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Dynamic Female Labor Supply
Zvi Eckstein and Osnat Lifshitz
November 5, 2010, CBCBased on the Walras-Bowley Lecture to the American Econometric Society
Summer meeting, June 2008
Why Do We Study Female Employment (FE)?
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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 2004year2006 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 2004year2006 prices.
43797 (244%)
40%
Central Question
Why Did Female Employment (FE)Rise Dramatically?
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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 2006yearAges 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 2006yearAges 22-65. Proportion of women working 10+ weekly hours.
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Why did Married Female Employment (FE) Rise Dramatically?
Main Empirical HypothesesSchooling 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 declineGronau(1973), Heckman(1974), Rosensweig and Wolpin(1980), Heckman and Willis(1977), Albanesi and Olivetti(2007) Attanasio at.al.(2008)
Marriage decline/Divorce increaseWeiss 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 2004yearAges 22-65.
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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 2006year
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 2006year
45%
50%
55%
60%
65%
70%
75%
80%
Ages 22-65. Full-time full-year workers with non-zero wages. 2006 Prices.
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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 2007yearAges 22-65. Extrapolated data for number of young children during 1968-1975.
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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 2006yearAges 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..
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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 62ageYears 1962-2007. Proportion of women working 10+ weekly hours.
An Accounting ExerciseMeasure 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 modelUse 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 ModelExtension 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
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Estimation Fit – 1955 cohort FE
Aggregate
High School Dropouts
Post College
20%
30%
40%
50%
60%
70%
80%
90%
100%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53age1953-1957 cohorts for the period 1964-2007.
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Estimation Fit – 1955 cohort FE
High School Graduates
Some College
College Graduates
50%
60%
70%
80%
90%
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53age1953-1957 cohorts for the period 1964-2007.
Back to Accounting ExerciseFor 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 53ageYears 1964-2007.
1%Other69%+ 4 Marital Status
69%+ 3 Children
69%1+ 2 Wage
71%1 - Schooling
68%Actual 1945Age Group: 38-42 1955:Actual: 74% Fitted: 74%
12%Other61%+ 4 Marital Status
+ 3 Children
63%1+ 2 Wage
63%1 - Schooling
49%Actual 1945Age Group: 28-32 1955: Actual: 65% Fitted: 65%
Accounting for changes in FE: 1945 cohort
Early age total difference 12% is Other
61%
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Accounting for the change in FE: Cohorts of 1925, 30, 35 based on 1955
Schooling: ~ 36% of the change in FE
Wages: ~ 24%
Fertility: ~ 3%
Marriage: ~ 0%
Other: ~ 37%45% at the early ages
34% for older ages
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Accounting for the change in FE: Cohorts of 1940, 45, 50: based on 1955 Cohort
Schooling : ~ 33% of the change in FE
Wages: ~ 22%
Fertility: ~ 8%
Marriage: ~ 1%
Other: ~ 36%
55% at the early ages
18% for older ages
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Accounting for the change in FE: Cohorts of 1960, 65, 70, 75: based on 1955 Cohort
Schooling : ~ 39% of the change in FE
Wages: ~ 16%
Fertility: ~ 2%
Marriage: ~ 1%
Other: ~ 43%
44% at the early ages
almost no data after age of 40
What are the missing factors for “other”?
What is missing factor for early ages?
Childcare cost if working
Change 1 parameter (α4) – get perfect fit1945 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 workingValue of staying at homeChange 2 parameters (α1,α4) – 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?
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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 Rates
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 2006yearAges 23-54.
Alternative Modeling for Explaining “Other Gap”
Unobserved heterogeneity regarding leisure/cost of children
Bargaining power of women changes
Household game: a “new” empirical framework
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Concluding remarksWe 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 FEOther – 25-45% of increase in Married FE Change in two parameters close the Other Gap
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Labor Supply of Couples: Classical and Modern Households –”new” Model
Internal family game (McElroy,1984, Chiappori, 1998)
New empirical dynamic models of household labor supply: Lifshitz (2004), Flinn (2007), Tartari (2007)
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Two types of household (unobserved)Classical (C): Husband is Stackelberg leader. Every period after state is realized the husband makes the decision before the wife, and then she responds.
Modern (M): Husband & Wife play Nash. Husband & wife are symmetric, act simultaneously after state is realized, taking the other person actions as given.
Both games are solved as sub-game perfect.
The Model: Household Dynamic Game
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Sketch of Model: Choices
Employment; Unemployment; Out of LF
Initially UE or OLF - two sub-periods Period 1: Search or OLF Period 2: Accept a potential offer E or UE
Initially E – one period Quit to OLFFired to UEEmployment in a “new” wage.
44
Sketch of Model: Dynamic program
Max Expected PV as in EWUtility functions are identical for both C and MCharacteristics of husband and wife different
Game solved recursively backwards to wedding
46
Sketch of model: Budget constraint
The household budget constraint
ttt1Ht
Ht
1Wt
Wt Ncxdydy ⋅+=⋅+⋅
Wty and H
ty are the wife's and husband's earnings;
ajtd equals one if individual WHj ,= chooses alternative a at time t , and zero otherwise;
tx is the joint couple consumption during period t;
tc is the goods cost per child, )(ct
1Ht
Ht
1Wt
Wt
Ndydy
t⋅+⋅⋅= α
tN is the number of children in the household.
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Sketch of model: Wage and probabilities (EW)
Mincerian wage functions for each j = H, W
.SKKyln 1jtj
j4
21jt
j31jt
j2
j1
jt εββββ ++++= −−
11 jtjtjt dkk += −
Logistic form for job offer probability, divorce probability and probability of having a new child (like EW model).
Endogenous experience
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Sketch of Model: Main Result
Wives work more in M than C family because:Husband earnings and offer rates are larger In M family she faces more uncertainty(Husband employment and earnings are uncertain when she makes the decision independently)
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2 sets of moments: Mean individual choice of (E; UE; OLF) by duration since marriage. Average predicted and actual wage for men and women by duration since marriage.
Estimation: SMMData
PSID – Panel - 863 couples who got married between 83-84 - Cohort of 1960
10 years (40 quarters) sample (at most)
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Estimation Results
90% of choices are correctly predicted61% is estimated proportion of C families
Husbands in C & M have similar labor supplyWives work 10% more in M families
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Fit: Employment rate
Actual - Men
Actual - Women
Predicted - Men
Predicted - Women
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39quarter
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Probability of Family type
Posterior probability of M family is:
Negatively correlated with: husband age at wedding, number of children, husband is black or Baptist.
Positively correlated with: couples education, wife age at wedding; husband is white, Catholic; potential divorce.
Counterfactual: 100% of Families are Modern
Predicted Employment Rates
Original Model - Men
Original Model - Women
100% Modern Households - Men
100% Modern Households - Women
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39quarter
Increase of female employment ~ 6%No impact on malesEmployment difference from males ~ 11%.
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Counterfactual: Full Equality - 100% of Families are Modern; Equal Wages & Job Offers for Males and Females
Predicted Employment Rates
Original Model - Men
Original Model - Women
Identical Wages and Offers - Men
Identical Wages and Offers - Women
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39quarter
Males employment decreases by 1.4%Females employment increases by 12.9%.Difference between males & females
employment (3.2%) due to higher risk aversion and higher cost/utility from home for females
Summary of results
Education – 35% of increase in Married FEOther – 25-45% of increase in Married FE Household game model for change in Social Norms (C and M families) can account to large change in Married FE – 5% to 10%
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Concluding remarks
The two examples 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
Dynamic couples game models are the framework for future empirical labor supply
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Percentage of HSG by Cohort - Married Women
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64age
192519351945195519651975
Years 1964-2007.
Percentage of HSG by Cohort - Married Men
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64age
192519351945195519651975
Years 1964-2007.
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Breakdown of Men by Level of Education
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004year
HSDHSGSCCGPC
Ages 22-65.
63
Appliances in U.S. Households, Selected Years, 1980-2001 (Percentage)
Survey Year
200119971993199019871984198219811980
575557535146454547Clothes Dryer
797777767573717374Clothes Washer
868384796134211714Microwave
535045454338363737Dishwasher
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Logistics form for probability of employment, children, marriage and divorce:
( )( ) ( )( )( )( )tt
tttt P
PP,exp1
,exp,PrΩ+
Ω=Ω
φφφ
Job Offer Probability
(function of: constant, schooling, experience and previous state):
( )( ) 1412
4121514131211, −−− ⋅+⋅+⋅+⋅+⋅+⋅+⋅+⋅=Ω ttttt PKKPCCGSCHSGHSDP ρρρρρρρρφ
Marriage Probability
(function of: constant, age, schooling, previously divorced):
( )( ) SmDmagemagemmPtt ⋅+⋅+⋅+⋅+=Ω 432
210,φ
Probability of Having a New Child
(function of: constant, age, schooling, marital status, number of children and previous state):
( )( ) 1712
6151432
210, −−−− ⋅+⋅+⋅+⋅+⋅+⋅+⋅+=Ω tttttt McNcNcPcScagecageccPφ
Divorce Probability
(function of: constant, years of marriage, schooling, number of children, husband wage and previous state):
( )( ) 16154132
210 __, −−− ⋅+⋅+⋅+⋅+⋅+⋅+=Ω tH
tttt ydPdSdNdmarriageydmarriageyddPφ
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Simulation 1945
67
Simulation 1965
68
Simulation 1975