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Dynamic Female Labor Supply. Zvi Eckstein and Osnat Lifshitz. The Walras-Bowley Lecture, Econometric Society Meeting, June 19-22, 2008 Pittsburgh, USA. Outline. Facts and Survey Decomposition of the growth in FE using standard DP: Eckstein and Wolpin (1989)

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dynamic female labor supply

Dynamic Female Labor Supply

Zvi Eckstein and Osnat Lifshitz

The Walras-Bowley Lecture, Econometric Society Meeting, June 19-22, 2008 Pittsburgh, USA


Facts and Survey

Decomposition of the growth in FE using standard DP: Eckstein and Wolpin (1989)

Traditional vs. Modern families: interpreting the growth in FE by cohorts.

employment by education
Employment by Education
  • Employment of married women was doubled – from 30% to 62%
  • Each education group work more, but not doubled:
    • HSD: from 28% to 41%
    • HSG: from 33% to 59%
    • SC: from 33% to 65%
    • CG: from 45% to 66%
    • PC : from 61% to 73%
  • But, there is a change in the composition of education! Is it enough to explain the increase in married women participation?
education becker
Education (Becker)

Women by cohort

Men composition s.s.


Increase Wages and Close the Gender GapHeckman and McCurdy (1980), Goldin (1990), Galor and Weil (1996), Blau and Kahn (2000), Jones, Manuelli and McGrattan (2003)

Decrease Fertility of Married WomenGronau(1973), Heckman (1974), Rosensweig and Wolpin(1980), Heckman and Willis (1977)


by cohort


Social Norms or/and Cost of ChildrenGoldin (1991), Fernandez, Fogli and Olivetti (2004), Mulligan and Rubinstein (2004)Technical Progress: Greenwood (2004)

models to interpret data
Models to Interpret Data
  • Eckstein-Wolpin (1989) reconstructed model: Fit 1955 cohort FE and measure the contribution of each “story” for the increase FE by fitting the other cohorts.
  • Internal family game (Browning and Chiappori (1998))– Traditional and Modern family games: New empirical dynamic estimable models of household labor supply (Lifshitz (2004), Flinn (2007)) parental impact on children (Tartari (2007))
female labor supply model

Female Labor Supply Model

Eckstein and Wolpin (EW, 1989) –

Model reconstructed

ew model outline
EW Model: Outline
  • The EW DP extended model.
  • Estimation using 1955 cohort CPS data
  • Discussion: DP vs. Reduced form MNL
  • Measure the predicted employment of other cohorts by main “explanations”, changes in: Education, Wages, Fertility, Marriage, Divorce and Cost\Utility.
  • A married woman takes the husband employment and wage as given (Becker, 1974): standard traditional family.

The Mincerian earning function for the woman:

Budget constraint and wage into utility imply:





We adopt a logistic form for the job offer probability, the marriage and divorce probability and the probability of having a new child


Backward Solution following Eckstein and Wolpin (1989) and Keane and Wolpin (1987)

discussion of estimation structural dp vs mnl keane and wolpin 2006
Discussion of Estimation: Structural DP vs. MNL (Keane and Wolpin, 2006)
  • Estimation EW: SGMM using 1955 (+-2 years) CPS data and choice of relevant cross-section moments. Joint estimation of the following equations :
    • Mix DP probit with logit FE offer rate – FE dynamic discrete choice model with cross equation restrictions and forwards RE internal consistency (Lucas, 1976, Sargent, 1983).
    • Log wage with endogenous experience (not age).
    • MNL of Children, Marriage, Divorce
    • Random choice of: husband characteristics and employment; Wage is predicted by Mincerian Eq.
  • Full Reduced form approximation: MNL and Log Wage (KW, 2006, Del-Boca and Sauer 2008)
  • or Logit/regression ( Heckman and Willis , 1977, Hyslop, 1999). .

FE by Age per Cohort

How much of the differences between the 1955 cohort and the other cohorts can be explained by changes in:

  • Education
  • (1)+(2) Wage Growth

(1)+(2)+(3) Number of Children

(1)+(2)+(3)+(4) Marital Status

Unexplained : Cost\Utility reduction in Home Production

decomposition of change in fe
Decomposition of change in FE

Schooling composition graph 1945

Schooling composition graph 1965

Schooling composition graph 1975

decomposition of change in fe cohorts of 45 65 75
Decomposition of change in FE:Cohorts of 45, 65, 75
  • Most of the change in FE in early and late age is due to change in schooling composition per cohort. About 60% of the FE gap per cohort.
  • About 10% of FE gap is due to change in fertility and the same for wages.
  • About 20% of FE gap is unexplained and it is 50% at the early (23-32) ages and zero for older ages.
decomposition of change in fe cohorts of 25 35
Decomposition of change in FE:Cohorts of 25, 35
  • Most of the change in FE in early and late age is due to change in schooling composition per cohort. About 47% of the FE gap per cohort.
  • About 3% of FE gap is due to change in fertility and 5% for wages.
  • About 45% of FE gap is unexplained.
  • The reduction in cost/utility is interpreted in the literature as:
  • Technical progress in home production (Greenwood et. al.)
  • Change in preferences – social norms related to children and intra- household standing of the female: Traditional vs. Modern families – Percent of M is slowly increasing.
labor supply of couples traditional and modern households

Labor Supply of Couples:Traditional and Modern Households

Model and measurement of employment of females and males for married couples with different cultural family background - Traditional and Modern – as different internal family games.


The Model: Household Game

Chiappori(1998): Bargaining

Ours: At the date of marriage each household is one of two types – unobserved heterogeneity:

  • Traditional (T): the game is characterized by the husband being a Stackelberg leader. The husband makes the decision before the wife, and then she responds.
  • Modern (M): the game within is a Nash equilibrium. The husband and the wife are symmetric players and they act simultaneously, each is taking the other person actions as given.
  • Both games are solved as sub-game perfect.
the model cont states
The model (cont.): States
  • Three states: 1- Employment; 2 - Unemployment;

3 - out of LF

  • If Initially UE or OLF there are two sub-periods: (a) search or OLF

(b) Accept a potential offer (E) or UE.

  • If initially E: One period decision to

quite to become OLF; fired to become UE; Continue employment in a “new” wage.

the model cont utility
The model (cont.): Utility
  • Max Expected PV as in EW
  • The husband (H) and wife (W) utilityfunctions are identical for both types of families.
  • Preferences parameters (leisure, children and consumption); wage and job offer rates parameters are potentially different (same format) between males and females but not by type of household.
the model cont budget constraint
The Model (cont.): Budget constraint

The household budget constraint

the model cont wage and probabilities as in ew
The model (cont.): Wage and probabilities – as in EW
  • Mincerian wage functions for each j = H, W
  • Endogenous experience
  • We adopt a logistic form for the job offer probability, the divorce probability and the probability of having a new child (like EW model).
the model cont
The model (cont.)
  • Model Solution:

From date of Marriage to 10 years later sub-game perfect solution as DDC with unobserved heterogeneity on type of households.

  • Data Description:
    • Data from the PSID – panel sample of American households.
    • 863 couples who got married between 83-84 (Cohort of 1960 – late baby boomers
    • 10 years (40 periods) sample at most (less if the couple divorced or left the sample).
estimation method sgmm simulated general method of moments
Estimation MethodSGMM (Simulated General Method of Moments)

2 sets of moments:

  • Mean individual choice of (E; UE; OLF) per period.
  • Difference of average predicted and actual wage for men and women per period.
  • Diagonal weighting matrix using the inverse of estimated standard error.
  • The model predicted correctly 89.9% of the choice moments.
  • The estimated proportion of the conservative families is 61.4% .
  • Husbands in both families have the same participation rate, females in M families participation rate is 9% higher then females is T families.
probability of family type
Probability of Family type
  • The posterior probability of being a modern family is consistent with common sense:
    • negatively correlated with the husband age at wedding, the number of children, and husband is black or Baptist.
    • positively correlated with the couples education, the wife age at wedding, husband is white, Catholic and potential divorce.
counterfactual 100 of families are modern
Counterfactual: 100% of Families are Modern
  • The increase of female employment and participation is about 5%.
  • No impact on males.
  • The employment/participation difference from males is about 10%.
Counterfactual: Full Equality - 100% of Families are Modern; Equal Wages and Job Offers for Males and Female
  • Males participation Rate decrease by 1.4%
  • Females participation Rate increase by 13.7%.
  • The difference between males and females employment/participation ( 3.7%) is due to risk aversion (females are more risk averse) and cost/utility from children/leisure that is higher for females.
concluding remark
Concluding remark
  • It is easy to do the analysis of this paper with “pure” approximate simple regressions.
  • The paper demonstrates the gain from using Stochastic Dynamic Discrete models with rational expectations and cross-equations restrictions for measuring and interpreting the rise in FE.