Macroeconomic costs of gender gaps in a model with entrepreneurship and household production

David Cuberes; Marc Teignier

doi:10.1515/bejm-2017-0031

Published by De Gruyter December 27, 2017

Macroeconomic costs of gender gaps in a model with entrepreneurship and household production

David Cuberes and Marc Teignier

From the journal The B.E. Journal of Macroeconomics

https://doi.org/10.1515/bejm-2017-0031

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Abstract

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.

Keywords: gender inequality; household production; factor misallocation; aggregate productivity

JEL Classification: E2; J21; J24; O40

Acknowledgement

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.

Appendix

A Model details

A.1 Agents’ optimization

A.1.1 Employers

Employers choose the units of labor and capital they hire in order to maximize their current profits π.

maxk,n{x(kαn1−α)η−rk−wn},

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:

(5)n(x)=[xη(1−α)(α1−α)αηwαη−1rαη]1/(1−η),

(6)k(x)=[xηα(1−αα)η(1−α)rη(1−α)−1wη(1−α)]1/(1−η).

A.1.2 Self-employed

When we solve for the problem of a self-employed agent with talent x who wishes to maximize his or her profits,

maxk{xk(x)αη−rk},

we find

(7)k~(x)=(τxαηr)11−αη.

A.1.3 Household production

Women can get extra earnings from household production, hence they choose the household units of capital k_h and labor n_h 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

maxkh,nh{(Akh+Bnh)η+wx(1−nh)},

with nh∈[0,1] and k_h ≥ 0.^[16] As a result, when AB>rwx, women choose to allocate all their time to the market sector and rent kh1≡(ηAηr)11−ηunits of capital. When AB<rwx, 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 nh0≡min{1,(ηBηwx)11−η}, 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 kh0≡max{0,(ηAηr)11−η−BA} units of capital.

In other words, when rB1−ηηA<1, women choose their labor allocation as follows:

(8)nh={0if x>BArw1otherwise

and their units of capital used in the household sector are equal to

(9)kh={(ηAηr)11−ηif x>BArw(ηAηr)11−η−BAotherwise,

producing the following units of output:

(10)yh=(ηAr)η1−η

in both cases.

On the other hand, when , when rB1−ηηA>1, women choose their labor allocation as follows:

(11)nh={0if x>BArw(ηBηwx)11−ηif ηBηw<x<BArw1if x<ηBηw

and their units of capital used in the household sector are equal to

(12)kh={(ηAηr)11−ηif x>BArw0otherwise

producing the following units of output:

(13)yh={(ηAr)η1−ηif x>BArw(ηBwx)η1−ηif ηBηw<x<BArwBηif x<ηBηw.

A.1.4 Occupational choice

Figure 1 displays the shape of the profit functions of employers (πe(x)) and self-employed (πs(x)) along with wage function earned by employees and the female household workers extra earning as a function of talent x.^[17] 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

(14)wz1=τz1k~(z1)αη−rk~(z1).

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

(15)τz2k~(z2)αη−rk~(z2)=z2x(k(z2)αn(z2)1−α)η−rk(z2)−wn(z2)

so that if x > z₂ an agent wants to become an employer.

Finally, the cutoff z0f, 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 rB1−ηηA<1, household workers get earnings(ηAr)η1−η−r((ηAηr)11−η−BA), while market workers get their wage income plus household earnings equal to (ηAr)η1−η−r(ηAηr)11−η. Hence, the difference between the household sector earnings is equal to rBA and the talent threshold z0f is defined as

(16)rBA=wz0f.

Therefore, if their talent is below z0f, women maximize their earnings as household workers, while above z0f their earnings are maximized as market workers.

When rB1−ηηA>1, 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 z00f, where z00f≡ηBηw, choose to work full time in the household sector, and earn B^η. Women with ability between z00f and z0f , where z0f 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 (ηBwx)η1−η from the household production plus wx(1−(ηBηwx)11−η) from the market sector, compared to total earnings of wx+(ηAr)η1−η−r(ηAηr)11−η by female workers.

When rB1−ηηA>1 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

πh00≡Bη−(1−η)(ηAr)η1−η

and

πh01≡wx+(1−η)((ηBwx)η1−η−(ηAr)η1−η),

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:

(17)k=12[∫z2∞k(x)dΓ(x)+∫z1z2k~(x)dΓ(x)]+λ2[∫z2∞μk(x)dΓ(x)+∫z1z2(μ+(1−μ)μ0)k~(x)dΓ(x)+∫z2∞(1−μ)μ0k~(x)dΓ(x)]+λ2[∫Bz0fkh0dΓ(x)+∫z0f∞kh1dΓ(x)]+1−λ2∫z0f∞kh0dΓ(x).

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

12[∫z2∞n(x)dΓ(x)]+λ2[∫z2∞μ(x)n(x)dΓ(x)]=12∫Bz1xdΓ(x)+λ2[∫z0fz1xdΓ(x)+∫z1∞((1−μ)(1−μ0))xdΓ(x)+∫Bz0fx(1−nh0(x))dΓ(x)],

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 (z00f,z0f,z1,z2), a set of quantities [n(x),nh0(x),k(x),k~(x),kh0,kh1],∀x, and prices (w,r) 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
Austria	6.41	17.38	12.77	5.11	11.75	11.75
Belarus	6.40	11.94	9.12	4.97	5.62	5.62
Belgium	7.31	20.09	14.82	5.91	13.83	13.83
Bulgaria	5.88	15.12	11.09	4.61	9.75	9.75
Croatia	5.08	16.27	11.96	4.01	11.88	11.88
Cyprus	8.99	19.85	14.58	7.33	11.65	11.65
Czech Republic	6.28	21.70	16.39	5.08	16.74	16.74
Denmark	7.89	18.14	13.34	6.33	10.92	10.92
Estonia	9.06	16.53	12.51	7.29	7.63	7.63
Finland	7.28	15.66	11.60	5.76	8.78	8.78
France	7.40	17.18	12.64	5.90	10.39	10.39
Germany	6.75	18.09	13.30	5.39	12.17	12.17
Greece	5.26	22.70	17.63	4.28	18.82	18.82
Hungary	5.96	16.95	12.46	4.71	11.72	11.72
Iceland	7.21	16.14	11.91	5.72	9.42	9.42
Ireland	7.80	19.28	14.16	6.26	12.34	12.34
Italy	5.33	23.23	18.13	4.34	19.34	19.34
Latvia	6.07	10.77	8.35	4.69	4.69	4.69
Lithuania	7.28	12.96	9.97	5.72	5.72	5.72
Luxembourg	5.49	20.01	15.04	4.42	15.62	15.62
Macedonia	4.54	23.33	18.52	3.69	20.13	20.13
Malta	5.18	29.42	24.99	4.37	26.37	26.37
Moldova	5.95	11.41	8.68	4.60	5.54	5.54
Netherlands	6.79	18.01	13.23	5.42	12.03	12.03
Norway	7.23	16.91	12.44	5.73	10.27	10.27
Poland	4.68	17.25	12.80	3.69	13.34	13.34
Portugal	6.42	15.45	11.37	5.07	9.54	9.54
Romania	6.13	18.73	13.85	4.88	13.53	13.53
Russian Federation	4.36	9.34	7.01	3.34	5.09	5.09
Serbia	4.72	20.55	15.73	3.77	16.92	16.92
Slovakia	5.67	19.15	14.26	4.51	14.45	14.45
Slovenia	6.33	17.71	13.02	5.02	12.16	12.16
Spain	5.35	17.63	13.04	4.23	13.11	13.11
Sweden	8.01	18.53	13.61	6.43	11.24	11.24
Switzerland	6.22	18.11	13.34	4.98	12.78	12.78
Ukraine	4.00	9.52	7.03	3.08	5.68	5.68
United Kingdom	6.89	17.89	13.15	5.48	11.77	11.77
United States	6.31	17.26	12.68	5.01	11.70	11.70

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Published Online: 2017-12-27

Macroeconomic costs of gender gaps in a model with entrepreneurship and household production

Abstract

Acknowledgement

Appendix

A Model details

A.1 Agents’ optimization

A.1.1 Employers

A.1.2 Self-employed

A.1.3 Household production

A.1.4 Occupational choice

A.2 Competitive equilibrium in a model with household sector

B Women occupational choice map

C Country-by-country results: long run income losses from labor market gender gaps

References

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