Income risk and fertility decision
Oliwia Komada
November 22, 2018
Doctoral Seminar
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 1

Motivation

Risky childless world...
• Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011;
Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2

Risky childless world...
• Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011;
Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016)
• Uncertainty meters a lot...
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2

Risky childless world...
• Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011;
Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016)
• Uncertainty meters a lot...
• Differences in income growth volatility account for 61% of fertility
variation between US states during the post WWII baby boom.
(Chabe-Ferret & Gobbi 2018)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2

Risky childless world...
• Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011;
Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016)
• Uncertainty meters a lot...
• Differences in income growth volatility account for 61% of fertility
variation between US states during the post WWII baby boom.
(Chabe-Ferret & Gobbi 2018)
• Increase of husband occupation earnings risk by 1sd yields to
decrease of completed fertility by 1.5 children. (Sommer JME 2016)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2

Risky childless world...
• Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011;
Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016)
• Uncertainty meters a lot...
• Differences in income growth volatility account for 61% of fertility
variation between US states during the post WWII baby boom.
(Chabe-Ferret & Gobbi 2018)
• Increase of husband occupation earnings risk by 1sd yields to
decrease of completed fertility by 1.5 children. (Sommer JME 2016)
• Idiosyncratic earnings risk increase explains nearly
50% of fertility drop. (Sommer JME 2016)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2

This study
1. Fertility is too low or just lower due to idiosyncratic income risk?
→ individual vs. social planer choice
→ open vs. closed economy
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3

This study
1. Fertility is too low or just lower due to idiosyncratic income risk?
→ individual vs. social planer choice
→ open vs. closed economy
2. If fertility is too low, is child benefit welfare improving?
→ PAYG pension system: social benefits and individual cost
→ immediate cost and future benefits
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3

This study
1. Fertility is too low or just lower due to idiosyncratic income risk?
→ individual vs. social planer choice
→ open vs. closed economy
2. If fertility is too low, is child benefit welfare improving?
→ PAYG pension system: social benefits and individual cost
→ immediate cost and future benefits
3. Does it matter how we finance child benefit?
→ taxes imply a redistribution
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3

This study
1. Fertility is too low or just lower due to idiosyncratic income risk?
→ individual vs. social planer choice
→ open vs. closed economy
2. If fertility is too low, is child benefit welfare improving?
→ PAYG pension system: social benefits and individual cost
→ immediate cost and future benefits
3. Does it matter how we finance child benefit?
→ taxes imply a redistribution
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3

This study
1. Fertility is too low or just lower due to idiosyncratic income risk?
→ individual vs. social planer choice
→ open vs. closed economy
2. If fertility is too low, is child benefit welfare improving?
→ PAYG pension system: social benefits and individual cost
→ immediate cost and future benefits
3. Does it matter how we finance child benefit?
→ taxes imply a redistribution
→ redistribution can amplify risk: lump-sum tax
→ ... or insure against labor income risk: capital tax
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3

Methodology

What do we do?
Our approach
We develop an overlapping generations model (OLG) with
endogenous fertility and idiosyncratic risk.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 4

What do we do?
Our approach
We develop an overlapping generations model (OLG) with
endogenous fertility and idiosyncratic risk.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 4

What do we do?
Our approach
We develop an overlapping generations model (OLG) with
endogenous fertility and idiosyncratic risk.
Main novelty
• Optimal fertility decision in the model with idiosyncratic risk.
• The computational model with endogenous fertility, idiosyncratic
risk and general equilibrium.
• Pronatalist policy effect with idiosyncratic risk captured.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 4

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
→ lump sum tax welfare deteriorating
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Results in a nutshell
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
→ lump sum tax welfare deteriorating
→ capital income tax brings welfare gains.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5

Part I - analytic framework

Model I

Consumers
Vt = ln(cy
t ) + φ ln(nt+1) + β ln(co
t+1(ζt+1))dΦ
subject to:
cy
t + at+1 + (p − ϕ)nt+1 = wt(1 − τ) − θt
co
t+1 = at+1Rt+1 + κζt+1wt+1 + ηt+1
where
ζt+1 ∈ {1 − δζ, 1 + δζ}
and probability of each stage is equal to 1
2
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 6

Government
• covers child benefit adjusting lump sum tax:
θt = ϕnt
• balances pension system
ηt+1 = wt+1τnt+1
Producers
Standard perfectly competitive representative firm with
Cobb-Douglas production function
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 7

Results I

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)
• steady state social planer fertility choice
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
y (δζ) is decreasing function
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)
• steady state social planer fertility choice
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
y (δζ) is decreasing function
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)
• steady state social planer fertility choice
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
y (δζ) is decreasing function
Individual consumer ignore pension benefits and fertility link
→ fertility too low
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)
• steady state social planer fertility choice
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
y (δζ) is decreasing function
Individual consumer ignore pension benefits and fertility link
→ fertility too low
Individual consumer ignore the cost of capital for future generation
→ fertility too high
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)
• steady state social planer fertility choice
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
y (δζ) is decreasing function
Individual consumer ignore pension benefits and fertility link
→ fertility too low
Individual consumer ignore the cost of capital for future generation
→ fertility too high
Idiosyncratic income risk has the same impact on the individual consumer and
social planer → higher the risk lower the optimal fertility
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings
• additional savings lower the interest rate and increase wages
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings
• additional savings lower the interest rate and increase wages
• ”risky” part of income increase
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings
• additional savings lower the interest rate and increase wages
• ”risky” part of income increase
• individual savings rate higher than social planer savings rate
→ (Ludwig Krueger 2018)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings
• additional savings lower the interest rate and increase wages
• ”risky” part of income increase
• individual savings rate higher than social planer savings rate
→ (Ludwig Krueger 2018)
• individual consumption lower than social planer choice
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings
• additional savings lower the interest rate and increase wages
• ”risky” part of income increase
• individual savings rate higher than social planer savings rate
→ (Ludwig Krueger 2018)
• individual consumption lower than social planer choice
• individual fertility lower than social planer choice
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9

Part II - computational model

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods,
• survival rate πj,t < 1
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods,
• survival rate πj,t < 1
• enter labor market at j = 5
• uninsurable earnings: endogenous labor with idiosyncratic
productivity process that follows AR(1) approximated by Markov
chain
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods,
• survival rate πj,t < 1
• enter labor market at j = 5
• uninsurable earnings: endogenous labor with idiosyncratic
productivity process that follows AR(1) approximated by Markov
chain
• endogenous fertility: discrete choice made at j = 8 ,
n ∈ {0, 1, 2, 3}
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods,
• survival rate πj,t < 1
• enter labor market at j = 5
• uninsurable earnings: endogenous labor with idiosyncratic
productivity process that follows AR(1) approximated by Markov
chain
• endogenous fertility: discrete choice made at j = 8 ,
n ∈ {0, 1, 2, 3}
• work till retirement age j = 14, later receive pension benefits
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods,
• survival rate πj,t < 1
• enter labor market at j = 5
• uninsurable earnings: endogenous labor with idiosyncratic
productivity process that follows AR(1) approximated by Markov
chain
• endogenous fertility: discrete choice made at j = 8 ,
n ∈ {0, 1, 2, 3}
• work till retirement age j = 14, later receive pension benefits
• pay Soc Sec contributions, labor, capital, consumption taxes
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods,
• survival rate πj,t < 1
• enter labor market at j = 5
• uninsurable earnings: endogenous labor with idiosyncratic
productivity process that follows AR(1) approximated by Markov
chain
• endogenous fertility: discrete choice made at j = 8 ,
n ∈ {0, 1, 2, 3}
• work till retirement age j = 14, later receive pension benefits
• pay Soc Sec contributions, labor, capital, consumption taxes
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10

Government
• Collects taxes from labor income, capital income, consumption and
lump sum tax.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 11

Government
• Collects taxes from labor income, capital income, consumption and
lump sum tax.
• Finances government spending.
• Balances pension system.
• Services debt.
Producers
Standard perfectly competitive representative firm with
Cobb-Douglas production function
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 11

Calibration
Preferences
• Preference for leisure γ matches average hours 33%
• Preference for children φ matches fertility rate 1.9
• Discounting rate δ matches interest rate 4%
Idiosyncratic productivity shock based on Kruger and Ludwig (2013):
• Persistence η = 0.95
• Variance ση = 0.0375
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 12

Calibration
Pension system
• Replacement rate ρ matches benefits as % of GDP 5.2%
• Contribution rate balances pension system in the initial steady
state
Child cost {pt = 0.15(1 − τ)(1 − τl )wt} matches average child cost in
terms of average wages
Taxes {τc, τl , τk} match revenue as % of GDP {9.2%, 3.8%, 3.6%}
Depreciation rate d matches investment rate of 25%
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 13

Results

Fertility rate decreases when income variance is higher
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 14

Fertility rate decreases when income variance is higher
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 15

Variance change explains 50 % of fertility drop
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 16

Child benefit raises fertility
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 17

Effects are similar for different fiscal tools
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 18

Fertility is higher. Does it make the World better place?
Measuring welfare effects
• Compare utility under the veil of ignorance
→ In which World would I rather be born?
• P − efficiency
→ care only about utility level, ignore cohort size
• express as a percent of consumption from pre-reform scenario
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 19

Welfare is lower when we use lump sum tax
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Welfare increase when we use capital tax
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 21

Summary

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
→ lump sum tax welfare deteriorating
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Insights from this study
• In standard OLG model fertility and idiosyncratic labor income risk
are negatively correlated.
• It reflects well pattern observed in the data.
• Child benefit increase fertility however welfare effects are
ambiguous.
• It matters how we finance child benefit:
→ lump sum tax welfare deteriorating
→ capital income tax brings welfare gains.
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22

Thank you for your attention!
w: grape.org.pl
t: grape org
f: grape.org
e: o.komada@grape.org.pl
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 23