## sipea2023030 — A New Growth Engine for Japan: Women in STEM Fields

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**Canonical URL:** [sipea2023030 — A New Growth Engine for Japan: Women in STEM Fields](https://www.imf.org/-/media/files/publications/selected-issues-papers/2023/english/sipea2023030.pdf)

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---

### A. Introduction
- Female labor force participation rate rose by 10 percentage points in the last 10 years, approaching the highest level among G7 countries.
- Share of women enrolled in STEM fields in university in Japan is around 7 percent (lowest among G7).
- Factors discouraging women from STEM (Homma et al. (2013)):
  - Few role models for younger women.
  - Unconscious bias among male researchers towards female colleagues.
  - Avoiding competition and underestimation of ability by women themselves.
- Cultural and workplace features compounding under-representation:
  - Social norm of long working hours and mandatory socializing after work.
  - Japan ranks second worst in The Economist’s Glass Ceiling index for environment for working women.
- Innovation trends and policy challenge:
  - Patent grants in Japan have declined since 2012.
  - With an ageing labor force and plateauing participation, boosting TFP through innovation is necessary.
- Key quantified claim:
  - Bridging the gender gap in STEM fields can boost TFP growth by 20 percent.

### B. Endogenous Growth Model with STEM Talent (Model Overview)
- Model structure:
  - Standard endogenous growth model with monopolistic competition in intermediate goods; final goods producers operate under perfect competition.
  - STEM workers ≡ researchers; R&D by researchers yields higher-quality intermediate goods and drives growth.
  - Research talent (for STEM) differs across individuals and follows a Pareto distribution; all agents have identical talent for final goods production.
  - Final goods wages are uniform; researcher pay depends on individual research talent. Only sufficiently talented individuals choose research.
- Modeling discrimination:
  - Schooling bias modeled as a uniform discount factor on women’s research talent (reduces productivity).
  - Labor market discrimination modeled as a uniform discount factor on female researchers’ wages (no productivity effect).
  - Schooling bias has a larger effect on growth because it lowers female researcher productivity.
- Misallocation mechanism:
  - Discrimination raises the talent cutoff for women to become researchers, reducing female participation in STEM and lowering aggregate research talent and long-term growth.
- Calibration strategy:
  - Baseline assumes all misallocation comes from labor market discrimination (conservative estimate).
  - Robustness check considers scenario where half of discrimination comes from schooling bias.
- Key model equations/assumptions (from Box 1 summary):
  - Agents maximize present discounted utility: U(ε,t)=∫_t^∞ e^{−ρ(τ−t)}⋅c(ε,τ)^{1−γ}−1 / (1−γ) dτ.
  - Final goods production: Y(t)=∫_0^1 A(i,t) x(i,t)^α di ⋅ L_Y(t)^{1−α}.
  - Aggregate idea arrival rate: z(t)=η⋅H_R(t); a successful idea raises machine quality by factor λ.

### Key Parameters (as calibrated for Japan)
- Parameters Set Externally:
  - α = 1 - labor share; Source: PWT10, Value: 0.4
  - ρ = Discount rate; Value: 0.02
  - γ = Risk Aversion (CRRA); Source: Hall (2009), Value: 2.0
- Parameter Set Independently:
  - θ = Pareto shape parameter; Source: Basic Survey on Wage Structure, Value: 3.5
- Parameters Estimated Jointly (targeted moments, values):
  - η = 0.024 (TFP growth rate; Source: PWT10)
  - λ = 2.4 (% of STEM workers among male: 10%; Source: Basic Survey on Wage Structure)
  - δ = 0.4 (% of STEM workers among female: 2%; Source: Basic Survey on Wage Structure)

### C. Results (Quantitative Findings)
- TFP growth:
  - Removing discrimination against female researchers raises TFP growth by 20 percent in the baseline scenario (all misallocation from labor market discrimination).
- Researcher composition and quantities:
  - Total number of researchers increases by about 20 percent as additional female researchers outnumber replaced male researchers.
  - Entry of new female researchers pushes down unit wage for researchers and crowds out marginal male researchers.
- Welfare impacts (consumption-equivalent, Lucas 1987 measure):
  - Old female researchers: CE Welfare change = 12.5 percent
  - New female researchers: CE Welfare change = 12.5 percent [4.2~12.5]
  - Remaining male researchers: CE Welfare change = -5.3 percent [-5.3,4.2]
  - Male researchers who dropped out: CE Welfare change = -5.3 percent
  - Workers (non-researchers): CE Welfare change = 4.2 percent
  - Average consumption-equivalent welfare rises by about 4 percent.
- Robustness scenario (half of distortion from schooling bias):
  - Removing schooling barriers and the pay gap can boost TFP growth by 26 percent and average welfare by 4.5 percent.
- Comparisons:
  - Welfare gains from removing gender barriers (average ~4 percent) exceed the gains from a 10-percentage point increase in female LFPR under current labor market structure (about 3.5 percent).

### D. Policy Implications (Prescriptive Findings)
- Address both financial and non-financial barriers:
  - Explicit pay gaps: Japan’s gender pay gap is the third highest among OECD countries.
  - Implicit pay gaps: disproportionate family care burdens, workplace discrimination, maternity harassment.
    - 30 percent of women quit their jobs when they give birth.
    - One out of every five pregnant full-time working women have experienced maternity harassment (Japan Institute for Labour Policy and Training).
  - Cultural bias and school-level stereotyping deter girls from STEM.
- Government actions to reduce explicit pay gap and lead by example:
  - “Framework policies” requiring companies to increase transparency of their gender wage gap.
  - Promote female leaders in public agencies.
  - Public universities may consider female-specific quotas to improve diversity in STEM.
- Work style reforms and labor market flexibility:
  - Increase male take-up of paternity leave; government target to double number of men taking paternity leave by 2025.
  - Consider mandatory leave policies if needed.
  - Reduce working hours and adopt flexible work arrangements (teleworking) to rebalance housework contributions.
  - Make hiring and promotion in STEM more merit-based and less seniority-based to facilitate reentry as full-time workers after childbirth (example: more flexible hiring in medical and legal fields aids female reentry).
- Education and societal measures:
  - Training and workshops for teachers and parents to counter gender bias.
  - Targeted research grants and special quotas for female scientists to correct for bias and improve diversity (Tokyo Tech’s decision to introduce special quotas noted as a welcome step).
  - Role models and mentoring: invite successful female scientists to speak and support mentoring by senior women on work-family conflict navigation.

### Section 2 — Decentralized equilibrium; gender discrimination details; welfare measurement
- Decentralized equilibrium: definition and conditions
  - A decentralized equilibrium of the model consists of time paths of individual choices {c(ε,t), a(ε,t)}_{t=0}^∞, average technology {A(t)}_{t=0}^∞, efficiency wage of each occupation {w_Y(t), w_R(ε,t)}_{t=0}^∞, labor demand in final goods sector {L_Y(t)}_{t=0}^∞, aggregate quantities {Y(t), X(t), C(t)}_{t=0}^∞, interest rate {r(t)}_{t=0}^∞ and talent cutoff of researchers {ε^*(t)}_{t=0}^∞ such that:
    - Agents maximize utility;
    - Demand of labor and intermediate goods is given by the final goods sector;
    - Each monopolist of intermediate goods maximizes profits;
    - There is free entry of intermediate firms, requiring w_R(t) to equal to the value of innovation;
    - An individual chooses to be a STEM worker if her talent ε is greater than the cutoff ε^*, where ε^* is pinned down by w_Y(t) = ε^*(t) w_R(t);
    - Growth is pinned down by the amount of total STEM talent among researchers.
- Gender discrimination in STEM: modeling approach
  - Gender discrimination in STEM fields incorporates both explicit pay gaps and implicit barriers.
  - For simplicity, the discrimination is captured by a discount factor (i.e., δ) on female researcher’s wages in the model.
  - The talent cutoff for female researchers ε_F^*(t) is pinned down by:
    - w_Y(t) = ε_F^*(t) (1−δ) ⋅ w_R^F(t).
- Consumption-equivalent welfare (Box 2)
  - As in Lucas (1987), an individual’s welfare change is defined as the amount of extra consumption ω(ε) that a rational consumer would require in order to be indifferent between the new equilibrium (after removing the barriers to women in STEM) and the old equilibrium. ω(ε) would differ across individuals depending on their research talent ε and gender.
  - Individual indifference condition (as presented):
    - ∫_0^∞ e^{−ρ t} ⋅ [ (1 + ω(ε)) ⋅ c_t^{표표표표표표}(ε) ]^{1−γ} / (1−γ) dt = ∫_0^∞ e^{−ρ t} ⋅ [ c_t^{닌닌닌닌}(ε) ]^{1−γ} / (1−γ) dt
    - (As shown in the source, the left-hand side uses (1 + ω(ε)) ⋅ c_t^{표표표표표표}(ε) inside the period utility; the right-hand side uses c_t^{닌닌닌닌}(ε).)
  - The average welfare change ω is calculated using the total welfare of all individuals:
    - ∫_0^∞ e^{−ρ t} ⋅ ∫_1^∞ [ (1 + ω) ⋅ c_t^{표표표표표표}(ε) ]^{1−γ} / (1−γ) f(ε) dε ⋅ dt = ∫_0^∞ e^{−ρ t} ⋅ ∫_1^∞ [ c_t^{닌닌닌닌}(ε) ]^{1−γ} / (1−γ) f(ε) dε ⋅ dt

_Italic source: IMF Selected Issues Paper SIP/2023/030 (Prepared by Rui Xu, March 2023)._

### Section 1

### A New Growth Engine for Japan: Women in STEM Fields

### A. Introduction
- Female labor force participation rate rose by 10 percentage points in the last 10 years, approaching the highest level among G7 countries.
- Share of women enrolled in STEM fields in university in Japan is around 7 percent (lowest among G7).
- Factors discouraging women from STEM (Homma et al. (2013)):
  - Few role models for younger women.
  - Unconscious bias among male researchers towards female colleagues.
  - Avoiding competition and underestimation of ability by women themselves.
- Cultural and workplace features compounding under-representation:
  - Social norm of long working hours and mandatory socializing after work.
  - Japan ranks second worst in The Economist’s Glass Ceiling index for environment for working women.
- Innovation trends and policy challenge:
  - Patent grants in Japan have declined since 2012.
  - With an ageing labor force and plateauing participation, boosting TFP through innovation is necessary.
- Key quantified claim:
  - Bridging the gender gap in STEM fields can boost TFP growth by 20 percent.

### B. Endogenous Growth Model with STEM Talent (Model Overview)
- Model structure:
  - Standard endogenous growth model with monopolistic competition in intermediate goods; final goods producers operate under perfect competition.
  - STEM workers ≡ researchers; R&D by researchers yields higher-quality intermediate goods and drives growth.
  - Research talent (for STEM) differs across individuals and follows a Pareto distribution; all agents have identical talent for final goods production.
  - Final goods wages are uniform; researcher pay depends on individual research talent. Only sufficiently talented individuals choose research.
- Modeling discrimination:
  - Schooling bias modeled as a uniform discount factor on women’s research talent (reduces productivity).
  - Labor market discrimination modeled as a uniform discount factor on female researchers’ wages (no productivity effect).
  - Schooling bias has a larger effect on growth because it lowers female researcher productivity.
- Misallocation mechanism:
  - Discrimination raises the talent cutoff for women to become researchers, reducing female participation in STEM and lowering aggregate research talent and long-term growth.
- Calibration strategy:
  - Baseline assumes all misallocation comes from labor market discrimination (conservative estimate).
  - Robustness check considers scenario where half of discrimination comes from schooling bias.

- Key model equations/assumptions (from Box 1 summary):
  - Agents maximize present discounted utility: U(ε,t)=∫_t^∞ e^{−ρ(τ−t)}⋅c(ε,τ)^{1−γ}−1 / (1−γ) dτ.
  - Final goods production: Y(t)=∫_0^1 A(i,t) x(i,t)^α di ⋅ L_Y(t)^{1−α}.
  - Aggregate idea arrival rate: z(t)=η⋅H_R(t); a successful idea raises machine quality by factor λ.

### Key Parameters (as calibrated for Japan)
- Parameters Set Externally:
  - α = 1 - labor share; Source: PWT10, Value: 0.4
  - ρ = Discount rate; Value: 0.02
  - γ = Risk Aversion (CRRA); Source: Hall (2009), Value: 2.0
- Parameter Set Independently:
  - θ = Pareto shape parameter; Source: Basic Survey on Wage Structure, Value: 3.5
- Parameters Estimated Jointly (targeted moments, values):
  - η = 0.024 (TFP growth rate; Source: PWT10)
  - λ = 2.4 (% of STEM workers among male: 10%; Source: Basic Survey on Wage Structure)
  - δ = 0.4 (% of STEM workers among female: 2%; Source: Basic Survey on Wage Structure)

### C. Results (Quantitative Findings)
- TFP growth:
  - Removing discrimination against female researchers raises TFP growth by 20 percent in the baseline scenario (all misallocation from labor market discrimination).
- Researcher composition and quantities:
  - Total number of researchers increases by about 20 percent as additional female researchers outnumber replaced male researchers.
  - Entry of new female researchers pushes down unit wage for researchers and crowds out marginal male researchers.
- Welfare impacts (consumption-equivalent, Lucas 1987 measure):
  - Old female researchers: CE Welfare change = 12.5 percent
  - New female researchers: CE Welfare change = 12.5 percent [4.2~12.5]
  - Remaining male researchers: CE Welfare change = -5.3 percent [-5.3,4.2]
  - Male researchers who dropped out: CE Welfare change = -5.3 percent
  - Workers (non-researchers): CE Welfare change = 4.2 percent
  - Average consumption-equivalent welfare rises by about 4 percent.
- Robustness scenario (half of distortion from schooling bias):
  - Removing schooling barriers and the pay gap can boost TFP growth by 26 percent and average welfare by 4.5 percent.
- Comparisons:
  - Welfare gains from removing gender barriers (average ~4 percent) exceed the gains from a 10-percentage point increase in female LFPR under current labor market structure (about 3.5 percent).

### D. Policy Implications (Prescriptive Findings)
- Address both financial and non-financial barriers:
  - Explicit pay gaps: Japan’s gender pay gap is the third highest among OECD countries.
  - Implicit pay gaps: disproportionate family care burdens, workplace discrimination, maternity harassment.
    - 30 percent of women quit their jobs when they give birth.
    - One out of every five pregnant full-time working women have experienced maternity harassment (Japan Institute for Labour Policy and Training).
  - Cultural bias and school-level stereotyping deter girls from STEM.
- Government actions to reduce explicit pay gap and lead by example:
  - “Framework policies” requiring companies to increase transparency of their gender wage gap.
  - Promote female leaders in public agencies.
  - Public universities may consider female-specific quotas to improve diversity in STEM.
- Work style reforms and labor market flexibility:
  - Increase male take-up of paternity leave; government target to double number of men taking paternity leave by 2025.
  - Consider mandatory leave policies if needed.
  - Reduce working hours and adopt flexible work arrangements (teleworking) to rebalance housework contributions.
  - Make hiring and promotion in STEM more merit-based and less seniority-based to facilitate reentry as full-time workers after childbirth (example: more flexible hiring in medical and legal fields aids female reentry).
- Education and societal measures:
  - Training and workshops for teachers and parents to counter gender bias.
  - Targeted research grants and special quotas for female scientists to correct for bias and improve diversity (Tokyo Tech’s decision to introduce special quotas noted as a welcome step).
  - Role models and mentoring: invite successful female scientists to speak and support mentoring by senior women on work-family conflict navigation.

_Italic source: IMF Selected Issues Paper SIP/2023/030 (Prepared by Rui Xu, March 2023)._

### Section 2

### sipea2023030 - Section 2

### Decentralized equilibrium: definition and conditions
- A decentralized equilibrium of the model consists of time paths of individual choices {c(ε,t), a(ε,t)}_{t=0}^∞, average technology {A(t)}_{t=0}^∞, efficiency wage of each occupation {w_Y(t), w_R(ε,t)}_{t=0}^∞, labor demand in final goods sector {L_Y(t)}_{t=0}^∞, aggregate quantities {Y(t), X(t), C(t)}_{t=0}^∞, interest rate {r(t)}_{t=0}^∞ and talent cutoff of researchers {ε^*(t)}_{t=0}^∞ such that:
  - Agents maximize utility;
  - Demand of labor and intermediate goods is given by the final goods sector;
  - Each monopolist of intermediate goods maximizes profits;
  - There is free entry of intermediate firms, requiring w_R(t) to equal to the value of innovation;
  - An individual chooses to be a STEM worker if her talent ε is greater than the cutoff ε^*, where ε^* is pinned down by w_Y(t) = ε^*(t) w_R(t);
  - Growth is pinned down by the amount of total STEM talent among researchers.

### Gender discrimination in STEM: modeling approach
- Gender discrimination in STEM fields incorporates both explicit pay gaps and implicit barriers.
- For simplicity, the discrimination is captured by a discount factor (i.e., δ) on female researcher’s wages in the model.
- The talent cutoff for female researchers ε_F^*(t) is pinned down by:
  - w_Y(t) = ε_F^*(t) (1−δ) ⋅ w_R^F(t).

### Consumption-equivalent welfare (Box 2)
- As in Lucas (1987), an individual’s welfare change is defined as the amount of extra consumption ω(ε) that a rational consumer would require in order to be indifferent between the new equilibrium (after removing the barriers to women in STEM) and the old equilibrium. ω(ε) would differ across individuals depending on their research talent ε and gender.
- Individual indifference condition (as presented):
  - ∫_0^∞ e^{−ρ t} ⋅ [ (1 + ω(ε)) ⋅ c_t^{표표표표표표}(ε) ]^{1−γ} / (1−γ) dt = ∫_0^∞ e^{−ρ t} ⋅ [ c_t^{닌닌닌닌}(ε) ]^{1−γ} / (1−γ) dt
  - (As shown in the source, the left-hand side uses (1 + ω(ε)) ⋅ c_t^{표표표표표표}(ε) inside the period utility; the right-hand side uses c_t^{닌닌닌닌}(ε).)
- The average welfare change ω is calculated using the total welfare of all individuals:
  - ∫_0^∞ e^{−ρ t} ⋅ ∫_1^∞ [ (1 + ω) ⋅ c_t^{표표표표표표}(ε) ]^{1−γ} / (1−γ) f(ε) dε ⋅ dt = ∫_0^∞ e^{−ρ t} ⋅ ∫_1^∞ [ c_t^{닌닌닌닌}(ε) ]^{1−γ} / (1−γ) f(ε) dε ⋅ dt

*Source: sipea2023030 - Section 2*

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_Source: https://www.imf.org/-/media/files/publications/selected-issues-papers/2023/english/sipea2023030.pdf_