Income risk and fertility decision

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

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)

• 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)

This study
1. Fertility is too low or just lower due to idiosyncratic income risk?
→ individual vs. social planer choice
→ open vs. closed economy

This study
2. If fertility is too low, is child benefit welfare improving?
→ PAYG pension system: social benefits and individual cost
→ immediate cost and future benefits

This study
3. Does it matter how we ﬁnance child beneﬁt?
→ taxes imply a redistribution

This study
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

What do we do?
Our approach
We develop an overlapping generations model (OLG) with
endogenous fertility and idiosyncratic risk.

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.

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.

ambiguous.
• It matters how we ﬁnance child beneﬁt:

ambiguous.
→ lump sum tax welfare deteriorating

ambiguous.
→ capital income tax brings welfare gains.

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

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

Fertility is just lower due to risk in open economy
• individual consumer fertility choice
n =
φ
p − ϕ
c∗
y (δζ)

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

n =
φ
p − ϕ
c∗
y (δζ)
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
Individual consumer ignore pension beneﬁts and fertility link
→ fertility too low

n =
φ
p − ϕ
c∗
y (δζ)
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
Individual consumer ignore the cost of capital for future generation
→ fertility too high

n =
φ
p − ϕ
c∗
y (δζ)
n =
φ + β
p + k − d
c∗
y (δζ)
where c∗
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

Fertility may be too low due to risk in closed economy
Intuition:
• idiosyncratic income risk → precautionary savings

Intuition:
• additional savings lower the interest rate and increase wages

Intuition:
• ”risky” part of income increase

Intuition:
• individual savings rate higher than social planer savings rate
→ (Ludwig Krueger 2018)

Intuition:
• individual consumption lower than social planer choice

Intuition:
• individual consumption lower than social planer choice
• individual fertility lower than social planer choice

Consumers
• uncertain lifetimes: live for j = 1, 2, ..., 20 ﬁve-year periods,
• survival rate πj,t < 1

Consumers
• enter labor market at j = 5
• uninsurable earnings: endogenous labor with idiosyncratic
productivity process that follows AR(1) approximated by Markov
chain

Consumers
chain
• endogenous fertility: discrete choice made at j = 8 ,
n ∈ {0, 1, 2, 3}

Consumers
chain
n ∈ {0, 1, 2, 3}
• work till retirement age j = 14, later receive pension beneﬁts

Consumers
chain
n ∈ {0, 1, 2, 3}
• work till retirement age j = 14, later receive pension beneﬁts
• pay Soc Sec contributions, labor, capital, consumption taxes

Government
• Collects taxes from labor income, capital income, consumption and
lump sum tax.

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

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

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%

Fertility rate decreases when income variance is higher

Variance change explains 50 % of fertility drop

Child beneﬁt raises fertility

Effects are similar for different fiscal tools

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

Welfare is lower when we use lump sum tax

Welfare increase when we use capital tax

Insights from this study

ambiguous.

ambiguous.
→ capital income tax brings welfare gains.

Thank you for your attention!
w: grape.org.pl
t: grape org
f: grape.org
e: o.komada@grape.org.pl

Income risk and fertility decision

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