal with this shortcoming, Hellerstein and Neumark (1999) and Hellerstein, Neumark and Troske (1999) exploit newly available matched employer-employee data to calculate a novel indicator for wage discrimination. They estimate the relative marginal products of various worker types, which are then compared with their relative wages. If productivity is the only wage determinant, which is true if there is perfect competition in the labor market, or if there are no significant differences in friction patterns or in the distribution of firms faced by both groups, any difference in wages that is not driven by a difference in productivity may be understood as discrimination.

However, comparing wages and productivity may provide an incomplete picture of the problem. For example, wage differentials across groups are often accompanied by unemployment-rate and job-duration differentials. There is a vast expanse of literature estimating differentials in job-finding and job-retention rates across groups, directly observing duration in unemployment and employment, or using experiments such as audit studies.2 Although there is agreement in predicting effects of frictions on wages,3 there is scarce empirical evidence as to how much of the wage gap can be accounted for by the differences in the friction patterns. Also, the variation in worker composition is likely to be correlated with heterogeneity in the production technology, which generates labor market segregation.4

Estimated structural models may provide a complete interpretation of observed wage gaps as a consequence of between-groups differences in every wage determinant. Nevertheless, progress in this direction has been slow, primarily due to the difficulty in separately identifying the impacts of worker productivity differentials and discrimination, solely from worker-level data. The main references are Eckstein and Wolpin (1999) and Bowlus and Eckstein (2002). Both papers are focused on racial discrimination in the United States and deal with this empirical identification problem through structural assumptions. Eckstein and Wolpin (1999) proposed a method based on a two-sided, search-matching model that formally accounts for unobserved heterogeneity and unobserved offered wages. They argued that differences in the bargaining power parameter (their index of discrimination) are not identified unless some firm-side data are available. They compute bounds for discrimination that were ultimately not informative on the estimation sample they worked with. Bowlus and Eckstein (2002) also proposed a search model with heterogeneity in worker productivity but including an appearance-based employer disutility factor. As long as there are firms that do not discriminate, they are able to identify between-groups differences in the skill distribution as well as the proportion of discriminatory employers. The first attempts to use an equilibrium search model to study gender discrimination were made by Bowlus (1997) and Flabbi (2010). Bowlus only focuses on the effect of gender differences in friction patterns on wage differentials without distinguishing between differences in productivity and discrimination. Flabbi (2010) uses the identification strategy proposed in Bowlus and Eckstein (2002) to additionally disentangle the effect of productivity differentials.5

In this paper, we link two independent branches of the wage-discrimination literature. We propose a natural step in extending the structural estimation literature focused on wage discrimination. The availability of better data enables us to estimate a more complete model,6 using a more transparent identification strategy to measure differences in productivity and taking into account the effect on wages of labor market segregation. This approach may also be understood as a step forward from the strategy proposed by Hellerstein and Neumark (1999), where only productivity gaps were estimated. Here, we provide a more complete interpretation of the observed wage gap, where the productivity gap is only one of the potential determinants of the difference in wages between males and females.

The model builds upon the equilibrium search model, with strategic wage bargaining and on-the-job search presented in Cahuc, Postel-Vinay, and Robin (2006). The model consents rent-splitting and, as in Eckstein and Wolpin (1999), we allow for different rent-splitting rules for male and female workers to capture wage discrimination. The model has two sources of heterogeneity. Workers are heterogeneous in terms of productive efficiency to capture the effect on equilibrium wages of differences across sexes in productivity. Firms technology is also heterogeneous and its distribution is group-specific. This feature allows the model to fit an economy with segregation. Workers do not find jobs instantaneously and, when working, there is a positive probability of losing the current job. The parameters that describe these events are also allowed to be gender-specific in order to capture the effect of frictions on the gender wage gap.

We use LIAB, a 1996–2005 matched employer-employee panel data made available by the German Labor Agency.7 This panel provides us with a unique opportunity to disentangle the different sources of the gender wage gap, because it contains valuable information on gender, wages and occupations but also because it is a panel that tracks firms as opposed to individuals. Tracking firms is essential in the estimation of production functions using panel estimation methods. To the best of our knowledge, this paper presents the first structural estimation using matched employer-employee data to study labor market discrimination.8

To have a more homogeneous sample, we only consider firms in West Germany. The gender wage gap in this part of Germany is particularly large. According to Blau and Kahn (2000) the gender hourly wage gap in West Germany is 32 percent; placing west Germany in position 6 in a ranking of 22 industrialized countries. Many researchers are trying to understand the nature of this large earning differential (Lauer 2000; Heinze and Wolf 2010; Antonczyk, Fitzenberger and Sommerfeld 2010).

The empirical analysis initially involves calculating the empirical distribution of firms’ productivity and differences in productivity between men and women. The linkage between worker-level information and firm-level data is essential at this stage. From the worker-level data, we recover the composition of the firm during each time period. The production function estimation exploits within firm variation in worker composition, capital, and output. We estimate group-specific productivity parameters and a firm-specific technology measure. We find large productivity differentials for women and noticeable differences in the distribution of firms faced by both kind of workers.

We then analyze group-specific friction patterns by survival analysis. We find that women have higher job-creation rates than men, and that females also have higher job-destruction rates than males. Finally, we estimate bargaining power for male and female workers by means of individual wages, gender-specific productivity measures for each firm, the gender-specific distribution of firms’ productivity, and gender-specific frictions patterns. In spite of the large wage differentials, on average, women are found to have only slightly lower bargaining power than men.

In terms of wages, the raw gender wage gap is 41 percent. It turns out that most of the gap—65 percent—is accounted for by differences in productivity. Differences in destruction rates explain 9 percent while differences in the distribution of the firm’s productivity faced by male and female workers explain 17 percent of the total wage-gap. Netting out differences in offer-arrival rates would increase the gap by 13 percent. Presumably, within differences in arrival rates, destruction rates, the distribution of employers and productivity there is some content of discrimination. The economic literature, as well as the legislation of many countries, certainly recognize these potential sources of discrimination. But if we focus our attention on direct wage discrimination, we find that differences in the rent-splitting parameter are responsible for 21 percent of the wage gap, implying that female workers receive wages that are 8.6 percent lower than equivalent males in terms of productivity and treated the same as males in terms of the offer arrival rate, destruction rate and distribution of employers.

The rest of this paper is organized as follows. In the next section, we describe the structural model. Section III describes the data. Section IV presents the estimation of the structural model inputs, namely the productivity measures and friction parameters. We present and discuss the intermediate results and then describe the empirical strategy used to estimate the structural wage equation and its results. In Section V, the counterfactual experiments are discussed and we compare our empirical results with those found using other strategies for detecting discrimination. Conclusions are offered in Section VI.

II. Structural framework

In this section we describe the behavioral model of labor market search with matching and rent-splitting. The primary goal of estimating a structural model is to clearly state a wage-setting equation that enables us to measure the effect of each wage determinant. Once this wage equation is estimated, it becomes straightforward to obtain the effect of discriminatory wage policies by comparing a man’s wage with the wage that a woman with the same wage determinants would receive. This comparison is equivalent to a standard Oaxaca-Blinder decomposition, the main difference lies in the definition of wage determinants. A Oaxaca-Blinder decomposition includes observable characteristics of the worker and the job that are potentially correlated with the wage. By comparison, in our decomposition we include wage determinants that are driven by economic theory. We model the labor market, and therefore we propose a theory that explains how wages are determined. According to that theory, wages are a function of the extent of frictions in the labor market, the productivity of the worker, the productivity of the firm and the bargaining power of the worker. Knowing the function that links wages to these wage determinants, we can calculate the portion of the wage gap that is driven by differences in each wage determinant.

Previous research has shown the aptitude of these models in describing the labor market outputs and dynamics. Building on these assessments, we are interested in using the structural model as a measurement tool that enables us to empirically disentangle the effect of each wage determinant on the gender wage gap. Search-matching models have been used as an instrument to address empirical questions in a variety of papers. Examples include the previously mentioned papers in the discrimination literature but there are also interesting contributions in measuring returns to education (Eckstein and Wolpin 1995) or in analyzing the effect of a change in the minimum wage (Flinn 2006).

A. Assumptions

We propose a continuous time, infinite horizon, stationary economy. This economy is populated by infinitely lived firms and workers. All agents are risk-neutral and discount future income at the rate ρ > 0.

Workers: We normalize the measure of workers to one. Workers may belong to one of the groups (k) defined in terms of gender.9 Workers have different abilities (ε) measured in terms of efficiency units they provide per unit of time. The distribution of ability in the population of workers is exogenous and specific to each group, with cumulative distribution function Lk(ε). Group-specific distributions of efficiency units provided by workers are crucial in considering the between-groups differences in productivity. This source of heterogeneity is perfectly observable by every agent in the economy. Each worker may be either unemployed or employed. The workers from a generic group k that are not actually working receive a flow utility proportional to their ability, bkε. The workers’ efficiency in home production is associated with their productivity in the labor market and the parameter that describes that association is allowed to be gender-specific.10

Firms: Every firm is characterized by its productivity (p). We assume that p is distributed across firms according to a given cumulative distribution function Hk(p), which is continuously differentiable with support [pmin,pmax]. The primitive distribution of firms’ productivity faced by workers may differ among groups, allowing the model to be robust to labor market segregation. This source of heterogeneity is perfectly observable by every agent in the economy. The opportunity cost of recruiting a worker is zero.

Each firm contacts a worker of a given group k at the same constant rate, regardless of the firm’s bargained wage, its productivity or how many filled jobs it has. Unemployed workers receive job offers at a Poisson rate λ0k > 0. Employed workers may also search for a better job while employed and receive job offers at a Poisson rate λ1k > 0 We treat λ0k and λ1k as exogenous parameters specific to each group k. Searching while unemployed and searching while employed has no cost. Employment relationships are exogenously destroyed at a constant rate δκ > 0, leaving the worker unemployed and the firm with nothing. The marginal product of a match between a worker with ability ε and a firm with productivity p is εp.

Whenever an employed worker meets a new firm, the worker must choose an employer and then, if she switches employers, she bargains with the new employer with no possibility of recalling her old job. If she stays at her old job, nothing happens. Consequently when a worker negotiates with a firm, her alternative option is always unemployment. The surplus generated by the match is split in proportions βk and (1 – βk), for the worker and the firm respectively. βk is exogenously given and specific to each group k. We will refer to βk as the rent-splitting parameter. As in Wolpin and Eckstein (1999), we interpret βmale – βfemale as an index of the level of discrimination in the labor market. A difference in β in the same kind of job and sector, reveals differential payments unrelated to productivity and outside options, which are only driven by belonging to a given group.

It is well known that many other factors may have an impact on the rent-splitting parameters. The main candidates are: negotiation skills, risk-aversion, and the discount factor. In this model agents are assumed to be risk-neutral and the discount rate is homogeneous across groups. Although this could be part of the story that explains differences in β, there is scant convincing empirical evidence of gender differences in these primitive parameters.11 This could be the reason why risk-aversion and the discount factor have been held constant across genders in most of the empirical studies on wage discrimination.

It is not clear whether β can be interpreted as a Nash bargaining power. Shimer (2006) argues that in a simple search-matching model with on-the-job search, the standard axiomatic Nash bargaining solution is inapplicable, because the set of feasible payoffs is not convex. This nonconvexity arises because an increase in the wage has a direct negative effect over the firm’s rents but an indirect positive effect raising the duration of the job. This critique will hold depending on the shape of the firm productivity distribution. Whether β can be understood as a Nash Bargaining power is not essential for this study. If this critique holds up, we still interpret β as a rent-splitting parameter that simply states the proportion of the surplus that goes to the worker. A difference in these parameters remains informative about wage-discrimination.

The model assumes that the worker does not have the option of recalling the old employer. Hence, there is no possibility of Bertrand competition between firms, as in Cahuc, Postel-Vinay, and Robin (2006). Whether to allow firm competition a la Bertrand is controversial. While the Cahuc et al. bargaining scenario may be conceptually more appealing and may help to avoid the Shimer critique, it is not clear how realistic this assumption is. Mortensen (2003) argues that counteroffers are empirically uncommon. Moscarini (2008) illustrates that, in a model with search effort, firms may credibly commit to ignore outside offers to their employees, letting them go without a counteroffer, and suffer the loss, in order to keep in line the other employees’ incentives to not search on the job. Moreover, it can be shown that including a marginally positive cost of negotiation, makes it unprofitable for firms to try to poach the worker from better firms, and then the Bertrand competition vanishes.

In an environment where contracts cannot be written and wages are continuously negotiated, the outside option of the job is always unemployment. In this context, if a worker receives an offer from a firm with higher productivity, she must switch. She cannot use this offer to renegotiate with her current firm, because she knows that this offer will not be available tomorrow, and then her future option will be the unemployment.12 This possibility is also discussed in Flinn and Mabli (2010).

Beyond the theoretical relevance of between-firms Bertrand competition, this assumption is not critical for most of the results presented in this paper. In the Appendix, we illustrate that using the same data with a variation of the model where between-firm Bertrand competition is allowed, the gender wage-gap decomposition remains practically unchanged.

This model is similar to the model presented in Flinn and Mabli (2010). The primary difference is in the distributions of productivity. To have a model that is estimable only with employee-level data, they assume that there is a technologically determined discrete distribution of worker-firm productivity. In other words, they assume discrete heterogeneity at the match level, while here we assume two-sided continuous heterogeneity. The model presented here also has the convenient property of producing a closed-form solution for the wage-setting equation.

B. Value Functions

The expected value of income for a worker with ability ε, who belongs to group k, currently employed at wage w(p,ε,k) is denoted by E(w(p,ε,k),ε,k) and it satisfies:

Embedded Image (1)

The expected value of being unemployed for a worker with ability ε, who belongs to group k is given by:

Embedded Image (2)

Finally, the value of the match with productivity pε for the firm when paying a wage w(p,ε,k) to a worker of group k is given by:

Embedded Image

where Embedded Image and F (w(p,ε, k) | ε, k) is the equilibrium cumulative distribution function of wages paid by firms with a productivity lower than p to workers with an ability ε who belong to group k. Note that every parameter is group-specific. As the alternative value of the match for the firm is always zero, this value does not depend on alternative matches and is therefore independent of the parameters of the other groups of workers. Although every group is sharing the same labor market, all value functions may be considered group-by-group as if they were in independent markets. For simplicity of the notation, we therefore omit the k-index. Note that w(p,ε) is a function of p and ε, therefore given p and ε, the wage is a redundant state variable which is only included for exposition simplicity.

These expressions are equivalent to the value functions of the model with heterogeneous firms presented in Shimer (2006), including heterogeneity in workers ability. Here, wages are determined by the following surplus splitting rule:

Embedded Image (3)

After some algebra (see the Online Appendix for the proof13), it can be shown that:

Embedded Image

Noting that Embedded Image and changing the variable within the integral, we obtain a first-order differential equation,

Embedded Image

After some algebra, solving for the differential equation yields:

Embedded Image (4)

This expression states a clear relationship between wages w(p,ε), workers’ ability (ε), firm productivity (p), the distribution of firms’ productivity (H(.)), friction patterns (λ1,d) and the rent-splitting parameter (β).14 This wage equation is relatively similar to the one proposed by Cahuc, Postel-Vinay, and Robin (2006) when the wage is bargained between a firm with productivity p and an unemployed worker with ability ε.15

As expected, the model predicts that the mean equilibrium wage increases in β, and that the mean wage paid by a firm with productivity p increases in p. Note in Equation 4 that if β = 1 ⇒ w(p,ε) = pε, the maximum wage that a firm with productivity p can pay to a worker with ability ε is the full productivity. If β = 0 ⇒ w(p,ε) = pminε that is the minimum wage that a worker would accept to leave unemployment. Figure 1 illustrates that the mean equilibrium wage increases when λ1 increases and when δ decreases.16 Many models in the literature predict that the mean equilibrium wage decreases in the amount of frictions (see, for example, the models in Burdett and Mortensen 1998, Bontemps, Robin, and van den Berg 2000; Postel-Vinay and Robin 2002; Cahuc, Postel-Vinay, and Robin 2006). Wages are decreasing in the degree of frictions (λ1 / d) due to a compositional effect and a direct effect. The compositional effect is due to the fact that when frictions decrease the workers are, on average, higher in the job ladder. The direct effect is because the model is asymmetric in workers and employers, when frictions decrease the outside option of the worker increases but the outside option of the firm is always zero.17

Figure 1
  • Download figure
  • Open in new tab
  • Download powerpoint
Figure 1

Wage-Setting Equation

We assumed that the economy is in a steady state. The standard stationary equilibrium conditions are exploited. The inflow must balance the outflow for every stock of workers, defined in terms of individual ability, employment status, and for those workers who are employed, firm productivity.

  • The inflow to unemployment must be equal to its outflow, λ0μ = δ(1−μ), where μ is the unemployment rate given by:

    Embedded Image (5)

  • The inflow to jobs in firms with productivity p or lower than p must be equal to its outflow:

    Embedded Image

    where G(p) is the fraction of workers employed at a firm with productivity p or lower than p. Using Condition 5 and rearranging:

    Embedded Image (6)

    This stationary condition, (or its counterpart in terms of wages) is quite common and has been broadly used after Burdett and Mortensen (1998) to infer the primitive distribution of productivity (or the primitive distribution of wages) when only the distribution of productivity (or distribution of wages) for employed workers is observable. Since we use matched employer-employee data, we can directly observe the empirical distribution of productivity at the firm level. We use this stationary condition to construct the likelihood for the duration analysis in Section IV.

  • The fraction of employed workers with ability ε or lower than ε that are working in firms with productivity p or lower than p are (1 – μ)F(ε,p), where F(ε,p) is the joint cdf of ε and p. These workers leave this group due to a better offer, or because they become unemployed; such event occurs with probability Embedded Image. The inflow to this group is given by the unemployed workers with ability ε or lower than ε, (that is, L(ε)μ) who receive an offer from a firm with productivity p or lower than p. This last event occurs with probability λ0H(p). We now obtain the following condition:

    Embedded Image

    Using Conditions 5 and 6 and rearranging:

    Embedded Image (7)

    This expression states that there is no sorting between firm’s productivity and worker‘s ability;18 this statement is controversial, and there is an active debate in the assortative matching literature.

Becker (1973) showed that in a model without search frictions but with transferable utility, if there are supermodular production functions, then any competitive equilibrium exhibits positive assortative matching. In a more recent work, Shimer and Smith (2000) and Atakan (2006) show that in search models, complementaries in production functions are not sufficient enough to ensure assortative matching.

After Abowd, Kramarz, and Margolis (1999), the empirical literature has primarily focused on estimating the correlation between worker’s and firm’s fixed effects, using matched employer-employee data. However, there are still no definitive results. Abowd et al. (1999) find a negative and small correlation between firms and workers fixed effects for France and a zero correlation for the United States. Lindeboom, Mendez, and van den Berg (2010), using a Portuguese matched employer-employee data set, and Bartolucci and Devicienti (2012) find that there is positive assortative matching.

III. Data

A. Linked Employer-Employee Data from the German Federal Employment Agency (LIAB).

We use the linked employer-employee data set of the IAB (denoted LIAB), covering the period of 1996–2005. LIAB was created by matching the data of the IAB establishment panel and the process-produced data of the Federal Employment Services (social security records). The distinctive feature of this data is the combination of information about individuals with details concerning the firms in which these people work. The workers source contains valuable data on age, sex, nationality, daily wage (censored at the upper earnings limit for social security contributions),19 schooling / training, the establishment number and occupation. Occupation is recorder using a three-digit code but in this paper is collapsed into two categories: high- and low-qualification occupations.20

The firm-level data come form IAB Establishment Panel. These data are drawn from a stratified sample of the plants, where the strata are defined over industries and plant sizes (large plants are oversampled), but the sampling within each cell is random. The firm’s data provide details on total sales, value added, investment, depreciation,21 number of workers, and sector.22 In particular, only firms with more than ten workers, a positive output and positive depreciated capital were included in our subsample. Since firms of different sectors do not share the same market, we construct separate samples for each sector. LIAB has a very detailed industry classification. We focus on four primary industries: Manufacturing, Construction, Trade, and Services.23 Participation of establishments is voluntary but the response rates are high (exceeding 70 percent). However, the response rate on some variables key for our purposes is lower. Among survey respondents, only 60 percent of firms in the previous four industries provided valid responses for output. To estimate productivity, we need data on output and number of workers in each category. We only consider observations from the old Federal Republic of Germany (West Germany). The final number of observations in our sample of firms is 15,174. Table 1 provides descriptive statistics of the final sample of the firms.

One of the main advantages of this data set is that it has information for all employees subject to social security in each firm.24 The employee data are matched to firms for which we have valid estimates of productivity through a unique firm identifier. The raw data contains 21,246,022 observations between 1996 and 2005. After the final trimming we have a ten-year unbalanced panel, including a total of 5,760,110 workers’ observations distributed into 15,174 firms’ observations.

View this table:
  • View inline
  • View popup
Table 1

Firms—Descriptive Statistics

Given this selection on top of the original oversampling of large plants, the sample becomes less representative. According to the Federal Statistical Office (Statistisches Bundesamt Deutschland), between 1996 and 2005, the proportion of the work force in the manufacturing sector ranges between 25.6 and 31.7 percent. In the sample used in this paper, this proportion exceeds 74 percent (Table 1). For that reason, the analysis is performed clustering at the industry and occupation level and when making inference on the total population, the between-clusters aggregation of results are calculated using weights obtained from the G-SOEP.25

In the sample, women are, on average, younger than men. They also have less tenure and less experience. Women are overrepresented in high-qualification occupations. The proportion of immigrants is larger within the male group. See Table 2 for details on the sample of workers.

View this table:
  • View inline
  • View popup
Table 2

Workers — Descriptive Statistics

The primary goal of this study is to understand the gender wage gap. In LIAB, individual wages are top-coded. Consequently, the wage gap is estimated by maximum likelihood assuming that log-wages are normally distributed within the firm. The mean of the log-wage for each group is estimated using worker-level data, maximizing saturated normal-likelihoods at the firm level. This is consistent with the model if we assume that, conditioning on the worker group, the ability is log-normally distributed.

The difference in conditional means is 21 percent (see Table 17 in the Appendix). This implies that women, on average, have salaries that are 21 percent lower than men with the same set of observable characteristics. The unconditional wage differential is 41 percent but it is not stable across sectors and occupations (see Table 3). Mean wages, estimated across industries and occupations, illustrate that the gap ranges between 30 and 45 percent. Wage gaps are significantly different from zero for every sector and for every group. Earning differentials are larger for highly qualified workers in manufacturing, construction, and trade sectors.

View this table:
  • View inline
  • View popup
Table 3

Gender Wage Gap

B. German Socio-Economic Panel

The LIAB version used in this paper is a panel of firms complemented by worker data. As it does not track workers, it is not possible to distinguish between attrition26 and job-termination.27 For that reason we use the G-SOEP (German Socio-Economic Panel) to estimate the group-specific transition parameters.28 The G-SOEP is a representative repeated survey of households in Germany. This survey has been carried out annually with the same people and families in Germany since 1984 (note that this study only analyzes the 1996–2005 data).29

IV. Empirical Strategy and Results

The discrete nature of annual data implies a complicated censoring of the continuous-time trajectories generated by the theoretical model. Because of these complications, a potentially efficient full-information maximum likelihood is not considered as a candidate for the estimation. Instead, we perform a multistep estimation procedure.30

Even though it may be asymptotically inefficient, we prefer a step-by-step method. One reason is that transition parameters are better estimated using a standard labor force survey, such as G-SOEP. Another reason is that the consistency of every parameter in full-information maximum likelihood is only guaranteed in the case of the correct specification of the full model. However, we are interested in obtaining productivity differences and transition parameter estimates that are robust to misspecification in other parts of the model, such as the wage setting mechanism. This facilitates the comparability of the intermediate results with previous reduced-form studies that measure gender differentials in productivity and job-retention rates. Moreover, even in an informal way, models are generally incomplete. Therefore, it seems prudent to use estimators that are as robust to misspecification as possible.

The structural model abstracts many dimensions that may be relevant in the wage setting (for example, amenities or union pressure). These omitted dimensions may be mainly associated with different job types. As can be seen in Tables 1 and 2, there are important differences between men and women in terms of occupation and sector. To compare jobs that are as similar as possible, the empirical analysis is clustered at the sector and occupation level. The model is estimated independently for each of the four sectors. In order to control for occupation, transition and the rent-splitting parameters are estimated independently for both types of jobs, in each sector and gender group. We only control for occupation parametrically when we estimate productivity, because we need to consider the full workforce at each firm.31

A. Productivity

We assume, as in the theory laid out in Section II, that the distribution of abilities in worker groups within each firm fluctuates around some fixed density, say l(ε | p,k). According to the model (see Condition 7), there is no assortative matching between workers and firms. Therefore, for a given worker group (k), the equilibrium distribution of worker types, conditional on the firm type, equals the marginal one: L(ε | p,k) = L(ε | k). The model describes the matching process, and the wage setting, for single-worker firms. For the sake of consistency with multi-worker firms, we assume that workers are perfectly substitutable in the production process, between and within skill categories (k’s). Equivalently to Cahuc, Postel-Vinay, and Robin (2006), we define the total amount of efficient labor employed at firm j at time t as:

Embedded Image

where Embedded Image is the total amount of workers of group k in firm j at time t, and Embedded Image is the steady-state mean ability of workers of group k. We then specify firm j’s total perperiod output at the constant-return Cobb–Douglas function of capital and quality adjusted labor input.

Embedded Image (8)

where, Yjt is the value added produced by firm j in period t, Kjt is the total capital, and Aj is a firm-specific productivity parameter. A similar specification, without imposing constant return to scale, has already been used in the discrimination literature to estimate between-group productivity gaps (for example, Hellerstein and Neumark 1999; Hellerstein, Neumark and Troske 1999). We are primarily interested in four groups of workers depending on gender (men and women) and occupation (high- and low-qualification). We normalize γhm = 1 considering highly qualified male workers as the reference group.32 As such, Embedded Image is the proportional productivity of group k relative to the productivity of highly qualified male workers.

We further assume that firms can adjust capital instantaneously, what makes Equation 8 totally consistent with the theory presented in Section II, where we have assumed that the productivity of a match is pε. If the firm chooses the level of capital, the firm solves the following problem:33

Embedded Image

where r is the cost of capital. Therefore—that is the optimal choice of capital given the stock of workers and the firm specific productivity parameter—is:

Embedded Image

Plugging Embedded Image into Equation 8 and rearranging, we have that:

Embedded Image (9)

Note that Equation 9 is equivalent to the production function presented in Section II, where pj is a function of the firm-specific productivity parameter (Aj) and the r; and Ljt is the total labor input in efficiency units. Using the panel with firm-level data on output (Embedded Image)34, depreciated capital Embedded Image35 and the number of workers in each category, we estimate the production function in logs imposing that the relative difference in productivity between low- and high-qualification occupations is constant across gender (γlw = γlγw).

Embedded Image (10)

where Embedded Image and Embedded Image are, respectively, the number of men and women in high-qualification occupations in firm j at time t while Embedded Image and Embedded Image are, respectively, the number of men and women in low-qualification occupations in firm j at time t, and ujt is a zero mean stationary productivity shock.

The model predicts that more productive firms are able to attract more workers of every type. Moreover, the optimal choice of capital depends on Aj. As a result, productive inputs are correlated with the firm fixed effect (that is cov(Aj, Ljt) ≠ 0 and cov(Aj, Kjt) ≠ 0), which would generates inconsistent estimates of α and γ if we used ordinary least squares in the estimation. Therefore, we estimate Equation 10 by within-firms nonlinear least squares to remove the firm fixed effects.

The within-firms nonlinear least squares results are presented in Table 4. Women’s productivity is lower than men’s productivity in similar jobs. This difference ranges from 20 to 41 percent. On average across sectors, female workers are 33 percent less productive than males in each job. One of the primary candidates to explain this large productivity gap, is that these estimates are not taking into account that women work, on average, fewer hours than men. Using the G-SOEP36, we find that the average hour-gap is 19.9 percent, hence, differences in hours are likely to be one of the main determinants of the productivity gap.37

View this table:
  • View inline
  • View popup
Table 4

Production Function Estimates

Low-qualification workers are also found to be between 51 percent and 70 percent less productive than highly qualified workers. As in most production function estimations using microdata, α is found to be very near one, and hence, the marginal productivity of capital is near zero but statistically different from zero. Although this finding is standard,38 the main results of this paper are not very sensitive to this issue. If instead of α = 0.96, we include an α more realistic like 0.6; the wage gap decomposition does not change significantly.

Pioneered by Hellerstein and Neumark (1999) and Hellerstein, Neumark and Troske (1999), differences in productivity across genders are now well documented in the literature. The first paper finds, with Israeli firm-level data, a productivity gap of 17 percent. The second paper, using a U.S. sample of manufacturing plants, reports a productivity gap of 15 percent. These studies have been criticized mainly due to the potential endogeneity of the proportion of female workers in the firm.39

In this paper, we treat the number of workers of each group as potentially correlated with the firm fixed effect.40 Estimating Equation 10 by within-firm non linear least-squares, the firm fixed effect is completely removed; hence, our estimates are robust to a correlation between the firm fixed effect and the firm labor input level but also robust to a correlation between the firm fixed effect and the labor composition of the firm. In this data set, we find a significant correlation between the firm’s fixed effect and the firm’s labor input. Estimating Equation 10 by NLLS without fixed effects, γ’s estimates are significantly lower, the average of Embedded Image across sectors is 0.38 and the average of Embedded Image across sectors is 0.26. See Table 12 in the Appendix.

The estimates presented in Table 4, require orthogonality of productive inputs to the sequence of shock ujt. In the theory presented in Section II, we abstract from productivity shock. Assuming that ujt is uncorrelated with the productive inputs would be consistent with the model. As we assume that capital is perfectly adjustable, if the productivity shock is observed by the manager after production takes place, capital is exogenous and our results are consistent. Nevertheless, this extra assumption could be avoided by dropping capital altogether and estimating Equation 9 directly. Results of this last exercise are presented in Table 11 in the Appendix. The estimates of γw and γl are not statistically different from the ones that come out from the estimation of Equation 10, what suggests that the productivity shock is not observed before the manager chooses the level of K. The current productivity shock also might affect the vacancy creation, making it possibly correlated with Embedded Image, which would go against the condition of strict exogeneity required for consistency of fixed-effects estimators. As in the case of capital, the number of vacancies opened by the firm would not be correlated with the productivity shock if ujt were realized ex-post the production takes place. However, there is large literature suggesting that productive inputs are determined simultaneously with the productivity shock.41 It is possible to estimate α and γk by GMM using internal instruments, assuming that Ljt and Kjt are predetermined. For the sake of robustness of our results, we have explored this possibility but unfortunately there is a severe problem of lack of precision on the GMM estimates of the γ parameters (See Section IA in the Appendix for details).

B. Labor Market Dynamics

In the model described is Section II, job terminations might occur endogenously, due to job-to-job transitions, or exogenously, due to job destruction. As both processes are Poisson, the model defines the precise distribution of job durations (t) conditional on the firm productivity (p):

Embedded Image (11)

We use the G-SOEP to estimate transition parameters. Unfortunately, this data set does not have productivity measures, so we estimate λ1 and δ treating p as an unobservable. To do this, we maximize the unconditional likelihood ℓ(t) = ∫ℓ(t | p)g(p)dp, where g(p) is the probability density function of the firm’s productivity among employed workers implied by the model.

Taking derivatives with respect to p in Equation 6, we obtain the density of firm productivity in the population of workers as:

Embedded Image (12)

In the Appendix we show the individual contributions to the unconditional likelihood become simple enough to be estimated and are given by:

Embedded Image

Integrating the unobserved productivity out of the conditional likelihood removes p and all reference to the sampling distribution H(p). This method is robust to any misspecification in wage bargaining. The only required property of the structural model is that there exists a scalar firm index, in this case p, which monotonously defines transitions.

In the Appendix42, we show how to obtain the exact form of the likelihood that takes into account that some durations are right-censored, while others started before the survey’s beginning. Finally, an individual contribution to the log-likelihood is:

Embedded Image

where ci is a right-censored spell indicator and Hi is the time period elapsed before the sample started.43

Maximum likelihood estimates are reported in Table 5. The average duration of an employment spell, 1 / δ (possibly changing employers), is between 10 and 32 years but the mean duration across sectors is 20.2 years. The average time between two outside offers, 1 / λ1, ranges from 1.7 to 4.6 years. These results seem to be fairly large but they are compatible with the previous literature. van den Berg and Ridder (2003) used a similar specification but with German aggregated data, and found δ to be equal to 0.060 and λ1 / δ equal to 6.5,44 Here, the weighted average of δ across sectors and groups is 0.0574 and the weighted average of λ1 / δ is 6.41.

View this table:
  • View inline
  • View popup
Table 5

Transition Parameters—Maximum Likelihood Estimates

Highly qualified workers have, in general, lower transition rates to unemployment and lower on-the-job offer arrival rates. Women are more mobile than men in terms of job-to-job transitions and, in general, have higher job-destruction rates. Considering λ1 / δ as an index of friction (van den Berg and Ridder 2003), we do not find significant differences in the extent of labor market friction between men and women.

C. The Wage Equation: Closing the Model

The structural wage Equation 4 can be written as:

Embedded Image

where wjti is the daily wage of worker i, who belongs to group k,45 in a firm j with productivity pj at time t, and:

Embedded Image

As illustrated in Equation 7, ε is statistically independent of p, thus

Embedded Image

Ek(εi) = γk is the mean efficiency units of workers in group k, relative to the male highly qualified group. Therefore, the predicted mean wage for workers of group k working in firms with productivity pj at time t is:

Embedded Image (13)

The group chosen for normalization is irrelevant. Changing this group to a generic group k, we would change our measure of productivity. Instead of pj, that is, the productivity measured in terms of efficiency units of highly qualified males, we would have Embedded Image—that is, the productivity measured in term of efficiency units of group k. To define Equation 13 in terms of the productivity of group k, we only need to put γk inside the expectation operator:

Embedded Image

Noting that dp / dpk = 1 / γk, and changing the variable within the integral, we obtain:

Embedded Image

For each firm in the sample we estimate the average daily wage Embedded Image paid to the workers of group k at time t. Since wages are top-coded, we estimate the firm mean wage for each worker group (that is, Embedded Image) by maximum likelihood at the firm level assuming that εi is distributed as a log-normal.46 Under the steady state assumption, and according to the theory presented in Section II, Embedded Image exhibits stationary fluctuation around the steady state mean wage E(wjtk) paid by firm j with productivity pj.

Writing Equation 13 in logs:

Embedded Image (14)

We estimate Equation 14 by weighted nonlinear least squares at the firm level, where γk, δk and λk are parameters estimated in the previous stages, pj is the productivity of firm j, and vjtk is a transitory shock that comes out from within firm aggregation. As usual, the discount factor has been set to an annual rate of 5 percent (daily rate of 0.0134 percent).

Standard errors have to take into account that pj, γ, λ1 and δ are estimated in previous stages. To solve this problem, we combine bootstrap for pj and γ with the analytical solution for λ1 and δ. Hence, we obtain standard errors replicating the productivity estimation and the bargaining power estimation in 200 resamples of the LIAB original sample, with replacement but considering the estimated transition parameters as the population parameters. To correct these preliminary standard errors, we add to them the analytical term corresponding to the standard errors of λ1 and δ reported in Table 5. The analytical correction is straightforward in this case, because the estimators come from different samples, such that we can omit the term corresponding to the outer product of the scores in the first and second stages.

Consistent standard errors are given by the squared root of:

Embedded Image

where Ξ is the objective function in the optimization, which, in this case is the weighted sum of squares and Embedded Image. Second derivatives of Embedded Image are obtained numerically.47

Results are presented in Table 6. Women are found to have lower rent-spitting parameters than men in construction and trade for both high- and low-qualification occupations, and in manufacturing highly qualified occupations. Female workers receive larger portions of the surplus than males in services and in manufacturing low-qualification occupations but these differences are not significant.

View this table:
  • View inline
  • View popup
Table 6

Rent-Splitting Parameter Estimates

There is a clear pattern in terms occupations. Low-qualification workers receive larger shares of the surplus in every sector, considering female and male workers.48 Union coverage, which is higher for low-qualification occupations, and differences in compensating differentials, are potential reasons to explain this difference.

Estimates of the rent-splitting parameter are considerably higher than the parameters reported in Cahuc, Postel-Vinay, and Robin (2006). This is probably due to the differences in our definition of match rents.49 In a similar model estimated with U. S. employee-level data by Flinn and Mabli (2010), the overall bargaining power is found to be 0.45. Here, the weighted average across cells is remarkably similar, 0.421.

Allowing between-firms Bertrand competition as in Cahuc, Postel-Vinay, and Robin (2006), changes the magnitude of β for males and females but not the difference across genders. In the Appendix, we present a numerical exercise, where β is recovered by the simulated method of moments using the same data and a model with between-firm Bertrand competition. The bargaining power is found to be significantly lower; the weighted average is 0.219 but the gender and occupation patterns do not change. Women are found to have lower bargaining power than males in construction and trade, while there is no clear pattern in manufacturing and services. As in the model without Bertrand competition, workers in low-qualification occupations are also found to have higher β than workers in high-qualification occupations. These findings are not consistent with results found in Cahuc, Postel-Vinay, and Robin (2006), where they find a positive association between bargaining power and job qualification in France. As in this case we are estimating a similar model to Cahuc, Postel-Vinay, and Robin (2006), this occupation pattern does not seem to be a modeling artifact but instead is a difference between German and French labor markets.50

Differences in rent-splitting parameters are not significant in every sector. We only find that male workers receive larger shares of the surplus than females in the construction sector, where bootstrap p-values of the differences in β are 4.5 percent for low-qualification workers and 9.6 percent for high-qualification workers.

V. Wage-Gap Decomposition

The structural wage setting equation provides us with a direct way to isolate the effect of each wage determinant on the overall wage differential. Hence, we are able to calculate what fraction of the wage gap is due to segregation or differences in the rent-splitting parameter, productivity, or friction patterns. Although the model takes into account the equilibrium effects of changes in the primitives, this is always conditional to what we have defined as primitives. For example, there are good reasons to think that the offer arrival rate might be a function of the distribution of offers and the bargaining power. Changes in the distribution of offers and the bargaining power might change the search effort of the worker but in the model we do not endogeneize wage effort. Moreover, differences in productivity also might be a function of frictions. If a demographic group faces a labor market with more frictions, its members are likely to accommodate their optimal investment in human capital. In principle every mechanism could be endogeneized, and for sure the decomposition would more complete and its interpretation would be cleaner. The purpose of the estimation presented in this paper is to provide a wage gap decomposition to have a better understanding of the main determinants of wage differentials between male and women. This is not a final answer because we are not explaining what is causing the difference in each wage determinant but our results provide insights of relative importance of each wage determinant in the determination of the wage gap.

To calculate our decomposition we proceed as follow. Using the structural wage equation

Embedded Image (4)

For each sector and each worker group, it is possible to measure the wage differential caused by the differences in each wage determinant. For example, we can estimate the wage gap accounted for by β as the relative difference between the mean wage that women actually receive and the mean wage that women would receive if they had the male rent-splitting parameter.

Embedded Image (15)

As shown in Equation 7 ε is independent of p, therefore we can estimate Equation 15 at the firm level:

Embedded Image

where Embedded Image is the number of female workers in each firm. To decompose the wage gap, we sequentially replace each female parameter with a male parameter until we reach the male predicted mean wage. Counterfactual wages are presented in Table 7.

View this table:
  • View inline
  • View popup
Table 7

Counterfactual wages

Differences in friction patterns imply differences in the observed distributions of firm productivity within the employed workers of different groups. This is also true when both groups face the same primitive distribution of productivity (see Condition 6). Consequently, a change in frictions generates a direct effect and a compositional effect on mean wages. The direct effect is the change in the wage of a worker ε, who belongs to the group k, working in a firm p, driven by the change in the value of the outside option of the worker; this is the effect displayed in Figure 1. The second effect is the one that comes from aggregation, due to the changes in the distribution of the accepted wages.

The wage setting equation implies that the higher the offer-arrival rate, the higher the wage and the higher the job destruction rate, the lower the wage (see Figure 1). In addition, increasing the offer-arrival rate makes the counterfactual firm productivity distribution among workers to stochastically dominate the original one, while increasing the destruction rate has the opposite effect.51 Hence, the direct effect and the aggregation effect follow the same pattern when we change λ1 and δ.

It is straightforward to calculate the counterfactual wage of one worker if we change δ or λ1. But, as the distribution of accepted wages change, it is more problematic to aggregate individual wages when some of this parameters change. Therefore, the counterfactual wages are calculated by simulating the distribution of productivity among employed female workers using the friction parameters of male workers.52

Considering the direct effect and the aggregation effect together, the effect of friction is significant. We find that, on average across sectors, gender differences in destruction rates, δ, explain 9 percent of the total wage gap, while decreasing the female offer arrival rate, λ1, to be equal to the male one would increase the gap by 13 percent. Differences in δ increase the gap, while differences in λ1 reduce the gap. Therefore, the effects of both type of frictions are partially compensated for. The sizes of these effects are consistent with Bowlus (1997), who analyzed samples of high school and college graduates from the National Longitudinal Survey of Youth (NLSY). These behavioral patterns were found to account for 20–30 percent of the wage differentials.

It is possible to disentangle the direct effect of friction on wages from the aggregation effect. For this purpose, we calculate the mean wage of women, changing the friction parameters but maintaining the original distribution of firm productivity, as is illustrated in Figure 1. These effects are surprisingly small; differences in δ explain, on average, 1.3 percent of the total wage gap, while netting out λ1 increases the wage-gap by 2.4 percent. In view of that, most of the effect of friction comes through the aggregation effect.

The proportion of the wage gap due to differences in productivity connects directly with a branch of the literature initiated by Hellerstein et al. (1999). In this line of work, they assumed proportionality between wages and productivity. Therefore, an inequality in wages that is not driven by a difference in productivity, suggests that there is discrimination. In this paper we impose more structure, which allows us to have a more complete interpretation of the fraction of the wage gap that is not explained by differences in productivity.

On average, 65 percent of the total wage gap is accounted for by differences in productivity. The role of productivity in explaining the wage gap is large but not surprising, given the definition of productivity used in this exercise. Behind these large productivity-gaps, there are important differences in productivity determinants. It can be seen on Table 2 that there are significant differences in age, tenure and potential experience. Moreover, in Lauer (2000), there is also evidence suggesting that a large part of the gender wage gap in Germany can be attributed to the fact that women have a lower endowment in human capital than men.

There is a large literature base investigating the effect of segregation on the gender wage gap.53 The structural estimation enables us to compare the current mean wages of female workers with the counterfactual female mean wages, if they faced the primitive distribution of firm productivity faced by male workers (that is, changing HW(p) for HM(p)). We find that 17 percent of the wage gap is accounted for by this difference. These results are consistent with the results of Bayard, Hellerstein, Neumark and Troske (2003). who found a negative and small effect of the proportion of women in the establishment, over wages in the U.S.. One of the advantages of the estimation of this structural model is that it enables us to empirically disentangle the effect of segregation from differences in the distribution of firm productivity generated by gender differences in friction patterns.54 In this exercise, we are not modeling the firm behavior explicitly and therefore differences in H(p) have no direct structural interpretation.

The effect of differences in productivity is not stable across occupations. Three quarters of the wage gap is explained by differences in productivity in low-qualification occupations, while this proportion reduces to 58 percent when considering high-qualification occupations. Finally, these productivity measures are not on an hourly basis: the numbers of hours significantly differs between male and female workers (see Section 5A for a more detailed discussion on this issue).

On average, 21 percent of the total wage gap is accounted for by the differences in the rent-splitting parameter. This means that women receive wages that are 9 percent lower than the wages received by equivalent men. This finding is not significantly different to what we obtained using the traditional approach based on Mincer-equations, where female workers are found to receive wages that are 15 percent lower than those of equivalent male workers (see Section A5 in the Appendix). The reported gender differences in bargaining power represent a potential explanation of the observed differences in destruction rates and in productivity. Neumark and McLennan (1995) show that as women experience labor market discrimination, they have more career interruptions, and therefore less human capital accumulation.

As in the case of differences in productivity, differences in the wage setting parameter are also occupation-specific. As can be seen from Table 8, the difference in rent-splitting parameters turns out to be an important determinant of the gender wage gap of workers in high-qualification occupations; this explains almost none of the wage gap in the low-qualification jobs. This result is consistent with the growing literature on glass ceilings. One potential reason to explain this pattern is the higher union coverage in low-qualification occupations. Collective bargaining agreements regulating wage rates and general working conditions may limit the extent of wage discrimination. See Heinze and Wolf (2010) and Antonczyk, Fitzenberger, and Sommerfeld (2010) for empirical evidence of a relationship between the gender wage gap and the coverage by collective wage bargaining in Germany.55

View this table:
  • View inline
  • View popup
Table 8

Gender Wage-Gap Decomposition

A. Productivity-gap and differences in hours

One possible explanation for the large estimated productivity and wage gaps may be that male workers work more hours than females. One of the main limitations of the LIAB is that it does not provide any measure of hours. Therefore, the estimated differences in productivity and the estimated differences in wages are not on an hourly basis. To tackle this problem, one alternative is to look for an external source of information about hours worked by each group in each sector. Using the G-SOEP, we find significant differences in mean hours between genders (see Table 9). On average, female workers work almost 20 percent fewer hours than their male counterparts.

View this table:
  • View inline
  • View popup
Table 9

Mean Hours Per Week

As the structural wage equation is linear in workers’ ability, correcting for hours does not affect the estimated rent-splitting parameters.56 Nevertheless, an interesting exercise is to have an hourly wage-gap decomposition directly plugging in the hour correction.57 Correcting mean wages using mean hours is going to be valid whenever hours worked are uncorrelated with hourly wages, and there is evidence suggesting that this may be the case.58

Results are presented in Table 10. When correcting for hours, the wage gap is significantly smaller. We find that the average hourly wage gap is 27.5 percent. A smaller fraction of this gap, 48 percent, is now explained by differences in productivity. On the other hand, a larger fraction of the gap, 32 percent,59 is due to differences in rent-splitting parameters. Segregation is responsible for 27 percent of the unconditional wage gap in hourly wages. Netting out the offer arrival rate would increase the hourly wage differential by 25 percent; if women had the male destruction rate, the gap would be 17 percent smaller.

View this table:
  • View inline
  • View popup
Table 10

Gender Wage-Gap Decomposition

VI. Concluding Remarks

This paper presents the first estimation of an equilibrium search model using matched employer-employee data to study wage discrimination. The combination of firm and worker data is crucial for these purposes for many reasons. Firstly, and most importantly, it allows us to separately identify differences in workers productivity across groups and differences in wage policies toward those groups. Secondly, better data makes the estimation simpler, and therefore, a more complete model can be estimated. Finally, it enables us to produce measures of the effect of labor market segregation, disentangled from the effect of friction on the distribution of accepted wages.

The structural estimation involved several steps. First, we estimated group-specific productivity for each firm, relying on the production function estimation at the firm-level, using LIAB. Second, we computed job-retention and job-locating rates using G-SOEP employee-level data. And third, we estimated the wage-setting parameters (bargaining power) using individual wage records in LIAB, and transition parameters and productivity measures specific to each group and firm estimated in the previous steps.

When analyzing productivity, we observe that women are 33 percent less productive than men in similar jobs. This difference is reduced to 17.5 percent if we control for differences in hours. The primary findings, in terms of friction patterns, are that women are, in general, more mobile than men in terms of job-to-job transitions and that they have higher job-destruction rates. In spite of having large wage differentials, women were only found to have significantly lower rent-splitting parameters than men in the construction sector.

In terms of wages, we find that the unconditional gender wage gap is 42 percent. It turns out that 65 percent of the gap is accounted for by differences in productivity. Differences in destruction rates explain 9 percent of the total wage-gap and segregation is responsible for 17 percent of this wage differential. Netting out differences in offer-arrival rates would increase the gap by 13 percent. Differences in the rent-splitting parameter generate 21 percent of the wage gap, which implies that female workers receive wages 9 percent lower than equivalent males. This is not a final word given that we still have to understand what is causing the difference in each wage determinant. Moreover, in the model all the parameters are considered as exogenous primitives. In reality, most of them are the outcome of individual behavior, and they are not independent. Still, the purpose of our decomposition is to identify which wage determinants are contributing the most to the wage gap. Since we find that the gender productivity gap is very large and it accounts for most of the wage differential between male and women. A promising area for future research is now understanding what is behind the productivity gap. Our model is not the most appropriate framework to analyze this question because the productivity of the worker is assumed to be a fixed primitive characteristic and not a result of a decision of investment in human capital. In a lifecycle model, it is likely that some of the difference in productivity between male and women is a response to a difference between both groups in β or H(p).60

Our results also rely on simplifying assumptions that would need further scrutiny. We now list two very desirable extensions. A first interesting extension is to relax the assumption of stationarity. Men and women have different levels of experience in the data. Differences in experience are immaterial in the model, which is in steady-state with infinitely lived agents. However, in the real world, workers with shorter experience are less productive and have had less time to climb the job ladder. To incorporate experience and human capital accumulation by learning-by-doing in the model would generate a much richer interpretations of the gender difference in H(p) and the gender differences in productivity. This extension is not trivial because the equilibrium allocation of workers to firms in such model has assortative matching (see Carrillo-Tudela 2009) and the estimation of the production function would have to account for it. A second desirable extension is to look into our reported gender differences in rent-splitting parameters. Within this difference, apart from pure wage discrimination, there can be primitive differences in bargaining performance (Croson and Gneezy 2009). To empirically disentangle wage discrimination from these behavioral differences is surely difficult but it would certainly yield further insight into the understanding of the gender wage gaps.

Appendix 1 Production Function—Specification Tests

The robustness of the productivity estimates are crucial to be able to reach reliable conclusions about wage discrimination. As robustness check, we present results of the productivity estimates under different sets of assumptions.

In Table 11, we report within-group nonlinear least squares estimates of Equations 10 and 9. In the estimation of Equation 9 we do not use measures of capital. Relative productivity estimates (that are γw and γl) are very similar in both estimations: differences between parameters are always smaller than a standard deviation. This robustness check is essential because in this kind of model, it is assumed that capital adjusts instantaneously to match the number of workers in each period. Although this assumption may seem controversial, it turns out that using observed capital or using the theoretical optimal choice of capital does not change the relative productivity estimates.

View this table:
  • View inline
  • View popup
Table 11

Production Function: Optimal Capital Input

Worker Composition Endogeneity

One of the main criticisms to the productivity estimates reported in Hellerstein and Neumark (1999) and in Hellerstein, Neumark, and Troske (1999) was that the proportion of women in the firm is likely to be correlated with the firm’s technology.61

Embedded Image (16)

Note that Equation 16 is the original Cobb-Douglas production function in logs without imposing constant returns to scale and including the depreciated capital instead of the optimal capital input. In this estimation we are assuming that the depreciation rate is constant, and hence depreciated capital is a constant fraction of the total capital.

The results are presented in Table 12. Female productivity estimates are significantly smaller. This finding is true for all sectors. The difference between results presented in Table 12 and results presented in Table 4, where firm’s fixed effects were removed, implies a nonzero correlation between the proportion women of women in the firm and the firm fixed effect. Hausman tests reject equality of γw in every sector. In terms of γl, the results are not significantly different and we only reject equality for manufacturing.

View this table:
  • View inline
  • View popup
Table 12

Production Function: Nonlinear Least Squares in Levels

A. Predetermined inputs:

It is possible to estimate αl and γk by GMM using internal instruments, assuming that Ljt and Kjt are predetermined. The estimates of γ’s by nonlinear GMM are imprecise in every sector and for every group. We have contrasted different identification strategies, in terms of the sets of internal instruments and optimization routines. γ has been estimated using only lagged levels as instruments in the equation in differences (Arellano and Bond 1991); lagged levels as instruments in the equation in differences jointly with lagged differences as instruments in the equation in levels (for example, Arellano and Bover 1995); and only lagged differences as instrument in the equation in levels (for example, Cahuc, Postel-Vinay, and Robin 2006). We obtained extremum estimators that minimize the two-stage robust GMM objective function and iterated-GMM objective function.62 We also calculated Monte Carlo Markov Chain type of estimators for continuously updated GMM (Chernozhukov and Hong 2003). Nonlinear System-GMM estimates of the Production Function 9 are reported in Table 13.63 The lack of precision in the quality parameter estimates is a pervasive problem in this kind of production function specification when the lag of capital and the lag of labor are used to instrument the current capital and labor, partialling out the firm fixed effects. See, for example, Cahuc, Postel-Vinay, and Robin (2006) or Hellerstein and Neumark (1998),

View this table:
  • View inline
  • View popup
Table 13

Production Function: Nonlinear SYSTEM-GMM

In Table 13 we report System-GMM estimates of Equation 16. However the precision in the γ’s GMM estimates is poor. Capital coefficients are not significantly different from zero and constant returns to scale are not rejected in any sector. Sargan tests do not reject compatibility of instruments in any sector. Haussman test of equality between γ’s reported in Table 13 and those in Table 4 do not reject equality in any group.

Footnotes

  • Cristian Bartolucci is an assistant professor of economics at Collegio Carlo Alberto. The author is specially grateful to Manuel Arellano for his guidance and constant encouragement. He would also like to thank Stéphane Bonhomme, Christian Bontemps, Raquel Carrasco, Zvi Eckstein, Chris Flinn, Andrés Erosa, Pietro Garibaldi, Carlos González-Aguado, José Labeaga, Joan Llull, Claudio Michelacci, Pedro Mira, Enrique Moral-Benito, Diego Puga, Jean-Marc Robin, Nieves Valdez, and seminar participants at Uppsala University, Bank of Canada, Collegio Carlo Alberto, Bank of Italy, Bank of France, PSE, UQAM, CEMFI, University of Tucuman, University College London, ICEEE (2011), European Meeting of the Econometric Society (2009), Cosme Workshop, EC-Squared Conference on Structural Microeconometrics, SEA meetings (2008), and IZA-ESSLE (2008) for very helpful comments. Special thanks is due to Emily Moschini for excellent research assistance and to Nils Drews, Peter Jacobebbinghaus, and Dana Muller at the Institute for Employment Research for invaluable support with the data. The data used can be made available to other researchers from December 2014 through November 2017 from IAB, BA, Postfach, Nuremberg 90327, Germany, subject to federal data protection regulations and the approval of the German Federal Employment Office. The computer code for replication of the results presented in this paper can be obtained from Cristian Bartolucci, Collegio Carlo Alberto, via Real Collegio, 30, Moncalieri TO, 10024, Italy. cristian.bartolucci{at}carloalberto.org

  • ↵1. See Blau and Kahn (2003) and Altonji and Blank (1999) for good surveys.

  • ↵2. See Chapter 4 in Altonji and Black (1999) for a good survey.

  • ↵3. See van den Berg and van Vuuren (2010) for a good discussion of this issue.

  • ↵4. See Altonji and Blank (1999) and Bayard, Hellerstein, Neumark, and Troske (2003).

  • ↵5. To have an estimable model with employee-level data, Flabbi (2010) only includes heterogeneity at the match level, not taking segregation into account, and not allowing for on-the-job search. Flabbi does allow for wage bargaining; however, the bargaining power is not estimated.

  • ↵6. Particularly related to Flabbi (2010), which at the moment is the most complete structural estimation in the wage-discrimination literature, the model presented in this paper allows for two-sided heterogeneity and on-the-job search. In the estimation, rent-splitting parameters are not imposed but are estimated. Note that we are not forcing the same firms distribution across gender. See Sections II and IV for details.

  • ↵7. This data set is subject to strict confidentiality restrictions. It is not directly available. After the IAB has approved the research project, The Research Data Center (FDZ) provides on-site use or remote access to external researchers. This study uses the Cross-sectional model of the Linked-Employer-Employee Data (LIAB) (Version 1, Years 1996–2005) from the IAB. Data access was provided via on-site use at the Research Data Centre (FDZ) of the German Federal Employment Agency (BA) at the Institute for Employment Research (IAB) and subsequently remote data access.

  • ↵8. There is a recent paper by Sulis (2011) that studies gender wage differentials in Italy, estimating a structural model. Sulis uses employee level data with firm identifiers, without data on firms, such as capital or output.

  • ↵9. The structural model abstracts many dimensions that may be relevant in the wage setting. In order to compare jobs that are as similar as possible, the empirical analysis is clustered at the sector and occupation level. See Section IV for details.

  • ↵10. The assumption that worker productivities “at home” and at work are proportional greatly simplifies the upcoming analysis. Furthermore, we allow b to be gender-specific to be consistent with a potential gender specialization in home production.

  • ↵11. The most convincing evidence comes from artificial experiments. See Croson and Gneezy (2009) for a good survey.

  • ↵12. If wages are continuously negotiated, firms could increase the wage of the worker at the same moment as the on-the-job offer to try to keep the worker from quitting. If the alternative employer is more productive, it can force the transition by also paying a premium. This auction for the worker finishes when the actual firm cannot pay more than the full productivity and transition holds, as in a Bertrand competition. This premium may be considered a hiring cost for the firm. Modeling this possibility is outside of the scope of this paper.

  • ↵13. Online Appendix available at http://sites.google.com/site/cristianbartolucci/DetectingWageDiscirmination_OA.pdf.

  • ↵14. Solving the differential equation we have:

    Embedded Image

    In Section A2 of the Online Appendix, we show that the minimum accepted productivity is independent of the worker type. Therefore we directly write pmin in the lower limit of integration.

  • ↵15. Note that in Cahuc et al. (2006), when the wage is bargained between a firm and an unemployed worker, Bertrand competition does not hold. Therefore, their proposed scenario and ours are equivalent. The only difference stems from the fact that both parts take into account future Bertrand competition.

  • ↵16. These simulations are calibrated using the estimated parameters of male highly qualified workers in the manufacturing sector, see Section IV. The parameters are: β = 0.292, λ−1 = 0.217 and δ = 0.034.

  • ↵17. See van den Berg and van Vuuren (2010) for a deeper discussion on the effect of friction on wages.

  • ↵18. To show that there is no sorting, Condition 7 is necessary but not sufficient. pmin, the minimum productivity, also needs to be independent of the worker ability. This second condition also holds in this model (the proof is in the Online Appendix at https://sites.google.com/site/cristianbartolucci/DetectingWageDiscirmination_OA.pdf).

  • ↵19. In the sample of firms used in this paper, 14.7 percent of the worker observations have censored information on wages. This proportion varies significantly across genders and occupations. 4.7 percent of female observations and 18.1 percent of males observations are censored. The proportion of worker observations in high-qualification occupations, with wages that exceed the upper earning limit for social security contributions, is 37.0 percent while the corresponding proportion of low-qualification occupations is 3.1 percent.

  • ↵20. We assigned the following groups to the low-qualification occupations: agrarian occupations, manual occupations, services and simple commercial or administrative occupations. We classified the following as high-qualification occupations: engineers, professional or semiprofessional occupations, qualified commercial or administrative occupations, and managerial occupations.

  • ↵21. The survey gives information about investment made to replace depreciated capital.

  • ↵22. For a more detailed description of this data set, see Alda et al. (2005).

  • ↵23. The service sector includes three kind of services defined in the survey: industrial, transport and communication, and other services. In the database, there is also information about firms in the financial and public sectors. No measure of output is well-defined for these sectors, so they have been excluded from the analysis.

  • ↵24. Employees subject to social security are workers, other employees and trainees who are liable to health, pension, and / or unemployment insurance or whose contributions to pension insurance is partly paid by the employer. We do not have information on workers who are not liable to social security. The following forms of employment are not considered liable to social security: civil servants, self-employed persons, unpaid family workers and so-called “marginal” part-time workers (A “marginal” part-time worker is a person who is either only employed for a short-term or paid a maximum wage of €400 per month).

  • ↵25. The weights for each groups are estimated with the relative frequencies in the 1996–2005 sample of the G-SOEP; these include manufacturing—high-qualification men 12.3 percent; manufacturing—low-qualification men 15.6 percent; manufacturing—high-qualification women 6.1 percent; manufacturing—low-qualification women 4.8 percent; construction—high-qualification men 4.1 percent; construction—low-qualification men 7.0 percent; construction—high-qualification-women 1.1 percent; construction—low-qualification women 0.2 percent; trade—high qualification-men 6.1 percent; trade—low-qualification men 2.9 percent; trade—high-qualification-women 10.5 percent; trade—low-qualification women 2.8 percent; services—high-qualification-men 10.3 percent; services—low-qualification men 4.2 percent; services—high-qualification-women 8.7 percent; and services—low-qualification women 3.1 percent.

  • ↵26. There is practically no attrition in a establishment level data. There is attrition in the worker-level data due to changes in the worker’s identifier and changes across establishments of the same firm.

  • ↵27. Unless the worker leaves the establishment and moves to another establishment within the panel.

  • ↵28. Cahuc, Postel-Vinay, and Robin (2006) follow the same strategy for estimating transition parameters with the French Labor Force Survey.

  • ↵29. See Wagner, Burkhauser, and Behringer (1993) for further details on the G-SOEP.

  • ↵30. Multistep estimation has been done in many papers. Good examples include Bontemps, Robin, and Van den Berg (2000), Postel-Vinay and Robin (2002), and Cahuc, Postel-Vinay and Robin (2006).

  • ↵31. We treat selection into occupations and sector as exogenous. Nevertheless, this selection also may have some content of discrimination (for example, Blau and Hendricks 1979).

  • ↵32. Due to this normalization, the firm specific productivity Ãj is redefined as Embedded Image

  • ↵33. Section A2 in the Appendix provides more detail and robustness checks on this assumption.

  • ↵34. There were problems of convergence in the estimation of Equation 8 using value added. For that reason, output measures where used in the estimation of α and γ in Equation 8. If a constant fraction of output is spent on materials, both estimators are consistent for α and γ. There is only a difference in the constant term of Equation 8.

    On the other hand, to estimate pj in Equation 9, the constant term matters, and hence we use measures of value-added.

  • ↵35. Assuming that a constant fraction (d) of capital depreciates by unit of time: Embedded Image. Therefore aklog(d) goes to the constant term.

  • ↵36. LIAB does not provide information on hours.

  • ↵37. Although differences in hours are illustrated as being important, the primary results of this paper remain valid. We only mention them in order to have a better understanding of the estimated productivity gap. See Section VA for a more detailed discussion of this issue.

  • ↵38. One interpretation of this result is that Embedded Image only captures variable capital whereas fixed capital is subsumed in the firm effect. If this is the case, the constant returns restriction is dubious.

  • ↵39. See Altonji and Blank (1999).

  • ↵40. Indeed, the model predicts that more productive firms are able to attract more workers of every type. Therefore, the total labor input will be correlated with the firm fixed effect but not with the labor input composition.

  • ↵41. If the firm has some knowledge of the productivity shock, it will adjust its choice of productive inputs accordingly. See, for example, Griliches and Mairesse (1998).

  • ↵42. Online Appendix available at http://sites.google.com/site/cristianbartolucci/DetectingWageDiscirmination_OA.pdf.

  • ↵43. The MATA code for computing the exponential integral and the MATA code to maximize this likelihood are available from the author upon request.

  • ↵44. van den Berg and Ridder (2003, p.237) report monthly rates for λ1 = 0.028 and λ1 / δ = 6.5.

  • ↵45. Notice that given the individual identifier i, the group k is fixed. Therefore we could replace k by k(i). To keep the notation as simple as possible we simply refer to k.

  • ↵46. The within-firm distribution of wages of each worker group is the same as the distribution of ability. As wages are linear in ε, to assume log-normality in the distribution of ε implies log-normal wages for each group within the firm.

  • ↵47. The analytical correction Embedded Image is not significant in any industry, neither for high-nor low-qualification workers.

  • ↵48. Differences between industries and occupations may be understood as consequence of compensating differentials or differences in union pressure. They cannot be understood as discrimination because we are comparing occupations and not workers.

  • ↵49. The surplus is defined in terms of the productivity of the match and the outside option. Both models imply different outside options. Without Bertrand competition the worker outside option is unemployment. While allowing for Bertrand competition, the worker’s outside option is the whole productivity of the poaching firm. As the outside option in the model with Bertrand competition dominates the one in the model without Bertrand competition, the estimated bargaining power is smaller.

  • ↵50. See Section A4 for details.

  • ↵51. Given that the offer arrival rate of women is higher than the one of men, the distribution of firms productivity across the population of female worker stochastically dominates the couterfactual distribution of firm’s productivity corresponding to female workers if they had the offer arrival rate of male workers. The proof is trivial, note that if Embedded Image :

    Embedded Image

    On the other hand, given that women have higher destruction rates than men

    Embedded Image

  • ↵52. The model used for simulations is a simplified version of the model presented in Section II, where worker heterogeneity has been omitted. Simulations use the punctual estimates of λ1, δ, γw, γl and α for every sector and worker group, reported in Section III. We assume that the primitive distribution of firm productivity is log-normal. The mean of the distribution of firm’s productivity is calibrated in equilibrium by matching mean wages for each occupation and for each sector. MATA codes for simulating the model previously described are available from the author upon request.

  • ↵53. See Altonji and Blank (1999).

  • ↵54. To the best of our knowledge, there is currently no available paper that disentangles both effects.

  • ↵55. The order of the sequential decomposition steps matters. As a robustness check, we reversed the order of the decomposition (see Table 16 in the Online Appendix). Results remain qualitatively similar.

  • ↵56. If wages and productivity are linear in time worked, the hour-correction only modifies the worker productivity and the wage. Consider the case where a worker i works h percent of time of a full-time worker.

    Embedded Image

    h is canceled out of both sides of the equation and the original wage setting equation holds.

  • ↵57. I must thank Zvi Eckstein for this suggestion.

  • ↵58. See Blundell and MaCurdy (1999).

  • ↵59. Female workers used to receive wages that were 6.2 percent lower than equivalent males, due to differences in the rent-splitting parameter. This number does not change because the rent-splitting parameter estimates don’t change.

  • ↵60. This kind of mechanisms was first proposed by Coate and Loury (1993).

  • ↵61. See Altonji and Blank (1999).

  • ↵62. See Arellano 2003, pp. 184–97

  • ↵63. MATA codes for computing the nonlinear estimators previously described are available from the author upon request.

  • Received October 2011.
  • Accepted November 2012.

References

  1. ↵
    1. Abowd John M.,
    2. Kramarz Francis,
    3. Margolis David
    . 1999. “High Wage Workers and High Wage Firms.” Econometrica 67(2):251–334.
    OpenUrlCrossRef
  2. ↵
    1. Antonczyk Dirk,
    2. Fitzenberger Bernd,
    3. Sommerfeld Katrin
    . 2010. “Rising Wage Inequality, the Decline of Collective Bargaining, and the Gender Wage Gap.” Labour Economics 17(5):835–47.
    OpenUrlCrossRef
  3. ↵
    1. Alda Holger,
    2. Bender Stefan,
    3. Gartner Hermann
    . 2005. “The Linked Employer-Employee Data set of the IAB (LIAB).” IAB-Discussion Paper 6/2005.
  4. ↵
    1. Altonji Joseph,
    2. Blank Rebecca
    . 1999. “Race and Gender in the Labor Market.” In Handbook of Labor Economics, ed. Ashenfelter O., Card D., Volume3(C):3143–259. Amsterdam: Elsevier Science.
    OpenUrlCrossRef
  5. ↵
    1. Arellano Manuel,
    2. Bond Stephen
    . 1991. “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Mquations.” Review of Economic Studies 58(2):277–97.
    OpenUrlCrossRef
  6. ↵
    1. Arellano Manuel,
    2. Bover Olympia
    . 1995. “Another Look at the Instrumental-Variable Estimation of Error-Components Models.” Journal of Econometrics 68(1):29–52.
    OpenUrlCrossRef
  7. ↵
    1. Atakan Alp
    . 2006. “Assortative Matching with Explicit Search Cost.” Econometrica 74(3):667–80
    OpenUrlCrossRef
  8. ↵
    1. Bartolucci Cristian,
    2. Devicienti Francesco
    . 2012. “Better Workers Move to Better Firms, A Simple Test to Identify Sorting.” Carlo Alberto Notebook No. 259. Unpublished.
  9. ↵
    1. Bayard Kimberly,
    2. Hellerstein Judith,
    3. Neumark David,
    4. Troske Kenneth
    . 2003. “New Evidence on Sex Segregation and Sex Differences in Wages from Matched Employee-Employer Data.” Journal of Labor Economics 21(4):887–922.
    OpenUrlCrossRef
  10. ↵
    1. Becker Gary
    . 1973. “A Theory of Marriage: Part I.” Journal of Political Economy 81(4): 813–46.
    OpenUrlCrossRef
  11. ↵
    1. Blau Francine,
    2. Hendricks Wallace
    . 1979. “Occupational Segregation by Sex: Trends and Prospects.” Journal of Human Resources 14(2):197–210.
    OpenUrlCrossRef
  12. ↵
    1. Blau Francine,
    2. Kahn Lawrence
    . 2000. “Gender Differences in Pay.” Journal of Economic Perspectives 14(49):75–99.
    OpenUrl
  13. ↵
    1. Blau Francine,
    2. Kahn Lawrence
    . 2003. “Understanding International Differences in the Gender Pay Gap.” Journal of Labor Economics 21(1):106–44.
    OpenUrlCrossRef
  14. ↵
    1. Blundell Richard,
    2. Macurdy Thomas
    . 1999. “Labor Supply: A Review of Alternative Approaches.” In Handbook of Labor Economics, ed. Ashenfelter O., Card D., Volume3(A):1559–1695. Amsterdam: Elsevier Science.
    OpenUrlCrossRef
  15. ↵
    1. Bontemps Christian,
    2. Robin Jean-Marc,
    3. van den Berg Gerard
    . 2000. “Equilibrium Search with Continuous Productivity Dispersion: Theory and Non-Parametric Estimation.” International Economic Review 41(2):305–58.
    OpenUrlCrossRef
  16. ↵
    1. Bowlus Audra
    . 1997. “A Search Interpretation of Male-Female Wage Differentials.” Journal of Labor Economics 15(4):625–57.
    OpenUrlCrossRef
  17. ↵
    1. Bowlus Audra,
    2. Eckstein Zvi
    . 2002. “ Discrimination and Skill Differences in an Equilibrium Search Model.” International Economic Review 43(4):1309–45.
    OpenUrlCrossRef
  18. ↵
    1. Burdett Kenneth,
    2. Mortensen Dale
    . 1998. “ Wage–Differentials, Employer Size and Unemployment.” International Economic Review, 39(2):257–73.
    OpenUrlCrossRef
  19. ↵
    1. Cahuc Pierre,
    2. Postel-Vinay Fabien,
    3. Robin Jean-Marc
    . 2006. “Wage Bargaining with On-the-job search: Theory and Evidence.” Econometrica 74(2):323–64.
    OpenUrlCrossRef
  20. ↵
    1. Carrillo-Tudela Carlos
    . 2009. “An Equilibrium Search Model when Firms Observe Workers’ Employment Status.” International Economic Review 50(2):485–506.
    OpenUrlCrossRef
  21. ↵
    1. Chernozhukov Victor,
    2. Hong Han
    . 2003. “An MCMC Approach to Classical Estimation.” Journal of Econometrics 115(2):293–346.
    OpenUrlCrossRef
  22. ↵
    1. Croson Rachel,
    2. Gneezy Uri
    . 2009. “Gender Differences in Preferences.” Journal of Economic Literature 47(2):448–74.
    OpenUrlCrossRef
  23. ↵
    1. Eckstein Zvi,
    2. Wolpin Kenneth
    . 1995. “Duration to First Job and Return to Schooling: Estimates from a Search-Matching Model.” Review of Economic Studies 62(2):263–86.
    OpenUrlCrossRef
  24. ↵
    1. Eckstein Zvi,
    2. Wolpin Kenneth
    . 1999. “Estimating the Effect of Racial Discrimination on First Job Wage Offers.” Review of Economics and Statistics 81(3):384–92.
    OpenUrlCrossRef
  25. ↵
    1. Flabbi Lucca
    . 2010. “Gender Discrimination Estimation in a Search Model with Matching and Bargaining.” International Economic Review 51(3):745–83.
    OpenUrlCrossRef
  26. ↵
    1. Flinn Christopher
    . 2006. “Minimum Wage Effects on Labor Market Outcomes under Search, Bargaining, and Endogenous Contact Rates.” Econometrica 74 (4):1013–62.
    OpenUrlCrossRef
  27. ↵
    1. Flinn Christopher,
    2. Mabli James
    . 2010. “On-the-Job Search, Minimum Wages, and Labor Market Outcomes in an Equilibrium Bargaining Framework.” Unpublished, NYU.
  28. ↵
    1. Griliches Zvi,
    2. Mairesse Jacques
    . 1998. «Production Functions: The Search for Identification. » Essays in Honour of Ragnar Frisch. ed. Strom S., Econometric Society Monograph Series, Cambridge University Press.
  29. ↵
    1. Heinze Anja,
    2. Wolf Elke
    . 2010. «The Intra-Firm Gender Wage Gap: A New View on Wage Differentials Based on Linked Employer–Employee Data.» Journal of Population Economics 23(3):851–79.
    OpenUrlCrossRef
  30. ↵
    1. Hellerstein Judith,
    2. Neumark David
    . 1998. “Wage Discrimination, Segregation, and Sex Differences in Wage and Productivity Within and Between Plants.” Industrial Relations 37(2):232–60.
    OpenUrlCrossRef
  31. ↵
    1. Hellerstein Judith,
    2. Neumark David
    . 1999. “Sex, Wages, and Productivity: An Empirical Analysis of Israeli Firm-Level Data.” International Economic Review 40(1):95–123.
    OpenUrlCrossRef
    1. Hellerstein Judith,
    2. Neumark David,
    3. Troske Kenneth
    . 1999. “Wages, Productivity, and Worker Characteristics: Evidence from Plant-Level Production Functions and Wage Equations.” Journal of Labor Economics 17(3):409–46.
    OpenUrlCrossRef
  32. ↵
    1. Lauer Charlotte
    . 2000. “Gender Wage Gap in West Germany: How Far Do Gender Differences in Human Capital Matter?” ZEW Discussion Paper No. 00–07.
  33. ↵
    1. Lindeboom Maarten,
    2. Mendes Rute,
    3. van den Berg Gerard
    . 2010. “An Empirical Assessment of Assortative Matching in the Labor Market.” Labour Economics 17(6):919–29.
    OpenUrlCrossRef
  34. ↵
    1. Mortensen Dale
    . 2003. Wage Dispersion, Cambridge, Mass.: MIT Press.
  35. ↵
    1. Moscarini Giuseppe
    . 2008. “Job-to-Job Quits and Corporate Culture.” Unpublished.
  36. ↵
    1. Neumark David,
    2. McLennan Michele
    . 1995. “Sex Discrimination and Women’s Labor Market Outcomes.” Journal of Human Resources 30(4):713–40.
    OpenUrlCrossRef
  37. ↵
    1. Postel-Vinay Fabien,
    2. Robin Jean-Marc
    . 2002. “ Equilibrium Wage Dispersion with Heterogeneous Workers and Firms.” Econometrica 70(6):2295–1350.
    OpenUrlCrossRef
  38. ↵
    1. Ridder Geert,
    2. van den Berg Gerard
    . 2003. “ Measuring Labor Market Frictions: A Cross-Country Comparison.” Journal of the European Economic Association 1(1):224–44.
    OpenUrlCrossRef
  39. ↵
    1. Shimer Robert
    . 2006. “On-the-Job Search and Strategic Bargaining.” European Economic Review 50(4):811–30
    OpenUrlCrossRef
  40. ↵
    1. Shimer Robert,
    2. Smith Lones
    .2000. “Assortative Matching and Search.” Econometrica 68(2):343–69
    OpenUrlCrossRef
  41. ↵
    1. Sulis Giovanni
    . 2011. “Gender Wage Differentials in Italy: A Structural Estimation Approach.” Journal of Population Economics 25(1):53–87.
    OpenUrl
    1. Van den Berg Gerard,
    2. van Vuuren Aico
    . 2010. “The Effect of Search Frictions on Wages.” Labour Economics 17(6):875–85.
    OpenUrlCrossRef
  42. ↵
    1. Wagner Gert,
    2. Burkhauser Richard,
    3. Behringer Friederike
    . 1993. “The English Language Public Use File of The German Socio-Economic Panel.” Journal of Human Resources 28(2):429–33.
    OpenUrl
PreviousNext
Back to top

In this issue

Journal of Human Resources: 48 (4)
Journal of Human Resources
Vol. 48, Issue 4
2 Oct 2013
  • Table of Contents
  • Table of Contents (PDF)
  • Index by author
Print
Download PDF
Article Alerts
Sign In to Email Alerts with your Email Address
Email Article

Thank you for your interest in spreading the word on Journal of Human Resources.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
Gender Wage Gaps Reconsidered
(Your Name) has sent you a message from Journal of Human Resources
(Your Name) thought you would like to see the Journal of Human Resources web site.
Citation Tools
Gender Wage Gaps Reconsidered
Cristian Bartolucci
Journal of Human Resources Oct 2013, 48 (4) 998-1034; DOI: 10.3368/jhr.48.4.998

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Share
Gender Wage Gaps Reconsidered
Cristian Bartolucci
Journal of Human Resources Oct 2013, 48 (4) 998-1034; DOI: 10.3368/jhr.48.4.998
Twitter logo Facebook logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Google Plus One
Bookmark this article

Jump to section

  • Article
    • Abstract
    • I. Introduction
    • II. Structural framework
    • III. Data
    • IV. Empirical Strategy and Results
    • V. Wage-Gap Decomposition
    • VI. Concluding Remarks
    • Appendix 1 Production Function—Specification Tests
    • Footnotes
    • References
  • Figures & Data
  • Supplemental
  • Info & Metrics
  • References
  • PDF

Related Articles

  • Google Scholar

Cited By...

  • No citing articles found.
  • Google Scholar

More in this TOC Section

  • Sexual Orientation and Multiple Job Holding
  • Owning the Agent
  • Understanding the Educational Attainment Polygenic Index and its Interactions with SES in Determining Health in Young Adulthood
Show more Articles

Similar Articles

UW Press logo

© 2025 Board of Regents of the University of Wisconsin System

Powered by HighWire