A General Equilibrium Analysis of Parental Leave Policies
Erosa A., Fuster L. and Restuccia D.
(Forthcoming RED)
Eva Garcia-Moran
March 2010
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
1 / 21
Outline
Question
Motivation
What do they do
Model
Calibration
Benchmark economy
Experiments
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
2 / 21
Question
Assess the quantitative impact of parental leave policies on the
economy
In particular:
Welfare
Fertility
employment
And improve understanding of mechanisms driving the e¤ects of
parental leave policies
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
3 / 21
Motivation
Mandated parental leave policies are common in most developed
countries
The channels through which they in‡uence economic decisions are
complex
Di¤erent e¤ects across heterogenous agents
Di¤erent welfare implications across agents
Empirically di¢ cult to disentangle the channels a¤ecting outcomes
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
4 / 21
Motivation
General equilibrium model of fertility and labor market decisions
Framework of Mortensen and Pissarides (94)
Benchmark: Voluntary leaves, there is no government intervention
Calibrate to USA economy before implementation of parental leave
policy at federal level in 1993
Implement di¤erent parental leave policies
Implement other policies
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
5 / 21
Motivation
Parental leave policies a¤ect decisions and welfare through 3 channels
Bargaining channel
General equilibrium channel
Redistributive channel
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
6 / 21
Model
Agents
Males and females searching for jobs
Females can be:
Fertile females
Non-fertile females
Males decisions will depend on human capital and employment status
Female decisions will also depend on number of kids and value of
staying home
Entrepreneurs: posting vacancies and making job o¤ers
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
7 / 21
Model
Environment
Large number of workers
Exponential life: probability of dying ρ each period
Equal proportion of males and females
Ex ante heterogeneity: Education levels
Females become infertile with probability φ each period
People derive utility from consumption
Females also get utility from spending time with kids and the number
of kids
Kids are costly in terms of time and goods
each kid reduces time working in η units
costs ψ units of good per period
Female becomes non-fertile, kids become adults and they are costless
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
8 / 21
Model
Environment
Utility is linear in consumption, time spent with children and concave
in the number of kids
Continuum of entrepreneurs
Linear preferences over consumption
post vacancies at cost c (in units of output good)
If a worker-vacancy is matched, next period the production unit can
Produce
be on leave
be destroyed
If the match is not destroyed, it faces …xed cost C whether producing
or not
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
9 / 21
Model
Problem of a Fertile Female
Decision divided into 3 stages:
Fertility stage
Labor stage
Matching stage
Beginning of period (j, d, h, n)
j 2 fe, u g, employment status
d 2 f0, 1g, domestic status
h: human capital
n : number of kids
Female draws 2 shock:
Fertility opportunity : they can have a kid with probability σ
Value of staying home v N µv , σ2v
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
10 / 21
Model
Problem of a Fertile Female
(j,d,h,n)
Shocks
υσ
Demographic
Human capital
Job destruction
Shocks
t+1
t
Fertility Stage
Labor Stage
Matching Stage
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
11 / 21
Model
Problem of a Fertile Female
Fertility stage
Wjf
(d, h, n) =
Z n
v
n
oo
σ max Vjf (d1 , h, n + 1, v ) , Vjf (d, h, n, v )
dF (v )
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
12 / 21
Model
Problem of a Fertile Female
Labor stage
If employed
n
o
Vef (d, h, n, v ) = max Af , R f , Lf
Af depends on wage, number of kids and the expected value of next
period (she could be employed, unemployed and become non fertile)
R f depends on value of staying home, kids and the expected value
next period(with probability p they receive an o¤er)
Lf depends on value of staying home, kids, a wage, and the expected
value of next period given that she was on leave (she could be
employed, unemployed and become non fertile)
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
13 / 21
Model
Problem of a Fertile Female
Matching state
Exogenous matching function, M (u, v ) = ku α v 1
α
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
14 / 21
Model
Value of a job for the entrepreneur
Output of a female
y f (h, n) = (1
wg ) ( 1
wf n ) ( 1
ηn) h
C
Value of a job for the entrepreneur
n
o
J f (d, h, n, v ) = max Jaf , Jlf , 0
Wage determination: Generalized Nash Bargaining
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
15 / 21
Experiments
1
Implement 1 period unpaid parental leaves (USA, 93)
2
Implement 1 and 2 periods fully paid parental leave
Check welfare, fertility, Labor market decisions, Work
Importance of Channels
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
16 / 21
Experiments
Welfare
Parental leave policies lead to welfare losses
Distortion of decision of destroying matches
Higher taxes for males and lower …nding rate, no bene…ts
High education females bene…t less
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
17 / 21
Experiments
Fertility and Work
Fertility increases
Distinction between employment and work
Benchmark
Paid 2
Mothers with
Employment
66.6
71
infants
Working
63
22
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
18 / 21
Experiments
Channels
Isolate general equilibrium e¤ect: keep job …nding rate constant
Eliminate redistribution e¤ect across gender: parental leave …nanced
with taxes on female workers
Eliminate redistribution e¤ect across education: taxes di¤er across
education groups
Bargaining: take other e¤ects out
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
19 / 21
Experiments
Channels
For females
Welfare
Employment of mothers
Employment of fertile females
Fertility
Paid 4
(1)
p=0.7
(Redistr.+Barg.) (2)
No red., p=0.7
(Bargaining) (3)
0.33
0.76
0.66
2.23
0.58
0.76
0.66
2.23
-0.34
0.76
0.64
2.26
General equilibrium channel: (1)-(2)
Redistributive channel: (2)-(3). Generates an increase in welfare of 0.92%
of GDP
Bargaining channel: (3). Generates a reduction in welfare of 0.34%
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
20 / 21
Model
Other policies
Work subsidy
For females
Welfare
Welfare for males
Employment of mothers
Employment of fertile females
Fertility
Paid 2
work subsidy
0.25
-0.81
0.70
0.66
2.2
0.78
-0.07
0.5
0.76
2.15
Erosa A., Fuster L. and Restuccia D. (Forthcoming
A General
RED)
Equilibrium
Eva Garcia-Moran
Analysis of()Parental Leave Policies
03/10
21 / 21