1. Dynamic Female Labor Supply
Zvi Eckstein and Osnat Lifshitz
December 27, 2010
Based on the Walras-Bowley Lecture to the American Econometric Society Summer meeting, June 2008

2. Why Do We Study Female
Employment (FE)?

3. Because they contribute a lot to US Per Capita GDP…3 3

4. Why Did Female Employment (FE)
Central Question
Why Did Female Employment (FE)
Rise Dramatically?

5. Because Married FE Rose…..!5 5

6. Why did Married Female Employment (FE) Rise Dramatically?

7. Main Empirical Hypotheses
Schooling Level increase (Becker)
Wage increase/Gender Gap decline
Heckman and McCurdy(1980), Goldin(1990), Galor and Weil(1996), Blau and Kahn(2000), Jones, Manuelli and McGrattan(2003), Gayle and Golan(2007)
Fertility decline
Gronau(1973), Heckman(1974), Rosensweig and Wolpin(1980), Heckman and Willis(1977), Albanesi and Olivetti(2007) Attanasio at.al.(2008)
Marriage decline/Divorce increase
Weiss and Willis(1985,1997), Weiss and Chiappori(2006)
Other – (unexplained)

8. Schooling Level Increase9

9. Wage increase – Gender Gap decline10 10

10. Fertility Decline
Ref.
by cohort 11 11

11. Marriage Declines – Divorce Increases13 13

12. What are the Other Empirical Hypotheses?
Social Norms
Fernandez, Fogli and Olivetti(2004), Mulligan and Rubinstein(2004), Fernandez (2007)
Cost of Children
Attanasio, Low and Sanchez-Marcos(2008) Albanesi and Olivetti(2007)
Technical Progress
Goldin(1991), Greenwood et. al.(2002),
Will show up as a cohort effects..

13. Post baby-boomers Cohort’s FE stabilized
Employment rates by Age
Post baby-boomers Cohort’s FE stabilized 15 15

14. An Accounting Exercise
Measure female’s employment due to:
Schooling Level increase
Wage increase/Gender Gap decrease
Fertility decline
Marriage decline/Divorce growth
The “unexplained” is Others
Lee and Wolpin, 2008

15. An Accounting Exercise
Need an empirical model
Use Standard Dynamic Female Labor Supply Model – Eckstein and Wolpin 1989 (EW): “old” model
Later extensions (among others..): van der Klauw, 1996, Altug and Miller, 1998, Keane and Wolpin, 2006 and Ge, 2007.

16. Sketch of the Model Extension of Heckman (1974)
Female maximizes PV utility
Chooses employment (pt = 1 or 0)
Takes as given:
Education at age 22
Husband characteristics
Processes for wages, fertility, marital status
Estimation using SMM and 1955 cohorts from CPS
Model

17. Estimation Fit – 1955 cohort FE

18. Estimation Fit – 1955 cohort FE

19. Estimation Fit – 1955 cohort FE

20. Back to Accounting Exercise
For the 1955 cohort we estimated:
p55= P55(S, yw, yh, N, M) for each age
Contribution of Schooling of 1945 cohort (S45) for predicted FE of 1945 cohort is:
predicted p45= P55(S45, yw55, yh55, N55, M55)
….Schooling and Wage
predicted p45= P55(S45, yw45, yh45, N55, M55)
….Etc

21. FE by Age per Cohort 28

22. Accounting for changes in FE: 1945 cohort Dynamic Model
Age Group: : Actual: 65% Fitted: 65%
Actual 1945
49%
1 - Schooling
63%
1+ 2 Wage
63%
+ 3 Children
61%
+ 4 Marital Status
61%
Other
12%
Age Group: :Actual: 74% Fitted: 74% 
Actual 1945
68%
1 - Schooling
71%
1+ 2 Wage
69%
+ 3 Children
69%
+ 4 Marital Status
69%
Other 1%
Early age total difference 12% is Other

23. Goodness of Fit Tests for the Three Models

24. Accounting for the change in FE: Cohorts of 1925, 30, 35 based on 1955

25. Accounting for the change in FE: Cohorts of 1940, 45, 50: based on 1955

26. What are the missing factors for “other”?
Accounting for the change in FE: Cohorts of 1960, 65, 70, 75: based on 1955
What are the missing factors for “other”? 37 37

27. What is missing factor for early ages?
Childcare cost if working
Change 1 parameter (a4) – get perfect fit
1945 cohort childcare cost: $3/hour higher
1965 cohort childcare cost: $1.1/hour lower
1975 cohort childcare cost: $1.1/hour lower

28. What is missing factor for all ages?
Childcare cost if working
Value of staying at home
Change 2 parameters (a1,a4) – get perfect fit
1935,1925 cohorts childcare cost: $3.2/hour higher
1935 cohort leisure value: $4.5/hour higher
1925 cohort leisure value: $5/hour higher
How can we explain results?

29. Actual and Predicted Employment Rates 1940 Cohort

30. Actual and Predicted Employment Rates 1930 Cohort

31. How can we explain results?
Change in cost/utility interpreted as:
Technical progress in home production
Change in preferences or social norms
How do we fit the aggregate employment/participation?

32. Aggregate fit Simulation
Simulate the Employment rate for all the cohorts:
Calculate the aggregate Employment for each cohort at each year by the weight of the cohort in the population.
Compare actual to simulated Employment

33. Predicted Aggregate Female Employment Rates
Dynamic Model

34. Predicted Aggregate Female Employment Rates
by Cohort and Age - Dynamic Model

35. Alternative Modeling for Explaining “Other Gap”
Unobserved heterogeneity regarding leisure/cost of children
Bargaining power of women changes
Household game: a “new” empirical framework 46

36. Concluding remarks
We demonstrate the gains from using Stochastic Dynamic Discrete models:
Dynamic selection method, rational expectations, and cross-equations restrictions are imposed
Accounting for alternative explanations for rise in US Female Employment
Better fit than static models (new version)
Education – 35% of increase in Married FE
Other – 25-45% of increase in Married FE
Change in two parameters close the Other Gap 47 47

37. Thanks!!
Thanks!!