dynamic female labor supplydynamic discrete models: dynamic selection method, rational expectations,...

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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)?

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 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?

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 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.

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 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.

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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

55

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