Gender Wage Gaps Reconsidered

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 L_k(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, b_kε. 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 H_k(p), which is continuously differentiable with support [p_min,p_max]. 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 λ_0k > 0. Employed workers may also search for a better job while employed and receive job offers at a Poisson rate λ_1k > 0 We treat λ_0k and λ_1k 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 δ_κ > 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 β_k and (1 – β_k), for the worker and the firm respectively. β_k is exogenously given and specific to each group k. We will refer to β_k as the rent-splitting parameter. As in Wolpin and Eckstein (1999), we interpret β_male – β_female 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:

(1)

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

(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:

where 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:

(3)

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

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

After some algebra, solving for the differential equation yields:

(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) = p_minε 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

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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:

  (5)

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

  

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

  (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 . 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:

  

  Using Conditions 5 and 6 and rearranging:

  (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.

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:

where is the total amount of workers of group k in firm j at time t, and 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.

(8)

where, Y_jt is the value added produced by firm j in period t, K_jt is the total capital, and A_j 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 γ_hm = 1 considering highly qualified male workers as the reference group.³² As such, 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

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:

Plugging into Equation 8 and rearranging, we have that:

(9)

Note that Equation 9 is equivalent to the production function presented in Section II, where p_j is a function of the firm-specific productivity parameter (A_j) and the r; and L_jt is the total labor input in efficiency units. Using the panel with firm-level data on output ()³⁴, depreciated capital ³⁵ 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 (γ_lw = γ_lγ_w).

(10)

where and are, respectively, the number of men and women in high-qualification occupations in firm j at time t while and are, respectively, the number of men and women in low-qualification occupations in firm j at time t, and u_jt 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 A_j. As a result, productive inputs are correlated with the firm fixed effect (that is cov(A_j, L_jt) ≠ 0 and cov(A_j, K_jt) ≠ 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

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 across sectors is 0.38 and the average of 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 u_jt. In the theory presented in Section II, we abstract from productivity shock. Assuming that u_jt 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 γ_w and γ_l 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 , 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 u_jt 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 γ_k by GMM using internal instruments, assuming that L_jt and K_jt 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):

(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:

(12)

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

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:

where c_i is a right-censored spell indicator and H_i 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.

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:

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

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

E_k(ε_i) = γ_k 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 p_j at time t is:

(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 p_j, that is, the productivity measured in terms of efficiency units of highly qualified males, we would have —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 γ_k inside the expectation operator:

Noting that dp / dp^k = 1 / γ_k, and changing the variable within the integral, we obtain:

For each firm in the sample we estimate the average daily wage 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, ) by maximum likelihood at the firm level assuming that ε_i is distributed as a log-normal.⁴⁶ Under the steady state assumption, and according to the theory presented in Section II, exhibits stationary fluctuation around the steady state mean wage E(w_jtk) paid by firm j with productivity p_j.

Writing Equation 13 in logs:

(14)

We estimate Equation 14 by weighted nonlinear least squares at the firm level, where γ_k, δ_k and λ_k are parameters estimated in the previous stages, p_j is the productivity of firm j, and v_jtk 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 p_j, γ, λ₁ and δ are estimated in previous stages. To solve this problem, we combine bootstrap for p_j 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:

where Ξ is the objective function in the optimization, which, in this case is the weighted sum of squares and . Second derivatives of 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.

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.

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.

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.