1

Household Interaction Impact on Married Female Labor Supply

Zvi Eckstein and Osnat Lifshitz

2

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.

4

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

5

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.

6

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

9

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.

10

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

13

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)

14

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.

15

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

16

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

17

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

18

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

19

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

23

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

24

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%.

27

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

28

Concluding remarks