The role of joint leisure in retirement decisions

The Role of Joint Leisure in Retirement Decisions
K. Makarski, J. Tyrowicz, Lucas van der Velde
FAME GRAPE
Warsaw School of Economics
10th
RCEA Macro-Money-Finance Conference
September 2019

Introduction
Motivation: little spotlight in macro on joint retirement
Rich literature on role of PS features in retirement: take-up and timing
French (2005), Cagetti (2006), French and Jones (2012), etc.
Models of men’s behavior with little attention to spouses
Second earner only in budget const. French (2005), French & Jones (2012)
Binary labor supply Casanova (2010), Knapp (2012), Jorgensen (2014)
Only binary leisure coplementarities Vermeulen et al (2006)
→ Missing spousal/household decision making

Introduction
Motivation: little spotlight in macro on joint retirement
Rich literature on role of PS features in retirement: take-up and timing
French (2005), Cagetti (2006), French and Jones (2012), etc.
Models of men’s behavior with little attention to spouses
Second earner only in budget const. French (2005), French & Jones (2012)
Binary labor supply Casanova (2010), Knapp (2012), Jorgensen (2014)
Only binary leisure coplementarities Vermeulen et al (2006)
→ Missing spousal/household decision making meanwhile:
women typically have lower eligibility age
most workers close to retirement age are married
age diﬀerence between spouses < age diﬀerence in the eligibility age

Introduction
Strong empirical evidence on coordinating in couples
Ubiquitous ﬁndings of spouses coordinating the retirement dates

Introduction
US: Coile (2003) , Bhatt(2017)
France: Goux et al (AER, 2014), Stancanelli and Soest (2017)
Sweden: Gustafson (2017) , Slin (2016)
Australia: Warren (2015), Brazil: Queiroz and Sousa (2017), Spain: Perez
et al (2015), Switzerland: Lalive and Parrota (2017),
Comparative (SHARE data): Hospido and Zamarro (2014)

Introduction
US: Coile (2003) , Bhatt(2017)
France: Goux et al (AER, 2014), Stancanelli and Soest (2017)
Sweden: Gustafson (2017) , Slin (2016)
Australia: Warren (2015), Brazil: Queiroz and Sousa (2017), Spain: Perez
et al (2015), Switzerland: Lalive and Parrota (2017),
Comparative (SHARE data): Hospido and Zamarro (2014)
Borella et al (2017) incorporating heterogeneity (marriage and
gender) into models improves the match to the data.

Introduction
Our contribution
A retirement decision model within couples

Introduction
Our contribution
Both agents are active decision makers
Generalize model used by literature ⇒ do not impose abrupt exits
Retirement timing is fully endogenous
(eligibility to pensions beneﬁts)

Introduction
Our contribution
Both agents are active decision makers
Generalize model used by literature ⇒ do not impose abrupt exits
Retirement timing is fully endogenous
(eligibility to pensions beneﬁts)
Calibrate the model to German economy
Analyze policy changes
1 Eligibility age of women ↑ on participation of men
2 (Partial) eligibility age of men ↓ on participation of women

Model
The model
Discrete time ﬁnite horizon collective household model in partial
equilibrium
Finite horizon
→ agents die at J
→ retire with certainty at jr
→ are eligible for retirement at je
Partial equilibrium: factor prices are given
Collective household model
In the spirit of Chiappori (1992,1996), Vermeulen et al (2010)
Individual maximization and bargaining (Pareto optimal equilibria)

Model
Household utility
U = θu1(c1, l1, l2) + (1 − θ)u2(c2, l2, l1)
where
θ bargaining power of agent 1
ui depends on consumption (ci ), leisure (1 − li ) and partner’s leisure
(1 − l¬i )
when i retires li = 0

Model
Household utility
U = θu1(c1, l1, l2) + (1 − θ)u2(c2, l2, l1)
Properties
1 Traditional, uc > 0, uc < 0
2 Joint leisure:
∂2ui
∂li ∂lj
= 0
3 Individual leisure: ∂ui
∂li
|lj =0 < 0 & ui (ci , li , 0) < ui (ci , 0, 0)

Model
Household utility
U = θu1(c1, l1, l2) + (1 − θ)u2(c2, l2, l1)
Agent’s utility function
ui = ln(ci ) −
φi
2
l2
i + ρi (1 − li )(1 − l¬i )
where
φi Agent i disutility of labor
ρi represents joint leisure enjoyment

Model
Budget constraint
ci + c¬i + a = (1 + r)a +
i∈1,2
1(i works)wi ωi li
+
i∈1,2
1(i retired)bi
where
a (a’) are assets in t (t+1)
wi , bi are wage rates and beneﬁts
ωi is a productivity shock
ωi = exp(z) z ∼ N(0, σi )

Model
The retirement decision: structure of the model
Both working
Both work
Agent 1 retires
Agent 2 retires
Both retired
Both retired
j < je je ≤ j < jr jr ≤ j
Agents choose their state when je ≤ j < jr
Retirement is an absorbing state

Model
The inter-temporal decision problem: easy cases
j < je
max V w,w
j (a, li , l¬i ) = u(a, li , lj ) + δπj+1|j E[(V w,w
(· )]
sub to i=1,2 ci + a = i=1,2 wi ωi,j li + (1 + r)a
jr ≤ j
max V r,r
j (a, li , l¬i ) = u(ci , c¬i ) + δπj+1|j E[V r,r
(· )]
sub to i=1,2 ci + a = i=1,2 bi + (1 + r)a

Model
The inter-temporal decision problem: je ≤ j < jr
Two-stage problem
max V s,s
j (a, li , l¬i ) = us,s
(ci , c¬i , li , lj ) + δπj+1|j E[V s ,s
(· )]
sub to i=1,2 ci + a =
i=1,2
wi ωi,j li,j +
i=1,2
1i bi + (1 + r)a
1i = 1 if agent i has retired
1 Agents choose continuous variables for all states (ci , c¬i , li , l¬i )
2 Agents choose their preferred state among feasible states (si , s¬i )
Discrete choice
Feasible = retirement in an absorbing state

Model
Mechanisms for coordinating retirement
1 Budget constraint
→ Retirement →↓ income (bi < wi ωi )
→↓ joint retirement
2 Leisure complementarities (ρi > 0)
→ Retirement →↓ ∂ui
∂li
→↑ joint retirement

Model
Estimation
We recover parameters using simulated method of moments
ˆθ minimizes the distance between observed and simulated moments
Formally
arg minˆθ
1
1 + τ
ˆφI (θ) ˆWI
ˆφI (θ)
where
ˆφI (θ) = moment data − moment model
ˆWI is a weighting matrix
→ Identity matrix (consistent, but not eﬃcient)
τ equals ratio of ndata to nsimulations

Model
Which moments should be matched?
Source German SOEP (Socio-Economic Panel)
Description Joint retirement

Model
Moments describing labor supply

Model
1 Hours worked — age & gender
1) Mean 2) Variance 3) Q1 4) Q3
2 Participation rate — age & gender

Model
1 Hours worked — age & gender
1) Mean 2) Variance 3) Q1 4) Q3
2 Participation rate — age & gender
# moments → 50 × 2 × 5 = 500

Results
Input parameters
Definition Value Source
w1 Men’s wage 1 Numeraire
w2 Women’s wage 0.8 literature
r Interest rate 0.03
bi Benefits 0.4 ∗ ¯wi OECD
je1 Eligibility age for men 62 OECD, Eff ret. age
je2
Eligibility age for men 60 OECD, Eff ret. age
jr Mandatory retirement 80 (NA)
πj+1|j Cond. prob survival ... Eurostat

Results
Estimated parameters
Deﬁnition Value
ˆθ Barg. power men 0.44
ˆφm Distate for 8.68
ˆφf work 10.57
ˆρm Preference for 0.11
ˆρf joint leisure 0.01
ˆδ Time discount 0.987
ˆσm Variance 0.003
ˆσf of shocks 0.05

Results
Model’s ﬁt
Observed Simulated
E(HoursM ) .364 .320
Var(HoursM ) .071 .038
E(HoursF ) .203 .140
Var(HoursF ) .052 .010
Correl(Hours) .238 .861

Results
Model’s ﬁt
Simulated vs real data: men’s labor supply
0
.2
.4
.6
Weeklyhoursworked(80hrs=1)
20 30 40 50 60 70
Age
95% CI Actual moments Simulated moments

Results
Model’s ﬁt
Simulated vs real data: female’s labor supply
0
.1
.2
.3
Weeklyhoursworked(80hrs=1)
20 30 40 50 60 70
Age
95% CI Actual moments Simulated moments

Policy experiment
A policy experiment
1 Raising females eligibility age
→ In many countries, jF
e < jM
e
→↑ jF
e ⇒↑ Male employment

Policy experiment
A policy experiment
e < jM
e
→↑ jF
Who will be affected by the policy?
Men in couples where difference in elligibility age < difference in
couple’s age
∼ one third of couples in SOEP (29.7%)

Policy experiment
A policy experiment
e < jM
e
→↑ jF
Who will be affected by the policy?
Men in couples where difference in elligibility age < difference in
couple’s age
∼ one third of couples in SOEP (29.7%)
2 Raising men’s eligibility age
→↑ jM
e ⇒↑ Female employment (?)

Policy experiment
1) Increasing women’s eligibility age0.1.2.3.4
Laborsupplymen(80=1)
50 55 60 65 70
age
Ret. age as in data Equal retirement age Women retire later

Policy experiment
2) Increasing men’s eligibility age0.05.1.15.2
Laborsupplymen(80=1)
50 55 60 65 70
age
Retirement as in data + 3 years mean + 10 year men

Policy experiment
Summary
This is still a work in progress
We propose a model to model joint retirement decisions
Joint leisure preference
Continuous labor decisions for both spouses in a household
Continuous choice between retirement & leisure × 2
We propose to use it for:
isolating the role of channels (preferences, joint shocks, policies)
quantifying the eﬀects of policy experiments
↑ eligibility age of women
costs of partial early eligibility for men

Policy experiment
Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: l.vandervelde@grape.org.pl

Policy experiment
SOEP - Description
A yearly panel data from Germany from 1984 - today
(East Germany included since 1991)
The sample comprises
Married individuals aged between 21 and 70
We focus on heterosexual couples
Years between 2010 and 2015
Our sample consists of
> 110 ths couple-year observations
> 18 ths unique couples
Back

Policy experiment
The extent of joint retirement in Germany (I)
→ Partner’s employment status aﬀects own employment
→ Preference for joint leisure or similar distaste for work?

Policy experiment
The extent of joint retirement in Germany (II)
Exits between 2000-2015
0.05.1.15.2
−10 0 10 −10 0 10 −10 0 10
−5 < Age Dif. <−2 −2 < Age Dif. <2 2 < Age Dif. <5
Density
Year retirement (m) − Year retirement (w)
→ Most retirement decisions are within 2 years
→ Age diﬀerence matters, but peak at zero persist
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The role of joint leisure in retirement decisions

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