Why not Choose a Better Job?

Flexibility, Social Norms, and Gender Gaps in Japan

Kazuharu Yanagimoto

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

Female Laborforce Participation 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?

Flexibility of the Job

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

Social Norms

Bertrand, Kamenica, and Pan (2015)

  • A gap in the density of the wife’s share of earnings at 50% in US
  • Interpreted as the existence of social norms

Japanese Data

  • A stark gap is seen in Japanese data
  • Rising pattern just before 50%
  • Marriage penalty Marriage Penalty

Before Going to the Model…

Key Features

  1. Job Flexibility (Regular vs. Non-regular)
  2. 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

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

Estimation

Parmeter Value Target Data Model

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

11.81

corr. of working hours, couples

0.19 0.18

Estimation

Parmeter Value Target Data Model

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

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

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

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

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

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

Occupational Choices (Not-Targeted)