happy together: a structural model of couples' joint retirement … · 2019. 3. 5. · happy...

Happy Together: A Structural Model of Couples’Joint Retirement Choices

Maria CasanovaUCLA

QSPS 2015 Summer Workshop

05/29/2015

Maria Casanova UCLA Couple’s Joint Retirement Choices

Introduction

This paper estimates a life cycle model of labor supply and saving ofolder couples.

Large literature aiming to understand why individuals retire when they doso as to predict effects of policy changes.

I Increase in full retirement age.

I Change in indexation of Social Security benefit formula andcost-of-living adjustments.

I Elimination of spousal benefit.

Main contribution of the paper is analysis of retirement at the couplelevel.

Introduction

Structural models of individual retirement

I Gustman and Steinmeier (1986), Stock and Wise (1990), Blau(1994, 2008), Rust and Phelan (1997), French (2005), French andJones (2010)

I Individuals respond to incentives fromI WealthI IncomeI Health StatusI Health InsuranceI Private PensionsI Social Security

Introduction

Structural models of couples’ retirement.

I Husband and wife are separate decision-making agents within thehousehold.

I Each spouse’s preferences represented by a separate utility function.

These models can be broadly divided in two groups:

1. Studies focused on modeling shared budget constraint.Blau and Gilleskie (2006), Van der Klaauw and Wolpin (2008)

2. Studies focused on modeling leisure complementarities. def.

Gustman and Steinmeier (2000, 2004), Maestas (2001)

This paper aims to bridge the gap between the two strands

Introduction

1. Studies focused on modeling shared budget constraint.

Blau and Gilleskie (2006), Van der Klaauw and Wolpin (2008)

Introduction

I Dynamic, stochastic model of labor supply and saving choices

I Agents maximize expected discounted utility

I At each period t, given i) initial assets ii) wage and iii) measure oflifetime earnings, households make decisions in two steps:

1. choose participation status

2. conditional on participation status, choose optimalconsumption/savings

I Agents face uncertainty on a) wages, b) survival, and c) medicalexpenditures

I Retirement is not an absorbing state

I Benefit receipt is an absorbing state

CHOICE SET

Discrete choices: d jt ∈ D j = {R,PT ,FT}, for j = m, f

Continuous choices: st ∈ Ct(zt , εt ; dt)

STATE SPACE

Observable variables

zt = {At ,Emt ,E

ft , agediff }

Unobservable variables

εt = {εt(dt)|dt ∈ D}

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

CHOICE SET

STATE SPACE

zt = {At ,Emt ,E

ft , agediff }

PREFERENCES

Household utility

U(dt , st ; zt , εt , θ1) = φUm(ct , lmt ) + (1− φ)U f (ct , l

ft ) + εt(dt)

Individual utility

U j =1

1− ρ

1t (l jt )1−α

)1−ρl jt = L− hj

t(d jt ) + α2I (dm

t = R, d ft = R)

PREFERENCES

Household utility

ft ) + εt(dt)

Individual utility

U j =1

1− ρ

1t (l jt )1−α

t(d jt ) + α2I (dm

t = R, d ft = R)

PREFERENCES

Household utility

ft ) + εt(dt)

Individual utility

U j =1

1− ρ

1t (l jt )1−α

t(d jt ) + α2I (dm

t = R, d ft = R)

PREFERENCES

Household utility

ft ) + εt(dt)

Individual utility

U j =1

1− ρ

1t (l jt )1−α

t(d jt ) + α2I (dm

t = R, d ft = R)

PREFERENCES

Household utility

ft ) + εt(dt)

Individual utility

U j =1

1− ρ

1t (l jt )1−α

)1−ρ

l jt = L− hjt(d j

t ) + α2I (dmt = R, d f

t = R)

PREFERENCES

Household utility

ft ) + εt(dt)

Individual utility

U j =1

1− ρ

1t (l jt )1−α

t(d jt ) + α2I (dm

t = R, d ft = R)

BUDGET CONSTRAINT

ct + st = At + Y (rAt ,wmt hm

t ,wft hf

t , τ) + Bmt × ssbm

t + B ft × ssbf

t + Tt

Next period’s asset:

At+1 = st + hct

Liquidity constraint:

st ≥ 0

BUDGET CONSTRAINT

t ,wft hf

t + B ft × ssbf

t + Tt

At+1 = st + hct

st ≥ 0

BUDGET CONSTRAINT

t ,wft hf

t + B ft × ssbf

t + Tt

At+1 = st + hct

st ≥ 0

BUDGET CONSTRAINT

t ,wft hf

t + B ft × ssbf

t + Tt

At+1 = st + hct

st ≥ 0

BUDGET CONSTRAINT

t ,wft hf

t + B ft × ssbf

t + Tt

At+1 = st + hct

st ≥ 0

BUDGET CONSTRAINT

t ,wft hf

t + B ft × ssbf

t + Tt

At+1 = st + hct

st ≥ 0

Social Security Function:

I Entitlement is a function of accumulated earnings (Et)

I Step formula applied to Et to obtain PIA

I Workers retiring at 65 receive full PIA

I Workers retiring at 62 receive 80% of PIA

I Workers retiring after 65 receive 5.5% increase per year

I Benefits are indexed to CPI

I Earnings test

I Dependent spouse benefit

I Surviving spouse benefit

I Earnings test

STOCHASTIC PROCESSES

ln wit = W (ageit) + ςI{dit = PT}+ υit

υit = υit−1 − δR I (dit−1 = R)− δPT I (dit−1 = PT ) + ξit

where:

ξi v N(0, σ2ξi )

For estimation purposes, υi0 is a fixed effect:

ln wit = υi0 + W (ageit) + ςI{dit = PT}+ υ∗it

ln wit = W (ageit) + ςI{dit = PT}+ υit

where:

ξi v N(0, σ2ξi )

Wage:ln wit = W (ageit) + ςI{dit = PT}+ υit

where:

ξi v N(0, σ2ξi )

υit = υit−1

− δR I (dit−1 = R)− δPT I (dit−1 = PT )

+ ξit

where:

ξi v N(0, σ2ξi )

where:

ξi v N(0, σ2ξi )

where:

ξi v N(0, σ2ξi )

where:

ξi v N(0, σ2ξi )

where:

ξi v N(0, σ2ξi )

where:

ξi v N(0, σ2ξi )

STOCHASTIC PROCESSES (contd.)

E (hct |agemt , agef

t ) = E (hct |agemt , agef

t , hc > 0)P(hct > 0|agemt , agef

ln hct = h(agemt , agef

t ) + ψt ,

ψ ∼ N(0, σ2ψ)

Survival:

s jt+1 = s(age jt)

t ) + ψt ,

ψ ∼ N(0, σ2ψ)

Survival:

s jt+1 = s(age jt)

t ) + ψt ,

ψ ∼ N(0, σ2ψ)

Survival:

s jt+1 = s(age jt)

t ) + ψt ,

ψ ∼ N(0, σ2ψ)

Survival:

s jt+1 = s(age jt)

t ) + ψt ,

ψ ∼ N(0, σ2ψ)

Survival:

s jt+1 = s(age jt)

t ) + ψt ,

ψ ∼ N(0, σ2ψ)

Survival:

s jt+1 = s(age jt)

Model Solution

I Framework introduced by Rust (1987, 1988) for the solution andestimation of stochastic Markov discrete processes.

I Extend framework in order to account for continuous decisions.

Model Solution

Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:

{T∑i=t

βi−tSi−tUt(θ1)

}subject to the corresponding constraints.

The expectation is taken with respect to the controlled stochastic process{zt , εt} with probability distribution:

f (zt+1, εt+1|dt , st , zt , εt , θ2, θ3) =

q(εt+1|zt+1, θ2)g(zt+1|zt , dt , st , θ3)

Model Solution

{T∑i=t

subject to the corresponding constraints.

Model Solution

{T∑i=t

Model Solution

{T∑i=t

Model Solution

{T∑i=t

Model Solution

{T∑i=t

Model Solution

The Bellman equation can be written as:

Vt(zt , εt , θ) = maxdt

{maxst{u(k, st , zt , θ1) + βEtVt+1(zt+1, k, st , θ)|dt = k}+ εt

}Inner maximization yields choice-specific value functions:

r(k, zt , θ) = maxst{[u(k, st , zt , θ1) + βEtVt+1(zt+1, k, st , θ)]|dt = k}

Outer maximization is random-utility model:

maxdt{r(zt , dt , θ) + εt(dt)}

Model Solution

{maxst{u(k , st , zt , θ1) + βEtVt+1(zt+1, k, st , θ)|dt = k}+ εt

Inner maximization yields choice-specific value functions:

Model Solution

r(k, zt , θ) = maxst{[u(k , st , zt , θ1) + βEtVt+1(zt+1, k, st , θ)]|dt = k}

Model Solution

Assumption: ε follows multivariate extreme value distribution

Conditional choice probabilities:

P(k|zt , θ) =exp{r(zt , k, θ)}∑

k∈D exp{r(zt , k, θ)}

Model Solution

P(k|zt , θ) =exp{r(zt , k, θ)}∑

k∈D exp{r(zt , k, θ)}

Model Solution

P(k |zt , θ) =exp{r(zt , k , θ)}∑

k∈D exp{r(zt , k , θ)}

Estimation

Vectors of parameters to be estimated: θ1 and θ3

Estimation takes place in two stages:

I First stage:

Estimate parameters which can be identified withoutspecific reference to dynamic model.

This yields θ̂3.

I Second stage:

Estimate θ1 using method of simulated moments.

Estimation

I First stage:

This yields θ̂3.

I Second stage:

Estimation

I First stage:

This yields θ̂3.

I Second stage:

Estimation

I First stage:

This yields θ̂3.

I Second stage:

Estimation

I First stage:

This yields θ̂3.

I Second stage:

Estimation

I First stage:

This yields θ̂3.

I Second stage:

Estimation

I First stage:

This yields θ̂3.

I Second stage:

I Health and Retirement Study (HRS)

I Panel data on households where at least one member is aged 51 to61 in initial wave.

I Extensive information on:

I Wealth and IncomeI HealthI RetirementI Demographics

I HRS data can be linked to Social Security Administration recordswhich provide information on covered earnings and benefits.

I Wealth and Income

I HealthI RetirementI Demographics

I Wealth and IncomeI Health

I RetirementI Demographics

I Wealth and IncomeI HealthI Retirement

I Demographics

Estimation sample:

I The model is estimated using the sample of HRS couples who donot have a defined benefit pension.

I For individuals with no private pension, Social Security providesmain age-specific incentives for retirement.

I The same is true for individuals with defined contribution pensions.

I Defined benefit pensions give very strong incentives for retirement atparticular ages, usually different from the Social Security ages.

Estimation sample:

Estimation: Second Stage

Table: Preference and Wage Process Parameter Estimates

Parameter and definition (1) (2)

αm1 Consumption share, male U function 0.5102

0.5274(0.0061)

αf1 Consumption share, female U function 0.4295

0.4334(0.0043)

α2 Value of shared retirement

0.0891(0.0079)

Male’s wage depreciation per year PT 0.9051

0.9258(0.0383)

Female’s wage depreciation per year PT 0.8933

0.9219(0.0334)

Male’s wage depreciation per year R 0.8092

0.8609(0.0436)

Female’s wage depreciation per year R 0.7795

0.7841(0.0336)

GMM criterion 0.2058 0.1404

αm1 Consumption share, male U function 0.5102

0.5274(0.0061)

αf1 Consumption share, female U function 0.4295

0.4334(0.0043)

α2 Value of shared retirement 0.0891(0.0079)

0.9258(0.0383)

0.9219(0.0334)

0.8609(0.0436)

0.7841(0.0336)

αm1 Consumption share, male U function 0.5102 0.5274

(0.0061)αf1 Consumption share, female U function 0.4295

0.4334(0.0043)

α2 Value of shared retirement 0.0891(0.0079)

0.9258(0.0383)

0.9219(0.0334)

0.8609(0.0436)

0.7841(0.0336)

(0.0061)αf1 Consumption share, female U function 0.4295 0.4334

(0.0043)α2 Value of shared retirement 0.0891

(0.0079)Male’s wage depreciation per year PT 0.9051

0.9258(0.0383)

0.9219(0.0334)

0.8609(0.0436)

0.7841(0.0336)

(0.0079)Male’s wage depreciation per year PT 0.9051 0.9258

(0.0383)Female’s wage depreciation per year PT 0.8933

0.9219(0.0334)

0.8609(0.0436)

0.7841(0.0336)

(0.0383)Female’s wage depreciation per year PT 0.8933 0.9219

(0.0334)Male’s wage depreciation per year R 0.8092

0.8609(0.0436)

0.7841(0.0336)

(0.0334)Male’s wage depreciation per year R 0.8092 0.8609

(0.0436)Female’s wage depreciation per year R 0.7795

0.7841(0.0336)

(0.0334)Male’s wage depreciation per year R 0.8092 0.8609

(0.0436)Female’s wage depreciation per year R 0.7795 0.7841

(0.0336)

Figure: Simulated vs. actual age profiles for total participation, men.

1Total Participation Rate. Men. Actual vs. Simulated

Percentag

Husbands' Total participation rate ‐ data

Husbands' Total participation rate ‐ simulated

55 57 59 61 63 65 67 69 71 73 75Age

Figure: Simulated vs. actual age profiles for total participation, women.

1Total Participation Rate. Women. Actual vs. Simulated

Wives' Total participation rate ‐ data

0.9Wives' Total participation rate ‐ simulated

Percentag

55 60 65 70 75Age

Figure: Simulated vs. actual age profiles for FT/PT participation, men.

Percen

Full‐time and Part‐time Participation Rate. Men. Actual vs. Simulated

Husbands' FT participation rate ‐ dataHusbands' PT participation rate ‐ dataHusbands' FT participation rate ‐ simulatedHusbands' PT participation rate ‐ simulated

55 57 59 61 63 65 67 69 71 73 75Age

Figure: Simulated vs. actual age profiles for FT/PT participation, women.

0.7Full‐time and Part‐time Participation Rate. Women. Actual vs. Simulated

Wives' FT participation rate ‐ data

0.6Wives' PT participation rate ‐ dataWives' FT participation rate ‐ simulatedWives' PT participation rate ‐ simulated

Percentag

55 57 59 61 63 65 67 69 71 73 75Age

Figure: Simulated vs. actual retirement frequencies, men.

0.25Retirement Frequencies. Men. Actual vs. Simulated

Husbands' retirement frequencies ‐ dataH b d ' ti t f i i l t d

Husbands' retirement frequencies ‐ simulated

Percentag

55 57 59 61 63 65 67 69Age

Figure: Simulated vs. actual retirement frequencies, women.

0.2Retirement Frequencies. Women. Actual vs. Simulated

Wives' retirement frequencies ‐ data

Wives' retirement frequencies ‐ simulated

Percentage

55 57 59 61 63 65 67 69Age

Figure: Simulated vs. actual joint retirement frequencies.

0.45Joint Retirement Frequencies. Actual vs. Simulated

Retirement age differences

0.4 ‐ data

Retirement age differences ‐ simulated

Percentage

from 5 to 10 from 2 to 4 from -1 to 1 from -4 to -2 from -10 to -5

Figure: Simulated vs. actual joint retirement frequencies.

Retirement age differences ‐data

0.35Retirement age differences ‐simulated

Experiement 1 ‐Without

Complementarities

Experiement 2 ‐Without Dependent Spouse Benefit

0.2Perce

from 5 to 10 from 2 to 4 from -1 to 1 from -4 to -2 from -10 to -5

Conclusions

I I develop a life-cycle model of couples’ choices which carefullymodels shared budget constraint and allows for leisurecomplementarities.

I Results show that positive complementarity parameters explain 8%of joint retirements...

I ...while social security’s spousal benefit accounts for another 13%.

Conclusions

Figure: Retirement frequencies for married men and women

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

Men - N=2,818 Women - N=2,339

Figure: Optimal participation choices as a function of Em, E f

INTRODUCTION

Figure 3: Optimal participation choices for baseline couple as a function of accumulated earnings

RESULTS FROM SIMULATIONS

1 2 3 4 5 6 7 8 9 10

30004000

X: 2985Y: 0Z: -6.977

SSbenefit, wife

X: 2985Y: 3134Z: -5.953

X: 0Y: 0Z: -11.74

SSbenefit, husband

X: 0Y: 3134Z: -7.013

Model Solution

Figure: Differences in retirement dates by age difference between spouses

−10 −5 0 5 10

Agediff < 0, N = 247

−10 −5 0 5 10

Agediff in [0,1], N = 382

−10 −5 0 5 10

Agediff in [2,3], N = 3970

−10 −5 0 5 10

Agediff in [2,3], N = 3970

−10 −5 0 5 10

Agediff > 5, N = 359

Introduction

Leisure Complementarities

A significant fraction of spouses retires together graph

Hurd (1990), Blau (1998), Gustman and Steinmeier (2000)

Joint retirements of spouses with different ages may be partly explainedby interactions in spouses’ preferences.

Complementarity of spouse’s leisure: one (or both) spouses enjoy theirleisure more if this is shared with their partner.

Reduced-form studies provide evidence that spouses enjoy theirretirement more if their partner is retired too.

I Coile (2004)

I Banks, Blundell and Casanova (2010)

Introduction

I Coile (2004)

Introduction

I Coile (2004)

Introduction

I Coile (2004)

Introduction

I Coile (2004)

Introduction

I Coile (2004)

Introduction

I Coile (2004)

Introduction

I Coile (2004)

happy together: a structural model of couples' joint retirement … · 2019. 3. 5. · happy...

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