A collective labor supply model with
externalities
Identification and estimation by means of
panel data
Pierre-Carl Michaud (RAND)
Frederic Vermeulen (Tilburg University)
F ACULTY
OF
E CONOMICS
AND
B USINESS ADMINISTRATION
Introduction
 Household labor supply usually rationalized by standard
unitary model

Households assumed to behave as single decision
makers

Utility function maximized subject to a budget constraint

Implies well-known theoretical restrictions

Unique preference ordering if restrictions are satisfied
 Unitary model suffers from methodological and empirical
shortcomings

Does not fit in methodological individualism

Unitary restrictions usually rejected when tested on multiperson households
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Introduction
 Collective approach to household behaviour

Chiappori (1988, 1992)

Multi-person households consist of different individuals
with own rational preferences

Intra-household allocations are Pareto-efficient

Theoretical restrictions that fit the data better than unitary
restrictions
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Introduction
 Crucial issue: can we identify individual preferences and the
intra-household bargaining process on couples’ labor supply
data alone?

No, if there are leisure externalities and consumption is
public

Yes, if leisure is exclusive

Yes, if individual preferences are egoistic or of the
Beckerian caring type
 Allows analyzing policy reforms in terms of individual
preferences
 But restrictive assumptions
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Introduction
 Novel approach to obtain identification when individual
preferences allow for general externalities with respect to
leisure
 Idea: make use of individuals who are observed as member
of a couple and as a single (widows and widowers)
 Core assumption: preferences can only change via
observable characteristics when somebody is widowed

Preferences are individual specific: can only change via
clear channel when spouse dies

Obvious candidate: mental health shocks that can in
principle be controlled for
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Introduction
 Application to sample of older Americans drawn from the
Health and Retirement Study
 HRS allows identification strategy: substantial number of
initial couples dissolved over time due to death of one of the
spouses
 Evidence for joint retirement: complementarities in leisure
 Social security simulations by collective model and related
unitary model
 What is value added of collective model?
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Overview
 Identifying a collective labor supply model with leisure
externalities
 Empirical specification
 Data
 Estimation results
 Simulation results
 Conclusion
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Overview
 Identifying a collective labor supply model with leisure
externalities
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Identifying a collective labor supply
model with leisure externalities
 Ingredients of a collective labor supply model

Individual preferences

Pareto-efficient intra-household bargaining process

Observed allocations result from the maximization of a
weighted sum of spouses’ utilities subject to a household
budget constraint

Pareto weights depend on wages and non-labor income
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Household maximization problem



m m
f
m
f
m
f
f






max

b
v
l
,
l
,
c
;
z

1


b
v
l
,
l
,
c
;
z
m f
l ,l , c

subject t o
c  wm h m  w f h f  y
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Identifying a collective labor supply
model with leisure externalities
 Individual preferences and Pareto weights are not identifiable
without additional assumptions

Continuum of utility functions and Pareto weights yield
same observed behavior
vm  v m  v f
vf  v f  v m
1      ;
  1
 
max 
,
   1
1 
1  
 
 Chiappori and Ekeland (2005) propose restrictions on
marginal utilities to secure identifiability
 
 Marginal utility of exclusive goods set to zero in other
individual’s utility function
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Identifying a collective labor supply
model with leisure externalities
 Approach not immediately applicable:

We only observe leisure and consumption of Hicksian
aggregate good in labor supply data sets

Evidence that there are leisure externalities
 Our identification strategy: make use of individuals who are
observed as member of a couple and as a single (panel data)
 Core assumption: preferences can only change via
observable characteristics when somebody becomes a
widow(er)
 Allows to pin one (and only one) structural model from the
continuum of structural models
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Identifying a collective labor supply
model with leisure externalities
 Recall: single’s optimization problem

j j
j
max
v
l
,
c
;
z
s
j
l ,c

s.t. c  w j h j  y;
j  m, f
 Assumption regarding preferences implies

l
 
  v l
vsm l m , c; z m  v m l m , l f , c; z m
vsf
f
, c; z f
f
m
, l f , c; z f


 Unidentified constant: leisure level associated with
deceased spouse
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Identifying a collective labor supply
model with leisure externalities
 ‘Household’ utility function:

 


 
k m 1  k f v m l m , l f , c; z m  k f 1  k m v f l m , l f , c; z f





 k m k f  b v m l m , l f , c; z m  1   bv f l m , l f , c; z f

 Three cases can be distinguished: couple, widows and
widowers
 Compare to Chiappori and Ekeland (2005): marginal
utility of partner’s leisure equals zero only when that
spouse died
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Overview
 Identifying a collective labor supply model with leisure
externalities
 Empirical specification
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Empirical specification
 Discrete choice framework
 Spouses choose between a limited number of working hours
choices

Husbands: 0, 25, 40 and 50 hours

Wives: 0, 15, 30 and 40 hours
 Nonlinear budget sets
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Empirical specification
 Preferences are of a modified Cobb-Douglas type
uitj   jj zitj ln litj  cj zitj ln cit  mfj zitj ln litm ln litf
 j  m, f 
 Discrete unobserved heterogeneity in marginal utility of own
leisure
 cj zitj   zitj '  cj
 z   z '   
j
j
j
it
j
it
j
j
j
 mfj zitj   zitj '  mfj
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Empirical specification
 Pareto weight
exp REC it , yit , SSit 
 bit  
1  exp REC it , yit , SSit 
 Fixed costs of participation taken into account via monetary
costs subtracted from after-tax income if one returns to work
(state dependence)
 Part-time specific utility costs
 Estimation in conditional logit framework with discrete
heterogeneity
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Empirical specification
 Unitary model’s specification
uit   m zit  ln litm   f zit  ln litf   c zit  ln cit
  mf zit  ln litm ln litf
 Also discrete heterogeneity, fixed costs of participation and
part-time specific utility costs taken into account
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Overview
 Identifying a collective labor supply model with leisure
externalities
 Empirical specification
 Data
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Data
 Health and Retirement Study
 Longitudinal survey that follows a cohort of individuals who
were born between 1931 and 1941, and their partners
 We use first six biennial waves (1992-2002)
 Sample selection

Married or cohabiting couples where both individuals
were alive in 1992

Sample of 2342 households that are potentially 6 times
observed (487 widows and 138 widowers in 2002)
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Overview
 Identifying a collective labor supply model with leisure
externalities
 Empirical specification
 Data
 Estimation results
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Estimation results
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Estimation results
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Overview
 Identifying a collective labor supply model with leisure
externalities
 Empirical specification
 Data
 Estimation results
 Some simulations
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Some simulations
 Simulation 1: Elimination of earnings test

Social security benefits are reduced if one has earnings
above a threshold if one is younger than the normal
retirement age

Reimers and Honig (1996), Friedberg (2000): men are
deterred from working by this rule, while women are not
affected

Gruber and Orszag (2000): no influence on husbands,
while there are disincentive effects for women
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Simulation 1
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Some simulations
 Simulation 2: Elimination of spouse allowance

Spouse is entitled to the maximum of the own benefit and
half of the spouse’s benefit given eligibility

Blau (1997): elimination of allowance with replacement
by earnings sharing has negative impact on husbands’
participation and positive impact on wives’ participation
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Simulation 2
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Welfare effects
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Overview
 Identifying a collective labor supply model with leisure
externalities
 Empirical specification
 Data
 Estimation results
 Some simulations
 Conclusion
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Conclusion
 Collective labor supply model
 Identification strategy in the presence of leisure externalities
 Application to Health and Retirement Study

Strong rejection of unitary model

Better fit of collective model

Simulations: depending on simulation and criterion
(participation/welfare) qualitatively different results
obtained
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