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
1
Why Do We Study Female
Employment (FE)?
Because they contribute a lot to US
Per Capita GDP…
45000
43797 (244%)
40000
Actual
40%
35000
30000
Labor Input Fixed at
25000 Labor Quality Input 1964
Fixed at 1964
20000
15000
1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
year
2006 prices.
3
Central Question
Why Did Female Employment (FE)
Rise Dramatically?
Because Married FE Rose…..!
Employment Rates by Marital Status - Women
100%
90%
80%
Single
70%
Divorced
60%
50%
40%
Married
30%
20%
10%
0%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
Ages 22-65. Proportion of women working 10+ weekly hours. year
5
Why did Married Female
Employment (FE)
Rise Dramatically?
7
Main Empirical Hypotheses
SchoolingLevel 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)
Schooling Level Increase
Breakdown of Married Women by Level of Education
50%
High School
45% Graduates
40%
35% High School Dropouts
30%
25%
College Graduates
20%
15% Some College
10%
5% Post College
0%
1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
Ages 22-65. year
Wage increase – Gender Gap decline
Annual Wages of Full-Time Workers
70000 80%
60000 75%
50000 70%
Men
40000 65%
Women
30000 60%
20000 Women to Men Wage 55%
Ratio (right axis)
10000 50%
0 45%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
Ages 22-65. Full-time full-year workers with non-zero wages. 2006 Prices. year
10
Fertility Decline
Number of Children per Married Women
1.8
1.6
Ref.
1.4
1.2
by cohort
Children under 18
1.0
0.8
0.6
0.4 Children under 6
0.2
0.0
1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007
Ages 22-65. Extrapolated data for number of young children during 1968-1975. year
11
Marriage Declines – Divorce Increases
Breakdown of Women by Marital Status
100%
90%
80%
70%
60% Married
50%
40%
30%
20%
Single (Never Married)
10% Divorced
0%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
year
Ages 22-65. 13
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..
Employment rates by Age
Post baby-boomers Cohort’s FE stabilized
Married Female Employment Rates by Cohort
80%
Born 1955
Born 1965
Born 1975
60%
40% Born 1925
Born 1945
20% Born 1935
0%
22 26 30 34 38 42 46 50 54 58 62
Years 1962-2007. Proportion of women working 10+ weekly hours. age 15
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
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.
Sketch of the Model
Extension of Heckman (1974)
Female maximizes PV utility
Chooses employment (pt = 1 or 0)
Takes as given:
Model
Education at age 22
Husband characteristics
Processes for wages, fertility, marital status
Estimation using SMM and 1955 cohorts from CPS
Estimation Fit – 1955 cohort FE
80%
Dynamic
70%
Actual
Static
Heckman
60%
50%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
age
1953-1957 cohorts for the period 1964-2007.
24
Estimation Fit – 1955 cohort FE
PC
85%
75%
65%
SC
55%
45%
HSD
35%
25%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
age
1953-1957 cohorts for the period 1964-2007.
25
Estimation Fit – 1955 cohort FE
90%
80%
CG
70%
HSG
60%
50%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
age
1953-1957 cohorts for the period 1964-2007.
26
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
FE by Age per Cohort
80%
Predicted 1955
Actual 1975
70%
Actual 1965
60% Actual 1955 Actual 1945
Actual 1935
50%
Actual 1925
40%
30%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
Years 1964-2007.
age
Accounting for changes in FE: 1945 cohort
Dynamic Model
Age Group: 28-32 1955: 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: 38-42 1955: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
Goodness of Fit Tests for the Three Models
Dynam ic Static Heckm an
Pearson* SSD** Pearson* SSD** Pearson* SSD**
HSD 7.96 71.93 26.65 238.42 112.53 897.94
HSG 6.24 83.44 12.58 167.33 29.60 394.77
SC 5.95 90.04 10.46 157.99 25.32 376.86
CG 4.69 75.73 10.89 175.86 11.49 180.97
PC 6.23 106.56 16.06 286.98 15.50 268.18
ALL 31.06 427.71 76.64 1026.59 194.43 2118.71
34
Accounting for the change in FE:
Cohorts of 1925, 30, 35 based on 1955
1925-1935
Dynamic Static Heckman
Schooling +initial 36% 33% 42%
Wage 23% 10% 0%
Children 4% 5% 14%
Martial Status 0% 1% 0%
Other 37% 51% 43%
Other - less than 38 no data
Other - over 38 34% 48% 45%
35
Accounting for the change in FE:
Cohorts of 1940, 45, 50: based on 1955
1940-1950
Dynamic Static Heckman
Schooling +initial 33% 32% 39%
Wage 22% 9% 1%
Children 8% 7% 5%
Martial Status 1% 0% 0%
Other 36% 51% 55%
Other - less than 38 55% 63% 55%
Other - over 38 18% 40% 55%
36
Accounting for the change in FE:
Cohorts of 1960, 65, 70, 75: based on 1955
1960-1975
Dynamic Static Heckman
Schooling +initial 35% 26% 20%
Wage 20% 11% 1%
Children 2% 6% 4%
Martial Status 1% 0% 0%
Other 42% 57% 75%
Other - less than 38 42% 50% 71%
Other - over 38 no data
What are the missing
factors for “other”? 37
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
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?
Actual and Predicted Employment Rates
1940 Cohort
80%
70%
60%
50%
40%
30%
α41=-2733.4;
Fitted estimated using the 1955 cohort.
α41=-8980.1;
Fitted estimated as the only additional free parameter, using the 1940 cohort.
Actual
20%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
age
40
Actual and Predicted Employment Rates
80%
1930 Cohort
70%
60%
50%
40%
30%
α1=-15658.1, α41=-2733.4; estimated using the 1955 cohort.
Fitted
α1=-25360.5, α41=-8818.8; estimated as the only additional free parameters, using the 1930 cohort.
Fitted
Actual
20%
32 34 36 38 40 42 44 46 48 50 52 54
41
How can we explain results?
Change in cost/utility interpreted as:
Technicalprogress in home production
Change in preferences or social norms
How do we fit the aggregate
employment/participation?
42
Aggregate fit Simulation
Simulate the Employment rate for all the
cohorts: 1923-1978.
Calculate the aggregate Employment for each
cohort at each year by the weight of the cohort
in the population.
Compare actual to simulated Employment
1980-2007.
Predicted Aggregate Female Employment Rates
Dynamic Model
80%
Actual - Unmarried
70% Predicted - Unmarried
Predicted - Married
60%
Actual - Married
50%
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Ages 23-54.
year
Predicted Aggregate Female Employment Rates
by Cohort and Age - Dynamic Model
Cohort
1925 1930 1935 1940 1945 1950 1960 1965 1970 1975
Age Group: 23-27 A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d A c t ua l F it t e d
married 0.32 0.30 0.39 0.39 0.48 0.48 0.60 0.61 0.64 0.63 0.66 0.64 0.65 0.65
unmarried 0.74 0.70 0.73 0.72 0.71 0.69 0.71 0.69 0.72 0.72 0.72 0.72 0.76 0.74
Age Group: 28-32
married 0.30 0.31 0.36 0.40 0.43 0.45 0.55 0.57 0.65 0.68 0.68 0.69 0.69 0.68 0.66 0.67
unmarried 0.71 0.70 0.69 0.71 0.70 0.69 0.73 0.71 0.72 0.71 0.73 0.73 0.79 0.75 0.76 0.75
Age Group: 33-37
married 0.36 0.38 0.41 0.41 0.47 0.49 0.56 0.59 0.63 0.64 0.70 0.71 0.70 0.71 0.68 0.71
unmarried 0.68 0.67 0.67 0.66 0.67 0.67 0.72 0.71 0.75 0.73 0.74 0.71 0.77 0.75 0.76 0.74
Age Group: 38-42
married 0.40 0.42 0.45 0.47 0.51 0.50 0.59 0.59 0.66 0.65 0.71 0.70 0.73 0.74 0.72 0.73
unmarried 0.72 0.73 0.69 0.67 0.67 0.66 0.72 0.73 0.75 0.76 0.78 0.75 0.78 0.75 0.76 0.75
Age Group: 43-47
married 0.48 0.46 0.51 0.49 0.58 0.57 0.64 0.63 0.72 0.71 0.75 0.74 0.75 0.75
unmarried 0.70 0.71 0.68 0.69 0.71 0.71 0.73 0.75 0.77 0.76 0.78 0.76 0.76 0.75
Age Group: 48-52
married 0.48 0.49 0.53 0.53 0.59 0.58 0.65 0.65 0.71 0.71 0.74 0.74
unmarried 0.66 0.70 0.67 0.67 0.69 0.68 0.73 0.73 0.76 0.75 0.76 0.77
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
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
Thanks!!