Why not Choose a Better Job?

Flexibility, Social Norms, and Gender Gaps in Japan

Kazuharu Yanagimoto

kazuharu.yanagimoto@cemfi.edu.es

CEMFI

June 7, 2023

Female Workers in Japan

Gap in Median Earnings of Full-time Workers in 2019

Fraction of Part-time in Female Workers in 2019

Large gap in earnings and high ratio of part-time jobs
Female participation is not low

Why is the gender wage gap large in Japan?

Why is the fraction of part-time workers large for women in Japan?

What Do I Do?

Document Female Employment in Japan

Large gender diff. in participation, occupations, working hours, and wage
Regular vs Non-regular job & Social norms on gender roles

Build a model

Choices on occupations and working hours
- Occupations differ in the way hours map into earnings (linear vs. convex)
Utility cost associated to social norms
- Wives earnings more than husbands

Model explains

All gender gaps in participation
33% in occupational choices, 74% in labor hours, and 34% in wage

Facts

Data

Japan Panel Study of Employment Dynamics (JPSED)

57,284 men and women older than 15 in Japan
Panel data 2015-2019
Earnings, working hours, housework, labor contracts
Use samples aged 25-59

Survey on Dual-Income Couples’ Household Economy and Attitudes

2200 couples, women (men) aged 35-49 (30-55), in the Greater Tokyo Area
One-year survey in 2014
Earnings, working hours, housework, types of contracts

Regular and Non-regular Jobs

In Japanese statistics, a definition is used: Regular and Non-regular jobs

Based on “how their occupations are classified in the company”
There is no precise definition, but typically,

	Regular	Non-Regular
Contract	Permanent	Temporary
Hours (week)	40/40+	Lower and Dispersed
Wage	High	Low

In JPSED,

92 % (91 %) of male (female) regular workers have permanent contracts
13 % (14 %) of male (female) non-regular workers have permanent contracts

Occupational Choices of Married Men and Women

Why Do Women Choose Non-regular Jobs?

Reasons for Choosing Non-regular Job, Women

Job Flexibility and Convex Earning

Goldin (2014) defines the two types of jobs by earning schedule

Linear jobs are lower wages and high flexibility
Non-linear (convex) jobs are high wage and low flexibility

These characteristics correspond to Regular and Non-regular jobs! Regression

Before Going to the Model…

Key Features

Job Flexibility (Regular vs. Non-regular)
Social Norm on Wife’s Earnings Cross-country Coparison

Gender Gaps

	Description	Gap	Men	Women
Partcipation	Participation rate	0.27	98%	70%
Ocuupation	Fraction of regular workers	0.59	89%	32%
Labor Hours	Mean of log weekly working hours	0.49	44.2h	20.3h
Wage	Mean of log hourly wage	0.76	2958 JPY	1534 JPY
Data: married, 25-59 aged in JPSED2016-2020

Model

Households’ Problem

Economy consists of couples, including husbands \((g = m)\) and wives \((g = f)\)
choose an occupation \(j_g\) from regular \(R\), non-regular \(NR\), not-working \(NW\)
Endowed one unit of time, and choose working hours \(h_m, h_f\), home hours \(T_m, T_f\), and leisure \(1 - h_m - T_m, 1 - h_f - T_f\)

\[ \max_{h_m, h_f, T_m, T_f, j_m, j_f} U = \log c + \gamma \log H(1 - h_m - T_m, 1 - h_f - T_f) - \delta \mathbb{1}\{e_m < e_f\} \]

subject to

\[\begin{aligned} c &= e(h_m, j_m) + e(h_f, j_f) \\ T &= T_m + T_f \end{aligned} \]

\(H(\cdot)\) : Joint leisure function
\(e(h, j)\) : Earning
\(T\) : Home hours requirement
\(\delta\) : Utility cost

Productivity

Each husband and wife is endowed job specific productivity:

\[ \begin{pmatrix}a_{m, R} \\ a_{f, R} \\ a_{m, NR} \\ a_{f, NR}\end{pmatrix} \sim \log\mathcal{N}\left(\begin{pmatrix}0 \\ 0 \\ \mu_{NR} \\ \mu_{NR}\end{pmatrix}, \begin{pmatrix} \sigma^2 & \rho_{mf}\sigma^2 & \rho_{R, NR}\sigma^2 & \rho_{R, NR}\rho_{mf} \sigma^2 \\ \cdot & \sigma^2 & \rho_{R, NR}\rho_{mf} \sigma^2 & \rho_{R, NR} \sigma^2 \\ \cdot & \cdot & \sigma^2 & \rho_{mf} \sigma^2 \\ \cdot & \cdot & \cdot & \sigma^2 \end{pmatrix}\right) \]

\(\mu_{NR} < 0 \Rightarrow\) Non-regular workers earns less than regular worker
\(\rho_{mf} > 0 \Rightarrow\) Assortative Mating
\(\rho_{R, NR} > 0 \Rightarrow\) Regular and Non-regular abilities are linked

No Gender Difference in Productivity

Convex Wage Schedules

Regular Jobs

\[ e(h, R) = \begin{cases} a_R h^{1 + \theta} & h < \bar{h} \\ a_R \left(\bar{h}^{1 + \theta} + \lambda_{R} \bar{h}^{\theta}(h - \bar{h})\right) & h > \bar{h} \end{cases} \]

Non-regular Jobs

\[ e(h, NR) = \begin{cases} a_{NR} h & h \le \bar{h} \\ a_{NR} \left(\bar{h} + \lambda_{NR} (h - \bar{h})\right) & h > \bar{h} \end{cases} \]

Leisure Function

\[ H = \left(\nu(1 - h_m - T_m)^{\xi} + (1 - \nu)(1 - h_f - T_f)^{\xi}\right)^{1/\xi} \]

\(\nu\) : share parameter. Each household is endowed \(\nu \sim Beta(\alpha_{\nu}, \beta_{\nu})\)
\(\xi\) : complementarity. \(\xi < 0 \Rightarrow\) complement

Home Hours Requirement

\[ \begin{aligned} T &= T_m + T_f \\ \frac{1}{2}T & \sim Beta(\alpha_T, \beta_T) \end{aligned} \]

Households has a home hours requirement \(T \in [0, 2]\)
\(T\) does not increase the utility
captures the heterogeneity of home hours requirements (children)

Estimation

Calibration Strategy

15 Parameters

\[ \{\underbrace{\lambda_{R}, \lambda_{NR},\theta, }_{\text{production function}} \underbrace{\mu_{NR}, \sigma^2, \rho_{R, NR}, \rho_{mf},}_{\text{productivity}} \,\, \underbrace{\gamma, \xi, \alpha_{\nu}, \beta_{\nu},}_{\text{leisure}} \underbrace{\alpha_{T}, \beta_{T},}_{\text{home hours }} \underbrace{\alpha_{\delta}, \beta_{\delta}}_{\text{social norm}}\} \]

Method of Simulated Moments

Model produces occupations, working hours, and wages of household
Compute 15 moments (e.g. ratio of regular workers, mean of working hours, gender correlation of wage…)
Minimize the distance between moments from data and model

Estimation

Parmeter	Value	Target	Data	Model
λ_R	0.57	mean of h_f for regular workers	0.50	0.48
λ_NR	0.63	mean of h_f for NR workers	0.30	0.27
θ	2.96	share of regular workers, females	0.32	0.37
μ_NR	−3.15	share of NR workers, females	0.38	0.28
σ	1.03	s.d. of ln w_f for R workers	0.72	0.72
ρ_{R, NR}	0.14	mean diff. of ln w_{f, R} and ln w_{f, NR}	0.62	0.62
ρ_mf	0.01	corr. of log wages, R×R couples	0.49	0.50
γ	0.84	s.d. of h_f for regular workers	0.11	0.11
ξ	−8.29	s.d. of h_f for NR workers	0.14	0.15
α_ν	13.04	mean of T_m for regular workers	0.14	0.13
β_ν	1.15	mean of T_m for NR workers	0.13	0.14
α_T	1.59	mean of T_f for regular workers	0.28	0.21
β_T	3.57	mean of T_f for NR workers	0.32	0.37
α_δ	0.59	share of couples with e_m < e_f	0.07	0.08
β_δ	11.81	corr. of working hours, couples	0.19	0.18

Estimation

Parmeter	Value	Target	Data	Model
λ_R	0.57	mean of h_f for regular workers	0.50	0.48
λ_NR	0.63	mean of h_f for NR workers	0.30	0.27
θ	2.96	share of regular workers, females	0.32	0.37
μ_NR	−3.15	share of NR workers, females	0.38	0.28
σ	1.03	s.d. of ln w_f for R workers	0.72	0.72
ρ_{R, NR}	0.14	mean diff. of ln w_{f, R} and ln w_{f, NR}	0.62	0.62
ρ_mf	0.01	corr. of log wages, R×R couples	0.49	0.50
γ	0.84	s.d. of h_f for regular workers	0.11	0.11
ξ	−8.29	s.d. of h_f for NR workers	0.14	0.15
α_ν	13.04	mean of T_m for regular workers	0.14	0.13
β_ν	1.15	mean of T_m for NR workers	0.13	0.14
α_T	1.59	mean of T_f for regular workers	0.28	0.21
β_T	3.57	mean of T_f for NR workers	0.32	0.37
α_δ	0.59	share of couples with e_m < e_f	0.07	0.08
β_δ	11.81	corr. of working hours, couples	0.19	0.18

\(\xi < 0\)

Leisure by husband and wife is complement

Estimation

Parmeter	Value	Target	Data	Model
λ_R	0.57	mean of h_f for regular workers	0.50	0.48
λ_NR	0.63	mean of h_f for NR workers	0.30	0.27
θ	2.96	share of regular workers, females	0.32	0.37
μ_NR	−3.15	share of NR workers, females	0.38	0.28
σ	1.03	s.d. of ln w_f for R workers	0.72	0.72
ρ_{R, NR}	0.14	mean diff. of ln w_{f, R} and ln w_{f, NR}	0.62	0.62
ρ_mf	0.01	corr. of log wages, R×R couples	0.49	0.50
γ	0.84	s.d. of h_f for regular workers	0.11	0.11
ξ	−8.29	s.d. of h_f for NR workers	0.14	0.15
α_ν	13.04	mean of T_m for regular workers	0.14	0.13
β_ν	1.15	mean of T_m for NR workers	0.13	0.14
α_T	1.59	mean of T_f for regular workers	0.28	0.21
β_T	3.57	mean of T_f for NR workers	0.32	0.37
α_δ	0.59	share of couples with e_m < e_f	0.07	0.08
β_δ	11.81	corr. of working hours, couples	0.19	0.18

\(\xi < 0\)

Leisure by husband and wife is complement

\(\alpha_{\nu} =\) 13.04, \(\beta_{\nu} =\) 1.15

\(E[\nu] =\) 0.92 > 0.5
Husbands have a higher weight on joint leisure

Estimation

Parmeter	Value	Target	Data	Model
λ_R	0.57	mean of h_f for regular workers	0.50	0.48
λ_NR	0.63	mean of h_f for NR workers	0.30	0.27
θ	2.96	share of regular workers, females	0.32	0.37
μ_NR	−3.15	share of NR workers, females	0.38	0.28
σ	1.03	s.d. of ln w_f for R workers	0.72	0.72
ρ_{R, NR}	0.14	mean diff. of ln w_{f, R} and ln w_{f, NR}	0.62	0.62
ρ_mf	0.01	corr. of log wages, R×R couples	0.49	0.50
γ	0.84	s.d. of h_f for regular workers	0.11	0.11
ξ	−8.29	s.d. of h_f for NR workers	0.14	0.15
α_ν	13.04	mean of T_m for regular workers	0.14	0.13
β_ν	1.15	mean of T_m for NR workers	0.13	0.14
α_T	1.59	mean of T_f for regular workers	0.28	0.21
β_T	3.57	mean of T_f for NR workers	0.32	0.37
α_δ	0.59	share of couples with e_m < e_f	0.07	0.08
β_δ	11.81	corr. of working hours, couples	0.19	0.18

\(\xi < 0\)

Leisure by husband and wife is complement

\(\alpha_{\nu} =\) 13.04, \(\beta_{\nu} =\) 1.15

\(E[\nu] =\) 0.92 > 0.5
Husbands have a higher weight on joint leisure

\(\alpha_{T} =\) 1.59, \(\beta_{T} =\) 3.57

Home hours requirement is 49 hours per week

Why not Choose a Better Job?

Female Workers in Japan

What Do I Do?

Document Female Employment in Japan

Build a model

Model explains

Facts

Data

Japan Panel Study of Employment Dynamics (JPSED)

Survey on Dual-Income Couples’ Household Economy and Attitudes

Regular and Non-regular Jobs

Occupational Choices of Married Men and Women

Why Do Women Choose Non-regular Jobs?

Job Flexibility and Convex Earning

Social Norms

Before Going to the Model…

Key Features

Gender Gaps

Model

Households’ Problem

Productivity

Convex Wage Schedules

Leisure Function

Home Hours Requirement

Estimation

Calibration Strategy

15 Parameters

Method of Simulated Moments

Estimation

Estimation

Estimation

Estimation

Occupational Choices (Not-Targeted)