This paper examines the quantitative effects of gender gaps in entrepreneurship and workforce participation in an occupational choice model with a household sector and endogenous female labor supply. Gender gaps in workforce participation have a direct negative effect on market, while gender gaps in entrepreneurship affect negatively market output not only by reducing wages and labor force participation but also by reducing the average talent of entrepreneurs and aggregate productivity. We estimate the effects of these gender gaps for 37 European countries, as well as the United States, and find that gender gaps cause an average loss of 17.5% in market output and 13.2% in total output, which also includes household output. Interestingly, the total output loss would be similar (12%) in a model without household sector, since the market output loss is larger when the female labor supply is endogenous. Eastern Europe is the region with the lowest income fall due to gender gaps, while Southern Europe is the region with the largest fall. Northern Europe is the region with the largest productivity fall, which is due to the presence of high gender gaps in entrepreneurship.
We would like to thank the editor, Tiago V. de V. Cavalcanti for his guidance to improve the article, as well as Joseph Kaboski, Rachel Ngai and seminar particiapants at Universitat de Girona and the Conference “Employment in Europe”, Cyprus 2016, for valuable comments and suggestions. Financial support from the Spanish Ministry of Economy and Competitiveness, Grant ECO2015-66701-R, and Generalitat of Catalonia, Grant SGR2014-493, is gratefully acknowledged. All remaining errors are ours.
A Model details
A.1 Agents’ optimization
Employers choose the units of labor and capital they hire in order to maximize their current profits π.
The optimal number of workers and capital stock, n(x) and k(x) respectively, depend positively on the productivity level x, as equations (5) and (6) show:
When we solve for the problem of a self-employed agent with talent x who wishes to maximize his or her profits,
A.1.3 Household production
Women can get extra earnings from household production, hence they choose the household units of capital kh and labor nh in order to maximize their total earnings, which are given by their market-sector plus their household sector earnings. Specifically, when their optimal occupational choice in the market is to become a worker, their optimization problem is
with and kh ≥ 0. As a result, when , women choose to allocate all their time to the market sector and rent units of capital. When , on the other hand, women allocate at least part of their time endowment to the household sector. In particular, their optimal time allocation to the household sector is , which implies that some women with high market productivity may choose to allocate part of their time to the household sector and part of their time to the market sector. Women supplying all their labor to the market sector choose to rent units of capital.
In other words, when , women choose their labor allocation as follows:
and their units of capital used in the household sector are equal to
producing the following units of output:
in both cases.
On the other hand, when , when , women choose their labor allocation as follows:
and their units of capital used in the household sector are equal to
producing the following units of output:
A.1.4 Occupational choice
Figure 1 displays the shape of the profit functions of employers and self-employed along with wage function earned by employees and the female household workers extra earning as a function of talent x. The figure also shows the relevant talent cutoffs for the occupational choices. Here we present the equations that define the three thresholds. The threshold, z1, determines the earnings such that agents are indifferent between becoming workers or self-employed and it is given by
If x ≤ z1 agents choose to become workers, while if x > z1 they become self-employed or employers. The cutoff, z2, on the other hand, determines the choice between being a self-employed or an employer and it is given by
so that if x > z2 an agent wants to become an employer.
Finally, the cutoff , defines the talent level at which women are indifferent between being household workers, who only get earnings from their household production, and market workers, who get wage income plus household income from the household capital production. Specifically, when , household workers get earnings, while market workers get their wage income plus household earnings equal to . Hence, the difference between the household sector earnings is equal to and the talent threshold is defined as
Therefore, if their talent is below , women maximize their earnings as household workers, while above their earnings are maximized as market workers.
When , on the other hand, there are some women working full time in the household sector, some working part-time in the household sector and part-time in the market sector, and some other women working full time in the market sector. Women with ability below , where , choose to work full time in the household sector, and earn Bη. Women with ability between and , where is defined in equation (16), choose to allocate part of their time to the market and part of their time to the household. Their total earnings are from the household production plus from the market sector, compared to total earnings of by female workers.
When women have actually five occupational choices, since some choose to work part time in the market and part time in the household sector. In this case, the earning functions are defined as
which correspond to the household workers earnings minus the household production earnings of female market workers.
A.2 Competitive equilibrium in a model with household sector
We assume that women represent half of the population in the economy and that there is no unemployment. Moreover, any agent in the economy can potentially participate in the labor market, except for the restrictions on women described above. Under these assumptions, in equilibrium, the total demand of capital by employers and self-employed must be equal to the aggregate capital endowment (in per capita terms), k:
The first line of equation (17) is the demand for capital by men, while the two lower lines are the women’s demand for capital. The demand for capital by male-run firms has two components: the first one represents the capital demand by employers, while the second represents the demand by self-employed.
The demand of capital by women has six components, the first three corresponding to the market-sector firms run by women and the last three corresponding to the household-sector capital. The first one represents the capital demand by female employers, i.e. those with enough ability to be employers and who are allowed to be so, while the second term represent the capital demand by women who have the right ability to be self-employed. The third term shows the capital demand by women who become self-employed because they are excluded from employership. The fourth term corresponds to the household-sector capital demand by women who choose to be household-sector workers, the fifth is the household-sector capital demanded by women supplying the entire labor supply to the market sector, and the last term is the household-sector capital demand by women who work in the household-sector because they are not allowed to work in the market sector.
Similarly, the labor market-clearing condition is given by
where the first line represents the skill-adjusted aggregate labor demand and the second line represents the skill-adjusted aggregate labor supply in the market sector. The aggregate labor demand is equal to the male employers demand (first term) and the female employers demand (second term), i.e. those women with enough ability to be employers who are allowed to choose their occupation freely. The aggregate labor supply is equal to the male workers supply (first term in second line) plus the female workers supply (second, third, and fourth term in second line). The female workers supply is given by the skill-adjusted labor of women who, given their talent, choose to be full-time workers, plus that of women who have enough ability to be employers or self-employed but are excluded from both occupations. Finally, some women working in the household sector may also choose to be part-time workers in the market sector.
A competitive equilibrium in this economy is a set of cutoff levels , a set of quantities , and prices such that entrepreneurs choose the amount of capital and labor to maximize their profits, and labor and capital markets clear.
B Women occupational choice map
C Country-by-country results: long run income losses from labor market gender gaps
|%||Baseline simulation||No household sector simulation|
|Loss in Y/N due to all gender gaps||Loss in Y/P due to all gender. gaps||Loss in Total Y/P due to all gaps||Loss in Y/N due to all gender gaps||Loss in Y/P due to all gender. gaps||Loss in Total Y/P due to all gaps|
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