[PPT] - Are marriage-related taxes and Social Security benefits holding back PowerPoint Presentation

SLIDE 1

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Are marriage-related taxes and Social Security benefits holding back female labor supply?

Margherita Borella1 Mariacristina De Nardi2 Fang Yang3

1University of Torino and CERP 2Federal Reserve Bank of Minneapolis, CEPR, and NBER 3Louisiana State University

September 2019

SLIDE 2

Question and data Approach and model Estimation Model fit Policy changes Conclusions

U.S. marriage-related policies

Taxes and old age Social Security benefits depend on marital status
Joint income tax
Social Security spousal benefit
Social Security survival benefit

SLIDE 3

Question and data Approach and model Estimation Model fit Policy changes Conclusions

U.S. marriage-related policies

Taxes and old age Social Security benefits depend on marital status
Joint income tax
Social Security spousal benefit
Social Security survival benefit
Question: how do marriage-related policies affect
Labor supply of women
Labor supply of men
Savings
Welfare

SLIDE 4

Question and data Approach and model Estimation Model fit Policy changes Conclusions

U.S. marriage-related policies

Taxes and old age Social Security benefits depend on marital status
Joint income tax
Social Security spousal benefit
Social Security survival benefit
Question: how do marriage-related policies affect
Labor supply of women
Labor supply of men
Savings
Welfare
Labor supply of married women has been changing over time. Do the effects of

these policies depend on the cohort?

Two cohorts (1945 cohort and 1955 birth cohorts)

SLIDE 5

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Why might they matter? Marginal tax rate for women

1 2 3 4 5 6 7 8 9 10

Women's income

104

0.1
0.05

0.05 0.1 0.15 0.2 0.25 0.3

Marginal tax rate Women's marginal tax rates

Married to 75th earner Married to 50th earner Married to 25th earner Single Women

0.2
0.1

0.1 0.2 0.3

Non-working wives' marginal tax rate

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cumulative probability Empirical cumulative distribution

SLIDE 6

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Why might they matter? Social Security benefits

1 2 3 4 5 6 7 8 9 10

Wife's own benefit decile

20000 25000 30000 35000 40000 45000 50000

Average Household Benefit Social Security Benefit

W/ m. benefit W/O m. benefit

1 2 3 4 5 6 7 8 9 10

Wife's own benefit decile

5000 10000 15000 20000 25000

Average Wife's Survivor Benefit Survivor Benefit

W/ m. benefit W/O m. benefit

SLIDE 7

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Participation for women, 1945 and 1955 cohorts

25 30 35 40 45 50 55 60 65

Age

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Labor Participation

Single women, 1945 Married women, 1945 Single women, 1955 Married women, 1955

Hours

SLIDE 8

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Participation for men, 1945 and 1955 cohorts

25 30 35 40 45 50 55 60 65

Age

0.4 0.5 0.6 0.7 0.8 0.9 1

Labor Participation

Single men, 1945 Married men, 1945 Single men, 1955 Married men, 1955

Hours

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Approach

Partial equilibrium, cohort level analysis

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Approach

Partial equilibrium, cohort level analysis
Data
Panel Study of Income Dynamics (PSID): working period
Health and Retirement Study (HRS): retirement period

SLIDE 11

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Approach

Partial equilibrium, cohort level analysis
Data
Panel Study of Income Dynamics (PSID): working period
Health and Retirement Study (HRS): retirement period
Estimate model on each cohort using the Method of Simulated moments (MSM)
Counterfactuals: eliminate marriage-related provisions

SLIDE 12

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Model’s key features

Single and married people
Endogenous human capital
Risks during working period and retirement
Self-insurance: saving and labor supply (hours)

SLIDE 13

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Model’s key features

Single and married people
Endogenous human capital
Risks during working period and retirement
Self-insurance: saving and labor supply (hours)
Government
Taxes married and single people + tax progressivity
Social Security payments (survival and spousal benefits)
Old-age means-tested transfer programs

SLIDE 14

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Model’s key features

Lifecycle model, period length: one year
Working stage (t0=25 to 61)
Alive for sure
Labor productivity shocks
Might get married if single
Risk divorce if married
Both spouses can work

SLIDE 15

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Model’s key features

Lifecycle model, period length: one year
Working stage (t0=25 to 61)
Alive for sure
Labor productivity shocks
Might get married if single
Risk divorce if married
Both spouses can work
Early retirement stage (62 to 65)
Can retire and claim Social Security. Couples retire at the same time.
No marriage and divorce risk

SLIDE 16

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Model’s key features

Lifecycle model, period length: one year
Working stage (t0=25 to 61)
Alive for sure
Labor productivity shocks
Might get married if single
Risk divorce if married
Both spouses can work
Early retirement stage (62 to 65)
Can retire and claim Social Security. Couples retire at the same time.
No marriage and divorce risk
Retirement stage (66 to T=99)
Health shocks
Medical costs
Exogenous probability of death → married people might lose their spouse

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Wages

Functions of
Human capital, measured as average past earnings
Wage shocks which follow an AR(1) that depends on gender

SLIDE 18

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Marriage and divorce

Marriage
Probability of marrying: function of age, gender, and wage shock
Conditional on getting married, probability of meeting with a partner with a certain

wage shock depends on your wage shock

Conditional partner’s productivity, distribution of partner’s characteristics are assets

and human capital

Divorce probability: function of age and wage shocks of both spouses

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Children

Exogenous fertility
Number and age structure of children depends on maternal age and marital status
Time costs of raising children
Monetary costs of raising children

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Health risks (after age 66)

Age, gender, marital status, and current health affect evolution of
Health
Medical expenses
Survival

SLIDE 21

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Government

Taxes income, progressive taxation of couples and singles

T(Y , i, j, t) = (1 − λi,j

t Y −τ i,j

t )Y .

Taxes labor income, up to Social Security cap

yt, at rate τ SS

t

to finance old-age Social Security

Old age means-tested cons. floor c(j) (Medicaid and SSI)

SLIDE 22

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Household preferences

β = discount factor, i = gender, j = marital status
Time endowment: Li,j
Leisure li,j

t

= Li,j − ni,j

t − φi,j t Ini,j

t

SLIDE 23

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Household preferences

β = discount factor, i = gender, j = marital status
Time endowment: Li,j
Leisure li,j

t

= Li,j − ni,j

t − φi,j t Ini,j

t

Singles

v(ct, lt) = ((ct/ηi,j

t )ωl1−ω t

)1−γ − 1 1 − γ

SLIDE 24

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Household preferences

β = discount factor, i = gender, j = marital status
Time endowment: Li,j
Leisure li,j

t

= Li,j − ni,j

t − φi,j t Ini,j

t

Singles

v(ct, lt) = ((ct/ηi,j

t )ωl1−ω t

)1−γ − 1 1 − γ

Couples

w(ct, l1

t , l2 t ) = ((ct/ηi,j t )ω(l1 t )1−ω)1−γ − 1

1 − γ + ((ct/ηi,j

t )ω(l2 t )1−ω)1−γ − 1

1 − γ

SLIDE 25

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Value functions for couples and people in couples

Working period
Early retirement
Retirement
People in couples

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Value functions for singles

Working period
Early retirement
Retirement

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Two-step estimation strategy

First step inputs for each cohort
Estimate from data directly (taxes, demographics, wage risk, health risk, human

capital accumulation function...)

Fix some parameters to calibrated or estimated values (externally to model)

SLIDE 28

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Two-step estimation strategy

First step inputs for each cohort
Estimate from data directly (taxes, demographics, wage risk, health risk, human

capital accumulation function...)

Fix some parameters to calibrated or estimated values (externally to model)
Second step, 1945 cohort
Estimate other parameters matching data targets for 1945 cohort

SLIDE 29

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Two-step estimation strategy

First step inputs for each cohort
Estimate from data directly (taxes, demographics, wage risk, health risk, human

capital accumulation function...)

Fix some parameters to calibrated or estimated values (externally to model)
Second step, 1945 cohort
Estimate other parameters matching data targets for 1945 cohort
Second step, 1955 cohort
Fix preference parameters and use rest of parameters to match data targets for 1955

cohort

SLIDE 30

Question and data Approach and model Estimation Model fit Policy changes Conclusions

PSID: Wage profiles, 1945 and 1955 cohorts

30 40 50 60

Age

15 20 25 30 35 40

Hourly wage

Single Men Single Women Married Men Married Women

30 40 50 60

Age

15 20 25 30 35 40

Hourly wage

Single Men Single Women Married Men Married Women Human Capital Shocks

SLIDE 31

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Other first-step inputs

Marriage
Divorce
Children
Health transitions
Health cost
Survival
Calibrated parameters

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Estimated parameters 1945 cohort 1955 cohort β: Discount factor 0.990 0.990 ω: Consumption weight 0.406 0.406 L2,1: Time endowment (weekly hours), single women 107 112 L1,2: Time endowment (weekly hours), married men 107 101 L2,2: Time endowment (weekly hours), married women 88 88 τ 0,5

c

: Prop. child care cost for children age 0-5 30% 25% τ 6,11

c

: Prop. child care cost for children age 6-11 7% 19% Φi,j

t : Partic. cost

Fig. 27
Fig. 27

Table: Second-step estimated model parameters

Participation cost

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Question and data Approach and model Estimation Model fit Policy changes Conclusions

Participation, 1945 cohort

25 30 35 40 45 50 55 60 65 Age 0.5 1 Labor Participation Married men Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 0.5 1 Labor Participation Married women Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 0.5 1 Labor Participation Single men Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 0.5 1 Labor Participation Single women Model Data Data, upper bound Data, lower bound

SLIDE 34

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Hours, 1945 cohort

25 30 35 40 45 50 55 60 65 Age 500 1000 1500 2000 2500 Hours among workers Married men Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 500 1000 1500 2000 2500 Hours among workers Married women Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 500 1000 1500 2000 2500 Hours among workers Single men Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 500 1000 1500 2000 2500 Hours among workers Single women Model Data Data, upper bound Data, lower bound

SLIDE 35

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Savings, 1945 cohort

25 30 35 40 45 50 55 60 65 Age 1 2 3 4 5 6 7 8 Average Household Asset #105 Couples Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 2 4 Average Household Asset #105 Single men Model Data Data, upper bound Data, lower bound 25 30 35 40 45 50 55 60 65 Age 2 4 Average Household Asset #105 Single women Model Data Data, upper bound Data, lower bound

SLIDE 36

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Labor supply elasticity, temporary wage change

Participation Hours among workers Married Single Married Single W M W M W M W M 30 1.0 0.0 0.5 0.2 0.2 0.3 0.4 0.3 40 0.7 0.1 0.4 0.2 0.3 0.5 0.5 0.5 50 0.6 0.2 0.4 0.5 0.5 0.5 0.8 0.5 60 1.1 0.8 1.4 2.0 0.4 0.2 0.5 0.3

Table: Labor supply elasticity, temporary wage change, 1945 cohort

SLIDE 37

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Labor supply elasticity, permanent wage change, 1945 cohort

25 30 35 40 45 50 55 60 65 Age

0.5

0.5 1 1.5 2 2.5 3 Elasticity in participation Raise wages of married women by:5% Single Men Single Women Married Men Married Women 25 30 35 40 45 50 55 60 65 Age

0.04
0.02

0.02 0.04 0.06 0.08 Change in participation Raise wages of married women by:5% Single Men Single Women Married Men Married Women

SLIDE 38

Question and data Approach and model Estimation Model fit Policy changes Conclusions

What is the effect of marriage-related policies?

In all cases, adjust the proportional component of the income tax to maintain revenue neutrality

Eliminating Social Security marital benefits, 1945 cohort
Taxing everyone as singles, 1945 cohort
Eliminating Social Security marital benefits and taxing everyone as singles, 1945 cohort
Eliminating Social Security marital benefits and taxing everyone as singles, 1955 cohort

SLIDE 39

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Welfare, 1945 cohort

All Winners Losers Couples SW SM Couples SW SM Couples SW SM Remove Social Security spousal benefits, unbalanced budget Avg

0.25
0.23

0.31 0.00 0.00 0.31

0.25
0.23
0.02

% 0.0 0.0 100.0 100.0 100.0 0.0 Remove Social Security spousal benefits, balanced budget Avg 0.71 0.20 1.30 0.71 0.22 1.30 0.00

0.04

0.00 % 100.0 93.4 100.0 0.0 6.6 0.0 Remove joint income taxation, balanced budget Avg 0.33

0.10

1.25 0.45 0.11 1.25

0.09
0.15

0.00 % 78.5 17.9 100.0 21.5 82.1 0.0 Remove all marital related polices, balanced budget Avg 0.83 0.03 2.24 0.84 0.31 2.24

0.04
0.13

0.00 % 98.9 35.8 100.0 1.1 64.2 0.0

SLIDE 40

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Welfare, remove all marital related polices, balanced budget, 1945 and 1955 cohorts

All Winners Losers Couples SW SM Couples SW SM Couples SW SM 1945 cohort Avg 0.83 0.03 2.24 0.84 0.31 2.24

0.04
0.13

0.00 % 98.9 35.8 100.0 1.1 64.2 0.0 1955 cohort Avg 0.75 0.21 1.31 0.77 0.31 1.31

0.05
0.05
0.02

% 97.2 70.9 100.0 2.8 29.1 0.0

SLIDE 41

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Conclusions

Estimate a rich life-cycle model of couples and singles with marriage-related

policies:

Marital income tax,
Social Security spousal benefits
Social Security survival benefits

SLIDE 42

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Conclusions

Estimate a rich life-cycle model of couples and singles with marriage-related

policies:

Marital income tax,
Social Security spousal benefits
Social Security survival benefits
Removal of marriage-related provisions
Increases participation of married women over their life cycle
Reduces participation of married men after age 55
Increases savings of couples
Is welfare improving for most

SLIDE 43

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Conclusions

Estimate a rich life-cycle model of couples and singles with marriage-related

policies:

Marital income tax,
Social Security spousal benefits
Social Security survival benefits
Removal of marriage-related provisions
Increases participation of married women over their life cycle
Reduces participation of married men after age 55
Increases savings of couples
Is welfare improving for most
Effects are also large for the 1955 cohort, who had much higher labor market

participation of married women to start with

SLIDE 44

Question and data Approach and model Estimation Model fit Policy changes Conclusions

Contributions

First estimated structural model of couples and singles with participation and

hours decisions (both men and women) and savings

Study all marriage-related taxes and benefits in a unified framework
Study two different cohorts
Rich framework
Labor market experience can affect wages
Survival, health, and medical expenses in old age, heterogeneous by marital status

and gender

Fit data for participation, hours worked, savings, and labor supply elasticities

SLIDE 45

Hours for women, 1945 and 1955 cohorts

25 30 35 40 45 50 55 60 65

Age

1300 1400 1500 1600 1700 1800 1900 2000

Average Working Hours (Workers)

Single women, 1945 Married women, 1945 Single women, 1955 Married women, 1955

back

Borella, De Nardi, Yang Marriage-related policies

A. 1

SLIDE 46

Hours for men, 1945 and 1955 cohorts

25 30 35 40 45 50 55 60 65

Age

1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

Average Working Hours (Workers)

Single men, 1945 Married men, 1945 Single men, 1955 Married men, 1955

back

Borella, De Nardi, Yang Marriage-related policies

A. 2

SLIDE 47

Recursive problem for working-age singles

W s(t, i, ai

t, ǫi t, ¯

yi

t) =

max

ct,at+1,ni

t

v(ct, li,j

t )+

β(1 − νt+1(·))EtW s(t + 1, i, ai

t+1, ǫi t+1, ¯

yi

t+1)+

βνt+1(·)Etξt+1(·)θt+1(·) ˆ W c(t + 1, i, ai

t+1 + ap t+1, ǫi t+1, ǫp t+1, ¯

yi

t+1, ¯

yp

t+1)

t : Age
i : Gender
at : Net worth from previous period
ǫi

t : Current productivity shock

¯

yi

t : Annual accumulated Social Security earnings

back

Borella, De Nardi, Yang Marriage-related policies

A. 3

SLIDE 48

Recursive problem for working-age singles

Y i

t = ei t ¯

yi

tǫi tni t

T(·) = τ(rat + Y i

t , j)

Borella, De Nardi, Yang Marriage-related policies

A. 4

SLIDE 49

Recursive problem for working-age singles

Y i

t = ei t ¯

yi

tǫi tni t

T(·) = τ(rat + Y i

t , j)

τc(i, j, t) = τ 0,5

c

f 0,5(i, j, t) + τ 6,11

c

f 6,11(i, j, t) ct + at+1 = (1 + r)ai

t + Y i t (1 − τc(i, j, t)) − τ SS t

min(Y i

t ,

yt) − T(·) ¯ yi

t+1 = (¯

yi

t(t − t0) + (min(Y i t ,

yt)))/(t + 1 − t0), at ≥ 0, nt ≥ 0, ∀t

back

Borella, De Nardi, Yang Marriage-related policies

A. 4

SLIDE 50

Early retirement stage, singles

Single individuals don’t get married anymore.
Decide whether to retire or not.

V s(t, i, ai

t, ǫi t, ¯

yi

t) = max Di

t

(1 − Di

t)Ns(t, i, ai t, ǫi t, ¯

yi

t)+

Di

tSs(t, i, ai t, ¯

yi

t, t)

If retire, no longer able to work.

back

Borella, De Nardi, Yang Marriage-related policies

A. 5

SLIDE 51

Early retirement stage, singles who decided not to claim SS

Ns(t, i, ai

t, ǫi t, ¯

yi

t) =

max

ct,at+1,ni

t

vi(ct, li,j

t ) + βEtV s(t + 1, i, ai t+1, ǫi t+1, ¯

yi

t+1)

Yt = ei,j

t (¯

yi

t)ǫi tni t,

T(·) = T(Yt + rat, j) ¯ yi

t+1 = (¯

yi

t(t − t0) + (min(Y i t ,

yt)))/(t + 1 − t0), ct + at+1 = (1 + r)ai

t + Y i t − τ SS t

min(Yt, yt) − T(·), at+1 ≥ 0.

back

Borella, De Nardi, Yang Marriage-related policies

A. 6

SLIDE 52

Early retirement stage, singles who have claimed SS

Ss(t, i, ai

t, ¯

yi

r, tr) = max ct,at+1

vi(ct, Li,j) + βEtSs(t + 1, i, ai

t+1, ¯

yi

r, tr)

Yt = SS(¯

yi

r, tr)

T(·) = T(Yt + rat, j) ct + at+1 = (1 + r)at + Yt − T(·) at+1 ≥ 0.

back

Borella, De Nardi, Yang Marriage-related policies

A. 7

SLIDE 53

Recursive problem for retired singles

Rs(t, i, at, ψi

t, ¯

yi

r, tr) = max ct,at+1

v(ct, Li,j) + βsi,j

t (ψi t)EtRs(t + 1, i, at+1, ψi t+1, ¯

yi

r, tr)

t : Age
i : Gender
at : Net worth from previous period
¯

yi

r : Annual accumulated social security earnings (PI)

ψi

t : Health status (good or bad)

tr: Retirement age

back

Borella, De Nardi, Yang Marriage-related policies

A. 8

SLIDE 54

Recursive problem for retired singles

Y i

t = SS(¯

yi

r)

T(·) = τ

Y i

t + rat, j

B(at, Yt, ψi

t, c(j)) = max

0, c(j) −
(1 + r)at + Yt − mi,j

t (ψi t) − T(·)

ct + at+1 = (1 + r)at + Yt + B(at, Y i

t , ψi t, c(j)) − mi,j t (ψi t) − T(·)

at+1 ≥ 0, ∀t

back

Borella, De Nardi, Yang Marriage-related policies

A. 9

SLIDE 55

PSID: Marriage, 1945 and 1955 cohorts

30 40 50 60 Age 0.05 0.1 0.15 0.2 0.25

Prob. of marriage

Men

Lowest 2nd 3rd 4th Highest 30 40 50 60

Age 0.05 0.1 0.15 0.2 0.25

Prob. of marriage

Women

Lowest 2nd 3rd 4th Highest 30 40 50 60

Age 0.05 0.1 0.15 0.2 0.25

Prob. of marriage

Men

Lowest 2nd 3rd 4th Highest 30 40 50 60

Age 0.05 0.1 0.15 0.2 0.25

Prob. of marriage

Women

Lowest 2nd 3rd 4th Highest

back

Borella, De Nardi, Yang Marriage-related policies

A. 10

SLIDE 56

PSID: Divorce, 1945 and 1955 cohorts

30 40 50 60 Age 0.01 0.02 0.03 0.04 0.05 0.06

Prob. of divorce

Men

Lowest 2nd 3rd 4th Highest 30 40 50 60

Age 0.01 0.02 0.03 0.04 0.05 0.06

Prob. of divorce

Women

Lowest 2nd 3rd 4th Highest 30 40 50 60

Age 0.01 0.02 0.03 0.04 0.05 0.06

Prob. of divorce

Men

Lowest 2nd 3rd 4th Highest 30 40 50 60

Age 0.01 0.02 0.03 0.04 0.05 0.06

Prob. of divorce

Women

Lowest 2nd 3rd 4th Highest

back

Borella, De Nardi, Yang Marriage-related policies

A. 11

SLIDE 57

PSID: number of children, 1945 and 1955 cohorts

30 40 50 60 Age of married woman 0.5 1 1.5 2 2.5 Children ages 0-17 Children ages 0-5 Children ages 6-11 30 40 50 60 Age of single woman 0.5 1 1.5 2 2.5 Children ages 0-17 Children ages 0-5 Children ages 6-11 30 40 50 60 Age of married woman 0.5 1 1.5 2 2.5 Children ages 0-17 Children ages 0-5 Children ages 6-11 30 40 50 60 Age of single woman 0.5 1 1.5 2 2.5 Children ages 0-17 Children ages 0-5 Children ages 6-11

back

Borella, De Nardi, Yang Marriage-related policies

A. 12

SLIDE 58

Recursive problem for working-age couples

W c(t, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) =

max

ct,at+1,n1

t ,n2 t

w(ct, l1,j

t , l2,j t )

+(1 − ζt+1(·))βEtW c(t + 1, at+1, ǫ1

t+1, ǫ2 t+1, ¯

y1

t+1, ¯

y2

t+1)

+ζt+1(·)β

2

i=1
EtW s(t + 1, i, at+1/2, ǫi

t+1, ¯

yi

t+1)

t : Age
at : Net worth from previous period
ǫi

t : Current productivity shock for each spouse

¯

yi

t : Annual accumulated SS earnings for each spouse

Divorce probability ζt(·) = ζt(ǫ1

t , ǫ2 t )

back

Borella, De Nardi, Yang Marriage-related policies

A. 13

SLIDE 59

Recursive problem for working-age couples

Y i

t = ei t(¯

yi

t)ǫi tni t,

T(·) = τ(rat + Y 1

t + Y 2 t , j)

Borella, De Nardi, Yang Marriage-related policies

A. 14

SLIDE 60

Recursive problem for working-age couples

Y i

t = ei t(¯

yi

t)ǫi tni t,

T(·) = τ(rat + Y 1

t + Y 2 t , j)

τc(i, j, t) = τ 0,5

c

f 0,5(i, j, t) + τ 6,11

c

f 6,11(i, j, t), ct + at+1 = (1 + r)at + Y 1

t + Y 2 t (1 − τc(2, 2, t))

−τ SS

t

(min(Y 1

t ,

yt) + min(Y 2

t ,

yt)) − T(·) at ≥ 0, n1

t , n2 t ≥ 0,

∀t

back

Borella, De Nardi, Yang Marriage-related policies

A. 14

SLIDE 61

Early retirement stage, couples

Couples don’t get divorced anymore.
Decide whether to retire or not at the same time.
If retire, no longer able to work.

V c(t, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) = max Dt

(1 − Dt)Nc(t, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) + DtSc(t, at, ¯

y1

t , ¯

y2

t , t)

back

Borella, De Nardi, Yang Marriage-related policies

A. 15

SLIDE 62

Early retirement stage, couples who decided not to claim SS

Nc(t, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) =

max

ct,at+1,n1

t ,n2 t

w(ct, l1,j

t , l2,j t )

+ βEtV c(t + 1, at+1, ǫ1

t+1, ǫ2 t+1, ¯

y1

t+1, ¯

y2

t+1)

,

li,j

t

= Li,j − ni

t − Φi,j t Ini

t,

Y i

t = ei,j t (¯

yi

t)ǫi tni t,

T(·) = T(rat + Y 1

t + Y 2 t , i, j, t)

ct + at+1 = (1 + r)at + Y 1

t + Y 2 t − τ SS t

(min(Y 1

t ,

yt) + min(Y 2

t ,

yt)) − T(·) ¯ yi

t+1 = (¯

yi

t(t − t0) + (min(Y i t ,

yt)))/(t + 1 − t0), at ≥ 0, n1

t , n2 t ≥ 0

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 63

Early retirement stage, couples who decided to claim SS

Sc(t, at, ¯ y1

r , ¯

y2

r , tr) = max ct,at+1

w(ct, L1,j, L2,j) + βEtSc(t + 1, at+1, ¯

y1

r , ¯

y2

r , tr)

,

Yt = max

(SS(¯

y1

r , tr) + SS(¯

y2

r , tr), 3

2 max(SS(¯ y1

r , tr), SS(¯

y2

r , tr))

T(·) = T(Yt + rat, i, j, t)

ct + at+1 = (1 + r)at + Yt − T(·) at+1 ≥ 0.

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SLIDE 64

Recursive problem for retired couples

Rc(t, at, ψ1

t , ψ2 t , ¯

y1

r , ¯

y2

r ) = max ct,at+1

w(ct, L1,j, L2,j)+

βs1,j

t (ψ1 t )s2,j t (ψ2 t )EtRc(t + 1, at+1, ψ1 t+1, ψ2 t+1, ¯

y1

r , ¯

y2

r )+

βs1,j

t (ψ1 t )(1 − s2,j t (ψ2 t ))EtRs(t + 1, 1, at+1, ψ1 t+1, ¯

¯ y1

r )+

βs2,j

t (ψ2 t )(1 − s1,j t (ψ1 t ))EtRs(t + 1, 2, at+1, ψ2 t+1, ¯

¯ y2

r )

t : Age.
at : Net worth from previous period.
¯

y1

r : PI for men.

¯

y2

r : PI women.

ψi

t : Health status (good or bad) for each spouse.

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SLIDE 65

Recursive problem for retired couples

¯ ¯ yi

r = max(¯

y1

r , ¯

y2

r ),

Yt = max

(SS(¯

y1

r ) + SS(¯

y2

r ), 3

2 max(SS(¯ y1

r ), SS(¯

y2

r ))

T(·) = τ(Yt + rat, j)

B(at, Yt, ψ1

t , ψ2 t , c(j)) = max

0, c(j)−
(1 + r)at + Yt − m1,j

t (ψ1 t ) − m2,j t (ψ2 t ) − T(·)

ct + at+1 = (1 + r)at + Yt + B(·) − m1,j

t (ψ1 t ) − m2,j t (ψ2 t ) − T(·)

at+1 ≥ 0, ∀t

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 66

Individual’s Discounted Present Value of Being in a Marriage

Evaluated under optimal policies ˆ W c(t, i, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) = v(ˆ

ct(·)/ηi,j

t , ˆ

li,j

t )+

β(1 − ζ(·))Et ˆ W c(t + 1, i, ˆ at+1(·), ǫ1

t+1, ǫ2 t+1, ¯

y1

t+1, ¯

y2

t+1)+

βζ(·)EtW s(t + 1, i, ˆ at+1(·)/2, ǫi

t+1, ¯

yi

t+1)

ˆ Rc(t, i, at, ψ1

t , ψ2 t , ¯

y1

r , ¯

y2

r ) = v(ˆ

ct(·)/ηi,j

t , Li,j)+

βsi,j

t (ψi t)sp,j t (ψp t )Et ˆ

Rc(t + 1, i, ˆ at+1(·), ψ1

t+1, ψ2 t+1, ¯

y1

r , ¯

y2

r )+

βsi,j

t (ψi t)(1 − sp,j t (ψp t ))EtRs(t + 1, i, ˆ

at+1(·), ψi

t+1, ¯

¯ yi

r)

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 67

Individual’s Discounted Present Value of Being in a Marriage

Evaluated under optimal policies ˆ Nc(t, i, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) = vi(ˆ

ct(·), ˆ li,j

t )

+ βEt ˆ V c(t + 1, i, ˆ at+1(·), ǫ1

t+1, ǫ2 t+1, ¯

y1

t+1, ¯

y2

t+1)

ˆ Sc(t, i, at, ¯ y1

r , ¯

y2

r , tr) = vi(ˆ

ct(·), Li,j) + βEtSc(t + 1, i, ˆ at+1(·), ¯ y1

r , ¯

y2

r , tr)

ˆ V c(t, i, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t ) = (1 − ˆ

Dt(·)) ˆ Nc(t, i, at, ǫ1

t , ǫ2 t , ¯

y1

t , ¯

y2

t )+

ˆ Dt(·) ˆ Sc(t, i, at, ¯ y1

r , ¯

y2

r , t)

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 68

PSID: Wage profiles, 1945 cohort

30 40 50 60

Age

10 15 20 25 30 35 40

Hourly wage rate Men

30 40 50 60

Age

10 15 20 25 30 35 40

Hourly wage rate Women

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SLIDE 69

PSID: Wage processes

Parameter Men Women Persistence 0.941 0.946 Variance prod. shock 0.026 0.015 Initial variance 0.114 0.095

Table: Estimated processes for the wage shocks for men and women, PSID data

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SLIDE 70

HRS: Health transition probabilities

70 80 90

Age

0.5 0.6 0.7 0.8 0.9 1

Prob. of staying in the same health

Singles

Men bad health Men good health Women bad health Women good health

70 80 90

Age

0.5 0.6 0.7 0.8 0.9 1

Prob. of staying in the same health

Couples

Men bad health Men good health Women bad health Women good health

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SLIDE 71

HRS: Survival rates

70 80 90

age

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

survival probability Singles

Men bad health Men good health Women bad health Women good health

70 80 90

age

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Couples

Men bad health Men good health Women bad health Women good health back

Borella, De Nardi, Yang Marriage-related policies

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SLIDE 72

HRS: Health costs

70 80 90

Age

0.5 1 1.5 2 2.5

Determinstic health cost in 2016$

104

Singles

Men bad health Men good health Women bad health Women good health

70 80 90

Age

0.5 1 1.5 2 2.5

Determinstic health cost in 2016$

104

Couples

Men bad health Men good health Women bad health Women good health

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 73

Second-step participation cost estimates

25 30 35 40 45 50 55 60 65 Age 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Participation cost SM SW MM MW 25 30 35 40 45 50 55 60 65 Age 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Participation cost SM SW MM MW

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 74

Fixed parameters Source Preferences and returns r Interest rate 4% De Nardi et al. (2016) γ Utility curvature parameter 2.5 see text ηt Equivalence scales PSID Government policy λi,j

t , τ i,j t

Income tax See text SS(¯ y i

r )

Social Security benefit See text τ SS

t

Social Security tax rate See text

yt

Social Security cap See text c(1) Minimum consumption, singles $8,687, De Nardi et al. (2016) c(2) Minimum consumption, couples $8,687*1.5 Social Security rules

Table: Additional first-step inputs

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SLIDE 75

Remove both Social Security benefits, 1945 cohort

25 30 35 40 45 50 55 60 65

Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3

Change in participation No spousal or survival benefit in SS

Single Men Single Women Married Men Married Women

Percentage asset change Couples Single men Single women Balanced government budget 14.9% 7.8% 11.2%

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SLIDE 76

Taxing everyone as singles, 1945 cohort

25 30 35 40 45 50 55 60 65

Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3

Change in participation No marital differential tax

Single Men Single Women Married Men Married Women

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SLIDE 77

Remove Social Security benefits + joint tax, 1945 cohort

25 30 35 40 45 50 55 60 65

Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3

Change in participation All policies change

Single Men Single Women Married Men Married Women

Percentage asset change Couples Single women Single men Balanced government budget 20.3% 14.8% 8.8%

Changing marriage and divorce pattern back

Borella, De Nardi, Yang Marriage-related policies

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SLIDE 78

Remove Social Security benefits + joint tax, 1955 cohort

25 30 35 40 45 50 55 60 65

Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3

Change in participation All policies change, fix G

Single Men Single Women Married Men Married Women

% asset change Couples Single women Single men Balanced government budget 19.7% 14.9% 8.4%

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Borella, De Nardi, Yang Marriage-related policies

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SLIDE 79

Remove Social Security benefits + joint tax, 1945 cohort

Left: ⇓ the marriage prob. and ⇑ the divorce rate by 20%
Middle: benchmark
Right: ⇑ the marriage prob. and ⇓ the divorce rate by 20%

25 30 35 40 45 50 55 60 65 Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3 Change in participation All policies change, lower marriage and higher divorce rates Single Men Single Women Married Men Married Women 25 30 35 40 45 50 55 60 65 Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3 Change in participation All policies change Single Men Single Women Married Men Married Women 25 30 35 40 45 50 55 60 65 Age

0.05

0.05 0.1 0.15 0.2 0.25 0.3 Change in participation All policies change, higher marriage and lower divorce rates Single Men Single Women Married Men Married Women

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