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1
Dynamic Female Labor Supply
Zvi Eckstein and Osnat Lifshitz
December 27, 2010Based on the Walras-Bowley Lecture to the American Econometric Society
Summer meeting, June 2008
Why Do We Study Female
Employment (FE)?
3
Because they contribute a lot to US Per Capita GDP…
Actual
Labor Input Fixed at 1964
15000
20000
25000
30000
35000
40000
45000
1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
year2006 prices.
43797 (244%)
40%Actual
Labor Input Fixed at 1964Labor Quality Input
Fixed at 1964
15000
20000
25000
30000
35000
40000
45000
1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
year2006 prices.
43797 (244%)
40%
Central Question
Why Did Female Employment (FE)
Rise Dramatically?
5
Because Married FE Rose…..!Employment Rates by Marital Status - Women
Married
Single
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
yearAges 22-65. Proportion of women working 10+ weekly hours.
Employment Rates by Marital Status - Women
Married
Single
Divorced
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
yearAges 22-65. Proportion of women working 10+ weekly hours.
7
Why did Married Female Employment (FE)
Rise Dramatically?
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)
Schooling Level IncreaseBreakdown of Married Women by Level of Education
High School Dropouts
High School Graduates
Some College
College Graduates
Post College
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
yearAges 22-65.
10
Wage increase – Gender Gap declineAnnual Wages of Full-Time Workers
Men
Women
Women to Men Wage Ratio (right axis)
0
10000
20000
30000
40000
50000
60000
70000
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
year
45%
50%
55%
60%
65%
70%
75%
80%
Ages 22-65. Full-time full-year workers with non-zero wages. 2006 Prices.
Annual Wages of Full-Time Workers
Men
Women
Women to Men Wage Ratio (right axis)
0
10000
20000
30000
40000
50000
60000
70000
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
year
45%
50%
55%
60%
65%
70%
75%
80%
Ages 22-65. Full-time full-year workers with non-zero wages. 2006 Prices.
11
Fertility Decline
Ref.
by cohort
Number of Children per Married Women
Children under 6
Children under 18
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007
yearAges 22-65. Extrapolated data for number of young children during 1968-1975.
13
Marriage Declines – Divorce Increases Breakdown of Women by Marital Status
Married
Single (Never Married)
Divorced
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
yearAges 22-65.
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..
15
Post baby-boomers Cohort’s FE stabilizedEmployment rates by Age
Married Female Employment Rates by Cohort
Born 1925
Born 1935
Born 1945
Born 1955
Born 1965Born 1975
0%
20%
40%
60%
80%
22 26 30 34 38 42 46 50 54 58 62
ageYears 1962-2007. Proportion of women working 10+ weekly hours.
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:
Education at age 22
Husband characteristics
Processes for wages, fertility, marital status
Estimation using SMM and 1955 cohorts from CPS
Model
Estimation Fit – 1955 cohort FE
24
Estimation Fit – 1955 cohort FE
25
Estimation Fit – 1955 cohort FE
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 Wagepredicted p45= P55(S45, yw45, yh45, N55, M55)
….Etc
FE by Age per Cohort
Actual 1925
Actual 1935
Actual 1945Actual 1955
Actual 1965
Actual 1975Predicted 1955
30%
40%
50%
60%
70%
80%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
ageYears 1964-2007.
1%Other
69%+ 4 Marital Status
69%+ 3 Children
69%1+ 2 Wage
71%1 - Schooling
68%Actual 1945
Age Group: 38-42 1955:Actual: 74% Fitted: 74%
12%Other
61%+ 4 Marital Status
+ 3 Children
63%1+ 2 Wage
63%1 - Schooling
49%Actual 1945
Age Group: 28-32 1955: Actual: 65% Fitted: 65%
Accounting for changes in FE: 1945 cohortDynamic Model
Early age total difference 12% is Other
61%
Goodness of Fit Tests for the Three Models
34
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
Dynamic Static Heckman
35
Accounting for the change in FE:Cohorts of 1925, 30, 35 based on 1955
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
Other - over 38 34% 48% 45%
1925-1935
no data
36
Accounting for the change in FE:Cohorts of 1940, 45, 50: based on 1955
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%
1940-1950
37
Accounting for the change in FE:Cohorts of 1960, 65, 70, 75: based on 1955
What are the missing factors for “other”?
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
1960-1975
no data
What is missing factor for early ages?
Childcare cost if working
Change 1 parameter (– get perfect fit
1945 cohort childcare cost: $3/hour higher 1965 cohort childcare cost: $1.1/hour lower1975 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 (– get perfect fit
1935,1925 cohorts childcare cost: $3.2/hour higher 1935 cohort leisure value: $4.5/hour higher1925 cohort leisure value: $5/hour higher
How can we explain results?
Actual and Predicted Employment Rates 1940 Cohort
40
Actual and Predicted Employment Rates 1930 Cohort
41
42
How can we explain results?
Change in cost/utility interpreted as:
Technical progress in home productionChange in preferences or social norms
How do we fit the aggregate employment/participation?
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 RatesDynamic Model
Actual - Married
Actual - Unmarried
Predicted - Married
Predicted - Unmarried
50%
60%
70%
80%
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
yearAges 23-54.
Predicted Aggregate Female Employment Ratesby Cohort and Age - Dynamic Model
Age Group: 23-27 Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Fitted ActualFitted
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
1960 1965 1970 1975
Cohort1925 1930 1935 1940 1945 1950
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
47
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 EmploymentBetter 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
Thanks!!