7 Equilibrium Counterfactuals
7.1 Sources of the Gender Pay Gap
With the estimated model in hand, we recompute equilibria while shutting down various gender differences. We consider four counterfactuals. First, we set the amenity cost shifters of women equal to those of men, cπ,0F = cπ,0M .36 Second, we shut down employer wedges, z = 0. Third, we only shut down differences in vacancy creation cost shifters cv,0g across genders. Fourth and finally, we shut down all of the above gender differences simultaneously.37 Table9 describes our baseline economy (column 0) and results from the four counterfactuals (columns 1–4).
Counterfactual 1: Shutting down gender differences in amenity costs. Gender differences in ameni-ties account for around 1.3 log points (18 percent) of the gender gap. Worker welfare increases by 0.5 percent in payroll-equivalent units. The increase in pay for women (Panel(a)of Figure8) is partly off-set by a corresponding decrease in mean amenity values (Panel(b)). Output increases slightly because high-productivity firms increase their amenities, thus attracting more women. As a consequence, pay inequality for women increases. However, employer welfare decreases: profits decline because firms now pay higher wages, and wedges increase because more women work at high-wedge firms. Finally, women’s employer rank-pay rank relationship becomes steeper (Panel(c)), becoming more like that of men documented in Section3.5. See column 1 of Table9.
36For robustness, we have simulated counterfactuals under a range of amenity cost elasticities. In AppendixF, we show a variant of the counterfactuals with exogenous amenities, i.e.,ηπ=∞. Our insights remain substantially unchanged.
37In all counterfactuals but the last, we keep single-gender employers unchanged. Single-gender employers are impor-tant because they make up a significant share of all employers and mediate the response of other firms to counterfactual parameter changes. For the gender-neutral economy, we set previously men-only firms to hire women in equal proportions, while previously women-only firms cease to exist. In essence, the gender-neutral economy is an economy that consists of two copies of the current market for men.
Table 9. Results from simulating equilibrium counterfactuals
Baseline Counterfactuals
Gender differences in... (0) (1) (2) (3) (4)
amenities X X X
employer wedges X X X
vacancy posting costs X X X
Gender pay gap... 0.074 0.061 0.020 0.018 0.000
between employers 0.055 0.056 0.047 0.016 0.000
within employers 0.018 0.005 −0.026 0.002 0.000
Output 1.000 1.001 1.012 1.033 1.035
Worker welfare from... 0.000 0.004 0.015 −0.004 0.027
payroll for women 0.000 0.010 0.026 0.019 0.029
amenity value for women 0.000 −0.006 −0.010 −0.022 −0.002 Payroll-equivalent welfare change 0.000 0.005 0.019 −0.004 0.033 Employer welfare from... 1.000 0.997 1.011 0.986 1.039
profits 1.004 1.002 1.011 1.039 1.039
employer wedges −0.004 −0.006 0.000 −0.053 0.000
Total employment for women 0.760 0.759 0.762 0.760 0.757
Source: Authors’ calculations based on RAIS.Note: Table reports simulation results from model-based coun-terfactuals. Baseline results (column 0) are compared against counterfactuals without gender differences in amenities (column 1), in employer wedges (column 2), in vacancy posting costs (column 3), and without any gender differences (column 4).
Figure 8. Effects of counterfactual 1 on amenities and pay for women
(a) Pay distribution
Source:Authors’ calculations based on RAIS.Note:Counterfactual corresponding to column 1 of Table9.
Counterfactual 2: Shutting down employer wedges. Employer wedges account for around 5.4 log points (73 percent) of the gender gap. Most of the decrease in the gender gap is within firms, but the between-firm gap also decreases due to equilibrium reallocation of women. The mean and dispersion of women’s wages increase (Panel (a) of Figure 9). Since wedges were positively correlated with productivity, removing them increases women’s dispersion in composite productivity and hence pay.
Output increases by 1.2 percent, worker welfare by 1.9 percent, and profits by 0.7 percent. Output increases due to women relocating to high-productivity, formerly high-wedge firms. The increase in
worker welfare is accounted for by a large rise in women’s payroll and partly offset by a decline in amenity values due to worker relocation (Panel(b)). That employer profits also increase reflects the fact that employers with a nonzero wedge were not maximizing monetary profits. Another result is a steepening of the productivity-pay relationship for women (Panel(c)) that resembles an increase in women’s “bargaining power” (Card et al.,2016). See column 2 of Table9.
Figure 9. Effects of counterfactual 2 on pay, amenities and offer distribution for women
(a) Pay distribution
0.00.51.01.52.02.53.0Density of women
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 Employer pay for women
Baseline Counterfactual 2
(b) Amenities distribution
0.00.20.40.60.81.01.21.41.6Density of women
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Amenities for women Baseline Counterfactual 2
(c) Pay vs. productivity
−0.2−0.10.10.20.40.5Employer pay for women
3.0 4.0 5.0 5.9 6.9 7.9 8.9 9.9 10.8 11.8 12.8
Productivity Baseline Counterfactual 2
Source:Authors’ calculations based on RAIS.Note:Counterfactual corresponding to column 2 of Table9.
Counterfactual 3: Shutting down gender differences in vacancy costs. Gender differences in va-cancy costs account for around 5.6 log points (76 percent) of the gender gap. Again, most of this decline is explained by a decline in the between-employer pay gap. More women become employed at high-paying firms (Panel(a)of Figure 10). There is a significant increase in output of around 3.3 percent due to the relocation of women to more productive firms (Panel(c)). However, the impact on worker welfare is net negative, around 0.4 percent. The reason for this is that especially high-wedge, high-productivity, but low-amenity employers increase their employment of women (Panel(c)). This also means that in spite of an increase in monetary profits of around 3.5 percent, employers are worse off on average. A key takeaway from this simulation is that gender differences in employer allocation are not necessarily inefficient. See column 3 of Table9.
Counterfactual 4: Moving to a gender-neutral economy. By construction, moving to a gender-neutral economy eliminates the gender gap. Put differently, women’s mean pay increases by 7.4 percent. Interestingly, this is also associated with large gains in output (3.5 percent), worker wel-fare (3.3 percent), and employer welwel-fare (3.9 percent). Output increases because women relocate to higher-productivity employers. Most of the increase in worker welfare is due to an increase in pay, not amenities. Additionally, employer welfare increases due to a combination of higher profits and
Figure 10. Effects of counterfactual 3 on the distribution of women’s employment.
(a) Women’s distribution over pay for women
0.00.51.01.52.02.53.0Density
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 AKM employer FE for women
Baseline Counterfactual 3
(b) Women’s distribution over amenities
0.00.20.40.60.81.01.21.41.6Density of women
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Amenities for women Baseline Counterfactual 3
(c) Women’s distribution over pro-ductivity
0.00.10.20.30.40.5Density
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 Productivity
Baseline Counterfactual 3
Source:Authors’ calculations based on RAIS.Note:Counterfactual corresponding to column 3 of Table9.
lower wedges. See column 4 of Table9.
Interaction effects and the distinction between output versus welfare. One important insight from our simulations is that the different structural gender differences interact nonlinearly. While removing all gender differences simultaneously leads to large output and welfare gains, addressing only one at a time may actually result in welfare losses. Another important insight is that output and welfare are fundamentally different, and that the two can move in opposite directions.