## wp18212 — Introduction, Model Overview, Calibration, and Gender-Specific Policies

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### Context and motivation
- Female entrepreneurs comprise about 10 percent of the total number of entrepreneurs in India.
- 98 percent of women-owned businesses are micro-enterprises.
- Approximately 90 percent of women-owned businesses operate in the informal sector.
- Over 90 percent of female entrepreneurs rely on informal sources of finance.
- Female labor force participation (FLFP) is at one-third of male labor force participation and has been falling over time.
- Informal (unorganized) sector employment constitutes more than 90 percent of total employment.
- Women receive lower wages for equal work, have lower average years of schooling, and perform a much larger share of household-related work than males.

### Research question and approach
- Core question: impact of eliminating gender gaps in access to formal finance on:
  - gender gaps in business opportunities (entrepreneurship);
  - gender gaps in the labor market (female labor force participation, female informality in employment, and wage gaps);
  - macroeconomic outcomes (GDP, unemployment, and overall formality).
- Method: two-sector small-open economy deterministic DSGE model (no uncertainty) with gender inequality in entrepreneurship and the labor market and with inter-linkages to the informal sector; calibrated to match Indian data.

### Model structure (high-level)
- Agents and sectors:
  - Households with male and female members choose entrepreneurship, market work, home work, job search, or leisure; decisions depend on intra-household bargaining and preferences.
  - Male and female entrepreneurs in formal (F) and informal (I) sectors hire male and female workers and rent capital (financed by bank loans).
  - Capital producers, formal and informal banks, government, and rest of the world complete the model.
- Two sectors: regulated formal sector and unregulated informal sector in goods, labor, and financial markets.
- Financial frictions: entrepreneurs face collateral constraints; capital serves as investment good and collateral.
- Formal-sector rigidities: higher entry costs, higher hiring/firing costs, higher wage bargaining power for formal workers, higher financial market frictions relative to informal sector.
- Gender heterogeneity via different access to finance, skills, safety, social norms, time use, and discrimination.

### Key channels and mechanisms emphasized
- Formal sector financial frictions and regulation drive size of informal finance and share/size of informal firms.
- Collateral constraints reduce borrowing capacity; shocks to productive capacity reduce collateral value and amplify downturns via reduced investment and borrowing.
- Increased female access to formal finance influences entrepreneurship entry, sectoral composition of firms, labor demand, labor market participation, and informality in employment.

### Main empirical and calibration targets (selected)
- Deterministic experiments correspond to permanent structural shifts in policies.
- Calibrated to Indian data (baseline and gender-related parameter tables referenced).
- Target matches include entrepreneurship and financial access shares, labor-market participation and formality shares, and wage gap targets.

### Major policy experiment: eliminate gender gap in access to formal finance
- Implementation in model: set LT V_f,F,t = LT V_m,F,t and β_f = β_m (example calibration: LT V_f,F,t = LT V_m,F,t = 0.7 and β_f = β_m = 0.98).
- Primary effects:
  - Greater financial inclusion of female entrepreneurs increases female entrepreneurship and female labor force participation.
  - Higher female labor force participation raises GDP and lowers unemployment.
  - More entrepreneurs set up in the formal sector, raising the share of formal sector output.
  - However, informality in the labor market increases because formal-sector entrepreneurs choose to hire workers informally due to stringent formal labor market regulations; a larger share of new labor market entrants find low-paying informal jobs.
- Interaction with formal labor market flexibility:
  - With lower hiring/firing costs (more flexible formal labor market), closing gender gaps in financial access leads to a higher share of formal sector employment for both females and males, and larger gains in GDP and unemployment.
  - Male workers tend to gain more because firms prefer hiring males as females on average have lower skills and/or face discrimination; gender gaps in formal employment and labor force participation can widen under this scenario.
- Interaction with policies that reduce gender-specific labor-market constraints:
  - Combining increased female access to finance with policies that lower demand-side constraints for females in the formal labor market (for example, closing skill gaps and improving female safety) yields substantially larger gains and improves gender parity in labor force participation, wages, and formal sector employment.

### Quantitative policy results (long-run GDP and macro impacts)
- Closing gender gaps in access to formal credit alone leads to a 1.6 percent increase in GDP.
- Closing gender gaps in access to formal credit combined with a 10 percent reduction in hiring/firing costs (more flexible formal labor market) leads to a 4.7 percent increase in GDP.
- Closing gender gaps in access to formal credit combined with policies that close gender gaps in worker skills leads to a 6.8 percent increase in GDP.
- Reported long-run changes (percentage deviations from steady state) for key scenarios (values preserved verbatim as presented):
  - Financial access:
    - GDP = 1.6
    - Unemp. = -5
    - Formality (Labor Product Formal Informal) = -2.1 0.9 0.6 1.8 0.07
    - LFP = 0.61
    - Entrepreneurship = 1.80.07
  - + Deregulation:
    - GDP = 4.7
    - Unemp. = -9.1
    - Formality = 11.5 14.1 2.14.5-1.5
  - + Skills:
    - GDP = 6.8
    - Unemp. = -6.8
    - Formality = 10 19.7 1.14.9-2.7
  - + Safety:
    - GDP = 0.9
    - Unemp. = -80.5
    - Formality = 0.5 0.51.1-0.2-0.4

### Baseline gender-inequality steady-state indicators (model India calibration)
- U = 0.13 unemployment rate
- LI/LF + LI = 0.75 share of informal employment
- YI/Y = 0.49 share of informal output
- Yf/Y = 0.06 share of female entrepreneurs’ output
- Loanf,F/Loanf,F+Loanf,I = 0.23 share of female entrepreneurs’ formal finances
- Lf/L = 0.12 share of female entrepreneurs’ employment
- Wm/Wf = 1.4 gender wage gap (male-to-female wage ratio)
- Lf I / (Lf F + Lf I) = 0.80 share of females’ informal employment
- Lm I / (Lm F + Lm I) = 0.70 share of males’ informal employment
- HPf t / HPm t = 14.19 gender gap in home-work
- Pf pf = 0.20 female labor force participation
- Pm pm = 0.85 male labor force participation

### Key quantitative findings (summary and distributional effects)
- Closing gender gaps in financial access (India calibration) yields:
  - GDP gains of 1.6 percent
  - Unemployment falls by 5 percent
  - Greater female entrepreneurial activity in formal sector; higher female labor force participation and employment
  - Share of informality increases due to labor market rigidities, limiting gains
- Financial access + Deregulation (10 percent lower hiring costs) yields:
  - GDP increase of 4.7 percent
  - Unemployment fall of 9 percent
  - 11.5 percent increase in share of formal employment of both males and females
  - Male workers gain more than females; gender gaps in labor market worsen
- Financial access + Skills (eliminate female skill gaps) yields:
  - Potential increase in India’s output by 6 percent (combined effect)
  - Larger reductions in gender inequality in LFP, formality, wages, and entrepreneurship; larger gains in GDP, employment, and formality
- Financial access + Safety yields:
  - Higher female participation but small GDP gains and increased female employment in informal jobs

### Policy implications and recommended complementarities
- Policies that lower barriers for females in obtaining formal finance are necessary to promote higher female entrepreneurship and yield economy-wide benefits.
- Full benefits of financial inclusion for female entrepreneurs require complementary reforms:
  - More flexible formal labor market (lower hiring/firing costs) to convert entrepreneurship gains into formal employment opportunities;
  - Policies that reduce gender-specific structural constraints in the formal labor market (e.g., closing skill gaps, improving safety and mobility);
  - Targeted policies that disproportionately benefit females and measures to reduce informality to better capture gains from financial inclusion and labor-market reforms.
- Trade-offs highlighted: increasing female participation can raise overall employment but also increase reliance on low-paying informal jobs unless demand-side and formality-enhancing reforms accompany financial inclusion.

### Financial inclusion and policy context (India, selected facts)
- More than 240 million previously unbanked individuals have gained access to bank accounts since the launch of the Pradhan Mantri Jan Dhan Yojana (PMJDY) in August 2014.
- About 47 percent of these newly banked individuals are females.
- Pradhan Mantri MUDRA Yojana (PMMY) scheme: womens’ businesses accounted for about one-half of the total amount lent under the scheme, and about four-fifths of the number of loans.
- Recent labor-market policy changes include allowing fixed-term employment across sectors; maternity benefits increased from 12 to 26 weeks.
- Recommended metrics to measure success of interventions:
  - Rise in females’ formal entrepreneurship.
  - Mobility of female-led firms to medium and large sizes.
  - Extent of improvement in females’ labor market participation.

*Source: IMF Working Paper (wp18212) — sections 1, 2 (model overview, retailers, market clearing) and 4.1 "Gender-Specific Policies".*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Context and motivation
- Female entrepreneurs comprise about 10 percent of the total number of entrepreneurs in India.
- 98 percent of women-owned businesses are micro-enterprises.
- Approximately 90 percent of women-owned businesses operate in the informal sector.
- Over 90 percent of female entrepreneurs rely on informal sources of finance.
- Female labor force participation (FLFP) is at one-third of male labor force participation and has been falling over time.
- Informal (unorganized) sector employment constitutes more than 90 percent of total employment.
- Women receive lower wages for equal work, have lower average years of schooling, and perform a much larger share of household-related work than males.

### Research question and approach
- Core question: What is the impact of an increase in female entrepreneurs’ access to formal finance (i.e. no gender gaps in financial access) on:
  - gender gaps in business opportunities (entrepreneurship);
  - gender gaps in the labor market (female labor force participation, female informality in employment, and wage gaps);
  - macroeconomic outcomes (GDP, unemployment, and overall formality)?
- Method: Build a two-sector small-open economy deterministic DSGE model (no uncertainty) with gender inequality in entrepreneurship and the labor market and with inter-linkages to the informal sector. The model is calibrated to match Indian data.

### Model structure (high-level)
- Agents and sectors:
  - Households with male and female members: each individual either owns a firm (entrepreneur), supplies labor to entrepreneurs, or stays at home. Labor-supply decision optimizes among entrepreneurial opportunities, paid market-good production, unpaid home-good production, job search, and leisure; depends on intra-household bargaining power.
  - Male and female entrepreneurs in each sector (formal and informal): hire male and female workers and rent capital (financed by bank loans) to produce final goods for domestic sale or export.
  - Capital producers: invest in new capital.
  - Formal and informal sector banks: provide loans to firms in their corresponding sector.
  - Government: taxes formal wage income to fund social spending and sets the interest rate.
  - Rest of the world.
- Two sectors: regulated formal sector and unregulated informal sector in goods, labor, and financial markets.
- Financial frictions: entrepreneurs face collateral constraints when borrowing; capital serves a dual role as investment good and collateral.
- Rigidities in formal sector (see model characterization):
  - Higher entry costs, higher hiring/firing costs, higher wage bargaining power for formal workers, higher financial market frictions relative to informal sector.
- Gender heterogeneity introduced via differences in access to finance, skills, safety, social norms, time use, and discrimination.

### Relation to prior literature
- Extends Khera (2016) by adding financial micro-foundations (banking sector) in spirit of Babilla et al. (2016).
- Addresses gaps: integrates gender gaps in access to credit and entrepreneurship with gender gaps in the labor market and with informality endogenously.

### Key channels and mechanisms emphasized
- Formal sector financial frictions and formal sector regulation drive size of informal finance and share/size of informal firms.
- Collateral constraints reduce borrowing capacity; shocks to productive capacity reduce collateral value, amplifying downturns via reduced investment and borrowing.
- Increased female access to formal finance affects entrepreneurship entry decisions, sectoral composition of firms, labor demand, labor market participation, and informality in employment.

### Main empirical and calibration targets (selected)
- Model calibrated to Indian data (baseline and gender-related parameter tables referenced).
- Deterministic experiments correspond to permanent structural shifts in policies.

### Major findings (policy experiment: eliminate gender gap in access to formal finance)
- Primary effects:
  - Greater financial inclusion of female entrepreneurs (no gender gaps in access to formal finance) increases female entrepreneurship and female labor force participation.
  - Higher female labor force participation raises GDP and lowers unemployment.
  - Increased access to formal finance induces more entrepreneurs to set up businesses in the formal sector, raising the share of formal sector output.
  - However, informality in the labor market increases because formal-sector entrepreneurs choose to hire workers informally due to stringent formal labor market regulations; thus a larger share of new labor market entrants find low-paying informal jobs.
- Interaction with formal labor market flexibility:
  - When labor markets are more flexible (modeled as lower regulations in the formal labor market), closing gender gaps in access to finance leads to a higher share of formal sector employment for both females and males, and larger gains in GDP and unemployment.
  - Nonetheless, male workers gain more because firms prefer hiring males as females on average have lower skills and/or face discrimination; gender gaps in formal employment and labor force participation can widen under this scenario.
- Interaction with policies that reduce gender-specific labor-market constraints:
  - Combining increased female access to finance with policies that lower demand-side constraints for females in the formal labor market (for example, closing the gender gap in skills via skill development and improving female safety) yields substantially larger gains and improves gender parity in labor force participation, wages, and formal sector employment.

### Quantitative policy results (long-run GDP impacts)
- Closing gender gaps in access to formal credit alone leads to a 1.6 percent increase in GDP.
- Closing gender gaps in access to formal credit combined with a 10 percent reduction in hiring/firing costs (i.e., more flexible formal labor market) leads to a 4.7 percent increase in GDP.
- Closing gender gaps in access to formal credit combined with policies that close gender gaps in worker skills leads to a 6.8 percent increase in GDP.

### Policy implications (concise)
- Policies that lower barriers faced by females in obtaining formal finance are necessary to promote higher female entrepreneurship and yield economy-wide benefits.
- Full benefits of financial inclusion for female entrepreneurs require complementary reforms:
  - More flexible formal labor market (lower hiring/firing costs) to convert entrepreneurship gains into formal employment opportunities;
  - Policies that reduce gender-specific structural constraints in the formal labor market (e.g., closing skill gaps, improving safety and mobility);
  - Without complementary labor-market and demand-side reforms, increased female entrepreneurial finance can raise overall employment but also increase reliance on low-paying informal jobs and may not close labor-market gender gaps.

*Source: IMF Working Paper (wp18212) — 1. Introduction*

### Box 4 in India, 2017). More than 240 million previously unbanked individuals, among whom

### Box 4 in India, 2017). More than 240 million previously unbanked individuals, among whom

### Financial inclusion, gender and labor-market reforms
- More than 240 million previously unbanked individuals have gained access to bank accounts since the launch of the Pradhan Mantri Jan Dhan Yojana (PMJDY) in August 2014.
- About 47 percent of these newly banked individuals are females.
- The Pradhan Mantri MUDRA 7 Yojana (PMMY) scheme has enabled women-led businesses to access collateral-free finance.
  - Womens’ businesses accounted for about one-half of the total amount lent under the scheme, and about four-fifths of the number of loans.
- Recent policy changes aimed at labor-market flexibility include allowing fixed-term employment across sectors.
  - Under fixed-term employment, workers are entitled to statutory benefits available to a permanent worker in the same factory, including work hours, wages, and allowances. However, employers need not give notice to fixed-term workers on non-renewal or expiry of contracts.
- Changes to women-oriented policy include increasing maternity benefits from 12 to 26 weeks.
- Recommended metrics to measure success of interventions:
  - Rise in females’ formal entrepreneurship.
  - Mobility of female-led firms to medium and large sizes.
  - Extent of improvement in females’ labor market participation (Box 6 and 7 in India, 2017).
- Caveat: analysis focuses on steady-state (long-run equilibrium) effects and abstracts from transitional impacts; transitional costs may exist and warrant future research (see Khera, 2016).

*Major themes of the model and paper organization: Section 2 — theoretical framework; Section 3 — calibration and equilibrium (steady state); Section 4 — policy experiments; Section 5 — conclusion.*

### Model overview (Baseline DSGE with financial micro‑foundations)
- Model basis: DSGE model in Khera (2016) augmented with a collateral constraint based on Kiyotaki and Moore (1997).
- Agents: households (male m and female f), entrepreneurs, retailers, capital producers, government.
- Goods:
  - Market-good: formal tradable goods (F), informal non-tradable goods (I), and imported goods (f*).
  - Home-good (H0): produced by household individuals working at home for household consumption only.
- Households: members either own a firm (entrepreneur), supply labor, or stay at home; employed agents work in one of four firm types:
  1. male entrepreneur in the formal sector,
  2. female entrepreneur in the formal sector,
  3. male entrepreneur in the informal sector,
  4. female entrepreneur in the informal sector.
- Formal and informal retailers purchase wholesale goods from entrepreneurs, differentiate varieties, and set retail prices under monopolistic competition with Rotemberg (1982) price adjustment costs.
- Capital producers combine formal market- and imported goods to produce final investment goods.
- Government: sets nominal interest rate via a Taylor-type rule; receives wage income taxes to finance public spending and unemployment benefits.

### Labor market structure and dynamics
- Population: continuum of households (0,1) with proportions pm (males) and pf = 1 − pm (females). Footnote: As per the 2001 consensus, females in India constitutes half of the country’s population and therefore we assumepm = pf = 1/2.
- Households decide on entrepreneurship, labor market participation, or non-participation.
- Notation for employment masses (examples):
  - Lm m,F,t, Lm m,I,t, Lm f,F,t, Lm f,I,t for male workers employed by male and female entrepreneurs across sectors.
  - Lf m,F,t, Lf m,I,t, Lf f,F,t, Lf f,I,t for female workers employed by male and female entrepreneurs across sectors.
  - Unemployment: Um t and Uf t.
  - Non-participants: NPm t and NPf t.
- Participation pools: Pm t = pm − NPm t and Pf t = pf − NPf t.
- Unemployment expressions:
  - Um t = pm − NPm t − Lm F,t − Lm I,t  (Eq. 2.3)
  - Uf t = pf − NPf t − Lf F,t − Lf I,t  (Eq. 2.4)
- Employment evolves with endogenous hiring and exogenous firing probability σs (sector-specific).
  - Fired at end of t−1: Ff m,F,t−1 = σF Lf m,F,t−1, etc.
  - New hires Hf m,F,t and Hf f,F,t from search pool Sf t.
- Evolution equations for female formal employment (examples):
  - Lf m,F,t = (1 − σF )Lf m,F,t−1 + p(Hf m,F,t)Sf t  (Eq. 2.5)
  - Lf f,F,t = (1 − σF )Lf f,F,t−1 + p(Hf f,F,t)Sf t  (Eq. 2.6)
- Job searcher pool and hiring probabilities:
  - Sf t + NPf t = Uf t−1 + NPf t−1 + σF Lf m,F,t−1 + σI Lf m,I,t−1 + σF Lf f,F,t−1 + σI Lf f,I,t−1  (Eq. 2.9)
  - Sf t = Pf t − (1 − σF )Lf m,F,t−1 − (1 − σI )Lf m,I,t−1 − (1 − σF )Lf f,F,t−1 − (1 − σI )Lf f,I,t−1  (Eq. 2.10)
  - Hiring probabilities: p(Hf m,s,t) = Hf m,s,t / Sf t ; p(Hf f,s,t) = Hf f,s,t / Sf t  (Eq. 2.15)
  - Probability of searching: p(Sf t) = Sf t / (Uf t−1 + NPf t−1 + Ff m,F,t−1 + Ff m,I,t−1 + Ff f,F,t−1 + Ff f,I,t−1)  (Eq. 2.16)
- Interpretation: female formal employment rises with higher female labor participation Pf t and higher hiring probability p(Hf m,F,t) (Eq. 2.11 and Eq. 2.12).

### Entrepreneurs: production, hiring costs, and financial constraints
- Continuum of male and female entrepreneurs in each sector s ∈ {F, I}.
- Production: Cobb-Douglas for female wholesalers:
  - YW f,F,t = θF,t (Kf,F,t−1)ψF (Lf,F,t)1−ψF  (Eq. 2.17)
  - YW f,I,t = θI,t (Kf,I,t−1)ψI (Lf,I,t)1−ψI  (Eq. 2.18)
  - ψs is the capital intensity parameter.
- Labor aggregation: CES aggregate of male and female workers with parameter ρs and firm preference ωh,s,t for male over female workers:
  - Lf,F,t = [ ωf,F,t (skillm F Lm f,F,t)pF + (1 − ωf,F,t)(skillf F Lf f,F,t)pF ]1/pF  (Eq. 2.19)
  - Lf,I,t analogous (Eq. 2.20)
  - ωs,t ∈ (0,1); ωs,t = 0.5 implies no gender discrimination; ωs,t > 0.5 implies discrimination against females.
- Hiring costs (real) HC h f,s,t depend positively on new hires and negatively on the unemployed pool:
  - HC h f,F,t = (βHC F,t)(p(Hh f,F,t))αHC F  (Eq. 2.23)
  - HC h f,I,t = (βHC I,t)(p(Hh f,I,t))αHC I  (Eq. 2.24)
  - αHC s > 0 elasticity of hiring cost w.r.t. hiring probability.
- Profits net of wages, hiring costs, capital rental and loan interest (examples):
  - ΠW f,F,t = PW f,F,t Pt YW f,F,t − Wm f,F,t Lm f,F,t − Wf f,F,t Lf f,F,t − RK t Kf,F,t−1 − HCm f,F,t Hm f,F,t − HCf f,F,t Hf f,F,t + Loanf,F,t − RK F,t−1 Loanf,F,t−1  (Eq. 2.21)
  - ΠW f,I,t analogous (Eq. 2.22)

### Financial frictions and collateral constraints
- Entrepreneurs borrow from sectoral banks; both formal and informal entrepreneurs are financially constrained by collateral value.
- Collateral = physical capital holdings; borrowing constrained by a loan-to-value ratio LT V f,s,t:
  - Rk f,F,t Loanf,F,t ≥ LT V f,F,t [ (1 − δK )Kf,F,t−1 Et(qt+1) ]  (Eq. 2.25)
  - Rk f,I,t Loanf,I,t ≥ LT V f,I,t [ (1 − δK )Kf,I,t−1 Et(qt+1) ]  (Eq. 2.26)
- The loan amount increases with expected collateral value Et(qt+1), higher LT V, and lower loan interest rates Rk s,t.

### Demand for capital, labor, loans and wage setting
- Female entrepreneurs maximize expected discounted profits subject to employment evolution and borrowing constraint (Eq. 2.27).
- First-order conditions yield demand relations:
  - Capital demand (Eq. 2.28):
    - RK t = ψs PW f,s,t Pt YW f,s,t / Kf,s,t−1 + (1 − δK ) LT V f,s,t Et[ (qt+1)(1 − (βf)Rk s,t+1) ] / Rk s,t
    - Interpretation: capital demand increases when RK t is lower; LT V f,s,t higher; Rk s,t and Rk s,t+1 lower; Et(qt+1) higher.
    - Policy implication: financial inclusion that increases LT V will raise capital demand and amplify investment via higher collateral prices.
  - Labor demand for males and females equates marginal product to marginal cost including wages and hiring costs (Eq. 2.29 and Eq. 2.30):
    - Male labor: (1 − ψs) ωf,s PW f,s,t Pt YW f,s,t / Lm f,s,t ( skillm s Lm f,s,t / Lf,s,t )ρs = Wm f,s,t + HCm f,s,t − Et( βf HCm f,s,t+1 (1 − σs) )
    - Female labor analogous.
- Wage setting: generalized Nash bargaining with worker bargaining weights λF h ∈ (0,1) and λh I ∈ (0,1); formal workers assumed to have higher bargaining power than informal workers; bargaining power may differ by gender to capture gender gaps in union access and leadership.
- Average wages define gender wage gap:
  - Wm t and Wf t defined as ratios of total after-tax wage income to total employed individuals (formulas given in text).
  - Gender wage gap = Wm t / Wf t.
- Example wage expression for female workers employed by female entrepreneurs in the formal sector (excerpted exact structure included in source):
  - Wf f,F,t (1 − τF) = λf F,t 1 − λf F,t (1 − τF)(HCf f,F,t) + WU,t − (1 − σF )Et{ ρt,k [ λf F,k 1 − λf F,k [1 − p(Sf k)p(Hf f,F,k)] (1 − τF)HCf f,F,k − λf I,k 1 − λf I,k (p(Hf f,I,k))HCf f,I,k − λf F,k 1 − λf F,k (p(Hf m,F,k))HCf m,F,k − λf I,k 1 − λf I,k (p(Hf m,I,k))HCf m,I,k + (1 − p(Sf k))WU,k + (1 − p(Sf k))p(le f k)MRSf le,C k + (1 − p(Sf k)) [1 − p(le f k) − τU] MRSm HP,C k ] }.
- Analogous expressions exist for other wage components Wf f,I,t, Wf m,F,t, Wf m,I,t, Wm m,I,t, Wm f,I,t, Wm m,F,t, and Wm f,F,t.

*Source: Excerpt from wp18212 (section containing Box 4 and Sections 2–2.2.1 of the Baseline model).*

### 2.3 Retailers

### 2.3 Retailers

### Retailer production technology and inputs
- Retailers introduce nominal rigidity and are modeled as a continuum F and I of monopolistically competitive formal and informal retailers.
- Retailers buy wholesale goods supplied by female entrepreneurs, Y_W_f,F,t and Y_W_f,I,t, and male entrepreneurs, Y_W_m,F,t and Y_W_m,I,t, and combine them using CES production functions to produce final market-good varieties Y_F,t(j_F) and Y_I,t(j_I):
  - Y_F,t(j_F) = [α_F^(1/η_F) Y_W_m,F,t^(η_F−1)/η_F + (1−α_F)^(1/η_F) Y_W_f,F,t^(η_F−1)/η_F]^(η_F/(η_F−1)) (2.31)
  - Y_I,t(j_I) = [α_I^(1/η_I) Y_W_m,I,t^(η_I−1)/η_I + (1−α_I)^(1/η_I) Y_W_f,I,t^(η_I−1)/η_I]^(η_I/(η_I−1)) (2.32)
- Parameters and interpretations:
  - α_s ∈ (0,1) is the relative weight on intermediate goods produced by male entrepreneurs.
  - η_s > 1 is the elasticity of substitution between goods produced by male and female entrepreneurs.
- Assumption: zero cost of differentiation.

### Retailer pricing as composite of input prices
- Retailer prices are CES composites of male and female entrepreneurs’ wholesale prices:
  - P_F,t(j_F) = [α_F P_W_m,F,t^(1−η_F) + (1−α_F) P_W_f,F,t^(1−η_F)]^(1/(1−η_F)) (2.33)
  - P_I,t(j_I) = [α_I P_W_m,I,t^(1−η_I) + (1−α_I) P_W_f,I,t^(1−η_I)]^(1/(1−η_I)) (2.34)

### Optimal input demand by retailers
- By minimizing expenditure on the composite demand, optimal demands for male and female entrepreneurs’ goods in each sector are:
  - Y_W_f,F,t = (1−α_F) (P_W_f,F,t / P_F,t)^(−η_F) Y_F,t
  - Y_W_m,F,t = α_F (P_W_m,F,t / P_F,t)^(−η_F) Y_F,t (2.35)
  - Y_W_f,I,t = (1−α_I) (P_W_f,I,t / P_I,t)^(−η_I) Y_I,t
  - Y_W_m,I,t = α_I (P_W_m,I,t / P_I,t)^(−η_I) Y_I,t (2.36)

### Composite output, aggregate prices, and demand facing each retailer
- Total composite output Y_s,t produced by retailers is a Dixit-Stiglitz (1977) CES aggregate of varieties Y_s,t(j_s):
  - Y_s,t = ( ∫_0^1 Y_s,t(j_s)^(ε_s−1)/ε_s d j_s )^(ε_s/(ε_s−1)) (2.37)
  - ε_s is the elasticity of substitution between different varieties.
- Composite price P_s,t:
  - P_s,t = ( ∫_0^1 P_s,t(j_s)^(1−ε_s) d j_s )^(1/(1−ε_s)) (2.38)
- Demand facing each retailer (firm-level demand):
  - Y_s,t(j_s) = (P_s,t(j_s) / P_s,t)^(−ε_s) Y_s,t (2.39)

### Tradability and consumption distinctions
- Formal final good Y_F,t is exportable and consumed domestically Q_d_F,t by households, capital producers and government, and exported Q_x_t.
- Informal sector good Y_I,t is nontradable and only consumed domestically by households Q_d_I,t.

### Price-setting and nominal rigidity
- Retailer j_s sets price P_s,t(j_s) to maximize expected discounted profits subject to Rotemberg (1982) adjustment costs. The price equation (in relative terms) is:
  - P_s,t(j_s) / P_t = ε_s/(ε_s−1) MC_W_j,t + φ_ad j_s (ε_s−1) ( (π_s,t / π^(−1)) (π_s,t / π) ) − E_t{ ρ_t,t+1 [ (φ_ad j_s (ε_s−1)) ( (π_s,t+1 / π^(−1)) (π_s,t+1 / π) ) Y_s,t+1(j_s) / Y_s,t(j_s) ] }^(ε_s/(ε_s−1)) (2.40)
- ε_s/(ε_s−1) is the desired (gross) mark-up resulting from retail market imperfections.
- φ_ad captures Rotemberg-style price adjustment costs, introducing nominal rigidity into price dynamics.

*Source: IMF Working Paper — section 2.3 Retailers.*

### 2.9 Market Clearing and Aggregation

### 2.9 Market Clearing and Aggregation

### Market definitions and aggregate identities
- Aggregate employment: L_F,t + L_I,t = L_t.
- Aggregate labor supply (participation): P_t = P_m,t + P_f,t.
- Aggregate unemployment: U_t = P_t − L_t; unemployment rate = U_t / P_t.

### Labor market equilibrium (male and female)
- Male supply–demand equilibrium:
  - P_m,t = L_mF,t + L_mI,t + U_m,t.
- Female supply–demand equilibrium:
  - P_f,t = L_fF,t + L_fI,t + U_f,t.
- Decomposition of employment by worker origin and sector:
  - L_mF,t = L_mm,F,t + L_mf,F,t
  - L_mI,t = L_mm,I,t + L_mf,I,t
  - L_fF,t = L_fm,F,t + L_ff,F,t
  - L_fI,t = L_fm,I,t + L_ff,I,t
- Unemployment as search minus hires:
  - U_m,t = S_m,t − H_mm,F,t − H_mm,I,t − H_mf,F,t − H_mf,I,t
  - U_f,t = S_f,t − H_fm,F,t − H_fm,I,t − H_ff,F,t − H_ff,I,t

### Asset market equilibrium
- Total bonds issued equals cost of desired capital:
  - D_t−1 = Q_t−1 (K_m,F,t−1 + K_m,I,t−1 + K_f,F,t−1 + K_f,I,t−1) (2.69)

### Resource constraints (formal and informal firms)
- Formal sector (female firm) resource constraint (equation numbering preserved):
  - P_Wf,F,t / P_t Y_WF,t = (1 − α_F) (1 / P_t) (P_Wf,F,t / P_F,t) − η_F Y_F,t (1 + φ^adj_F / 2 (π_F,t π^−1)^2) + HC_mf,F,t H_mf,F,t + HC_ff,F,t H_ff,F,t (2.70)
- Total demand for formal good:
  - Y_F,t = C_F,t + I_F,t + G_F,t + Q_x,t
- Informal sector resource constraint:
  - P_WI,t / P_t Y_WI,t = P_I,t / P_t Y_I,t (1 + φ^adj_I / 2 (π_I,t π^−1)^2) + HC_mI,t H_mI,t + HC_fI,t H_fi,t (2.71)
- Informal good demand:
  - Y_I,t = Q_dI,t = C_I,t

### Trade and GDP identity
- Total foreign imports: Q_m = C_f∗,t + I_f∗,t + G_f∗,t.
- 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)

### Calibration approach (section 3 summary)
- Nonlinear equilibrium conditions require numerical solution; periods interpreted as quarters.
- Calibration matches Indian macro data from 1996:Q1 to 2008:Q2 using CEIC for: GDP, private consumption expenditure, investment, government consumption expenditure, exports, imports (constant prices), real exchange rate, wholesale price inflation (WPI), nominal interest rate.
- Parameter choices follow standard business-cycle literature and Khera (2016) for formal/informal sector parameters.

### Parameter calibration, Baseline model for India (Table 4 selected entries — values preserved exactly)
- β 0.994 discount rate
- δ_K 0.025 capital depreciation rate
- 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)
- (P_Inv / P_G / Y) 0.11 government spending-to-GDP ratio in the steady state
- W_U / Y 0.014 social spending-to-GDP ratio in the steady state
- (P_F / P Q_x / Y) 0.19 export-to-GDP ratio in the steady state
- (P_f∗ / P Q_m / Y) 0.21 import-to-GDP ratio in the 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
- ψ_F 0.34 capital share in formal production function
- ψ_I 0.34 capital share in informal production function
- ε_F / (ε_F − 1) 1.2 price mark-up in formal sector
- ε_I / (ε_I − 1) 1.09 price mark-up in informal sector
- θ_F / θ_I 1.5 relative formal-to-informal productivity
- HC_s m,F / W_s m,F , HC_s f,F / W_s f,F 1.3 share of formal hiring costs in formal wages
- HC_s m,I / W_s m,I , HC_s f,I / W_s f,I 0.2 share of informal hiring costs in informal wages
- α_F , α_I 0.5 share of male intermediate good in final retail goods
- η_F , η_I 1.1 substitutability between male and female intermediate goods
- σ_F 0.1 formal worker firing rate in steady state
- σ_I 0.75 informal worker firing rate in steady state

### Matching gender inequality statistics (objectives)
- Targets calibrated to match Indian statistics on:
  - Entrepreneurship and financial access: Y^f / Y, L^f / L, Loan_f,F / (Loan_f,F + Loan_f,I)
  - Labor market: P_f, P_m, L_mF / (L_mF + L_mI), L_fF / (L_fF + L_fI), W_m / W_f

### Gender-related parameter calibration and targets (Table 5 values preserved)
- 1 / v^m_le 1.2 male’s Frisch elasticity of labor supply
- 1 / v^f_le 3.61 female’s Frisch elasticity of labor supply
- β_m 0.98 male entrepreneur’s discount factor
- β_f 0.97 female entrepreneur’s discount factor
- 1 / (1 − ρ_F) 2.5 substitutability between male & female formal workers
- 1 / (1 − ρ_I), 1 / (1 − ρ_H) 5 substitutability between male & female informal workers
- skill_mF / skill_fF 1.7 male-to-female skill ratio in formal employment
- skill_mI / skill_fI 1 male-to-female skill ratio in informal employment
- λ_mF 0.7 bargaining power of male formal worker
- λ_mI 0.3 bargaining power of male informal worker
- λ_fF 0.6 bargaining power of female formal worker
- λ_fI 0.01 bargaining power of female informal worker
- ω_m,F , ω_m,I 0.62 male entrepreneur’s relative preference for male worker
- ω_f,F , ω_f,I 0.5 female entrepreneur’s relative preference for male worker
- LT V_m,F,t 0.7 loan-to-value ratio of formal male entrepreneur
- LT V_f,F,t 0.5 loan-to-value ratio of formal female entrepreneur
- LT V_m,I,t , LT V_f,I,t 0.8 loan-to-value ratio in the informal sector
- φ^m_le 0.7 male utility weight on leisure
- φ^f_le 0.1 female utility weight on leisure
- φ^m 0.7 male utility weight on staying at home
- φ^f 1 female utility weight on staying at home

### Gender calibration details and steady-state matches
- Female entrepreneurs’ discount factor set at 0.97 vs male entrepreneurs at 0.98 to reflect lower female demand for credit and higher impatience.
- Loan-to-value ratios: LT V_f,F,t = 0.5 (formal female) vs LT V_m,F,t = 0.7 (formal male); LT V_f,I,t = LT V_m,I,t = 0.8 (informal, same for both).
- Hiring-cost-to-wage ratios: male workers formal = 1, informal = 0.2; female workers formal = 2, informal = 0.5 (same for male and female entrepreneurs).
- These calibrations produce targets:
  - Y^f / Y = 6 percent
  - Female entrepreneurs’ formal finances share Loan_f,F / (Loan_f,F + Loan_f,I) = 23 percent
  - Share of labor employed by female entrepreneurs = 12 percent
- Substitution elasticities between female and male workers:
  - Formal sector: 1 / (1 − ρ_F) = 2.5
  - Informal sector: 1 / (1 − ρ_I) = 5
- Labor supply Frisch elasticities solved from aggregation condition (female share 0.33) yield:
  - 1 / ν^m_le = 1.20
  - 1 / ν^f_le = 3.61
- Skill ratios:
  - Formal sector male-to-female skill ratio calibrated to 1.7 (matching education gaps)
  - Informal sector skill ratio set to 1
- Wage gap and bargaining:
  - World Economic Forum reports females earn 62 percent of male salary for equal work => W_m / W_f = 1.62 target.
  - Bargaining parameters λ_mF = 0.7, λ_mI = 0.3, λ_fF = 0.6, λ_fI = 0.01 yield W_m / W_f = 1.4 in the model.
- Formality shares:
  - Female formality L_fF / (L_fF + L_fI) = 20 percent (model)
  - Male formality L_mF / (L_mF + L_mI) = 30 percent (model)
  - These reflect higher female employment in informal sector: NSSO-based targets of 86 percent female informal employment vs 74 percent male informal employment inform calibration.
- Home-work and participation:
  - Female-to-male ratio of home-work HP_f,t / HP_m,t obtained at 14.19 given φ^m_le = 0.7 and φ^f_le = 0.1.
  - Participation calibration: NSSO 2015 female labor force participation rate P_f / p_f ≈ 25 percent; male P_m / p_m ≈ 80 percent.
  - Model yields P_f / p_f = 20.3 and P_m / p_m = 85.4 by setting φ_m = 0.7 and φ_f = 1.

### Policy assessment (section 4 preview)
- After matching the steady state to the Indian economy, permanent deterministic changes in structural policy variables are analyzed to assess transitions to new steady states following reforms.

*Source: wp18212 - 2.9 Market Clearing and Aggregation (IMF working paper PDF).*

### 4.1 Gender-Specific Policies

### 4.1 Gender-Specific Policies

### Policy setup and scenarios
- Objective: study long-run impact of closing gender gaps in access to formal credit (no gender gaps in access to credit).
  - Implementation in model: set LTVf,F,t = LTVm,F,t and βf = βm (example calibration used: LTVf,F,t = LTVm,F,t = 0.7 and βf = βm = 0.98).
- Three additional scenarios studied in combination with financial inclusion:
  - Deregulation: lower hiring costs in the formal sector (10 percent permanent decrease in βHC F).
  - Skills: eliminate gender gaps in skill (skillm s = skillf s).
  - Safety: eliminate gender differential disutility from working outside home (φf t = φm t).

### Baseline gender-inequality steady-state indicators (as reported)
- U = 0.13 unemployment rate
- LI/LF + LI = 0.75 share of informal employment
- YI/Y = 0.49 share of informal output
- Yf/Y = 0.06 share of female entrepreneurs’ output
- Loanf,F/Loanf,F+Loanf,I = 0.23 share of female entrepreneurs’ formal finances
- Lf/L = 0.12 share of female entrepreneurs’ employment
- Wm/Wf = 1.4 gender wage gap (male-to-female wage ratio)
- Lf I / (Lf F + Lf I) = 0.80 share of females’ informal employment
- Lm I / (Lm F + Lm I) = 0.70 share of males’ informal employment
- HPf t / HPm t = 14.19 gender gap in home-work
- Pf pf = 0.20 female labor force participation
- Pm pm = 0.85 male labor force participation

### Transmission channels—Financial access (no gender gaps in formal credit)
- Direct effects of higher LTV and equal β:
  - Female entrepreneurs obtain greater access to formal credit → boosts investment and demand for capital → raises price of capital and collateral value → eases access to credit further.
  - More female entrepreneurs set up businesses in the formal sector.
  - Demand for male and female workers in formal sector increases → higher overall labor force participation.
  - Female entrepreneurs in formal sector hire without gender discrimination → female labor force participation rises more than male participation → gender wage gaps fall (limited).
  - Consumption increases; demand for both formal and informal goods rises → demand for informal labor and informal entrepreneurship increases.
- Offsetting effect due to labor market rigidities:
  - Increase in labor supply not matched by formal job creation → large share of new labor market participants enter informal, low-paying jobs.
  - Overall share of formal employment falls; fall in gender wage gaps remains small.

### Transmission channels—Deregulation (financial access + lower βHC F)
- Lower hiring costs in formal sector amplify financial-access effects:
  - Formal firms hire more; more firms operate formally → increase in formal employment and entrepreneurship (male and female).
  - Formal price mark-ups εF/(εF−1) fall → external competitiveness and exports improve → investment and GDP rise.
- Distributional effect:
  - Substitution effect (higher job-finding in formal sector) and household income effect both raise Pm and Pf, but substitution dominates.
  - Gender gaps in participation widen (Pm increases more than Pf) because gender-related constraints (lower skills and discrimination) limit female gains.
  - Male workers gain more; increase in male formal entrepreneurship exceeds female increase.

### Transmission channels—Skills (financial access + equalized female skills)
- Eliminating skill gaps raises female productivity:
  - Entrepreneurs substitute male workers with more productive female workers; female hiring in formal sector increases relative to informal.
  - Female job-finding rates and Pf rise; female wages WfF and WfI increase in both sectors.
  - Male participation effect is muted due to (i) household income effect and (ii) lower male job-finding.
  - Higher aggregate formality and lower unemployment boost GDP; combined effect of higher female skills and financial inclusion yields much larger increases in GDP, employment, and formality.

### Transmission channels—Safety (financial access + equalized disutility φ)
- Eliminating gender differential disutility from working outside home increases Pf:
  - Pf rises more than in Financial access scenario, reducing female wages, increasing hiring and employment.
  - Gains in GDP are small relative to other scenarios because increase in entrepreneurship (especially female entrepreneurship) is lowest.
  - Females tend to be employed more in informal sector jobs → quality of female employment may worsen even as participation rises.
  - Model links safety only to female labor supply decision, not entrepreneurship; allowing effects on entrepreneurship could change results substantially.

### Long-run macroeconomic impacts (Table 8: percentage deviations from steady state)
- Financial access:
  - GDP = 1.6
  - Unemp. = -5
  - Formality (Labor Product Formal Informal) = -2.1 0.9 0.6 1.8 0.07 (table columns correspond to: Labor Product Formal Informal ? — preserve values exactly as presented)
  - LFP = 0.61
  - Entrepreneurship = 1.80.07
- + Deregulation:
  - GDP = 4.7
  - Unemp. = -9.1
  - Formality = 11.5 14.1 2.14.5-1.5 (preserve verbatim row entries)
- + Skills:
  - GDP = 6.8
  - Unemp. = -6.8
  - Formality = 10 19.7 1.14.9-2.7 (preserve verbatim row entries)
- + Safety:
  - GDP = 0.9
  - Unemp. = -80.5
  - Formality = 0.5 0.51.1-0.2-0.4 (preserve verbatim row entries)
Note: All values are percentage deviations from steady state. Unemp. is unemployment, LFP is labor force participation, formality is the share of formal sector in each market.

### Long-run impacts on gender gaps (Table 9: percentage deviations from steady state)
- Financial access (columns: Entrepreneurship M F; LFP M F; Formal share of employment M F; Wage gap):
  - Entrepreneurship Formal: -0.84 1.5
  - Entrepreneurship Informal: -1.5 0.4
  - LFP M F: 1.4 -31.2 -0.8 (preserve verbatim row entries)
- + Deregulation:
  - Entrepreneurship: 6.6 2.7 -1.7 -1.2 5.3 4.5 12.19.3-6.4 (preserve verbatim row entries)
- + Skills:
  - Entrepreneurship: 3.3 6.3 -3.7 -1.6 0.4 4.3-2.526-18.7 (preserve verbatim row entries)
- + Safety:
  - Entrepreneurship: -1.4 0.8 -0.7 -0.1 3.3 0.61.4-2.2-0.9 (preserve verbatim row entries)
Note: All values are percentage deviations from steady state. LFP is labor force participation. M and F correspond to male and female. Wage gap is male-to-female wage ratio.

### Key quantitative findings (from Conclusion)
- Closing gender gaps in financial access (India calibration) yields:
  - GDP gains of 1.6 percent
  - Unemployment falls by 5 percent
  - Greater female entrepreneurial activity in formal sector; higher female labor force participation and employment
  - Share of informality increases due to labor market rigidities, limiting gains
- Financial access + Deregulation (10 percent lower hiring costs) yields:
  - GDP increase of 4.7 percent
  - Unemployment fall of 9 percent
  - 11.5 percent increase in share of formal employment of both males and females
  - Male workers gain more than females; gender gaps in labor market worsen
- Financial access + Skills (eliminate female skill gaps) yields:
  - Potential increase in India’s output by 6 percent (combined effect)
  - Larger reductions in gender inequality in LFP, formality, wages, and entrepreneurship; larger gains in GDP, employment, and formality
- Financial access + Safety yields:
  - Higher female participation but small GDP gains and increased female employment in informal jobs

### Policy implications and trade-offs
- Policy objectives must be explicit: increase number of female entrepreneurs versus female share in formal entrepreneurship; increase female labor force participants versus female share in labor force; increase female employment versus female share in formal sector.
- For India, priorities could include stimulating the share of females and formality in economic activities.
- Recommended strategy: implement policies that disproportionately benefit females (e.g., targeting constraints more binding for women) simultaneously with policies that lower informality to better capture gains from financial inclusion and labor-market reforms.

*Source: IMF Working Paper — section 4.1 "Gender-Specific Policies" (wp18212 — 4.1 Gender-Specific Policies)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18212.pdf_