E.1 Sensitivity Analysis Across Different Employer Rank Measures
To check how sensitive our results are to the choice of ranking, we re-estimate employer-specific parameters—productivity p, amenity valuesπM andπF, and employer wedges z—by applying our estimation routine to three alternative ranking measures: the Pagerank (as in the main text), the poaching index (Moscarini and Postel-Vinay, 2008; Bagger and Lentz, 2018), and the net poaching index (Haltiwanger et al.,2018; Moscarini and Postel-Vinay, 2018). Table 21 presents employment-weighted correlations between various estimation objects across different employer rank measures.
Estimates across rank measures are significantly positively, albeit not perfectly, correlated. For our baseline analysis in the main text, we use the Pagerank index because it utilizes the most information per observed worker transition.
Table 21. Counterfactual simulations, shutting down differences across gender Panel A. Productivity estimates
Pagerank Poaching index Net poaching index
Pagerank 1.000
Poaching index 0.338 1.000
Net poaching index 0.457 0.379 1.000
Panel B. Male amenity estimates
Pagerank Poaching index Net poaching index
Pagerank 1.000
Poaching index 0.442 1.000
Net poaching index 0.437 0.648 1.000
Panel C. Female amenity estimates
Pagerank Poaching index Net poaching index
Pagerank 1.0000
Poaching index 0.420 1.000
Net poaching index 0.446 0.864 1.000
Source: Authors’ calculations based on RAIS. Note: Table reports pairwise correlations between estimates of productivity, male amenities, and female amenities based on different employer rank measures.
E.2 Details on Covariates for Analysis of Amenity Estimates
We include as covariates inEg,jin equation (25) the following fourteen variables that we construct us-ing the RAIS data: an indicator for whether the employer provides in-kind remuneration in the form of food stamps; the shares of workers with part-time contracts, with hours changes since the previous year, with paid sick leave, with parental leave, with unpaid leave, with earnings cuts since the pre-vious year, with noncontractual earnings fluctuations, with work-related accidents, with commute-related accidents; the shares of worker separations due to firing for unjust reasons and due to worker death; 5-digit industry dummies, and municipality dummies.
E.3 Details on Covariates for Analysis of Employer Wedge Estimates
We include as covariates in the vector Ej in equation (26) the following twelve variables, which we construct using the RAIS data: the mean intensity for routine-manual tasks, nonroutine-manual tasks, routine-cognitive tasks, nonroutine cognitive tasks involving interpersonal skills, nonroutine cogni-tive tasks involving analytical skills;44the share of worker separations due to worker death, the share of workers with work-related accidents; the female employment share, an indicator for whether the highest-paid worker is a woman; an indicator for whether an employer has no major financial stake-holder (as proxied by their participation in the small-business tax regimeSimples Nacional);455-digit industry dummies, and municipality dummies.
E.4 Basic Solution Algorithm
We start by feeding to the model the estimated labor market parameters{λuM,λuF,seM,seF,sGM,sGF,δM,δF} and the firm-level estimates of{p,πM,πF,z,cv,0M,cv,0F }. Then, we rank firms according to “composite productivity” ˜pgfor each gender. This is useful because, as stated in Lemma4, firms that have higher
“composite productivity” will pay higher effective wages.
We must first find the equilibrium level of aggregate vacanciesVg. We invert the equation for the offer arrival rate from unemployment in (13) to obtain:
Va,g=Ua,g
λug χa,g
1/α
.
Now consider the firm’s first order conditions for vacancies in equation (38) and the rewritten first-order condition with respect to flow utility in equation (42). We use the same transformations that we have used to prove Lemma 4. Define hg(p˜g) = F(x∗g(pg)). Thus, h′g(p˜g) = fg(x∗g(p˜g))x′g(p˜g), therefore f(x∗g(p˜g)) = h′g(p˜g)/x′g(p˜g). Also,v(p˜g) = Vgγh(′gp˜(p˜g)
g) , so we can rewriteh′g(p˜g) = vgV(pgg)γ(p˜g). We assumecvg(v) =cv,0g v2
2. Thus, we rewrite the first-order conditions as h′g(pg) = Tg(p˜g−xg(p˜g))
44We define task intensity as the mean z-score of a given task measures across occupations of workers at a given estab-lishment. We obtain task measures for the BrazilianClassificação Brasileira de Ocupaçoes (CBO)occupation codes by hand-matching them to US Census occupation codes, which are then linked to the Occupational Information Network (O*NET) task scales constructed byAutor and Dorn(2009) andAcemoglu and Autor(2011).
45Eligibility for the Simples Nacional tax regime requires that the enterprise is a micro- or small business with annual rev-enues below BRL 1,200,00 (around USD 200,000), that it has no other companies as stakeholders, that it is not internationally owned, that it has no shareholder or partner with significant financial stakes in other companies, and that the enterprise itself has no stake in other companies.
vacancies posted by integrating the functions above by gender and firm-by-firm. For every firmj:
h′g,j = Tg(p˜g,j−xg,j) Vgcv,0g,j
1
δ+λGg +λeg(1−hg,j) 2
γg(p˜g,j)
x′g,j = 2λ
egTg(p˜g,j−xg,j)2 Vgcv,0g,j
1
δ+λGg +λeg(1−hgg,j) 3
γg(p˜g,j) hg,j+1=hg,j+h′g,j(p˜g,j+1−p˜g,j)
xg,j+1= xg,j+x′g,j(p˜g,j+1−p˜g,j)
(54)
and we calculate total vacancies obtained in equilibrium as Vg∗ =
∑
j
vg,jγg(p˜g,j)(p˜g,j− p˜g,j−1). We solve the algorithm setting the initial conditionsxg,0 =φgandhg,0=0, and we loop over a multiplier of all vacancy cost shifterscv,0g,j until we obtain thatVg∗ =Vg. Our solution algorithm produces gender-specific firm-level flow utilityxg,j, easily converted to wageswg,j = xg,j−πg,j, gender-specific firm-level recruiting intensitiesvg,j and gender-specific firm-level ranks in the offer distributionFg,j that are exactly identical to those observed in the data, except for small rounding errors: the correlation between the data and the model-generated data is larger than 0.99999 for all variables, and it’s equal to 1 by definition for ranks.
When we perform counterfactuals that involve equalizing female amenities to male amenities, we assume thatcπj,g(πg) =cπ,0j,g π22g. We estimate the cost shiftercπ,0j,g by solving this equation forcπ,0j,g given our estimates ofπj,g. Thus, when a firm jwas previously posting amenitiesπj,Ffor women in equi-librium, and now this level is equalized to the level of menπj,M, we readjust composite productivity of firmjas follows:
p˜baselinej,F =p˜−z−cπj,Fπ2j,F 2 p˜counter f actual
j,F =p˜−z−cπj,Mπ2j,M 2
=p˜baselinej,F +cπj,Fπ2j,F,a
2 −cπj,Mπ2j,M 2