1 household interaction impact on married female labor supply zvi eckstein and osnat lifshitz
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1
Household Interaction Impact on Married Female Labor Supply
Zvi Eckstein and Osnat Lifshitz
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Introduction
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
year
Figure 1: Employment Rates by Marital Status - Women
Women aged 22-65.Proportion of women working 10+ weekly hours.
3
Introduction (Cont.)
0%
20%
40%
60%
80%
22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
age
Figure 2: Married Female Employment Rates by Cohort
Proportion of women working 10+ weekly hours.
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Two types of householdClassical (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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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 OLF Fired to UE Employment in a “new” wage.
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Dynamic program
Max Expected Present ValueUtility functions are identical for both C and MCharacteristics of husband and wife different
Game solved recursively backwards to wedding
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Budget constraint
The household budget constraint:
ttt1Ht
Ht
1Wt
Wt Ncxdydy
Wty and
Hty 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
tN is the number of children in the household.
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Wage and probabilities
Mincerian wage functions for each j = H, W
11 tjjttj dkk
Logistic form for job offer probability
Endogenous experience
.exp1
expPr
31213
032
021
01
31213
032
021
01
yearKSddd
yearKSdddob
jjtjjjtjjtjjtjj
jjtjjjtjjtjjtjjtj
.ln 14
213121 jtj
jjt
jjt
jjtj SKKy
Probability of Having an Additional Child
The probability of having an additional child is given as (Van der Klaauw, 1996):
function of the woman's employment state in the previous period,
the woman's age and education and those of her husband, current
number of children and the age of the youngest child. is the standard normal distribution function.
11
tttHtWHWH
tWt
Wttt ageNddSSAGEAGEAGENN 98
17
16543
2
211 )1Pr(
Probability of Divorce
The probability of divorce:
function of how long the couple has been married (t), current
number of children, the female's education and the
employment states of the woman and her husband.
12
.)1/0Pr( 16
1543
2211 tHtW
Wtttt ddSNttMM
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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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Data
PSID - 863 couples who got married between 83-84, start from the date of the wedding.
10 years (40 quarters) sample (at most). During the sample period:
36.3 percent of the couples divorced or separated 14.5 percent left the sample for other reasons after 10 years 49.2 percent of the couples remained in the
sample.
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Data – Descriptive Statistics
CPS DATA (for comparison)
End of first year (1984) End of last year (1993) 1993
Husbands
Age 30 39.1 30.1
Years of Schooling 12.6 12.8 12.7
Participation Rate 92.60% 93.70% 94.60%
Employment Rate 84.30% 89.90% 84.90%
Hours of w ork per w eek 43.2 43.5 43.5
Monthly Salary Income* 1566 4494 1565
Wives
Age 27.8 36.7 27.8
Years of Schooling 12.7 12.9 12.4
Participation Rate 72.10% 79.10% 60.50%
Employment Rate 67.80% 77.40% 54.90%
Hours of w ork per w eek 36.3 34.6 34.3
Monthly Salary Income* 1051 2569 881
# of children 0.8 1.7 1.2
Observations 863 425** 6429
* US dollars, 1984 prices
** 36.3% divorced, 14.5% dropped out of sample
PSID DATA
Table 1: Descriptive Statistics
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Data – Descriptive Statistics
Husband's Labor State Employed Unemployed Out of Labor Force
Employed 75.4% 3.5% 21.0%Unemployed 64.5% 6.5% 29.0%Out of Labor Force 65.0% 3.4% 31.6%
Table 2: Wives' employment states conditional on their husbands' employment states
Wife's Labor State
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2 sets of moments:
Individual choice of (E; UE; OLF) by duration since
marriage, those choices include the transition probabilities.
Average predicted and actual wage for men and women by duration since marriage.
Estimation: SMM
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Estimation Results
90% of choices are correctly predicted 61% is estimated proportion of C families
Husbands in C & M have similar labor supply Wives work 10% more in M families
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Fit: Employment rate
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
quarter
Figure 3: Actual and Predicted Choice Distribution
Male Employment Rate
Female Employment Rate
Male Unemployment Rate Female Unemployment Rate
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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.
Main Estimated Parameters
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Male Female Male Female Male Female
γj - risk aversion0.948
(0.886)0.849
(0.151)β1 -
constant
1.135(4.912)
0.89(0.212)
ρ01 - employed
in previous period
2.852(0.511)
2.973(0.688)
αj - value of
leisure
8.215(1.32)
9.188(2.874)
β2 -
experience
0.066(0.011)
0.057(0.21)
ρ02 - unemployed
in previous period
-0.439(0.067)
-0.966(0.288)
SC - search cost
β3 -
experience2
-0.00001(0)
-0.00001(0)
ρ03 - OLF
in previous period
-2.466(0.397)
-2.801(0.563)
γ1 - leisure per
child
β4 -
schooling
0.081(0.043)
0.087(1.626)
ρ1 - schooling0.018
(0.002)0.016
(0.005)
γ2 -
consumption per child
ρ2 - experience0.005
(0.003)0.006
(0.001)
ρ3 - trend0.03
(0.006)0.018
(0.003)
Classic family0.612
(0.027)
Standard errors appear in parentheses.
* See equations 2.4, 2.5 and 2.6 (note that γ0 is unidentif ied).
** See equation 2.2.
*** See equation 2.7.
**** The estimated parameter is 0.455, the probability w as calculated as exp(0.455)/(1+exp(0.455))
and the standard error w as calculated using bootstrapping.
Table 4: Estimated Parameters
Type Proportion****
Job Offer Probability***Wage**Utility*
4.802(1.293)
7.386(1.903)
0.606(0.278)
Counterfactual: 100% of Families are Classical
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
quarter
Figure 6: Simulation 1 - Predicted Employment Rates with 100% Classical Families
Males with 100% Classical Families
Females with 100% Classical Families
Males in Original Model
Females in Original Model Decrease of female employment ~ 3.5% No impact on males
Counterfactual: 100% of Families are Modern
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
quarter
Figure 7: Simulation 2 - Predicted Employment Rates with 100% Modern Families
Females with 100% Modern Families
Males with 100% Modern Families
Males in Original Model
Females in Original Model
Increase of female employment ~ 6% No impact on malesEmployment difference from males ~ 11%.
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Counterfactual: Full Equality: 100% Modern Families and Identical Wages & Job Offer Probabilities for Men and 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 39
quarter
Figure 8: Simulation 3 - Predicted Employment Rates with 100% Modern Families and Identical Wages and Job Offer Probabilities for Men and Women
Males in Original Model
Females in Original Model
Female in Identical Wages and Offers Model
Males in Identical Wages and Offers Model
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
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Concluding remarks
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