## 3. Changes in Households’ Per Capita Income, by Decile of Income Distribution

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### I. Introduction and research question
- Links recent improvements in Senegalese women’s education and employment and quantifies the impact of the rise in females’ years of education on female-to-male employment.
- Framework: a micro-founded overlapping generations (OLG) model analyzing consequences of education changes on labor outcomes, macro aggregates, and distributional variables.
- Model features: gender-differentiated life-cycle barriers (less education provision to women, home and family care costs, labor-market discrimination) and is suited to simulate fiscal and gender-equality policies (tax code changes, conditional cash transfers, government-funded education expenditure, female work regulation, childcare subsidies, family/social costs from female employment, gender-based anti-discrimination policies).
- Calibration: uses micro and macro data for Senegal (formal/informal sector sizes relative to GDP; labor force shares in formal/informal sectors; income distribution; effective tax rates; government education expenditure; distribution of education; female labor force participation relative to male; gender wage gaps in formal and informal sectors; returns to education and work experience; family consumption patterns).

### Main quantitative finding
- The increase in years of education of the working age population and the reduction of gender gaps in education between 2006 and 2011 can explain up to 44 percent of the growth in female-to-male employment ratio.
- The remaining 56 percent can potentially be explained by a reduction in gender discrimination in the labor market that would have meliorated females’ earnings and productivity by 4.7 percentage points.

### Economic mechanism and predicted aggregate impacts
- Mechanism (effects of higher education and lower discrimination):
  - raise women’s competitiveness and returns from working;
  - induce some women to enter the labor force;
  - induce shifts from informal to formal sector for some men and women;
  - generate general-equilibrium productivity and female income gains that positively affect male earnings.
- Predicted aggregate impacts (from simulations):
  - Education improvements contributed to both higher economic growth and lower income inequality, with households from lower income deciles gaining relatively more.
  - Reductions in discrimination predicted large effects on female employment and GDP but with more uneven distributional outcomes; could be slightly detrimental to some low-income families.

### Background on Senegal — key stylized facts and statistics
- Female-to-male employment ratio: increased by 14 percentage points between 2006 and 2011.
- Women’s share in total labor force participation: rose from 35 percent to 38 percent between 2006 and 2011.
- Primary education completion rates (UNESCO):
  - 2000: girls 33 percent, boys 43 percent;
  - 2016: girls 64 percent, boys 54 percent.
- Secondary completion (DHS 2012): average female completion rate 13 percent, male 21 percent.
- Education attainment increases (DHS 2005 vs 2011) for youth:
  - females 15–19 with some secondary education: from 18 percent to 35 percent;
  - males 15–19 with some secondary education: from 24 percent to 43 percent;
  - females 20–24 with some secondary education: from 12 percent to 19 percent;
  - males 20–24 with some secondary education: from 21 percent to 29 percent.
- Largest percentage improvements in education occurred in the bottom 60 percent of the income distribution.
- Government spending on education as share of GDP: from 3.2 percent in 2000 to 6.1 percent in 2011.
- Blinder-Oaxaca decomposition (2011 Household Survey, n = 37,969):
  - Prediction male (ln_hrwage): 5.2912 (Std. Err. 0.0010554; z 42.91; [95% Conf. Interval] 5.2893 5.2930)
  - Prediction female (ln_hrwage): 4.8225 (Std. Err. 0.0010469; z 95.40; [95% Conf. Interval] 4.8205 4.8245)
  - Difference: 0.4686 (Std. Err. 0.0014334; z 34.21; [95% Conf. Interval] 0.4659 0.4714)
  - Decomposition:
    - Explained: 0.1568 (Std. Err. 0.0010158; z 8.71; [95% Conf. Interval] 0.1548 0.1587)
    - Unexplained: 0.3118 (Std. Err. 0.0012270; z 70.96; [95% Conf. Interval] 0.3096 0.3141)
  - Percentage: Explained 0.3346; Unexplained 0.6654
  - Interpretation: total gender wage gap of 47 percent (from OLS estimation); about one third explained by observable characteristics; about two thirds unexplained.

### Legal and institutional constraints summarized
- Persisting gender-based discriminatory legal restrictions reported (examples in source): restrictions preventing non-pregnant, non-nursing women from performing the same job as men; no laws mandating equal remuneration for work of equal value; no laws censuring discrimination based on gender in hiring, promotions, or dismissal; discrimination in access to finance based on gender or marital status not prohibited by law; constitution does not formally recognize nor prohibit discrimination arising from customary laws; Family Code gives husbands decision-making power and inherits advantages to men.

### IV. Model structure — concise technical summary
- Model: overlapping generations (OLG) model; small open economy; three periods of life; agents heterogeneous by generation, gender, initial endowment ε, and access to savings market.
- Household composition:
  - Period 1: husband, wife, and two children.
  - Periods 2 and 3: husband and wife only.
- Financial market access: richer households can save/borrow at exogenous interest rate r*; poor are hand-to-mouth.
- Decisions: household jointly chooses labor supply (husband: formal/informal; wife: participation and formal/informal allocation), consumption of formal and informal goods, savings/borrowing (richer households).
- No unemployment: all participating individuals are employed.
- Utility specification (per period t):
  - u(c_t(ε), l_t^f(ε)) = ξ_f o log(c_t^fo(ε)) + ξ_inf log(c_t^inf(ε)) − ξ_l(ε) I(l_t^f > 0)
  - female labor supply l_t^f(ε) = l_t^{f,fo}(ε) + l_t^{f,inf}(ε)
- Human capital:
  - initial ε ~ lognormal(0, σ^2), passed deterministically.
  - period 1 human capital: h_1 = ε(e_i(ε))^{α_e}, i ∈ {f,m}
  - periods 2,3: h_{t,i} = (1 + g_{t,i}) h_{t−1,i} if l_{t−1,i} > 0; h_{t−1,i} if l_{t−1,i}=0
- Technologies:
  - Formal sector production: Y_fo = K^{α_fo} (L_{m,fo} + φ_fo L_{f,fo})^{1−α_fo}
  - Informal production (male): y_{t}^{m,inf} = [ l_{t}^{m,inf} h_{t}^{m} ]^{1−α_inf}
  - Informal production (female): y_{t}^{f,inf} = φ_inf [ l_{t}^{f,inf} h_{t}^{f} ]^{1−α_inf}
- Government and budget constraints summarized (education expenditure functional form preserved in model description).

### Sources of gender inequality captured
- Four sources:
  1. Utility cost ξ_l(ε) when wife works (coordination/home production/social/cultural barriers).
  2. Gender-differentiated government-provided education by ε and gender.
  3. Different returns to labor experience for men and women (g_{t,i} differentiation).
  4. Residual labor-market discrimination captured by φ_fo and φ_inf.
- φ_fo and φ_inf calibrated endogenously to match female-to-male earnings ratios in formal and informal sectors.

### V. Benchmark calibration — selected parameters and targets
- Model period: 18 years.
- Measure of households at each period: 1/3 (agents die at 72; savers stop working at 54).
- Number of children per percentile approximation:
  - n(ptile) = −0.0004 ptile^2 − 0.0028 ptile + 6.7072
  - Using approximation ptile = ε: n(ε) = −0.0004 ε^2 − 0.0028 ε + 6.7072
- Calibrated family disutility:
  - ξ_l(ε) = 0.0776 n(ε)
- Consumption goods weights:
  - ξ_inf = 45 percent
  - ξ_fo = 55 percent
- Discount factor:
  - β = 0.96 annually
- Equivalence scale calibration:
  - θ1 = 2
- Discrimination parameters (calibrated):
  - Formal sector female-to-male wage ratio = 0.74 → φ_fo = 0.92
  - Informal sector female-to-male wage ratio = 0.64 → φ_inf = 0.74
- Informal production curvature:
  - 1−α_inf = 0.65 (target: share of formal labor in total labor = 14 percent in data)
- Labor share in formal Cobb-Douglas:
  - 1−α_fo = 0.63
- Initial endowments:
  - 100 initial shocks discretizing log normal of ε.
  - Variance σ calibrated to match Gini (income) = 0.63 → σ = 1.22
  - Percentage of savers = 20
- Human capital formation:
  - α_e = 0.342
  - g2_f = 0.16
  - g2_m = 0.34
  - g3_f = 0.07
  - g3_m = 0.09
- Fiscal and interest parameters:
  - τ_c = 0.18
  - τ_v = 2.63%
  - ω = 0.0467
  - G = 0.085
  - r* = 6.84% per year
- Selected calibration results (model vs data where reported):
  - ξ_l(ε) functional form — Target: Female-to-male employment ratio = 0.60 (Model 0.60, Data 0.60)
  - σ = 1.22 — Target: Gini coefficient (income) = 0.63 (Model 0.63, Data 0.63)
  - 1−α_inf = 0.65 — Target: Share of formal labor force = 0.21 (Model) vs 0.14 (Data)
  - φ_fo = 0.921 — Target: Female-to-male per hour wage in the formal sector = 0.74 (Model 0.74, Data 0.74)
  - φ_inf = 0.743 — Target: Female-to-male per hour wage in the informal sector = 0.64 (Model 0.64, Data 0.64)
  - τ_v = 2.63% — Government Revenues on corporate taxes (as % of GDP) Target/Data 1.45
  - ω = 0.0467 — Government Expenditure on education as % of GDP: Target/Data 6.1
  - G = 0.085 — Government Expenditure on formal goods as % of GDP: Target/Data 5.2
  - r* = 6.84% per year — Size of formal sector (as % of GDP) Target/Data 55

### Experimental design — two experiments
1. Impact of observed improvement in years of education of the working age population on female labor force participation and other variables (GDP, inequality).
2. Hypothetical role of improvements in labor market discrimination parameters (φ_fo and φ_inf) to explain remaining female labor force participation growth; quantify required changes and analyze effects.
- Note: General equilibrium effects unfold over decades; baseline year set to 2011.

### A. Simulating the observed increase in years of education (2006 → 2011)
- Method:
  - Starting from 2011 baseline, reduce years of education to estimated 2006 levels by income level and gender.
  - Reduce government education spending from 6.1 percent of GDP (2011) to 5.1 percent of GDP (2006).
- Main simulated effects and exact quantitative outcomes:
  - Female-to-male labor force participation increases in the long run by 6.1 percentage points — representing 44 percent of the total percentage gains of 14 points observed in 2006–2011.
  - Women in deciles 1, 2, and 3 (lower skills), notably younger women, enter the labor force through the informal sector.
  - Women from 4th to 10th deciles shift time from informal to formal sector; biggest shifts in 5th and 6th deciles, increasing aggregate hours women work in the formal sector by 7.8 percent.
  - Male workers from 4th decile up (notably 6th to 8th deciles) also shift some time from informal to formal, increasing male formal hours by 2.1 percent.
  - Productivity (total product per worker) increases:
    - Formal sector: 0.8 percent
    - Informal sector: 1.3 percent
  - Price effects:
    - Informal goods price increases by 0.3 percent.
  - Labor earnings changes:
    - Women’s average labor earnings grow by 7.1 percent.
    - Men’s wages increase by 3.6 percent.
  - Gender pay gap shrinks by 2.2 percentage points.
  - Income distribution effects:
    - Income ratio between richest ten percent and poorest ten percent falls by 2.3 percent.
    - Income ratio between richest 50 percent and poorest 50 percent falls by 4.6 percent.
    - Gini index decreases by 1 percentage point.
  - Aggregate economy:
    - Increase in education has a positive impact on GDP (level and magnitude reported in source figures; specific percent change not provided in supplied excerpt).

### Marginal effects and calibration note on savers and lifecycle
- Savers stop working at 54 and start using only their savings to consume; all agents die at 72.
- Measure of households at each period = 1/3.
- Number of children approximation and family disutility functional form preserved in calibration.

### Simulating the reduction in discrimination in the labor market
- Setup:
  - Change φ_fo and φ_inf so that, together with the boost in education simulated above, the model can explain all of the observed rise in female employment from 2006 to 2011.
  - Assume both φ_fo and φ_inf improved by the same amount.
  - Necessary change in these parameters: 4.7 percentage points.
- Two exercises:
  - (i) Keep 2006 education levels and increase φ_fo and φ_inf by 4.7 percentage points to measure marginal impact of reducing discrimination.
  - (ii) Improve education levels (2006 → 2011) and increase φ_fo and φ_inf by 4.7 percentage points so the model explains the full observed boost in female employment.

### Marginal effects of reducing labor-market discrimination (exact outcomes)
- Distributional impacts:
  - More beneficial to deciles 2 and 6.
  - Marginally detrimental to the poor (deciles 1 and 3).
- Labor-force and sectoral changes:
  - Policy induces women in the 2nd decile to enter the labor force, particularly the informal sector.
  - Entrance of lower skilled labor reduces productivity in the informal sector by 2.1 percent.
  - Prices of informal goods fall by 1.2 percent.
  - Larger labor force participation raises aggregate consumption by 3.5 percent, inducing more production in the formal sector.
  - Men from the 6th to the 10th decile shift some work from informal to formal sector.
  - Mid-to-high skilled working women (6th to 10th deciles) shift some time to the formal sector.
  - Lower discrimination in the formal labor market boosts productivity in the formal sector by 1.9 percent.
- Earnings and wage effects:
  - Women’s average labor earnings rise by 6.4 percent.
  - Men’s wages decline by 0.1 percent.
  - Total female-to-male labor earnings ratio improves by 4.0 percentage points.
- Inequality measures:
  - Income ratio between richest 10 percent and poorest 10 percent rises by 3.1 percent.
  - Ratio between richest 50 percent and poorest 50 percent grows by 1.4 percent.
  - Gini index decreases marginally, by less than one percentage point.
- Aggregate output and fiscal effects:
  - Reduction in discrimination raises GDP by 4.0 percent.
  - Aggregate consumption increases by 3.5 percent.
  - Government revenue collection rises by 0.6 percent of GDP due to higher labor income taxes and consumption taxes.
- Cost considerations:
  - Cost of this policy to government coffers cannot be estimated here; could be low if driven by perception/legal changes (example: 2010 gender parity law).

### Combined simulation: anti-discrimination plus education policies
- Combined effects:
  - GDP growth of 10 percent from the combined package (noted as "a ted higher than the sum" in source).
  - Package explains all 14 points increase in female-to-male employment ratio observed between 2006 and 2011.
- Distributional outcomes:
  - Most positively affected deciles: 2nd and 6th.
  - Both Gini coefficient and top 50 versus bottom 50 income ratio improve.
  - Top 10 percent to bottom 10 percent per capita income ratio becomes larger because income gains in the 10th decile exceed gains in the 1st decile.
- Redistribution option:
  - Increased government revenues amount to 1.6 percent of GDP and could be used for redistribution (e.g., cash transfers) to compensate adverse effects on the poorest.

### Conclusions and policy implications (from the model)
- Education:
  - Increase in education levels and reduction in gender gaps in education during 2006–2011 could have added up to 6.1 percentage points to the female-to-male employment ratio (44 percent of the observed growth).
  - Higher education provision contributed to larger economic growth and lower income inequality.
- Discrimination:
  - A 4.7 percent reduction in the unexplained wage gap could boost female labor force participation by an additional 7.9 percentage points in the long run (56 percent of the 14 percentage point total gain).
  - Anti-discrimination policies have large effects on employment and GDP but can be slightly detrimental to some lower income families (deciles 1 and 3).
  - Fiscal gains from higher tax collections (1.6 percent of GDP under combined policy) can fund redistribution to the poor; policy costs could be low if achieved via legal/perception changes.
- Suggested further research using this framework:
  - Simulations of changes in taxes and transfers; improvements in health outcomes for women; reduction in fertility rates; ameliorations in infrastructure with differential benefits for women and men.

*Source: wpiea2019241-print-pdf — https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019241-print-pdf.pdf*

### References .............................................................................................................

### References ................................................................................................................................27

### Tables
- 1. Blinder-Oaxaca Decomposition .............................................................................................7
- 2. Calibration Results ...............................................................................................................18
- 3. Parameters ............................................................................................................................19

### Figures
- 1. Background on Senegal .........................................................................................................8
- 2. Results of the Education and Anti-Discriminatory Policies ................................................25

*Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019241-print-pdf.pdf*

### 3. Changes in Households’ Per Capita Income, by Decile of Income Distribution.................26

### 3. Changes in Households’ Per Capita Income, by Decile of Income Distribution

### I. Introduction and Research Question
- Paper links recent improvements in Senegalese women’s education and employment and quantifies the impact of the rise in females’ years of education on female-to-male employment.
- Framework: a micro-founded overlapping generations model that analyzes consequences of education changes on labor outcomes, macro aggregates, and distributional variables.
- Model features: gender-differentiated life-cycle barriers (less education provision to women, home and family care costs, labor-market discrimination) and is suited to simulate fiscal and gender-equality policies (tax code changes, conditional cash transfers, government-funded education expenditure, female work regulation, childcare subsidies, family/social costs from female employment, gender-based anti-discrimination policies).
- Calibration: uses micro and macro data for Senegal (formal/informal sector sizes relative to GDP; labor force shares in formal/informal sectors; income distribution; effective tax rates; government education expenditure; distribution of education; female labor force participation relative to male; gender wage gaps in formal and informal sectors; returns to education and work experience; family consumption patterns).

### Main quantitative finding
- The increase in years of education of the working age population and the reduction of gender gaps in education between 2006 and 2011 can explain up to 44 percent of the growth in female-to-male employment ratio.
- The remaining 56 percent can potentially be explained by a reduction in gender discrimination in the labor market that would have meliorated females’ earnings and productivity by 4.7 percentage points.

### Economic mechanism summarized
- Higher education levels (especially for women) and lower labor-market discrimination:
  - raise women’s competitiveness and returns from working;
  - induce some women to enter the labor force;
  - induce shifts from informal to formal sector for some men and women;
  - generate general-equilibrium productivity and female income gains that positively affect male earnings.
- Predicted aggregate impacts:
  - observed improvement in education contributed to both higher economic growth and lower income inequality, with households from lower income deciles gaining relatively more.
  - reductions in discrimination predicted large effects on female employment and GDP but with more uneven distributional outcomes; could be slightly detrimental to some low-income families.

### II. Related literature (concise pointers present in text)
- Theoretical and empirical antecedents include Mincer and Polachek (1974); Becker (1985); Eckstein and Lifshitz (2011) (education explained about 33 percent of US female employment increase, 1964–2007); Steinberg and Nakane (2012) (one standard deviation in education in OECD countries associated with a 3-percentage point increase in female labor force participation); Bowen and Finegan (1966) (one extra year of schooling associated with about three percentage points higher labor force participation for married women in US).
- Cross-country and policy-related findings noted: public education expenditure associated with smaller gender gaps in labor force participation (Jain-Chandra and others, 2018); government policies (parental leave, childcare subsidies, flexible work, cash transfers, infrastructure improvements, tax policy) affect female labor force participation (Jacobsen 1998; Kalb 2018; IMF 2016; IMF 2017a-e).

### III. Background on Senegal — stylized facts and statistics from surveys and administrative sources
- Female-to-male employment ratio: increased by 14 percentage points between 2006 and 2011 (Figure reference in source).
- Women’s share in total labor force participation: rose from 35 percent to 38 percent between 2006 and 2011.
- Primary education completion rates (UNESCO):
  - in 2000: girls 33 percent, boys 43 percent;
  - in 2016: girls 64 percent, boys 54 percent.
- Secondary completion (DHS 2012): average female completion rate 13 percent, male 21 percent.
- Education attainment increases (DHS 2005 vs 2011) for youth:
  - females 15–19 with some secondary education: from 18 percent to 35 percent;
  - males 15–19 with some secondary education: from 24 percent to 43 percent;
  - females 20–24 with some secondary education: from 12 percent to 19 percent;
  - males 20–24 with some secondary education: from 21 percent to 29 percent.
- Largest percentage improvements in education occurred in the bottom 60 percent of the income distribution (Figure reference).
- Government spending on education as share of GDP: from 3.2 percent in 2000 to 6.1 percent in 2011.
- PDEF program and USAID assistance noted as contributors to expanded access and quality improvements (school construction, teachers recruitment, middle school programs, latrines and clean water, textbooks, teacher training, data collection).
- Blinder-Oaxaca decomposition (using 2011 Household Survey micro data, number of observations = 37,969):
  - Prediction male (ln_hrwage): 5.2912 (Std. Err. 0.0010554; z 42.91; [95% Conf. Interval] 5.2893 5.2930)
  - Prediction female (ln_hrwage): 4.8225 (Std. Err. 0.0010469; z 95.40; [95% Conf. Interval] 4.8205 4.8245)
  - Difference: 0.4686 (Std. Err. 0.0014334; z 34.21; [95% Conf. Interval] 0.4659 0.4714)
  - Decomposition:
    - Explained: 0.1568 (Std. Err. 0.0010158; z 8.71; [95% Conf. Interval] 0.1548 0.1587)
    - Unexplained: 0.3118 (Std. Err. 0.0012270; z 70.96; [95% Conf. Interval] 0.3096 0.3141)
  - Percentage: Explained 0.3346; Unexplained 0.6654
  - Interpretation: total gender wage gap of 47 percent (from OLS estimation); about one third explained by observable characteristics; about two thirds unexplained (possible discrimination and unobserved factors).

### Legal and institutional constraints affecting women in Senegal (as reported)
- World Bank (2018) and source statements indicate:
  - gender-based discriminatory legal restrictions persist (e.g., prevent non-pregnant, non-nursing women from performing the same job as men — Figure reference).
  - no laws mandating equal remuneration for work of equal value nor laws censuring discrimination based on gender in hiring, promotions, or dismissal.
  - discrimination in access to finance based on gender or marital status is not prohibited by law.
  - constitution does not formally recognize nor prohibit discrimination arising from customary laws.
  - Family Code gives husbands decision-making power in the household and inherits advantages to men, reducing women’s asset ownership and legal protection.

### IV. Model structure (concise technical summary and key equations preserved)
- Model type: overlapping generations (OLG) model; small open economy; three periods of life; agents heterogeneous by generation, gender, initial endowment ε, and access to savings market.
- Household composition:
  - Period 1: husband, wife, and two children.
  - Periods 2 and 3: husband and wife only.
  - Each couple has two children; population constant.
- Financial market access:
  - richer households can save/borrow at exogenous interest rate r*; poor are hand-to-mouth.
- Decisions:
  - household jointly chooses labor supply (husband: formal/informal; wife: participation and formal/informal allocation), consumption of formal and informal goods, savings/borrowing (richer households).
  - no unemployment: all participating individuals are employed.
- Utility specification (per period t):
  - u(c_t(ε), l_t^f(ε)) = ξ_f o log(c_t^fo(ε)) + ξ_inf log(c_t^inf(ε)) − ξ_l(ε) I(l_t^f > 0)
  - female labor supply l_t^f(ε) = l_t^{f,fo}(ε) + l_t^{f,inf}(ε)
  - ξ_f o and ξ_inf: preferences over formal and informal goods; ξ_l(ε): utility cost parameter when wife participates.
- Human capital:
  - initial ε ~ lognormal(0, σ^2), passed deterministically.
  - period 1 human capital: h_1 = ε(e_i(ε))^{α_e}, i ∈ {f,m}
  - periods 2,3: h_{t,i} = (1 + g_{t,i}) h_{t−1,i} if l_{t−1,i} > 0; h_{t−1,i} if l_{t−1,i}=0
  - distinct returns to experience g_{t,i} for men and women.
- Technologies:
  - Formal sector production: Y_fo = K^{α_fo} (L_{m,fo} + φ_fo L_{f,fo})^{1−α_fo}, where φ_fo captures discrimination reducing female labor efficiency.
  - Informal production (male): y_{t}^{m,inf} = [ l_{t}^{m,inf} h_{t}^{m} ]^{1−α_inf}
  - Informal production (female): y_{t}^{f,inf} = φ_inf [ l_{t}^{f,inf} h_{t}^{f} ]^{1−α_inf}, where φ_inf captures discrimination in informal sector.
- Household budget constraints and government:
  - consumption tax τ_c on formal goods; effective labor income taxes τ_f (female) and τ_m (male); firm tax τ_v.
  - government expenditures: formal goods G_t, education E_t, transfers O_t; education spending E_t = μ ω ∫ (e_f(ε) + e_m(ε)) dε, with ω calibrated as expenditure per year of education.
  - government budget constraint: D_{t+1} = (1 + r*) D_t + E_t + G_t + O_t − R_t^c − R_t^w − R_t^v
  - current account zero condition: Y_fo − C_fo − δK − E − G = r* (D + K − S)
- Stationary equilibrium characterized by allocations for each household type, firms’ allocations, government policy vector, and prices {w_f, w_m, p_inf, r*}, satisfying household optimization, firm profit maximization, market clearing for informal goods, formal labor market clearing, government budget with debt stabilization, and current account condition.

### Sources of gender inequality captured in the model
- Four main sources:
  1. Utility cost ξ_l(ε) incurred when wife works (coordination/home production/social/cultural barriers).
  2. Gender-differentiated government-provided education by ε and gender.
  3. Different returns to labor experience for men and women (g_{t,i} differentiation).
  4. Residual labor-market discrimination captured by φ_fo and φ_inf in formal and informal production functions.
- φ_fo and φ_inf are calibrated endogenously to match female-to-male earnings ratios in formal and informal sectors and represent residual differences after accounting for education, experience, and household utility costs.
- The model labels labor-market discrimination as any differential treatment not based on endowments (skills, education, experience).

### V. Benchmark calibration and data
- Calibration uses Senegal’s 2011 Household Survey and aggregate data from 2011 (earlier surveys lacked individual earnings information).
- Almost half of parameters calibrated jointly in equilibrium to match Senegalese aggregated and disaggregated moments in 2011.
- Model period equals 18 years; hand-to-mouth agents work from ages 18 to 72 and die at end of life (calibration section continues beyond excerpt).

*Source: wpiea2019241-print-pdf - 3. Changes in Households’ Per Capita Income, by Decile of Income Distribution.................26*

### 72. Savers stop working at 54 and start using only their savings to consume. Because all agents

### wpiea2019241-print-pdf - 72. Savers stop working at 54 and start using only their savings to consume. Because all agents

### Preferences
- Measure of households (휇) at each period is equal to 1/3 because all agents die at 72 and savers stop working at 54.
- Family disutility when women enter the labor market: endogenously calibrated 휉_l(휀) to match aggregate female-to-male employment ratio and heterogeneity of time women spend in home production across income distribution.
- Number of children per percentile of income distribution n(ptile) approximated by quadratic:
  - n(ptile) = −0.0004 ptile^2 − 0.0028 ptile + 6.7072
- Using approximation ptile = 휀:
  - n(휀) = −0.0004 휀^2 − 0.0028 휀 + 6.7072
- Calibrated family disutility:
  - 휉_l(휀) = 0.0776 n(휀)
- Weights of consumption goods in utility:
  - 휉_inf = 45 percent
  - 휉_fo = 55 percent
- Discount factor:
  - 훽 = 0.96 annually
- Equivalence scale calibration:
  - 휃1 = 2 using OECD’s modified equivalence scale for increase in household consumption when 5 children are added (5 is average number of children in Senegalese households)
- Parameters 휃 and 휉_l(휀) correct for model implication of only two children per married couple.

### Production
- Discrimination parameters calibrated to match female-to-male wage ratios (net of taxes):
  - Formal sector female-to-male wage ratio = 0.74 → calibrated 휙_fo = 0.92
  - Informal sector female-to-male wage ratio = 0.64 → calibrated 휙_inf = 0.74
- Definition in survey: formal worker = paid worker with formal contract and/or affiliation to social security; informal used interchangeably with informal sector here.
- Curvature of informal production function with respect to labor (1−훼_inf) calibrated to match share of formal labor in total labor = 14 percent → 1−훼_inf = 0.65.
- Labor share in Cobb-Douglas production function used:
  - 1−훼_fo = 0.63

### Initial Endowments
- 100 initial shocks/endowments discretizing log normal distribution of 휀.
- Variance of shock calibrated to match Senegal’s Gini coefficient of income inequality:
  - Gini (income) = 0.63 (calculated from household survey micro-data) → σ = 1.22
- Measure of agents with access to savings:
  - Percentage of savers = 20 (households with 20 percent largest endowment shocks are savers; bottom 80 percent are hand-to-mouth)
  - Justification: World Bank reports 15 percent of Senegalese above 15 had bank accounts; model considers agents above 18 hence upward approximation.

### Human Capital Formation Function
- Curvature parameter 훼_e calibrated to 0.34 by regressing log education on log hourly wages of formal workers controlling for individual characteristics.
- Human capital growth parameters (exogenously calibrated by estimating contribution of 18 years of experience in two phases for men and women):
  - g2_f = 0.16
  - g2_m = 0.34
  - g3_f = 0.07
  - g3_m = 0.09
- Note: for informal workers, earnings are elevated to the power of 훼_e 훼_inf where 훼_inf is endogenously calibrated.

### Calibration Results (selected parameters and targeted statistics)
- 휉_l(휀) = 0.077∗(−0.0004 ptile^2 − 0.0028 ptile + 6.7072) — Target: Female-to-male employment ratio = 0.60 (Model 0.60, Data 0.60)
- σ = 1.22 — Target: Gini coefficient (income) = 0.63 (Model 0.63, Data 0.63)
- 1−훼_inf = 0.65 — Target: Share of formal labor force = 0.21 (Model) vs 0.14 (Data)
- 휙_fo = 0.921 — Target: Female-to-male per hour wage in the formal sector = 0.74 (Model 0.74, Data 0.74)
- 휙_inf = 0.743 — Target: Female-to-male per hour wage in the informal sector = 0.64 (Model 0.64, Data 0.64)
- 휏_v = 2.63% — Government Revenues on corporate taxes (as % of GDP) Target/Data 1.45
- 휔 = 0.0467 — Government Expenditure on education as % of GDP: Target/Data 6.1
- G = 0.085 — Government Expenditure on formal goods as % of GDP: Target/Data 5.2
- r* = 6.84% per year — Size of formal sector (as % of GDP) Target/Data 55

Additional parameters (Table 3):
- 휉_inf = 0.45
- 휉_fo = 0.55
- β = 0.96
- Percentage of savers = 20
- 훼_e = 0.342
- 훼_fo = 0.37
- g2_f = 0.16
- g2_m = 0.34
- g3_f = 0.07
- g3_m = 0.09
- 휏_c = 0.18

### Fiscal Policy and International Interest Rate
- Effective income tax rates: calculated by applying 2011 tax rules on average income from work in each percentile of income distribution.
  - Bottom 42 percent of income distribution did not pay taxes in the formal sector.
  - For percentiles 43rd to 100th, smoothed effective income tax rates range from 0.01 to 0.31.
- Consumption tax:
  - 휏_c = 18 percent (statutory rate)
- Companies’ revenue tax calibrated:
  - 휏_v calibrated to match corporate tax revenue = 1.45 percent of GDP → resulting in 2.6 percent hypothetical effective tax rate on revenues.
- Government spending on formal goods:
  - G = 5.2 percent of GDP (national accounts)
- Government spending on education parameter:
  - 휔 calibrated to match total education spending = 6.1 percent of GDP (national accounts)
- International real interest rate calibrated to match relative size of formal sector (55 percent of GDP):
  - r* = 6.8 percent per year

### Results — Experimental Design
- Two experiments to quantify importance of women’s schooling and working conditions on increase in female labor force participation and employment in Senegal from 2006 to 2011:
  1. Impact of observed improvement in years of education of the working age population on female labor force participation and other variables (GDP, inequality).
  2. Hypothetical role of improvements in labor market discrimination parameters (휙_fo and 휙_inf) to explain remaining female labor force participation growth; quantify required changes and analyze effects.
- Note: General equilibrium effects unfold over decades; presented results provide upper bounds of the role of education and labor market discrimination. Baseline year set to 2011.

### A. Simulating the Observed Increase in Years of Education of the Labor Force
- Method:
  - Starting from 2011 baseline, reduce years of education to estimated 2006 levels by income level and gender.
  - Reduce government education spending from 6.1 percent of GDP (2011) to 5.1 percent of GDP (2006).
  - Analyze impacts on labor market outcomes by income decile and gender, productivity, inequality, and growth.
- Main simulated effects:
  - Education increases reduce gender gaps in years of education; human capital and wages of all workers increase; competitiveness and incentives for some women to join labor force increase.
  - Household per capita income increases for all deciles of income distribution.
  - Women in 1st, 2nd, and 3rd deciles (lower skills), notably younger women, enter the labor force through the informal sector.
  - Female-to-male labor force participation increases in the long run by 6.1 percentage points (Figure 2a) — representing 44 percent of the total percentage gains of 14 points observed in 2006–2011.
  - Women from 4th to 10th deciles shift time from informal to formal sector; biggest shifts in 5th and 6th deciles, increasing aggregate hours women work in the formal sector by 7.8 percent.
  - Male workers from 4th decile up (notably 6th to 8th deciles) also shift some time from informal to formal, increasing male formal hours by 2.1 percent.
  - Productivity (total product per worker) increases:
    - Formal sector: 0.8 percent (Figure 2d)
    - Informal sector: 1.3 percent (Figure 2d)
  - Price effects:
    - Informal goods price increases by 0.3 percent.
  - Labor earnings changes:
    - Women’s average labor earnings grow by 7.1 percent.
    - Men’s wages increase by 3.6 percent (Figure 2b).
  - Gender pay gap shrinks by 2.2 percentage points (Figure 2c).
  - Income distribution effects:
    - Income ratio between richest ten percent and poorest ten percent falls by 2.3 percent.
    - Income ratio between richest 50 percent and poorest 50 percent falls by 4.6 percent.
    - Gini index decreases by 1 percentage point.
    - Explanation: Gini reduction limited because absolute income increases in top deciles remain large in absolute terms despite smaller percentage changes.
- Aggregate economy:
  - Increase in education has a positive impact on GDP (level and magnitude reported in Figure 2; specific GDP percent change not provided in supplied excerpt).

*Source: wpiea2019241-print-pdf (chapter/section content supplied above).*

### 5.7 percent. The effect is due to gains in production (increase in labor force participation) and

### Simulating the Reduction in Discrimination in the Labor Market

### Context and simulation setup
- Change gender discrimination parameters 휙푓표 and 휙푖푛푓 so that, together with the boost in education simulated in A, the model can explain all of the observed rise in female employment from 2006 to 2011.
- Assume both 휙푓표 and 휙푖푛푓 improved by the same amount.
- Necessary change in these parameters: 4.7 percentage points.
- Two exercises presented:
  - (i) Keep 2006 education levels and increase 휙푓표 and 휙푖푛푓 by 4.7 percentage points to measure the marginal impact of reducing discrimination.
  - (ii) Improve education levels (2006 → 2011) and increase 휙푓표 and 휙푖푛푓 by 4.7 percentage points so the model explains the full observed boost in female employment from 2006 to 2011.

### Marginal effects of reducing labor-market discrimination
- Distributional impacts:
  - More beneficial to deciles 2 and 6 of the income distribution.
  - Marginally detrimental to the poor (deciles 1 and 3).
- Labor-force and sectoral changes:
  - Policy induces women in the 2nd decile to enter the labor force, particularly the informal sector.
  - Entrance of lower skilled labor reduces productivity in the informal sector by 2.1 percent.
  - Prices of informal goods fall by 1.2 percent.
  - Larger labor force participation raises aggregate consumption by 3.5 percent, inducing more production in the formal sector.
  - Men from the 6th to the 10th decile shift some work from informal to formal sector.
  - Mid-to-high skilled working women (6th to 10th deciles) shift some time to the formal sector.
  - Lower discrimination in the formal labor market boosts productivity in the formal sector by 1.9 percent.
- Earnings and wage effects:
  - Women’s average labor earnings rise by 6.4 percent.
  - Men’s wages decline by 0.1 percent.
  - Total female-to-male labor earnings ratio improves by 4.0 percentage points.
- Inequality measures:
  - Income ratio between richest 10 percent and poorest 10 percent rises by 3.1 percent.
  - Ratio between richest 50 percent and poorest 50 percent grows by 1.4 percent.
  - Gini index decreases marginally, by less than one percentage point, driven by higher gains for the middle class (notably deciles 5 and 6) and the second decile.
- Aggregate output and fiscal effects:
  - Reduction in discrimination raises GDP by 4.0 percent.
  - Aggregate consumption increases by 3.5 percent (see above).
  - Government revenue collection rises by 0.6 percent of GDP due to higher labor income taxes and consumption taxes.
  - Cost of this policy to government coffers cannot be estimated here; cost could be low if driven by changes in perceptions or legal framework (e.g., the 2010 gender parity law).

### Combined simulation: anti-discrimination plus education policies
- Combined effects:
  - GDP growth of 10 percent from the combined package — noted as "a ted higher than the sum" of separate policies in the source.
  - Package explains all 14 points increase in female-to-male employment ratio observed between 2006 and 2011.
- Distributional outcomes:
  - Most positively affected deciles: 2nd and 6th.
  - Both Gini coefficient and top 50 versus bottom 50 income ratio improve.
  - Top 10 percent to bottom 10 percent per capita income ratio becomes larger because income gains in the 10th decile exceed gains in the 1st decile.
- Policy offset and redistribution:
  - Increased government revenues amount to 1.6 percent of GDP and could be used for redistribution (e.g., cash transfers) to compensate adverse effects on the poorest.

### Conclusions and policy implications (from the model)
- Model: micro-founded overlapping generations framework capturing life-cycle gender barriers (early education, childbearing costs, labor-market discrimination).
- Education findings:
  - Increase in education levels and reduction in gender gaps in education during 2006–2011 could have added up to 6.1 percentage points to the female-to-male employment ratio (44 percent of the observed growth).
  - Higher education provision contributed to larger economic growth and lower income inequality.
- Discrimination findings:
  - A 4.7 percent reduction in the unexplained wage gap could boost female labor force participation by an additional 7.9 percentage points in the long run (56 percent of the 14 percentage point total gain).
  - Anti-discrimination policies have large effects on employment and GDP but can be slightly detrimental to some lower income families (deciles 1 and 3).
  - Costs of anti-discrimination policy could be relatively low if achieved through legal or perception changes; fiscal gains from higher tax collections can fund redistribution to the poor.
- Suggested further research using this framework:
  - Simulations of: changes in taxes and transfers; improvements in health outcomes for women; reduction in fertility rates; ameliorations in infrastructure with differential benefits for women and men.

*Source: wpiea2019241-print-pdf (excerpt).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019241-print-pdf.pdf_