happy together: a structural model of couples' joint retirement … · 2019. 3. 5. · happy...
TRANSCRIPT
![Page 1: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/1.jpg)
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
![Page 2: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/2.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 3: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/3.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 4: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/4.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 5: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/5.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 6: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/6.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 7: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/7.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 8: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/8.jpg)
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
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 9: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/9.jpg)
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
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 10: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/10.jpg)
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
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 11: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/11.jpg)
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
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 12: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/12.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 13: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/13.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 14: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/14.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 15: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/15.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 16: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/16.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 17: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/17.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 18: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/18.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 19: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/19.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 20: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/20.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 21: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/21.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 22: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/22.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 23: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/23.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 24: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/24.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 25: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/25.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 26: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/26.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 27: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/27.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 28: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/28.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 29: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/29.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 30: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/30.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 31: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/31.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 32: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/32.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 33: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/33.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 34: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/34.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 35: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/35.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 36: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/36.jpg)
Model
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 ,w
mt ,w
ft ,B
mt ,B
ft , agediff }
Unobservable variables
εt = {εt(dt)|dt ∈ D}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 37: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/37.jpg)
Model
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
(cαj
1t (l jt )1−α
j1
)1−ρl jt = L− hj
t(d jt ) + α2I (dm
t = R, d ft = R)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 38: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/38.jpg)
Model
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
(cαj
1t (l jt )1−α
j1
)1−ρl jt = L− hj
t(d jt ) + α2I (dm
t = R, d ft = R)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 39: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/39.jpg)
Model
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
(cαj
1t (l jt )1−α
j1
)1−ρl jt = L− hj
t(d jt ) + α2I (dm
t = R, d ft = R)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 40: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/40.jpg)
Model
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
(cαj
1t (l jt )1−α
j1
)1−ρl jt = L− hj
t(d jt ) + α2I (dm
t = R, d ft = R)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 41: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/41.jpg)
Model
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
(cαj
1t (l jt )1−α
j1
)1−ρ
l jt = L− hjt(d j
t ) + α2I (dmt = R, d f
t = R)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 42: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/42.jpg)
Model
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
(cαj
1t (l jt )1−α
j1
)1−ρl jt = L− hj
t(d jt ) + α2I (dm
t = R, d ft = R)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 43: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/43.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 44: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/44.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 45: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/45.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 46: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/46.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 47: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/47.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 48: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/48.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 49: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/49.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 50: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/50.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 51: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/51.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 52: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/52.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 53: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/53.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 54: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/54.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 55: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/55.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 56: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/56.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 57: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/57.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 58: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/58.jpg)
Model
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 59: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/59.jpg)
Model
STOCHASTIC PROCESSES
Wage:
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 60: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/60.jpg)
Model
STOCHASTIC PROCESSES
Wage:
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 61: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/61.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 62: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/62.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 63: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/63.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 64: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/64.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 65: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/65.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 66: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/66.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 67: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/67.jpg)
Model
STOCHASTIC PROCESSES
Wage: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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 68: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/68.jpg)
Model
STOCHASTIC PROCESSES (contd.)
E (hct |agemt , agef
t ) = E (hct |agemt , agef
t , hc > 0)P(hct > 0|agemt , agef
t )
ln hct = h(agemt , agef
t ) + ψt ,
ψ ∼ N(0, σ2ψ)
Survival:
s jt+1 = s(age jt)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 69: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/69.jpg)
Model
STOCHASTIC PROCESSES (contd.)
E (hct |agemt , agef
t ) = E (hct |agemt , agef
t , hc > 0)P(hct > 0|agemt , agef
t )
ln hct = h(agemt , agef
t ) + ψt ,
ψ ∼ N(0, σ2ψ)
Survival:
s jt+1 = s(age jt)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 70: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/70.jpg)
Model
STOCHASTIC PROCESSES (contd.)
E (hct |agemt , agef
t ) = E (hct |agemt , agef
t , hc > 0)P(hct > 0|agemt , agef
t )
ln hct = h(agemt , agef
t ) + ψt ,
ψ ∼ N(0, σ2ψ)
Survival:
s jt+1 = s(age jt)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 71: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/71.jpg)
Model
STOCHASTIC PROCESSES (contd.)
E (hct |agemt , agef
t ) = E (hct |agemt , agef
t , hc > 0)P(hct > 0|agemt , agef
t )
ln hct = h(agemt , agef
t ) + ψt ,
ψ ∼ N(0, σ2ψ)
Survival:
s jt+1 = s(age jt)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 72: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/72.jpg)
Model
STOCHASTIC PROCESSES (contd.)
E (hct |agemt , agef
t ) = E (hct |agemt , agef
t , hc > 0)P(hct > 0|agemt , agef
t )
ln hct = h(agemt , agef
t ) + ψt ,
ψ ∼ N(0, σ2ψ)
Survival:
s jt+1 = s(age jt)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 73: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/73.jpg)
Model
STOCHASTIC PROCESSES (contd.)
E (hct |agemt , agef
t ) = E (hct |agemt , agef
t , hc > 0)P(hct > 0|agemt , agef
t )
ln hct = h(agemt , agef
t ) + ψt ,
ψ ∼ N(0, σ2ψ)
Survival:
s jt+1 = s(age jt)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 74: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/74.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 75: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/75.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 76: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/76.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 77: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/77.jpg)
Model Solution
Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:
Et
{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)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 78: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/78.jpg)
Model Solution
Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:
Et
{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)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 79: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/79.jpg)
Model Solution
Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:
Et
{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)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 80: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/80.jpg)
Model Solution
Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:
Et
{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)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 81: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/81.jpg)
Model Solution
Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:
Et
{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)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 82: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/82.jpg)
Model Solution
Households choose a series of decision rules Π = {π0, π1, ..., πT}, whereπt(zt , εt) = (dt , st), to maximize:
Et
{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)
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 83: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/83.jpg)
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)}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 84: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/84.jpg)
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)}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 85: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/85.jpg)
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)}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 86: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/86.jpg)
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)}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 87: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/87.jpg)
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)}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 88: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/88.jpg)
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)}
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 89: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/89.jpg)
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)}
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 90: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/90.jpg)
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)}
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 91: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/91.jpg)
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)}
graph
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 92: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/92.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 93: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/93.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 94: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/94.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 95: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/95.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 96: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/96.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 97: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/97.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 98: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/98.jpg)
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 99: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/99.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 100: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/100.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 101: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/101.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 102: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/102.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 103: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/103.jpg)
Data
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 Income
I HealthI RetirementI Demographics
I HRS data can be linked to Social Security Administration recordswhich provide information on covered earnings and benefits.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 104: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/104.jpg)
Data
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 Health
I RetirementI Demographics
I HRS data can be linked to Social Security Administration recordswhich provide information on covered earnings and benefits.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 105: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/105.jpg)
Data
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 Retirement
I Demographics
I HRS data can be linked to Social Security Administration recordswhich provide information on covered earnings and benefits.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 106: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/106.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 107: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/107.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 108: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/108.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 109: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/109.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 110: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/110.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 111: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/111.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 112: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/112.jpg)
Data
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.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 113: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/113.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 114: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/114.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 115: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/115.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 116: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/116.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 117: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/117.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 118: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/118.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 119: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/119.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 120: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/120.jpg)
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
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 121: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/121.jpg)
Figure: Simulated vs. actual age profiles for total participation, men.
1Total Participation Rate. Men. Actual vs. Simulated
0.8
0.9
0.6
0.7
ge
0.4
0.5
Percentag
0 2
0.3
0.1
0.2
Husbands' Total participation rate ‐ data
Husbands' Total participation rate ‐ simulated
0
55 57 59 61 63 65 67 69 71 73 75Age
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 122: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/122.jpg)
Figure: Simulated vs. actual age profiles for total participation, women.
0 9
1Total Participation Rate. Women. Actual vs. Simulated
Wives' Total participation rate ‐ data
0.8
0.9Wives' Total participation rate ‐ simulated
0.6
0.7
ge
0.4
0.5
Percentag
0.3
0.4
0.1
0.2
0
55 60 65 70 75Age
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 123: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/123.jpg)
Figure: Simulated vs. actual age profiles for FT/PT participation, men.
0.4
0.5
0.6
0.7
0.8
0.9
1
Percen
tage
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
0
0.1
0.2
0.3
55 57 59 61 63 65 67 69 71 73 75Age
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 124: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/124.jpg)
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
0 4
0.5
ge
0.3
0.4
Percentag
0.2
0.1
0
55 57 59 61 63 65 67 69 71 73 75Age
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 125: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/125.jpg)
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
0.2
Husbands' retirement frequencies ‐ simulated
0.15
ge
0 1
Percentag
0.1
0.05
0
55 57 59 61 63 65 67 69Age
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 126: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/126.jpg)
Figure: Simulated vs. actual retirement frequencies, women.
0.2Retirement Frequencies. Women. Actual vs. Simulated
Wives' retirement frequencies ‐ data
0.15
q
Wives' retirement frequencies ‐ simulated
0.15
e
0.1
Percentage
0.05
0
55 57 59 61 63 65 67 69Age
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 127: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/127.jpg)
Figure: Simulated vs. actual joint retirement frequencies.
0.45Joint Retirement Frequencies. Actual vs. Simulated
Retirement age differences
0.35
0.4 ‐ data
Retirement age differences ‐ simulated
0.3
e
0.2
0.25
Percentage
0.15
0.05
0.1
0
from 5 to 10 from 2 to 4 from -1 to 1 from -4 to -2 from -10 to -5
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 128: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/128.jpg)
Figure: Simulated vs. actual joint retirement frequencies.
0.4
0.45
Retirement age differences ‐data
0 3
0.35Retirement age differences ‐simulated
Experiement 1 ‐Without
0.25
0.3
ntage
Complementarities
Experiement 2 ‐Without Dependent Spouse Benefit
0.15
0.2Perce
0.1
0
0.05
from 5 to 10 from 2 to 4 from -1 to 1 from -4 to -2 from -10 to -5
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 129: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/129.jpg)
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%.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 130: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/130.jpg)
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%.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 131: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/131.jpg)
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%.
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 132: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/132.jpg)
Figure: Retirement frequencies for married men and women
0
5
10
15
20
25
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
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 133: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/133.jpg)
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
1
2
3
4
5
6
7
8
9
10
0
1000
2000
3000
01000
2000
30004000
-12
-10
-8
-6
-4
X: 2985Y: 0Z: -6.977
SSbenefit, wife
X: 2985Y: 3134Z: -5.953
X: 0Y: 0Z: -11.74
SSbenefit, husband
X: 0Y: 3134Z: -7.013
(1,1)
(0,1)
(0,0)
Model Solution
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 134: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/134.jpg)
Figure: Differences in retirement dates by age difference between spouses
0.0
5.1
.15
.2
−10 −5 0 5 10
Agediff < 0, N = 247
0.0
5.1
.15
.2
−10 −5 0 5 10
Agediff in [0,1], N = 382
0.0
5.1
.15
.2
−10 −5 0 5 10
Agediff in [2,3], N = 3970
.05
.1.1
5.2
−10 −5 0 5 10
Agediff in [2,3], N = 3970
.05
.1.1
5.2
−10 −5 0 5 10
Agediff > 5, N = 359
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 135: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/135.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 136: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/136.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 137: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/137.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 138: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/138.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 139: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/139.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 140: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/140.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 141: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/141.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices
![Page 142: Happy Together: A Structural Model of Couples' Joint Retirement … · 2019. 3. 5. · Happy Together: A Structural Model of Couples ... I Husband and wife are separate decision-making](https://reader033.vdocuments.site/reader033/viewer/2022051604/600691040d893b65350ee4df/html5/thumbnails/142.jpg)
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)
back
Maria Casanova UCLA Couple’s Joint Retirement Choices