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### Introduction — gender inequality and informality in India
- Female labor force participation rate is 27 percent in 2011-12; male labor participation is 84 percent; female participation fell from 34 percent in 1999-00 to 27 percent in 2011-12.
- More than 80 percent of the workforce is employed informally in India; among those in the formal sector females constitute only 19-20 percent.
- Women receive lower wages, are overrepresented in informal and unpaid domestic work; routine housework and care make up the greatest proportion of unpaid care work.
- Rising female education has not halted the decline in female labor participation; lack of decent formal jobs and labor market rigidities (modeled as hiring costs) drive high informality.
- Labor supply and demand gender constraints modeled:
  - Demand-side: lower female skill (World Bank (2013a)); lower bargaining power (ILO (2011)); firm-based gender bias against females in formal employment (ILO (2012), Campbell and Ahmed (2012), OECD (2008)).
  - Supply-side (utility): lower preference for working outside home (safety/mobility concerns) (World Bank (2011)); higher preference for home-production relative to leisure (social norms, lack of public provisions, Duflo (2012)).
- Policy experiments: increase in female education; stronger enforcement against gender discrimination; increase in public provisions and improvements in female safety and mobility; increasing formal-sector labor market flexibility (lowering labor regulations).
- Key general finding: Gender-targeted policies boost female labor force participation and lead to gains in GDP in the long run, but labor market rigidities limit formal job creation.

### The Model — structure, labor markets, and gender mechanisms
- Economy: small open economy DSGE with households (male m and female f), wholesale producers, retailers, capital producers, and government; two goods: market-good and home-good (H0).
- Market-good composition and aggregators: C_t = [α^{1/η} C_{D,t}^{(η−1)/η} + (1−α)^{1/η} C_{f∗,t}^{(η−1)/η}]^{η/(η−1)}; C_{D,t} = [w^{1/μ} C_{F,t}^{(μ−1)/μ} + (1−w)^{1/μ} C_{I,t}^{(μ−1)/μ}]^{μ/(μ−1)}.
- Labor market: participation P_{m,t} = p_m − NP_{m,t}, P_{f,t} = p_f − NP_{f,t}; unemployment U^h_t = p_h − NP_{h,t} − L^F_{h,t} − L^I_{h,t} (Eqs. 3.1–3.2).
- Employment dynamics and hiring probabilities:
  - L^h_{s,t} evolution with firing probability σ_s and hiring probability p(H^h_{s,t}) = H^h_{s,t} / S_{h,t} (Eqs. 3.3–3.4, 3.13).
  - Job searcher pools S_{h,t} defined in Eqs. 3.7–3.8; search probability p(S_{h,t}) defined in Eqs. 3.14–3.15.
- Wholesale production (Cobb-Douglas): Y^W_{s,t} = θ_{s,t} (K_{s,t−1})^{ψ_s} (L_{s,t})^{1−ψ_s} (Eqs. 3.16–3.17).
- Labor aggregation across genders: L_{s,t} = [ω_{s,t} (skill^m_s L^m_{s,t})^{p_s} + (1−ω_{s,t}) (skill^f_s L^f_{s,t})^{p_s}]^{1/p_s} (Eqs. 3.18–3.19).
- Hiring costs: HC^h_{s,t} = (β_{HC_s,t}) (p(H^h_{s,t}))^{α_{HC_s}} with β_{HC_s,t}, α_{HC_s} > 0 (Eqs. 3.22–3.23).
- Wage bargaining: generalized Nash bargaining with worker bargaining power λ^h_s ∈ (0,1); wage relation V^h_{s,t} − V^h_{U,t} = [λ^h_{s,t} / (1−λ^h_{s,t})] (1−τ_s) J^h_{s,t} and J^h_{s,t} = HC^h_{s,t} (Eq. 3.34).
- Average wages and gender wage gap: W^m_t and W^f_t defined as weighted averages across sectors; Gender wage gap = W^m_t / W^f_t.
- Households: aggregate utility Λ_t = E_t ∑ β^t [ (BP_t)(p_m) Λ^m_t + (1−BP_t)(p_f) Λ^f_t ], BP_t intra-household bargaining weight increasing with male-to-female wage income ratio (Eq. 3.42).
- Home-good production: H^0_t = θ_{H,t} { [ (1−BP_t)(HP^m_t + τ_U U^m_t)^{p_H} + BP_t (HP^f_t + τ_U U^f_t)^{p_H} ]^{1/p_H} }^{1−α_H} (Eq. 3.45).
- Labor supply first-order conditions (examples):
  - MRS^h_{HP,t,C_t} = (1−τ_F) W^h_{F,t} p(H^h_{F,t}) + W^h_{I,t} p(H^h_{I,t}) + W_{U,t} [1 − p(H^h_{F,t}) − p(H^h_{I,t})] (Eq. 3.57).
- Capital accumulation and Tobin’s Q:
  - K_t = (1−δ_K) K_{t−1} + (P^{Inv}_t / P_t) I_t − κ/2 ( ... ) (Eq. 3.59).
  - Q_t [1 − κ ( (P^{Inv}_t / P_t) I_t / K_{t−1} − δ_K )] = 1 (Eq. 3.62).
- Rest of the world and external premium: (1 + i^f_t) = (1 + i^*_t) − χ ( B^*_t − B^*_P_F(RER) P Q^x ) (Eq. 3.64).
- Government policy: Taylor-type rule i_t / i = (i_{t−1} / i)^{α_i} (π_t / π)^{α_π} (Y_t / Y)^{α_Y} ε_{i,t} (Eq. 3.65); fiscal rule balances investment-price-weighted G_t and unemployment benefits with formal wage tax revenue (Eq. 3.66).
- Shocks: fourteen exogenous shocks (thirteen domestic, two foreign); domestic gender-specific shocks include ω_{F,t}, θ_{H,t}, skill^f_{F,t}, skill^f_{I,t}, φ^f_t, φ^f_{le,t}; most shocks follow AR(1) in logs (Eq. 3.71).

### Estimation methodology — data, calibration, and Bayesian estimation
- Data: GDP, private consumption, investment, government consumption, exports, imports, real exchange rate, wholesale price inflation (WPI), nominal interest rate (3-month T-bill); sample 1996Q1 to 2012Q1 (65 observations).
- Pre-processing: series converted to real per capita, HP-filter detrended (percent deviation from steady state), seasonal effects removed with X12 arima filter (except REER and nominal interest rate); data source CEIC.
- Calibration (Baseline India) — selected calibrated values:
  - β = 0.994; δK = 0.025 (quarterly; annual rate 10 percent); α = 0.8; η = 1.2; π = 4.5 (gross inflation steady state, % annually); π* = 2.5 (% annually); (PInv/P G / Y) = 0.11; WU/Y = 0.014; (PFPQx/Y) = 0.19; (Pf*PQm/Y) = 0.21; μ = 1.5; w = 0.39; η^*_x = 4.5; ψF = 0.34; ψI = 0.34; εF/(εF−1) = 1.2; εI/(εI−1) = 1.09; θF/θI = 1.5; HCmF/WmF, HCfF/WfF, HCmF/WmF = 3; HCmI/WmI, HCfI/WfI = 0.5; σF = 0.1; σI = 0.75.
- Matching informality and gender statistics via calibration:
  - εF = 6 and εI = 12; θI = 1, θF = 1.5; formal hiring cost ratio calibrated at 3; informal hiring cost ratio at 0.5.
  - Exogenous firing probabilities σF = 0.1 and σI = 0.75 yield Informal employment share LI/(LF+LI) = 68 percent and Unemployment rate UP = 17 percent.
- Gender-specific calibration:
  - 1/(1−ρF) = 2.5; 1/(1−ρI) = 5.
  - Frisch elasticities: 1/vm le = 1.2; 1/vf le = 3.61.
  - skillmF/skillfF ; skillmI/skillfI = 1.7.
  - Bargaining powers: λmF = 0.67; λmI = 0.27; λfF = 0.46; λfI = 0.02.
  - World Economic Forum (2010) benchmark: Wm/Wf = 1.62 implied; calibration pins Wm/Wf at 1.7.
  - Female informal employment LfI/(LfF+LfI) = 0.86; Male informal employment LmI/(LmF+LmI) = 0.74.
  - Firm gender preference: ωF = 0.62; ωI = 0.5.
  - Resulting formality shares: Male formality LmF/(LmF+LmI) = 32 percent; Female formality LfF/(LfF+LfI) = 26 percent.
  - Household utility weights: φm le = 0.7; φf le = 0.5; φm = 0.7; φf = 1.
  - Female-to-male home-work HPf/HPm = 1.65.
  - Female labor force participation calibration target Pf pf = 39.9 percent; calibrated Pf pf = 39.6.
  - Male labor force participation target Pm pm = 84.8 percent; calibrated Pm pm = 81.3.
- Bayesian estimation in Dynare: priors chosen (diffuse due to scarce India-specific evidence); posterior means reported; robustness checks conducted.

### Estimation results — selected posterior means and robustness
- Price adjustment/posterior means:
  - φadj I = 24.15; φadj F = 64.54; φadj f* = 42.44 — formal sector more price-sticky than informal; import-price rigidity between.
- Monetary policy posterior means:
  - α_π = 3.2; α_Y = 0.32; α_i = 0.86.
- Shock persistence: most ρ_z in range 0.58 to 0.97; sd(ε_z) posterior means generally higher than priors, reflecting higher volatility.
- Appendix A selected posterior table (examples):
  - Habit h_C Posterior Mean 0.3993 95% CB [0.3406, 0.4523]
  - κ Posterior Mean 6.3579 [5.0900, 7.3700]
  - χ Posterior Mean 0.0009 [0.0007, 0.0010]
  - ρ_{θF} Posterior Mean 0.9718 [0.9579, 0.9883]
  - sd(ε_{θF}) Posterior Mean 0.1271 [0.1061, 0.1495]
- Robustness: alternative less-informative priors produce qualitatively similar core conclusions though some quantitative differences occur (examples provided in Appendix A).

### Policy results — gender-specific reforms, labor deregulation, and combinations
- Gender-specific policies overview: permanent shocks to relevant variables; impacts reported as percent deviations from steady state (SR = first 20 quarters; LR = 100 quarters).

- Female labor supply reforms
  - Increase in public provisions (including childcare):
    - Numerical examples from model (Table 5):
      - SR: Output Y = 1; Formality L_F/(L_F+L_I) = -0.3; Unemp. U/P = 1; Female LFP P_f/p_f = 2; Female Formal = -0.5; Wage gap W_m/W_f = 1.04.
      - LR: Y = 1.45; Formality = -0.1; Unemp. = 1; Female LFP = 1.5; Female Formal = -0.1; Wage gap = 0.7.
    - Mechanism: lowers home-work burden (θH up) and targets childcare (falls in 1/φfle) raising female participation by example of 1.5 percent → GDP +1.4 percent, unemployment +1 percent, informality +0.1 percent; most new female entrants go to informal jobs or remain unemployed, widening gender gaps in wages/formality; HPf/HPm falls.
  - Increase in female safety and mobility:
    - Numerical example: improvement that increases female participation by 1.5 percent → GDP +1.15 percent, unemployment +0.5 percent, informality +0.2 percent.
    - Mechanism: fall in φf (example induced by 10 percent fall in φf); Pf rises, female wages fall in both sectors, male participation rises, aggregate unemployment and informality rise; HPf/HPm increases.

- Female labor demand reforms
  - Increase in female education:
    - Numerical example (5 percent increase in skillfF and skillfI inducing Pf +1.5 percent): LR GDP +1.25 percent, unemployment −1.75 percent, labor formality +0.9 percent.
    - Table 5 entries:
      - SR: Y = 0.8; Formality = 0.1; Unemp. = -1.3; Female LFP = 2.4; Female Formal = -1.1; Wage gap = 0.5.
      - LR: Y = 0.7; Formality = 0.15; Unemp. = -1.4; Female LFP = 1.5; Female Formal = 0.25; Wage gap = -0.4.
    - Mechanism: higher female productivity raises formal hiring of females in long run; short run female formality can fall and gender wage gaps widen due to slow reallocation.
  - Stronger enforcement against firm-based gender discrimination (fall in ωF):
    - Table 5 entries:
      - SR: Y = -5.7; Formality = -2; Unemp. = -1.5; Female LFP = 3.1; Female Formal = 6; Wage gap = -34.
      - LR: Y = -8.3; Formality = -1.5; Unemp. = -1.3; Female LFP = 1.5; Female Formal = 17.5; Wage gap = -39.5.
    - Mechanism: fall in ωF raises female formality but can reduce formal-sector productivity and GDP unless accompanied by higher female education; result hinges on homogeneous-worker assumption.

- Labor market deregulation (lowering formal hiring costs and male bargaining power)
  - Numerical example (model reference): lowering formal regulations to decrease informality by 1.5 percent would increase GDP by 2 percent and lower unemployment by 1.5 percent in the long run, but female participation Pf falls by 0.5 percent.
  - Table 5 entries:
    - SR: Y = -0.45; Formality = 0.4; Unemp. = 0.3; Female LFP = 0.2; Female Formal = 0.5; Wage gap = -3.
    - LR: Y = 2; Formality = 1.5; Unemp. = -1.4; Female LFP = -0.5; Female Formal = 2.2; Wage gap = -3.5.
  - Mechanism: deregulation raises formal hiring and GDP but household income effects and unchanged female constraints can lower Pf; males tend to gain more.

- Reform interactions — combined policies (Table 6 highlights combinations; impacts are percent deviations)
  - Increase in female safety & education:
    - SR: Y = 1.5; Formality = -0.2; Unemp. = 0.2; Female LFP = 4.5; Female Formal = -1.5; Wage gap = 1.5.
    - LR: Y = 2; Formality = -0.1; Unemp. = -1; Female LFP = 3.5; Female Formal = 0.2; Wage gap = 0.2.
    - Finding: combination offsets adverse outcomes of safety/mobility alone and yields larger GDP gains; complements supply and demand improvements for female access to formal jobs.
  - Increase in female safety & public provisions:
    - SR: Y = 1; Formality = -0.4; Unemp. = 2; Female LFP = 3; Female Formal = -0.7; Wage gap = 1.6.
    - LR: Y = 2.1; Formality = -0.1; Unemp. = 0.8; Female LFP = 2.5; Female Formal = -0.15; Wage gap = 1.07.
    - Finding: both are supply-side lifts that can raise Pf substantially but risk larger informality and unemployment absent formal-job creation.
  - Increase in female safety & labor deregulation:
    - SR: Y = 2.2; Formality = 0.2; Unemp. = 1.5; Female LFP = 2.2; Female Formal = 0.1; Wage gap = -2.
    - LR: Y = 3.5; Formality = 1.7; Unemp. = -0.1; Female LFP = 1; Female Formal = 2.2; Wage gap = -3.
    - Finding: combining supply-side improvements with deregulation improves Pf, formality, and GDP, and can overturn Pf declines from deregulation alone.

- Policy implication and recommendation:
  - Standalone gender-targeted supply policies raise Pf and GDP but often increase informality and unemployment due to formal-sector rigidities; they can worsen gender gaps in wages and informal employment.
  - The exception is female education, which raises female efficiency and formal employment in the long run but may widen short-run gaps.
  - Complementary packages that combine lowering female supply constraints with (i) boosting formal job creation (lowering formal-sector labor market rigidities) and (ii) improving female access to formal jobs (education, anti-discrimination) yield the best outcomes for gender equality and aggregate gains.

### Conclusion — synthesis of results
- The DSGE framework integrating gender frictions and labor market rigidities shows:
  - Gender-targeted policies increase female labor force participation and GDP, but limited formal job creation constrains benefits and raises informality and unemployment.
  - Labor market deregulation expands formal employment and GDP, but male workers tend to benefit more unless female supply and demand constraints are simultaneously addressed.
  - Combined reforms that lower female participation constraints and expand access to formal jobs produce the largest gains in GDP, employment, formality, and gender equality.
- The model and estimates provide a starting point for policy design that emphasizes complementarities between gender-targeted interventions and reforms that facilitate formal job creation and female access to formal employment.

*Source: _wp1616*

### 1. Introduction

### 1. Introduction

### Gender inequality in India: scope and stylized facts
- Female labor force participation rate is the third lowest in the South Asian region at 27 percent in 2011-12; and less than one-third of male labor participation of 84 percent.
- Female labor participation fell from 34 percent in 1999-00 to 27 percent in 2011-12, in both rural and urban areas.
- More than 80 percent of the workforce is employed informally in India.
- Among those employed in the formal sector, females constitute only 19-20 percent.
- Women receive lower wages, are overrepresented in informal and unpaid domestic work, with gender gaps along several other dimensions including education, access to productive inputs, and bargaining power at home.
- Routine housework (cooking, cleaning, home maintenance etc.) and care for household members makes up the greatest proportion of India’s unpaid care work (OECD Gender Data Portal, as cited).

### Labor market informality and female participation
- Rising education levels amongst women have not halted the decline in female labor participation.
- Lack of decent quality jobs in the formal economy discourages female participation.
- Labor market rigidities (modeled as hiring costs) are identified as main drivers of high informality; informality results from significantly higher rigidities in the formal sector.
- Wages are determined through Nash bargaining between workers and firms; intra-household bargaining power is related to relative female-to-male earnings and captures feedback from female employment and wages on bargaining at home.
- Labor force participation rates only provide a partial analysis of women’s work in India because many women are engaged in vulnerable, low paid jobs in the informal sector.

### Theoretical framework and modeling approach
- The paper builds an open economy dynamic stochastic general equilibrium (DSGE) model with both informality and gender inequality in the labor market; estimated using Bayesian techniques and applied to quarterly data from India.
- Production structure:
  - Two goods produced: a market-good and a home-good.
  - Firms in formal and informal sectors combine labor with capital to produce different varieties of market goods.
  - Home goods produced by individuals working at home in home production.
- Household structure and choices:
  - Households consist of males and females.
  - Individual labor supply decisions allocate time among paid market-good production, unpaid home-good production, job search, and leisure.
  - Decisions depend on intra-household bargaining power.
- Modeling gender constraints (demand-side):
  - (i) Lower education (skill) level of female relative to male workers (World Bank (2013a)).
  - (ii) Lower bargaining power in the wage bargaining process (ILO (2011)).
  - (iii) Firm-based gender bias against females in formal employment (ILO (2012), Campbell and Ahmed (2012), OECD (2008)).
- Modeling gender constraints (supply-side via utility):
  - (i) Lower preference for working outside home in paid market-good production relative to staying at home (concerns regarding female safety and mobility) (World Bank (2011)).
  - (ii) Higher preference for working in home-production relative to leisure (related to social norms and lack of public provisions, including childcare support) (Duflo (2012)).
- The model links gender inequality to informality within a unified theoretical framework and captures short-run as well as long-run effects of policy.

### Policy experiments studied
- Gender-specific policies:
  - Increase in female education (lowers constraints on female labor demand).
  - Stronger enforcement of laws against gender discrimination (lowers constraints on female labor demand).
  - Increase in public provisions and improvements in female safety and mobility (lower constraints on female labor supply).
- Labor market policy:
  - Increasing labor market flexibility in the formal sector (lowering labor regulations) to boost formal job creation.

### Key policy findings (quantitative examples preserved exactly as presented)
- General result: Gender-targeted policies boost female labor force participation and lead to gains in GDP in the long run, but labor market rigidities limit formal job creation.
- Example 1 — public provisions:
  - An increase in public provisions that increases female participation by 1.5 percent would increase GDP by 1.25 percent, but it would also increase unemployment and informality by 1 and 0.1 percent, respectively.
  - Most of the increased female participants are either employed in low paying informal jobs or remain unemployed, widening gender gaps in wages and informal employment, and increasing aggregate informality and unemployment.
  - Exception: the policy that increases female education increases female workers’ efficiency in employment, leads to an increase in female formal employment, raises overall productivity in the formal sector, and creates more formal jobs for both males and females. However, due to slow reallocation to the formal sector, female formality falls and gender wage gaps are higher in the short run.
- Example 2 — labor market deregulation:
  - Lowering formal regulations that increase labor market flexibility allows more women and men to be employed in the formal sector, which lowers aggregate informality and unemployment and boosts GDP in the long run.
  - Quantitative example: lower labor regulations that decrease informality by 1.5 percent would increase GDP by 2 percent and lower unemployment by 1.5 percent, but it would also lower female participation by 0.5 percent.
  - Male workers gain more because unchanged constraints on female labor supply and demand, together with a positive household income effect, lower female labor force participation and lead to a smaller increase in female formality relative to males.
- Combined policies:
  - Combining gender-targeted policies that lower constraints on female labor participation with reforms that boost formal job creation improves gender equality in the labor market and leads to significantly larger gains in GDP, employment and formality, while minimizing short run losses.

### Positioning in the literature and contribution
- Existing literature relates gender inequality to growth largely via female labor force participation and productivity, often using talent allocation, occupational choice, OLG, or CGE models, and typically assumes labor market flexibility or exogenous wages.
- Limitations of prior work:
  - Many models do not account for labor market rigidities that vary by gender, or they shut down important transmission channels by assuming exogenous wage gaps or flexible labor markets.
  - CGE models are typically non-stochastic and static, capturing long-run effects but not dynamic short-run impacts.
- Contribution of this paper:
  - Integrates frictions on female labor supply and demand with labor market rigidities to model informality in a DSGE framework, enabling analysis of both short-run and long-run effects of gender-targeted and labor market policies.

*Source: _wp1616 - 1. Introduction*

### 3. The Model

### 3. The Model

### Overview
- Small open economy with households (male m and female f), wholesale producers, retailers, capital producers, and a government.
- Two goods: market-good and home-good (H0). Market-good consists of formal tradable goods (F), informal non-tradable goods (I), and imported goods (f*).
- Home goods (H0) produced by household individuals for own consumption.
- Government: sets nominal interest rate via Taylor-type rule, taxes formal wage income to finance public spending and unemployment benefits.
- Shocks: 14 exogenous shocks (13 domestic, 2 foreign) including gender-specific shocks used in policy experiments.

### Agents and Goods
- Market-good aggregation:
  - Composite consumption: C_t = [α^{1/η} C_{D,t}^{(η−1)/η} + (1−α)^{1/η} C_{f∗,t}^{(η−1)/η}]^{η/(η−1)} (Eq. 3.48).
  - Domestic composite: C_{D,t} = [w^{1/μ} C_{F,t}^{(μ−1)/μ} + (1−w)^{1/μ} C_{I,t}^{(μ−1)/μ}]^{μ/(μ−1)} (Eq. 3.50).
  - Price aggregates: P_t (Eq. 3.49), P_{D,t} (Eq. 3.51).
- Investment and government consumption use the same CES structure as consumption (Eqs. 3.60–3.61, 3.67).

### Labor Market: structure, dynamics, and hiring
- Population and participation:
  - Continuum of households (0,1) with proportions p_m and p_f = 1 − p_m.
  - Participants: P_{m,t} = p_m − NP_{m,t} and P_{f,t} = p_f − NP_{f,t}.
- Unemployment:
  - U_{m,t} = p_m − NP_{m,t} − L^F_{m,t} − L^I_{m,t} (Eq. 3.1).
  - U_{f,t} = p_f − NP_{f,t} − L^F_{f,t} − L^I_{f,t} (Eq. 3.2).
- Employment evolution (firing probability σ_s and endogenous hires H):
  - L^m_{s,t} = (1−σ_s) L^m_{s,t−1} + p(H^m_{s,t}) S_{m,t} (Eq. 3.3).
  - L^f_{s,t} = (1−σ_s) L^f_{s,t−1} + p(H^f_{s,t}) S_{f,t} (Eq. 3.4).
- Job searcher pools:
  - S_{m,t} = P_{m,t} − (1−σ_F) L^F_{m,t−1} − (1−σ_I) L^I_{m,t−1} (Eq. 3.7).
  - S_{f,t} = P_{f,t} − (1−σ_F) L^F_{f,t−1} − (1−σ_I) L^I_{f,t−1} (Eq. 3.8).
- Formal employment dynamics (s = F):
  - L^m_{F,t} = (1−σ_F)(1−p(H^m_{F,t})) L^m_{F,t−1} + p(H^m_{F,t}) P_{m,t} − p(H^m_{F,t})(1−σ_I) L^m_{I,t−1} (Eq. 3.9).
  - L^f_{F,t} = (1−σ_F)(1−p(H^f_{F,t})) L^f_{F,t−1} + p(H^f_{F,t}) P_{f,t} − p(H^f_{F,t})(1−σ_I) L^f_{I,t−1} (Eq. 3.10).
- Hiring probability:
  - p(H^m_{s,t}) = H^m_{s,t} / S_{m,t}, p(H^f_{s,t}) = H^f_{s,t} / S_{f,t} (Eq. 3.13).
- Search probability:
  - p(S_{m,t}) = S_{m,t} / (U_{m,t−1} + NP_{m,t−1} + F^m_{F,t−1} + F^m_{I,t−1}) (Eq. 3.14).
  - p(S_{f,t}) = S_{f,t} / (U_{f,t−1} + NP_{f,t−1} + F^f_{F,t−1} + F^f_{I,t−1}) (Eq. 3.15).

### Wholesale producers: production, costs, and labor
- Production (Cobb-Douglas):
  - Y^W_{F,t} = θ_{F,t} (K_{F,t−1})^{ψ_F} (L_{F,t})^{1−ψ_F} (Eq. 3.16).
  - Y^W_{I,t} = θ_{I,t} (K_{I,t−1})^{ψ_I} (L_{I,t})^{1−ψ_I} (Eq. 3.17).
- Labor aggregation (CES across genders):
  - L_{F,t} = [ω_{F,t} (skill^m_F L^m_{F,t})^{p_F} + (1−ω_{F,t}) (skill^f_F L^f_{F,t})^{p_F}]^{1/p_F} (Eq. 3.18).
  - L_{I,t} = [ω_{I,t} (skill^m_I L^m_{I,t})^{p_I} + (1−ω_{I,t}) (skill^f_I L^f_{I,t})^{p_I}]^{1/p_I} (Eq. 3.19).
- Hiring costs (Blanchard and Gali (2006)-type):
  - HC^h_{F,t} = (β_{HC_F,t}) (p(H^h_{F,t}))^{α_{HC_F}} (Eq. 3.22).
  - HC^h_{I,t} = (β_{HC_I,t}) (p(H^h_{I,t}))^{α_{HC_I}} (Eq. 3.23).
  - β_{HC_F,t}, β_{HC_I,t} > 0; α_{HC_s} > 0.
- Wholesaler profit (real):
  - Π^W_{F,t} = (P^W_{F,t}/P_t) Y^W_{F,t} − W^m_{F,t} L^m_{F,t} − W^f_{F,t} L^f_{F,t} − R^K_t K_{F,t−1} − HC^m_{F,t} H^m_{F,t} − HC^f_{F,t} H^f_{F,t} (Eq. 3.20).
  - Π^W_{I,t} analogous (Eq. 3.21).
- First-order conditions (capital and labor demand):
  - R^K_t = ψ_s (P^W_{s,t}/P_t) Y^W_{s,t} / K_{s,t−1} (Eq. 3.25).
  - Male labor condition: (1−ψ_s) ω_s (P^W_{s,t}/P_t) Y^W_{s,t} L^m_{s,t} ( (skill^m_s L^m_{s,t} / L_{s,t}) )^{ρ_s} = W^m_{s,t} + HC^m_{s,t} − E_t[ρ_{t,t+1} HC^m_{s,t+1} (1−σ_s)] (Eq. 3.26).
  - Female labor condition analogous (Eq. 3.27).

### Wage bargaining and wages
- Generalized Nash bargaining:
  - Worker bargaining power λ^h_s ∈ (0,1), with formal λ higher than informal; gender differences allowed.
  - Division of surplus: max_{W^h_{s,t}} (V^h_{s,t} − V^h_{U,t})^{λ^h_{s,t}} (J^h_{s,t})^{1−λ^h_{s,t}}.
  - Wage relation: V^h_{s,t} − V^h_{U,t} = [λ^h_{s,t} / (1−λ^h_{s,t})] (1−τ_s) J^h_{s,t} (Eq. 3.34).
  - J^h_{s,t} = HC^h_{s,t}.
- Average wages and gender wage gap:
  - W^m_t = [W^m_{F,t} L^m_{F,t} (1−τ_F) + W^m_{I,t} L^m_{I,t}] / (L^m_{F,t} + L^m_{I,t}).
  - W^f_t analogously. Gender wage gap = W^m_t / W^f_t.

### Retailers: differentiation, pricing, and nominal rigidities
- Retail production: Dixit-Stiglitz aggregator of varieties (Eq. 3.35).
- Demand for each variety: Y_{s,t}(j_s) = (P_{s,t}(j_s) / P_{s,t})^{−ε_s} Y_{s,t} (Eq. 3.37).
- Profit (formal retailer variety j_F):
  - Π^R_{F,t}(j_F) = (P_{F,t}(j_F)/P_t − MC^W_{F,t}) (P_{F,t}(j_F)/P_{F,t})^{−ε_F} (Q^d_{F,t} + Q^x_t) − φ^{adj}_F / 2 ( (P_{F,t}(j_F)/P_{F,t−1}(j_F) / π) − 1 )^2 (Q^d_{F,t} + Q^x_t) (Eq. 3.39).
- Price-setting condition (Rotemberg costs):
  - P_{s,t}(j_s) / P_t = [ε_s/(ε_s − 1)] MC^W_{j,t} + φ^{adj}_{j_s} (ε_s − 1)^{−1} (π_{s,t}/π − 1) (π_{s,t}/π) − E_t{ρ_{t,t+1} [ ... ] } (Eq. 3.41).
- Import prices follow similar pricing rule with φ^{adj}_{f∗} ≥ 0.

### Households: preferences, home production, and constraints
- Household aggregate utility:
  - Λ_t = E_t ∑_{t=0}^∞ β^t [ (BP_t)(p_m) Λ^m_t + (1−BP_t)(p_f) Λ^f_t ] (Eq. 3.42).
  - BP_t ∈ (0,1) intra-household bargaining weight; BP_t increases with male-to-female wage income ratio (specified formula).
- Individual utility components (male and female):
  - Λ^m = (1−h_c) ln(C_t − h_c C_{t−1}) + φ^m_t [ (H^0_t)^{1+ν^m_{H,t}} / (1+ν^m_{H,t}) + φ^m_{le,t} (le^m_t)^{1+ν^m_{le,t}} / (1+ν^m_{le,t}) ] (Eq. 3.43).
  - Λ^f analogously (Eq. 3.44).
  - h_c ∈ [0,1) external habit formation.
  - φ^h_t captures utility weight on staying at home (gender-specific), φ^h_{le} weight on home-work vs leisure.
- Home-good production (decreasing returns):
  - H^0_t = θ_{H,t} { [ (1−BP_t)(HP^m_t + τ_U U^m_t)^{p_H} + BP_t (HP^f_t + τ_U U^f_t)^{p_H} ]^{1/p_H} }^{1−α_H} (Eq. 3.45).
  - θ_{H,t} AR(1) shock to home productivity; τ_U ∈ (0,1) proportion of unemployed time in home production.
- Partial derivatives: household first-order conditions incorporate how home-work and leisure of each gender affect aggregate utility (Eqs. 3.46–3.47).
- Labor supply FOCs (from household optimization):
  - MRS^h_{HP,t,C_t} = (1−τ_F) W^h_{F,t} p(H^h_{F,t}) + W^h_{I,t} p(H^h_{I,t}) + W_{U,t} [1 − p(H^h_{F,t}) − p(H^h_{I,t})] (Eq. 3.57).
  - MRS^h_{le,t,C_t} = (1−τ_F) W^m_{F,t} p(H^m_{F,t}) + W^m_{I,t} p(H^m_{I,t}) + W_{U,t} [1 − p(H^m_{F,t}) − p(H^m_{I,t})] (Eq. 3.58).
- Budget constraint (real terms, with RER_t = e_t P^*_t / P_t):
  - C_t + RER_t B^*_{t} + D_t = (e_t / e_{t−1}) (1 + i^f_{t−1}) / π_t (RER_{t−1} B^*_{t−1}) + (1 + i_{t−1}) / π_t D_{t−1} + after-tax wage incomes + W_{U,t} (U^m_t + U^f_t) + Π^R_{F,t} + Π^R_{I,t} (Eq. 3.54).
- Euler equations:
  - 1 = β E_t { ( (C_t − h_c C_{t−1}) / (C_{t+1} − h_c C_t) ) (1 + i_t) / π_{t+1} } (Eq. 3.55).
  - 1 = β E_t { ( (C_t − h_c C_{t−1}) / (C_{t+1} − h_c C_t) ) (1 + i^f_t) / π_{t+1} (e_{t+1}/e_t) } (Eq. 3.56).
  - UIP (log-linear): (1 + i_t)/π_{t+1} = (1 + i^f_t)/π_{t+1} (e_{t+1}/e_t).

### Capital producers and Tobin’s Q
- Capital accumulation:
  - K_t = (1−δ_K) K_{t−1} + (P^{Inv}_t / P_t) I_t − κ/2 ( (P^{Inv}_t / P_t) I_t / K_{t−1} − δ_K )^2 K_{t−1} (Eq. 3.59).
  - κ ≥ 0 capital adjustment coefficient; δ_K depreciation.
- Investment aggregator (same α and η as consumption):
  - I_t = [α^{1/η} I_{F,t}^{(η−1)/η} + (1−α)^{1/η} I_{f∗,t}^{(η−1)/η}]^{η/(η−1)} (Eq. 3.60).
  - P^{Inv}_t = [α P_{F,t}^{1−η} + (1−α) P_{f∗,t}^{1−η}]^{1/(1−η)} (Eq. 3.61).
- Q-equation (Tobin’s Q):
  - Q_t [1 − κ ( (P^{Inv}_t / P_t) I_t / K_{t−1} − δ_K )] = 1 (Eq. 3.62).
- Wholesalers’ capital demand condition:
  - E_t(R_{t+1} Q_t) = E_t { ψ_F (P^W_{s,t+1} / P_{t+1}) (Y^W_{s,t+1} / K_{s,t}) + (1 − δ_K) Q_{t+1} }.

### Rest of the World and external borrowing premium
- Small open economy: foreign output Y^*_t, π^*_t, i^*_t exogenous (Y^*_t normalized to 1).
- Export demand:
  - Q^x_t = α^*_x (P^*_{X,t} / P^*_t)^{−η^*_x} Y^*_t (Eq. 3.63), with P^*_{X,t} = P_{F,t} e_t under LOOP.
- Foreign interest rate on bonds:
  - (1 + i^f_t) = (1 + i^*_t) − χ ( B^*_t − B^*_P_F(RER) P Q^x ) (Eq. 3.64).
  - χ is foreign-currency borrowing premium friction.

### Government policy
- Monetary policy: Taylor-type rule:
  - i_t / i = (i_{t−1} / i)^{α_i} (π_t / π)^{α_π} (Y_t / Y)^{α_Y} ε_{i,t} (Eq. 3.65).
  - α_i interest rate smoothing, α_π and α_Y policy response coefficients, ε_{i,t} monetary shock (white noise).
- Fiscal rule (wage-tax financed government consumption and unemployment benefits):
  - (P^{Inv}_t / P_t) G_t + W_{U,t} (U^m_t + U^f_t) = τ_F (W^m_{F,t} L^m_{F,t} + W^f_{F,t} L^f_{F,t}) (Eq. 3.66).
- Government consumption basket G_t follows same CES structure (Eq. 3.67).

### Market clearing, aggregation, and equilibrium conditions
- Employment aggregation: L_{F,t} + L_{I,t} = L_t.
- Labor force participation: P_t = P_{m,t} + P_{f,t}.
- Aggregate unemployment: U_t = P_t − L_t; unemployment rate = U_t / P_t.
- Male/female labor market equilibrium: P_{m,t} = L^m_{F,t} + L^m_{I,t} + U^m_t; analogous for females.
- Unemployment flow form:
  - U^m_t = S^m_t − H^m_{F,t} − H^m_{I,t}; U^f_t analogous.
- Asset market equilibrium:
  - D_{t−1} = Q_{t−1} (K_{F,t−1} + K_{I,t−1}) (Eq. 3.68).
- Sectoral resource constraints:
  - Formal: (P^W_{F,t} / P_t) Y^W_{F,t} = (P_{F,t} / P_t) Y_{F,t} [1 + φ^{adj}_F / 2 (π_{F,t}/π − 1)^2] + HC^m_{F,t} H^m_{F,t} + HC^f_{F,t} H^f_{F,t} (Eq. 3.69).
  - Informal: (P^W_{I,t} / P_t) Y^W_{I,t} = (P_{I,t} / P_t) Y_{I,t} [1 + φ^{adj}_I / 2 (π_{I,t}/π − 1)^2] + HC^m_{I,t} H^m_{I,t} + HC^f_{I,t} H^f_{I,t} (Eq. 3.70).
- Aggregate GDP:
  - Y_t = C_t + (P^{Inv}_t / P_t) (I_t + G_t) + (P_{F,t} / P_t) Q^x_t − (P_{f∗,t} / P_t) (C_{f∗,t} + I_{f∗,t} + G_{f∗,t}).

### Shocks and stochastic processes
- Fourteen shocks: domestic (thirteen) and foreign (two).
- Domestic shocks include gender-specific:
  - male gender bias in formal employment ω_{F,t};
  - home productivity θ_{H,t};
  - female skill efficiencies skill^f_{F,t}, skill^f_{I,t};
  - female relative utility preference for staying at home φ^f_t;
  - female relative utility preference for home-work vs leisure φ^f_{le,t}.
- Other domestic shocks: sectoral productivities θ_{F,t}, θ_{I,t}; government spending G_t; monetary shock ε_{i,t}; wholesaler hiring cost β_{HC_F,t}; wage bargaining shock λ^m_{F,t}.
- Foreign shocks: foreign inflation π^*_t and foreign interest rate i^*_t.
- All shocks except ε_{i,t} follow AR(1) in logs:
  - log(z_t / z) = ρ_z log(z_{t−1} / z) + ε_{z,t} (Eq. 3.71), where ρ_z ∈ (0,1) and ε_{z,t} i.i.d. mean zero with sd(ε_z).

*Source: _wp1616 - 3. The Model*

### 4. Estimation Methodology

### 4. Estimation Methodology

### 4.1. Data
- Variables used (all in constant prices unless noted): GDP, private consumption expenditure, investment, government consumption expenditure, exports, imports, the real exchange rate, wholesale price inflation (WPI), and the nominal interest rate.
- Nominal interest rate proxy: 3-month Treasury bill rate.
- Real exchange rate proxy: real effective exchange rate (REER).
- Sample period: 1996Q1 to 2012Q1 (65 observations per series).
- Pre-estimation transformations:
  - GDP, exports, imports, consumption, investment, and government spending converted to real per capita measures to align with the Baseline model steady state.
  - Time trends removed using the Hodrick-Prescott (HP) filter; series measured as percent deviation from steady state (HP trends corresponding to each).
  - Seasonal effects removed with the X12 arima filter (except the real exchange rate and the nominal interest rate).
- Data source: CEIC database.

### 4.2. Calibration
- Calibration approach: calibrate parameters important for matching first moments; estimate remaining parameters via Bayesian estimation in Dynare.
- Key calibrated parameter values (Baseline model for India):
  - β = 0.994 (discount rate)
  - δK = 0.025 (capital depreciation rate, quarterly; annual rate 10 percent)
  - α = 0.8 (share of home-good in consumption)
  - η = 1.2 (substitutability between domestic and foreign goods)
  - π = 4.5 (gross inflation in the steady state, % annually)
  - π* = 2.5 (gross foreign inflation in the steady state, % annually)
  - (PInv/P G / Y) = 0.11 (government spending-to-GDP ratio in steady state)
  - WU/Y = 0.014 (social spending-to-GDP ratio in steady state)
  - (PFPQx/Y) = 0.19 (export-to-GDP ratio in steady state)
  - (Pf*PQm/Y) = 0.21 (import-to-GDP ratio in steady state)
  - μ = 1.5 (substitutability between formal and informal goods)
  - w = 0.39 (share of formal goods in consumption)
  - η* x = 4.5 (price elasticity of exports)
  - ψF = 0.34 (capital share in formal production function)
  - ψI = 0.34 (capital share in informal production function)
  - εF/(εF−1) = 1.2 (price mark-up in formal sector)
  - εI/(εI−1) = 1.09 (price mark-up in informal sector)
  - θF/θI = 1.5 (relative formal-to-informal productivity)
  - HCmF/WmF, HCfF/WfF, HCmF/WmF = 3 (share of formal hiring costs in formal wages)
  - HCmI/WmI, HCfI/WfI = 0.5 (share of informal hiring costs in informal wages)
  - σF = 0.1 (formal worker firing rate in steady state)
  - σI = 0.75 (informal worker firing rate in steady state)
- Steady-state and calibration notes:
  - Steady state inflation, π = 4.5 percent corresponds to average seasonally adjusted quarterly WPI on an annualized basis.
  - Discount rate β = 0.994 corresponds to an annual nominal interest rate, i, of 7 percent (matching sample mean).
  - Foreign inflation π* = 2.5 percent corresponds to annual foreign interest rate, i*, of 5 percent.
  - Depreciation rate of the nominal exchange rate, dep, set at 2 percent annually.
  - Government expenditure share calibrated at 11 percent (matches data).
  - Social protection spending calibrated at 1.4 percent of GDP (basis for unemployment benefits to GDP ratio).
  - Substitution elasticity between imported and domestically produced goods, η = 1.2, and α = 0.8 yield steady state import-to-GDP ratio of 21 percent.
  - Elasticity of substitution of exports, η* x = 4.5, consistent with calibrated steady state export-to-GDP ratio of 19 percent.

### Matching informality statistics (calibration choices and implications)
- Retail mark-ups and substitution elasticities:
  - εF = 6 and εI = 12 → retail firms’ desired mark-ups: εF/(εF−1) = 1.2 and εI/(εI−1) = 1.09.
- Production and productivity:
  - ψF = ψI = 0.34 (cost share of capital in wholesalers’ production).
  - θI = 1 (informal wholesalers productivity normalized).
  - θF = 1.5 (formal firms productivity; 50 percent differential).
  - Home production productivity θH = θI; (1−ψH) = 0.67.
- Hiring/firing cost calibration:
  - World Economic Forum redundancy cost: 55.9 weeks annual salary → 4.53 times quarterly wage rate.
  - Formal sector hiring cost to wage ratio calibrated at 3 (corresponds to 38 weeks annual salary).
  - Informal sector hiring cost ratio set at 0.5.
  - Steady-state exogenous hiring cost variables βHC F and βHC I, and elasticity coefficients αHC F and αHC I, obtained endogenously to be higher in formal relative to informal sector.
- Employment and unemployment targets:
  - Exogenous firing probabilities σF = 0.1 and σI = 0.75 yield:
    - Informal employment share LI/(LF+LI) = 68 percent.
    - Unemployment rate UP = 17 percent.
  - Substitution elasticity between formal and informal goods μ = 1.5.
  - Formal goods bias w = 0.39 → share of informal sector output in GDP = 44 percent (close to NCEUS estimate of 49 percent).

### Matching gender inequality statistics (calibration choices and implications)
- Labor supply elasticities and substitution between genders:
  - 1/(1−ρF) = 2.5 (substitutability between male & female formal workers).
  - 1/(1−ρI) = 5 (substitutability between male & female informal workers).
  - Frisch elasticities of labor supply:
    - 1/vm le = 1.2 (male’s Frisch elasticity of labor supply)
    - 1/vf le = 3.61 (female’s Frisch elasticity of labor supply)
  - Calibration rationale: assume average elasticity of 2 in economy and female share in employment 0.33 → yields 1/vm le = 1.20 and 1/vf le = 3.61 via 0.33*(3/νf le) + 0.67*(1/νm le) = 2.
- Skill ratios and bargaining power:
  - skillmF/skillfF ; skillmI/skillfI = 1.7 (male-to-female skill ratio; consistent with NSSO 2004-05 education gap).
  - Bargaining powers:
    - λmF = 0.67 (male formal worker)
    - λmI = 0.27 (male informal worker)
    - λfF = 0.46 (female formal worker)
    - λfI = 0.02 (female informal worker)
- Gender wage gap and formal/informal shares:
  - World Economic Forum (2010): females earn 62 percent of male’s salary for equal work → implies Wm/Wf = 1.62; calibration pins Wm/Wf at 1.7.
  - Gender employment shares (NSSO/other sources targeted):
    - Female informal employment LfI/(LfF+LfI) = 0.86 (86 percent)
    - Male informal employment LmI/(LmF+LmI) = 0.74 (74 percent)
  - Firm-level gender preference parameters:
    - ωF = 0.62 (male gender bias in formal employment)
    - ωI = 0.5 (male gender bias in informal employment; implies no discrimination in informal sector)
  - Resulting formality shares:
    - Male formality LmF/(LmF+LmI) = 32 percent.
    - Female formality LfF/(LfF+LfI) = 26 percent.
- Household work and participation:
  - Relative utility weights on leisure and staying at home:
    - φm le = 0.7 (male utility weight on leisure)
    - φf le = 0.5 (female utility weight on leisure)
    - φm = 0.7 (male utility weight on staying at home)
    - φf = 1 (female utility weight on staying at home)
  - Female-to-male ratio of home-work HPf/HPm obtained at 1.65.
  - Female labor force participation calibration target: Pf pf = 39.9 percent (NSSO 2009-10); calibrated Pf pf = 39.6.
  - Male labor force participation calibration target: Pm pm = 84.8 percent; calibrated Pm pm = 81.3.

### 4.3. Bayesian Estimation
- Estimation method: Bayesian approach implemented in Dynare.
- Rationale for Bayesian-Maximum Likelihood:
  - Allows incorporation of prior information from empirical studies.
  - Facilitates representation and accounting for parameter and model uncertainties.
  - Enables formal comparison among potentially mis-specified models.
  - Consistent with growing trend among central banks to use Bayesian methods for policy analysis.
- Priors:
  - Choice of prior distributions summarized in Table 3 (not reproduced here).
  - Priors chosen considering theoretical restrictions and empirical evidence.
  - Due to scarce empirical evidence on India, relatively diffuse priors are used to cover wide parameter ranges; this reduces the influence of prior means on estimation outcomes.

### 5. Empirical Results (summary from estimation)
- Price adjustment costs (posterior means):
  - φadj I = 24.15 (informal sector price re-setting parameter; highest)
  - φadj F = 64.54 (formal sector price re-setting parameter; lowest)
  - φadj f* = 42.44 (import price rigidity)
  - Interpretation: formal sector fluctuations are more persistent (higher stickiness) than informal sector; import prices change more frequently than formal prices but less frequently than informal prices.
- Monetary policy reaction function (posterior means):
  - απ = 3.2 (RBI response to inflation deviations)
  - αY = 0.32 (RBI response to output deviations)
  - αi = 0.86 (policy inertia)
  - Comparison to literature: απ is slightly higher than previous values (range 1.5 to 2.9); αY and αi are in ranges reported in previous studies.
  - Possible interpretation: higher απ may reflect shock-absorbing role of the informal sector and low skilled female workers requiring stronger RBI response to stabilize prices.
- Shock persistence and volatility:
  - Persistence of most shocks estimated high (range 0.58 to 0.97), with exceptions for a few shocks.
  - Posterior means for standard deviations of shocks are significantly higher than prior means, consistent with higher business cycle volatility in emerging economies.
- Overall assessment:
  - Estimates for common parameters are statistically significant and largely within ranges of other Bayesian DSGE studies for emerging economies.
  - Some parameters (κ, φadj F, φadj I, φadj f*, and ρπ, ρθF, ρθI) show posterior means away from prior means, indicating the data is informative about them.
  - Robustness checks (Appendix A) indicate estimation is robust to prior specification for most parameters; for some parameters data provides limited additional information.
  - Authors consider these estimates preliminary and note further work is necessary to robustly identify key gender-related parameters.

*Source: 4. Estimation Methodology (extracted from the supplied content).*

### 6. Policy Results

### 6. Policy Results

### 6.1. Gender-Specific Policies
- Policies analyzed: (i) increase in public provisions (including childcare), (ii) improvements in female safety and mobility, (iii) increase in female education, and (iv) stronger enforcement of laws against employment based gender discrimination. The first two lower constraints on female labor supply; the latter two lower female labor demand constraints.

- Method: permanent shocks to relevant variables; Table 5 (in source) summarizes short-run and long-run impacts on GDP, formality, unemployment, female labor force participation, female formality, and gender wage gaps.

- Female Labor Supply Reforms
  - (i) Increase in Public Provisions (including childcare)
    - Mechanism: increase in home-production technology, θH, and targeted fall in 1/φfle (childcare targeted to females).
    - Numerical example: an improvement that increases female labor participation by 1.5 percent leads to a 1.4 percent gain in GDP; increases aggregate unemployment by 1 percent and informality by 0.1 percent; widens gender gaps in unemployment and informality (as described).
    - Transmission: higher θH lowers home-work burden, raising male and female participation (Pf, Pm). Childcare targeted at females (fall in 1/φfle) raises Pf more, lowering Pf/Pm. Labor market rigidities mean increased labor supply is not fully met by formal hiring, raising unemployment U and shifting employment toward informal wholesalers (reducing LF/(LF+LI)). Female formality falls relative to males, widening Wm/Wf. At home, female-to-male home-work burden HPf/HPm falls (improving gender equality at home).
    - Short run: qualitatively similar but formal wholesalers increase hiring gradually, so unemployment rises more and aggregate, female, and male formality fall more in the short run.

  - (ii) Increase in Female Safety and Mobility
    - Mechanism: fall in φf lowers females’ relative disutility from working outside home.
    - Numerical example: an improvement that increases female labor participation by 1.5 percent leads to a 1.15 percent gain in GDP; increases unemployment by 0.5 percent and informality by 0.2 percent.
    - Transmission: Pf rises; female wages WfF and WfI fall in both sectors. Higher male participation Pm as labor demand expands; male wages fall less than female wages, widening Wm/Wf. Aggregate unemployment and informality rise due to insufficient formal job creation; female formality falls more. Home-work burden HPf/HPm increases (females substitute into market-work and home-work), contrasting with the public provisions reform where HPf/HPm falls.
    - Shock inducing value: this is induced by a 10 percent fall in φf.

- Female Labor Demand Reforms
  - (iii) Increase in Female Education
    - Mechanism: increase in female skill in both sectors, skillfF and skillfI.
    - Numerical example: an increase that raises Pf by 1.5 percent leads to a 1.25 percent increase in GDP, a 1.75 percent decrease in unemployment, and a 0.9 percent increase in labor formality in the long run.
    - Transmission: higher female productivity leads wholesalers to substitute male for more productive female workers; more females hired in formal relative to informal sector increasing female formality LfF/(LfF+LfI) in the long run. Short run (up to 4 quarters): fall in female formality and wider gender wage gaps due to immediate increase in female informal employment and slow formal job creation. Female wages WfF and WfI rise in the long run (short-run decline due to supply effects); male participation Pm falls (household income and substitution effects), raising male wages. Home: HPf/HPm falls as females shift out of home-work into market-work and leisure.
    - Shock inducing value: this is induced by a 5 percent increase in both skillfF and skillfI.

  - (iv) Lower Gender Discrimination in Formal Employment
    - Mechanism: fall in ωF (formal wholesalers’ relative preference for males) — stronger enforcement of anti-discrimination laws; ωI unchanged.
    - Outcomes: gender gaps in participation, wages, formal employment, and home-work burden are reduced. However, unless accompanied by higher female education, aggregate activity falls: GDP and formality are lower in the long run.
    - Transmission: formal firms substitute higher-skilled male workers for relatively lower-skilled female workers, increasing female formality but reducing formal-sector productivity and profits — shrinking aggregate formality and lowering GDP. Female returns to job search rise, increasing Pf. Female wages rise, male wages in both sectors fall (WmF falls, WfF rises). Females move from informal to formal jobs (WfI rises); male supply to informal increases (WmI falls). Male participation Pm falls. Home dynamics mirror the female skill reform.
    - Caveat: effect driven by assumption of homogeneous male and female workers; heterogeneous skill assumptions could alter outcome.

- Summary findings from gender-specific policies:
  - Supply-targeted policies directly increase Pf and reduce Pf/Pm, but labor market rigidities mean formal job creation lags, increasing informality and unemployment; gender gaps in wages and informal employment can worsen. Public provisions improve HPf/HPm, while safety/mobility can worsen it.
  - Demand-targeted policies differ: increasing female skills reduces participation, wage, and formality gaps and raises aggregate formality and employment in the long run (short-run female formality can fall); enforcing anti-discrimination without higher female education can reduce formal-sector productivity and shrink GDP and formality.
  - Comparison to literature: impacts on female participation and GDP are consistent qualitatively and quantitatively; this framework additionally captures impacts on female employment quality, female unemployment rate, and gender wage gaps.

### 6.2. Labor Market Deregulation
- Reform analyzed: decrease in formal wholesalers’ labor hiring cost, βHCF, and fall in bargaining power of male workers in formal sector, βmF (βfF not shocked).
- Numerical example: lowering regulations to decrease informality by 1.5 percent would increase GDP by 2 percent and lower unemployment by 1.5 percent in the long run; female participation Pf falls by 0.5 percent.
  - Inducing shocks: a 5 percent fall in βHCF and βmF is referenced as inducing Pf decline.
- Transmission:
  - Two opposing effects on Pf and Pm:
    - Substitution effect: higher formal job-finding raises returns to job search, increasing Pf and Pm.
    - Household income effect: more household income from formal jobs decreases Pf and Pm.
  - For males: substitution outweighs income effect in short run (Pm up), but income effect dominates in long run (Pm down).
  - For females: household income effect outweighs substitution effect in both short and long run (Pf down) due to smaller increase in female job-finding (gender constraints), widening Pf/Pm.
  - Male labor supply increase depresses male wages; female labor supply decrease raises female wages, reducing Wm/Wf. At home, male aggregate wage gains lower female intrahousehold bargaining power, increasing HPf/HPm.
- Short run transition: unemployment increases and GDP falls for up to 4 quarters post-reform.

### 6.3. Reform Interactions
- Question: optimal strategy to achieve aggregate gains while improving gender equality (participation, wages, formality).
- Cases analyzed: (i) female labor supply reform + female labor demand reform; (ii) female labor supply reform + labor market deregulation; (iii) two female labor supply reforms.

- Combining female safety/mobility (supply) with increased female education (demand)
  - Figure 8 findings: combined package overturns adverse outcomes of safety/mobility alone (which reduced formality, raised unemployment, widened wage gaps). Combination mitigates short-run fall in female formality from education reform and yields significantly higher GDP gains. Mechanism: safety/mobility raises Pf; simultaneous skill increase raises productivity so a larger share of females are hired formally at higher wages, reinforcing Pf gains. Male Pf/Pm falls; HPf/HPm falls (female intra-household bargaining power rises).

- Combining female safety/mobility with labor market deregulation
  - Figure 9 findings: combined package leads to lower unemployment, increased female and male formality, lower gender wage gaps, and Pf increases (contrast to Pf decline with deregulation alone). GDP increases and even rises in short run (unlike deregulation alone) but the short-run increase in unemployment is larger due to increased participation and slower formal job creation versus informal sector.
  - Note: combined package of deregulation + female education can overturn short-run unemployment increase.

- Combining female safety/mobility with public provisions (both supply-side)
  - Figure 10 findings: both lower female labor supply constraints, so Pf increases by more than either alone; however, both are associated with inadequate formal job creation, reinforcing individual impacts and resulting in even larger increases in informality and unemployment.

- Policy implication and recommendation:
  - Not all combined packages yield better outcomes. Complementarity exists between policies that lower constraints on female labor supply and policies that boost formal job creation and ensure female access to formal jobs.
  - Suggested policy design: prioritize getting females into paid work outside home (lower supply constraints), while simultaneously (i) making sure there are enough formal job opportunities (lower formal-sector labor market rigidities), and (ii) ensuring females have access to formal jobs (lower demand-side constraints such as education gaps and discrimination).

*Source: _wp1616 - 6. Policy Results*

### 7. Conclusion

### 7. Conclusion

### Model and methodology
- Built a small open economy DSGE model that incorporates both gender inequality and informality.
- Households consist of males and females; gender inequality is modeled as various frictions on labor supply and demand that are higher for females relative to males.
- Two sectors: formal and informal, where informality results from significantly higher rigidities in the formal sector.
- The model is estimated using Bayesian techniques and applied to Indian data.
- Framework integrates the literature on gender with the literature on labor market rigidities and is detailed enough to provide a starting point for studying the impact of various public policies.

### Policy experiments studied
- (i) increase in female education;
- (ii) increase in public provisions (including childcare);
- (iii) increase in female safety and mobility to work;
- (iv) fall in gender-based discrimination by firms in formal employment;
- impact of lowering labor market rigidities (i.e. labor market deregulation) in the formal sector.

### Main findings — gains and limits of gender-targeted policies
- Gender-targeted policies increase female labor force participation and GDP in both the short run and long run.
- Due to labor market rigidities, gender-specific policies do not generate sufficient formal job creation.
- As a result, a larger share of increased female participants either:
  - are employed informally at low wages, or
  - stay unemployed.
- These dynamics increase aggregate unemployment and informality and further widen gender gaps in wages and informal employment.
- The only exception is the policy that increases female education:
  - by increasing female workers’ efficiency at work, it leads to higher formal employment of females;
  - this increase in female efficiency leads to an expansion of the formal sector, engendering an increase in both female and male formal employment.
  - however, slow reallocation of workers due to labor market rigidities leads to a fall in female formality and widens gender wage gaps in the short run.

### Findings on labor market deregulation
- Labor market deregulation in the formal sector increases formal employment of both males and females.
- Male workers gain more:
  - constraints on female labor supply and demand combined with the household income effect lower female participation,
  - leading to a smaller increase in female formality in comparison to males.

### Policy implication: combined reforms
- Simultaneously implementing gender-based policies that lower constraints on female participation combined with policies that boost formal job creation, as opposed to a piecemeal approach, generates substantial gains in:
  - gender equality in participation,
  - formal employment,
  - wages;
  - along with larger gains in GDP and formality.

* _wp1616 - 7. Conclusion_*

### References

### References and Appendices (excerpts)

### Key bibliographic scope
- References list cites empirical and theoretical work on gender, labor markets, macroeconomic modeling, and Indian economy dynamics. Notable topics/authors include:
  - Women, war, and wages; labor supply and wages (Acemoglu, Autor, Lyle).
  - Computable OLG and gender-growth models (Agenor).
  - Macrofinancial DSGE/estimated models for India and small open economies (Anand et al.; Gabriel et al.; Mendoza; Medina and Soto).
  - Labor market participation, informality, regulation, and gender discrimination studies (Blundell & MaCurdy; Klasen; Klasen & Pieters; Ulyssea; Sahoo & Raa).
  - Policy-focused reports on gender and development (World Bank; World Economic Forum; IMF Staff Discussion Notes).

*From the supplied References list (selected titles and topics only).*

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### Appendix A — Estimation Results (Baseline model for India)
- Table 3: Prior and Posterior Distributions, Baseline Model (India)
  - Habit h_C: Prior B0.6 Std. Dev.0.25 Posterior Mean 0.3993 95% CB [0.3406, 0.4523]
  - φ_adj_F (Price A.C. in F): Prior G50 Posterior Mean 64.546 [60.710, 68.270]
  - φ_adj_I (Price A.C. in I): Prior G50 Posterior Mean 24.1511 [20.240, 27.860]
  - φ_adj_f* (Price A.C. in f*): Prior G20 Posterior Mean 42.4417 [38.750, 45.610]
  - κ (Cap. A.C. IG): Prior G20 Posterior Mean 6.3579 [5.0900, 7.3700]
  - χ (Country premium IG): Prior 0.002 Posterior Mean 0.0009 [0.0007, 0.0010]
  - α_i (Coef. of i_{t−1} B): Prior 0.75 Std. Dev.0.2 Posterior Mean 0.862 [0.8249, 0.9000]
  - α_π (Coef. of π G33): Posterior Mean 3.2349 [2.8987, 3.5581]
  - α_Y (Coef. of GDP G0.4): Posterior Mean 0.3246 [0.2821, 0.3675]
  - Persistence parameters (examples):
    - ρ_{θF} Posterior Mean 0.9718 [0.9579, 0.9883 ]
    - ρ_{θI} Posterior Mean 0.3301 [0.2731, 0.4147]
    - ρ_G Posterior Mean 0.7886 [0.7050, 0.8782]
    - ρ_{θH} Posterior Mean 0.6989 [0.6493, 0.7559]
  - Std. dev. of shocks (selected):
    - sd(ε_{θF}) Posterior Mean 0.1271 [0.1061, 0.1495]
    - sd(ε_{θI}) Posterior Mean 0.0307 [0.0253, 0.0356]
    - sd(ε_G) Posterior Mean 0.1265 [0.1016, 0.1517]
    - sd(ε_{skillI}) Posterior Mean 1.1785 [0.9458, 1.4203]
    - sd(ε_{ωF}) Posterior Mean 0.211 [0.1622, 0.2645]
    - sd(ε_i) Posterior Mean 0.0084 [0.0074, 0.0096]

- Robustness checks (Alternative model with less informative priors; Table 4 compares alternative vs baseline)
  - Prior changes: uniform distributions assigned to many parameters originally bounded in (0,1) and to α_π (bounded 0–3).
  - Core robustness conclusions (preserved under alternative priors):
    - Policy inertia remains considerable; RBI responds aggressively to inflation deviations and not much to output deviations.
    - Formal price rigidity > informal price rigidity; import price rigidity lies between formal and informal rigidity.
    - Shock processes retain high persistence and volatility — shocks are more persistent and volatile in emerging economies.
  - Selected alternative vs baseline posterior comparisons (exact values from Table 4):
    - h_C: Alternative Posterior Mean 0.04 [0.02,0.07]; Baseline Posterior Mean 0.3993
    - φ_adj_F: Alternative Posterior Mean 64.6 [61.52,67.43]; Baseline 64.546
    - φ_adj_I: Alternative Posterior Mean 12.95 [7.08,19.62]; Baseline 24.1511
    - φ_adj_f*: Alternative Posterior Mean 40.49 [35.33,43.32]; Baseline 42.4417
    - κ: Alternative Posterior Mean 3.86 [3.40,4.32]; Baseline 6.3579
    - χ: Alternative Posterior Mean 0.001 [0.0008,0.0012]; Baseline 0.0009
    - α_i: Alternative Posterior Mean 0.79 [0.74, 0.84]; Baseline 0.862
    - α_π: Alternative Posterior Mean 2.84 [2.62,3.00]; Baseline 3.2349
    - α_Y: Alternative Posterior Mean 0.05 [0.02,0.09]; Baseline 0.3246
    - ρ_{θF}: Alternative Posterior Mean 0.97 [0.95,0.99]; Baseline 0.9718
    - ρ_{θI}: Alternative Posterior Mean 0.14 [0.09,0.18]; Baseline 0.3301
    - sd(ε_{θF}): Alternative Posterior Mean 0.30 [0.25,0.35]; Baseline 0.1271
    - sd(ε_{θI}): Alternative Posterior Mean 0.13 [0.11,0.16]; Baseline 0.0307
    - sd(ε_G): Alternative Posterior Mean 0.77 [0.63,0.94]; Baseline 0.1265
    - sd(ε_{HCF}): Alternative Posterior Mean 3.64 [3.23,4.23]; Baseline 0.0103
    - sd(ε_{i*}): Alternative Posterior Mean 5.85 [5.26,6.33]; Baseline 0.015

- Robustness summary:
  - Despite quantitative differences in some parameter estimates across specifications, Bayesian estimates are similar and the main arguments are strongly supported by the data.
  - Note (from text): mean value of parameters constrained to 0.5 where applicable.

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### Appendix B — Technical Appendix: model derivations and policy-impact tables

- Household and production first-order conditions, MRS expressions, and Euler equations are derived explicitly. Key analytical results:
  - Marginal utility of market-good consumption:
    - ∂Λ_t/∂C_t = 1/2 (1−h_c) / (C_t − h_c C_{t−1})  (Eq. B.5; assumption p_m = p_f = 1/2)
  - MRS definitions:
    - MRS^f_{HP_t,C_t} = (∂Λ_t/∂HP^f_t) / (∂Λ_t/∂C_t)  (Eq. B.6 & B.5)
    - MRS^m_{HP_t,C_t} analogous (Eq. B.7 & B.5)
    - MRS between market-good and leisure for each gender similarly defined (Eqs. B.8–B.9)
  - Household first-order conditions yield:
    - Euler equations for domestic and foreign bonds (Eqs. B.12–B.14 → text Eqs. 3.55–3.56)
    - Optimal labor/home-leisure tradeoffs expressed as equalities between MRS and wage-related terms (e.g., MRS^f_{HP_t,C_t} = (1−τ_F)(W^f_{F,t}−W_{U,t}) p(H^f_{F,t}) + (W^f_{I,t}−W_{U,t}) p(H^f_{F,t}) + W_{U,t})

- Wholesaler, retailer, capital-producer, and wage-bargaining solutions are derived with explicit first-order conditions:
  - Wholesaler demand for capital: R^K_t − (P^W_{s,t}/P_t) ψ_s Y^W_{s,t} / K_{s,t−1} = 0 (K first-order condition)
  - Labor demand conditions for male and female labor include Lagrange multipliers and expected continuation terms (Eqs. for [L_m] and [L_f]).
  - Price-setting (retailer) equations (formal sector example):
    - P_{F,t}/P_t = ε_F/(ε_F−1) MC^W_{F,t} − φ^{adj}_F/(ε_F−1) (π_{F,t}/π) (π_{F,t}/π − 1) + ρ_{t,t+1} φ^{adj}_F/(ε_F−1) (π_{F,t+1}/π) (π_{F,t+1}/π − 1) (Y_{F,t+1}/Y_{F,t})
    - Analogous expression for the informal sector (P_{I,t}/P_t).
  - Tobin’s Q from capital producer:
    - Q_t = [1 − κ (P^{Inv}_t / P_t I_t / K_{t−1} − δ_K)]^{−1} (Eq. B. for Q; corresponds to text Eq. 3.62).

- Policy-impact quantitative results (Tables 5 and 6: impacts expressed as percentage deviations from steady state)
  - Table 5: Impact of Gender-Specific and Labor Market Reforms (SR = short run within first 20 quarters; LR = long run 100 quarters)
    - Increase in public provisions:
      - SR: Output Y = 1; Formality L_F/(L_F+L_I) = -0.3; Unemp. U/P = 1; Female LFP P_f/p_f = 2; Female Formal L_f^F/(L_f^F+L_f^I) = -0.5; Wage gap W_m/W_f = 1.04
      - LR: Y = 1.45; Formality = -0.1; Unemp. = 1; Female LFP = 1.5; Female Formal = -0.1; Wage gap = 0.7
    - Increase in female safety & mobility:
      - SR: Y = 0.62; Formality = -0.25; Unemp. = 1.28; Female LFP = 1.96; Female Formal = -0.48; Wage gap = 1.07
      - LR: Y = 1.35; Formality = -0.18; Unemp. = 0.51; Female LFP = 1.5; Female Formal = -0.1; Wage gap = 0.70
    - Increase in female education:
      - SR: Y = 0.8; Formality = 0.1; Unemp. = -1.3; Female LFP = 2.4; Female Formal = -1.1; Wage gap = 0.5
      - LR: Y = 0.7; Formality = 0.15; Unemp. = -1.4; Female LFP = 1.5; Female Formal = 0.25; Wage gap = -0.4
    - Lower firm-based gender discrimination:
      - SR: Y = -5.7; Formality = -2; Unemp. = -1.5; Female LFP = 3.1; Female Formal = 6; Wage gap = -34
      - LR: Y = -8.3; Formality = -1.5; Unemp. = -1.3; Female LFP = 1.5; Female Formal = 17.5; Wage gap = -39.5
    - Labor market deregulation:
      - SR: Y = -0.45; Formality = 0.4; Unemp. = 0.3; Female LFP = 0.2; Female Formal = 0.5; Wage gap = -3
      - LR: Y = 2; Formality = 1.5; Unemp. = -1.4; Female LFP = -0.5; Female Formal = 2.2; Wage gap = -3.5

  - Table 6: Impact of Combined Package of Reforms (SR = first 20 quarters; LR = 100 quarters)
    - Increase in female safety & education:
      - SR: Y = 1.5; Formality = -0.2; Unemp. = 0.2; Female LFP = 4.5; Female Formal = -1.5; Wage gap = 1.5
      - LR: Y = 2; Formality = -0.1; Unemp. = -1; Female LFP = 3.5; Female Formal = 0.2; Wage gap = 0.2
    - Increase in female safety & public provisions:
      - SR: Y = 1; Formality = -0.4; Unemp. = 2; Female LFP = 3; Female Formal = -0.7; Wage gap = 1.6
      - LR: Y = 2.1; Formality = -0.1; Unemp. = 0.8; Female LFP = 2.5; Female Formal = -0.15; Wage gap = 1.07
    - Increase in female safety & labor deregulation:
      - SR: Y = 2.2; Formality = 0.2; Unemp. = 1.5; Female LFP = 2.2; Female Formal = 0.1; Wage gap = -2
      - LR: Y = 3.5; Formality = 1.7; Unemp. = -0.1; Female LFP = 1; Female Formal = 2.2; Wage gap = -3

- Note on interpretation (from table footnotes):
  - SR denotes short run impact (first 20 quarters or within first 20 quarters as noted).
  - LR denotes long run impact (100 quarters).
  - All values reported are percentage deviations from steady state.

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*Source: _wp1616 - References (PDF content unit provided).*

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