Back Matter
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund
  • | 2 https://isni.org/isni/0000000404811396, International Monetary Fund
  • | 3 https://isni.org/isni/0000000404811396, International Monetary Fund
  • | 4 https://isni.org/isni/0000000404811396, International Monetary Fund

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Annex I. Modeling Framework

A. Model for Advanced Economies

Environment

We study a stationary overlapping generations economy populated by a continuum of married males (m) and females (f). Let j ε {1,2,...,j} denote the age of each individual. We assume that the population grows at rate n and that the population structure is stationary.

In the model, individuals are endowed with a given level of education and start their adult life married. They retire at age Jr and collect pension benefits until they die at age J. We assume for simplicity that agents are married to individuals of the same age. Married individuals differ in their education and number of children, and the latter is a function of the couple’s education. Children appear in the beginning of parents’ lifetime and stay with them for three periods.

Each period, working households make labor supply, consumption, and saving decisions. Households cannot borrow but can save. If a woman with children works, the household pays for childcare. Households differ according to the childcare costs, which in turn depend on the household education level and the children’s age. Childcare costs are mitigated by childcare transfers that depend on households’ total income. In addition, if the female member of the household works, the household incurs a utility cost related to the female labor force participation that is not captured in the model, such as support of relatives, heterogeneity in the preferences of educating her own children, and availability of childcare. Females who decide not to work incur labor efficiency costs in the next period due to loss of experience.

The government taxes households and provides transfers. Child-related transfers include childcare subsidies, child tax credits, and childcare tax credits. The government also administers the earned income tax credit (EITC), which works as a wage subsidy for households below a certain income and as a means-tested welfare system, providing transfers for low-income households.

Technology

There is an aggregate firm that operates constant returns to scale technology. The firm rents capital and labor services from households at rates R and w. Using K units of capital and L units of labor, the firm produces F(K,L) = KαL1-α units of consumption goods. Capital depreciates at rate δ.

Childcare services are provided using labor services only in a linear way. Thus, the price of childcare services is wage rate w. Total labor services available are divided between childcare services and the production of goods. Households save in the form of a risk-free asset that pays the competitive rate of return r = R — δ.

Demographics

Individuals differ in terms of their labor efficiency at the beginning of their lives; each individual is endowed with an exogenous type z for males and x for females. Males’ productivity at age j and type z is denoted by hm(z,j) . As opposed to males’, females’ productivity evolves endogenously. Each female starts her life with productivity that depends on her education level, denoted by hf(x, 1). After age 1 her productivity level hf depends on her past level of productivity hf, age j, education level x, and labor supply lf and is given by

hf=exp(hf+α(x,j)I(lf>0)δ(x,j)(1I(lf>0)))

in which α(x,j) is the female’s productivity growth rate associated with her work experience, δ(x,j) is her productivity depreciation rate for not working, and I is an indicator function that is equal to 1 when the woman works and zero otherwise. The growth and depreciation rates depend on her education, which captures the difference in age-earning profiles of females with different levels of education.

Preferences, Children, and Childcare Costs

If a female works, the household must pay childcare costs. The cost depends on the husband’s and wife’s education, the age of the children, and the number of children. The childcare cost is paid as a fraction of household income and is denoted by θ.

At the start of their lives, married households draw a utility cost q that represents the cost of joint market work. Following Guner, Kaygusuz, and Ventura (2012), we assume that the initial utility cost depends on the husband’s education. The momentary utility function for a married household is then given by

u(c,lm,lf,q)=2log(c)φ(lm)χφ(lf)χq(I{1}(lf>0))

in which c is consumption, lf and lm are the time devoted to market work, φ is the parameter for the disutility of work, χ is the intertemporal elasticity of labor supply, and q is the utility cost incurred by the family when the female works (lf > 0).

Government

The government collects various taxes: value-added taxes τc and progressive labor income τi (·) and capital income taxes τk and uses tax collection to pay for government consumption, tax credits, transfers, and childcare subsidies. It also collects payroll taxes τss and pays social security benefits.

Income, Taxation, and Social Security

Income for tax purposes is defined as total labor and capital income, which is equal to

I=ra+w(lmhm(z,j)+lfhf(x,j)).

We assume that social security benefits are not taxed and that retired households’ income for tax purpose is just ra. The total tax income liability depends on the presence of children in the household and is represented by τi(I, k). These functions are continuous in I, increasing, and convex. Each household can also receive the EITC, which is a fully refunded tax credit that works as a wage subsidy for low-income households. We assume that the social security system balances its budget every period.

Retired households have access to social security benefits. We assume that social security benefits depend on agents’ education type; that is, more educated agents receive larger social security benefits. This allows us to capture in a parsimonious way the positive relationship between lifetime earnings and social security benefits. Households receive childcare subsidies to cover a share of childcare costs when their total income is below τd and the wife works.

Decision Problem

Households maximize the sum of the utilities of husband and wife. Consumption is a public good. Let s = (z,x,q) be the exogenous state for married couples. Couples maximize household utility by choosing consumption, labor supply, and saving according to the following:

V(a,h,s,j)=max{a,lf,lm}u(c,lm,lf,q)+βV(a,h,s,j+1)

subject to

(1+τc)c+a=(wlmhm+whflf+ra)(1τi(I)τssθ(j)k(s,j)(lf>0))+a(1+r(1τk))

in which lm, lf > 0 and I = w hmlm + w hflf + ra.

Equilibrium

The stationary equilibrium of this economy consists of a stationary distribution of types over assets and human capital space, policy functions, and value functions such that given prices and government policies, they satisfy households’ maximization problems, government budget constraints, distribution’s law of motion, and labor and capital market clearing conditions.

Calibration

The model is calibrated to match data from the US 2018 Current Population Survey. A large share of the parameters is calibrated jointly, in equilibrium, allowing the model to match the moments from US aggregated and disaggregated characteristics in 2018. The US tax code is calibrated using the Organisation for Economic Co-operation and Development tax base. Table A1 reports the results for the parameters calibrated endogenously, and Table A2 and Table A3 reports some exogenous parameterization values. Some of the parameters calibrated draw on Guner, Kaygusuz, and Ventura (2019) and Hannusch (2019) as their main source.

Table A1.

Parameters Calibrated Endogenously

article image
Source: Guner, Kaygusuz, and Ventura (2019).Note: FLFP = female labor force participation.
Table A2.

Parameters (Exogenously input)

article image
Source: Guner, Kaygusuz, and Ventura (2019).
Table A3.

Demographics

article image
Source: Guner, Kaygusuz, and Ventura (2019).Note: <HS (less than high school), HS (high school), SC (some college), C (college), COL + (post-college), Total gain (weighted average of gains by level of education).

B. Model for Low-Income Countries

A detailed description of the model is provided by Malta, Martinez, and Tavares (2019). Its main features are described below.

  • It is an overlapping generations model in which various families live in a small open economy for three periods and die at the end of the third period. Individuals initially differ from each other by generation, gender, endowment, and access to the saving market. Only individuals with higher initial endowments save and borrow. In the first period, a household comprises a husband and wife and two children. In periods two and three, the children have left to form their own households, and the original household comprises only the husband and the wife.

  • The husband and wife make decisions together. They determine the husband’s labor supply in the formal and/or informal sector and the woman’s labor force participation and, in the case of participation, how much time she will spend in the formal and informal sectors. There is no unemployment in the model; all individuals participating in the labor force are employed. They also decide how much to consume of each of the two types of goods in the economy (formal versus informal goods). Richer couples also decide how much to save and borrow.

  • Education for children and adolescents is provided by the government, and the amount of education is not equal across gender and initial endowments, reflecting heterogeneity in the data. Whenever women supply labor there is a utility cost incurred by the family. This cost relates to the difficulty in coordinating multiple household activities, such as home production, child and elderly care, and other unpaid work. For some countries, this cost can also be interpreted as social and cultural barriers to a woman working outside the home.

  • Production in the formal sector uses capital and labor, while the informal sector uses only labor. The formal sector in this economy is modeled as a representative firm that hires both male and female effective hours of labor and rents capital at rate r* from rich households or from abroad to produce formal goods. Besides being produced domestically, formal goods can be imported from abroad. Formal goods can be used as consumption goods, capital, or education.

  • The model also captures discrimination that women face in the workplace in both the formal and informal sectors. This discrimination constrains women’s ability to achieve their full salary, productivity, and career potential.

  • The government collects taxes on labor income, consumption, and firms’ profits and spends on education, formal goods, and cash transfers. The government has access to external financial markets and can finance its debt by borrowing at interest rate r* from abroad or from domestic households with access to the financial sector.

Calibration

The model is calibrated to match data from Senegal’s 2011 Household Survey and aggregate data from that same year. Almost half of the parameters are calibrated jointly, in equilibrium, so that the model matches the moments from Senegal’s aggregated and disaggregated characteristics in 2011. Table A4 reports the results for the parameters calibrated endogenously, and Table A5 reports some exogenous parameterization values.

Table A4.

Parameters Calibrated Endogenously

article image
Source: Female-to-male employment ratio, Gini coefficient (income), Share of formal labor force, Female-to-male per hour wage in the formal and in the informal sector are authors’ calculations using Senegal’s 2011 Household Survey. The remaining parameters’ sources are World Bank, IMF and Unesco.
Table A5.

Parameters (Exogenously input)

article image
Source: Authors’ calculations using Senegal’s 2011 Household Survey and Iberglobal.

C. Comparing the Models for Advanced Economies and for Low-Income Countries

Both advanced economy and low-income country models are overlapping generations macroeconomic general equilibrium models that capture gender inequalities in their micro-foundation. The main differences between the two frameworks are summarized as in Table A6.

  • The framework for low-income countries replicates households’ income distribution through an initial endowment shock, while the framework for advanced economies bases its distribution on different education levels.

  • The low-income country framework contains two sectors, producing one good each—the formal and the informal, while the advanced economy framework has only one good being produced in only one sector in the economy.

  • In the low-income country framework all men work; women may or may not work. In addition, all workers work full-time—as seen in the data (full-time work is defined as more than 30 hours a week). In the advanced economy framework, men’s and women’s labor supply decisions are made endogenously and are not imposed.

  • In both frameworks there is human capital accumulation, but only the advanced economy framework features human capital depreciation when a person temporarily stops working.

  • Both frameworks feature utility cost for families when a woman decides to work and different education levels for men and women. In the low-income country framework there is also gender discrimination in the labor market; in the advanced economy framework, families face the financial cost of childcare.

  • The low-income country model is calibrated to reflect lower education levels and higher inequality and poverty than the advanced economy model.

Table A6.

Main Differences between the Analytical Models for Low-Income Countries and Advanced Economies

article image
1

Research assistance was provided by Sibabrata Das, Angelica Martinez, and Carine Meyimdjui and production assistance by Natalia Romanova and Elisavet Zachou. The note draws on research produced under the project on macroeconomic research on low-income and developing countries (project id: 60925) supported by the UK Department for International Development (DFID). The views expressed herein are those of the authors and should not be attributed to the IMF, its Executive Board, or its management.

2

Our sample comprises 190 countries for which information on labor force participation is available in the World Bank World Development Indicators.

5

For instance, Stotsky and Zaman (2016) show that Indian states that adopted pro-female fiscal policies have made more progress on gender equality in primary school enrollment than those that have not adopted such policies.

6

A comprehensive assessment of all gender-responsive fiscal interventions is beyond the scope of this note.

7

This note focuses on pro-female fiscal policy measures; it does not cover the broader approach to gender budgeting, which includes budget institutions.

8

The analysis assumes only public education.

9

Average years of education of the workforce are lower than for the average low-income country.

10

“Unexplained” pay gap is the portion of the wage gap that cannot be explained by observed data, such as education differentials, location, type of work, years of experience, and so on. Unexplained wage gaps are associated with labor market discrimination. For a thorough analysis of Senegal’s gender gaps, see Malta, Martinez, and Tavares (2019).

11

In the analysis, the cost of childcare per child is reduced from 10 percent of family income to 5 percent. Currently, the United States offers a federal government program, the Child Care Development Fund (CCDF), for poor families. The exercise in this subsection envisages that women who already benefit from CCDF would be excluded from the extension of childcare subsidies. The cost of this intervention is estimated at 0.6 percent of GDP.

12

It should be noted that if the analysis were to assume further subsidization of childcare (for example, for families currently eligible for CCDF), the impact on poverty and inequality could be much larger.

13

While we consider only the extension of maternity leave (due to modeling constraints), gender-neutral parental leave might have even stronger benefits for women by leveling the playing field and reducing discrimination against mothers (IMF 2018a). However, there is evidence that an excessively long period of parental leave (in particular maternity leave) could be detrimental to female labor force participation because it leads to detachment from the labor force (IMF 2018a; Ruhm 1998).

14

In the United States, married women with less than a high school education have on average 2.8 children, while married women with a college degree or more have on average 1.6 children. In addition, poorer families face higher costs of childcare as a share of their total income. According to Herbst (2015), using data from the Survey of Income and Program Participation (SIPP), families in the top quartile of the income distribution spend on average 7.8 percent of their income on childcare, while families in the bottom quartile spend 17.4 percent.

15

According to the Internal Revenue Service, fewer than 3 percent of married couples file under separate status in the United States. This is likely because various credits and tax breaks are available only for joint filing (examples include earned income credits, credits for adoption-related expenses, student loan interest deductions, and interest income from qualified US savings bonds used for higher education). There are other nonnegligible costs associated with switching from one system to the other.

16

Different exercises have been performed using the same calibration (see Malta, Martinez, and Tavares 2019), which produced robust results. The model has also been extensively applied to different countries (see Box 2).

17

Based on survey data from 45 developing economies, the World Health Organization estimates that women are about three times more likely than men to fetch water (UN-WHO 2010). A similar pattern is also observed in Senegal.

18

The average years of education of the workforce in Senegal is calibrated at 3.8 years for men and 2.5 years for women. There is a 41 percentage point gap in years of education for working women at the bottom 50 percent of the income distribution compared with men, while among the top 50 percent of the distribution this gap drops to 30 percentage points.

19

Female labor force participation increases by 18 percentage points from its initial level of 39 percent, which was calibrated in the model based on household survey data. The share of the informal labor market is calibrated at 79 percent. The data indicate that women working in the informal sector face larger gender pay gaps (after controlling for other factors, such as education, experience, and location), suggesting that the larger the informal sector, the lower the economic incentives for women to join the labor force.

20

Using Gaspar and others (2019) costing methodology, we estimate the cost of this policy to be about 0.4 percent of GDP a year.

21

Household survey data show that women spend on average 1.9 hours a day fetching water (while men report spending on average 1.5 hours a day), and that poorer households tend to spend more time than richer households fetching water.

22

Using Gaspar and others (2019) costing methodology, the cost associated with this measure is estimated at 0.74 percent of GDP.

23

We assume an extension of the current cash transfer program in Senegal to all working women below the poverty line (38 percent of the population). Based on the current cash transfer values, the cost of the program is estimated at 1 percent of GDP.

24

Note that the model does not allow for unemployment and assumes that all women looking for a job would find one.

25

The model-based analysis captures only long-term effects. That said, because cash transfers would immediately increase the disposable income of poor women, the measure is expected to have an impact on poverty and inequality in the short run, too.

26

The Social Institutions and Gender Index (SIGI) measures gender discriminatory social institutions: formal and informal laws, social norms, and access to empowerment opportunities and resources (OECD 2019).

27

In which AW is the average income in the economy.

Women in the Labor Force: The Role of Fiscal Policies
Author: Anna Fruttero, Daniel Gurara, Ms. Lisa L Kolovich, Vivian Malta, Ms. Marina Mendes Tavares, Nino Tchelishvili, and Ms. Stefania Fabrizio