Evaluating welfare and economic effects of raised fertility

Evaluating welfare and economic eﬀects of raised fertility
Magda Malec
with Krzysztof Makarski and Joanna Tyrowicz
19th-20th of April 2018
PenCon 2018 in Lodz
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 1

Motivation
• Policy call for costly natalist policies and instruments – are they worth it?
• substantial decline in population due to lowering fertility and longevity in most of
advanced and middle income economies
• declining population and multiple long-term implications
=⇒ social security, pension system and health care expenditures
• mixed empirical literature on previous policy interventions – can we explain why?
=⇒ negligible eﬀects, ”too soon to tell”, methodological issues

Literature review
• empirical evaluation with negative eﬀects
Olivetti and Petrongolo (2017), Baizan et al. (2016), Rossin-Slater (2018)
• empirical evaluation with positive eﬀects
Drago et al. (2011), Milligan (2005), Brewer et al. (2012), Frejka and Zakharov (2013), Garganta et al. (2017),
Lalive and Zweimueller (2009), Rindfuss et al. (2010), Havnes and Mogstad (2011), Bauernschuster et al. (2015),
Del Boca et al. (2009)
• OLG framework with more explicit fertility
Fehr et al. (2017), Georges and Seekin (2016), Mamota (2016), Hock and Weil (2012)
• fertility may be endogenous
Liao (2011), Ludwig et al. (2012), Hock and Weil (2012)

Our questions
1. What are welfare effects of fertility changes?
⇒ costs are immediate and private, gains are delayed and public
2. What are macroeconomic effects of fertility changes?
⇒ assuming we know how to achieve given rise in fertility, how much to spend
3. Does it matter what kind of policy we do?
⇒ intensive (families with kids have more) vs extensive (more families has kids)
Potential effects
• time mismatch: immediate costs and delayed benefits
• beneficiary mismatch: private costs and public gains
• general equilibrium effects: people adjust to expected fertility

What do we do?
Our approach
We develop large OLG model with family structure and types of agents in a
household. Things we really care for:
• family structure – households with κ = 0, 1, 2, 3+ children
• heterogeneity – two types of agents within a household
• exogenous fertility
• extensive and intensive margin adjustments
• calibrating the model closely to the data
Main novelty
We can analyze various paths of fertility ⇒ sensitivity of macro to demographics
Model Calibration Demography

Fertility scenarios
What is baseline?
• status quo demographic projection
• unchanged fertility 1.44 (data averaged for 2006-2014)
• data on household structure
What is fertility change scenario?
• 1.44 −→some higher level
• How many combinations of household structure can generate a given fertility
increase path? Countless.
• Does it matter? Yes.
Generating scenarios

Measuring macroeconomic effects
• net surplus of the government budget
difference between government spending in baseline (GB
t ) and reform (GR
t )
discounted for the moment of fertility change and expressed in terms of GDP
per capita
• it acounts for GE effects (i.e. publc gains from fertility increase)

Measuring fiscal effects
• fiscally beneficial
• (−) labor market (women)
(−) higher government expenditures
• (+) labor market (men)
(+) higher consumption tax base
(+) higher labor tax base
• effects are small

How much can we spend every year, assuming increase of fertility?
target fertility 1.50 target fertility1.85

Distribution of the ﬁscal eﬀects over time

Measuring welfare effects
Do I prefer to live in the world with increased fertility?
(discounted expected utility in the form of consumption equivalent)
• raised fertility is not increasing
individually measured utility
• negative effect:
wages ↓ > pension benefits ↑
• really small effects: individual
welfare is not particularly responsive
to the population dynamics

Measuring welfare eﬀects
Does intensive and extensive margin matter?

Fiscal eﬀect
Fertility rate prior to the simulated increase
1.20 1.70

Welfare eﬀect
Fertility rate prior to the simulated increase
1.20 1.70

Insights from our study
1. Fiscal: net surplus in government budget, but small
• small, but universal fiscal gains
• for central path 0.2% GDP
• not in the long run (!)
2. Welfare: negative welfare effect
• fertility↑ −→ welfare↓
• intensive and extensive margin matters (change in sign), but extensive margin can
be unrealistic (no trend in data)
3. Methodology: mixed empirical results make sense
• intensive vs exensive fertility margin tilts the sign of the outcomes
• even with unidirectional labor supply effects
• effects are small (false rejection of null hypothesis in empirical research)
• labor supply of men dominates that of women
• potential perverse incentives should drag even further towards zero
• it is not likely that technological progress is a “replacement” for fertility

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

Producers – very standard
• Perfectly competitive representative ﬁrm
• Standard Cobb-Douglas production function
Yt = Kα
t (zt Lt )1−α
,
• Proﬁt maximization implies
wt = (1 − α)Kα
t zt (zt Lt )−α
rt = αKα−1
(zt Lt )1−α
− d
where d is the capital depreciation rate and zt is technological progress
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

Consumers
• live up to j = 1, 2, ..., J years (J = 100)
• face time and age speciﬁc mortality
• labor supply l endogenous until retirement age ¯J = 65
• until adult j < 21 they live in the household of birth
• reaching adulthood j = 21 they form their own household
• and observe the realization of the fertility

Households
• consist of men and women (the latter denoted by *)
• diﬀer by the number of children κ = 0, 1, 2, 3+
• collective decision making within households
• optimize lifetime utility derived from leisure and consumption
J
j=21
βj−21
πj,t+j−21[uj (˜cκ,j,t+j−21, lκ,j,t+j−21)
+ u∗
j ˜cκ,j,t+j−21, l∗
κ,j,t+j−21 ]
• with individual consumption as follows
˜cκ,j,t =
1
(2 + ϑκ)
cκ,j,t = Ξκcκ,j,t
ϑ child consumption scaling factor,
consumption scaling factor, Ξκ scale eﬀect

Households II
• during child rearing “female” labor supply is reduced following ϕκ
• households maximize utility:
men in age j < ¯J : uj (˜cκ,j,t , lκ,j,t ) = log ˜cκ,j,t + φ log(1 − lκ,j,t )
women in age j < 41 : u
∗
j (˜cκ,j,t , l
∗
κ,j,t ) = log ˜cκ,j,t + φ log(1 − l
∗
κ,j,t − ϕ(κ))
women in age 41 ≤ j < ¯J : u
∗
j (˜cκ,j,t , l
∗
κ,j,t ) = log ˜cκ,j,t + φ log(1 − l
∗
κ,j,t )
men in age j ≥ ¯J : uj (˜cκ,j,t , lκ,j,t ) = log ˜cκ,j,t
women in age j ≥ ¯J : u
∗
j (˜cκ,j,t , l
∗
κ,j,t ) = log ˜cκ,j,t
• subjected to:
(1 + τc )cκ,j,t + ˜sκ,j+1,t+1 = (1 − τ − τl )wj,t lκ,j,t + (1 − τ − τl )wj,t l
∗
κ,j,t
+ (1 + rt (1 − τk )) ˜sκ,j,t
+(1 − τl )bκ,j,t + (1 − τl )b
∗
κ,j,t
+beqκ,j,t + Υt (1)

Government
• collects taxes
Tt = τl (1 − τ)wt Lt + τl Bt + τc Ct + τk rt St + Υt
where Lt , Ct , St , Bt denote labor, consumption, savings and benefits
• finances spending on public goods and service Gt = gt Yt ,
• and services debt ∆Dt = (1 + rt )Dt−1 − Dt
Tt = Gt + ∆Dt
• PAYG defined contribution pension system with mandatory τ
bκ,¯J,t =
¯Jt −1
s=1
Πs
ι=1(1 + rI
t−j+ι−1) τwt−j+s−1lκ,s,t−j+s−1
J
s=¯J
πs,t
• pensions indexed annually with the rate of payroll growth

Calibration
Economics
Demographics

Calibration to replicate 2014 Polish economy
• Discounting rate (δ) matches interest rate of 6.5%
• Depreciation rate (d) matches investment rate of 21%
• Contribution rate (τ) matches beneﬁts to GDP ratio of 7%
• Labor income tax (τl ) matches revenues to GDP ratio of 4.5%
• Consumption tax (τc ) matches revenues to GDP ratio of 11%
• Capital tax (τk ) de iure = de facto
• Technological progress according to EC AWG projections, growth at 1.4%
Note: averages for 2000-2010 (investment rate) and 2005-2014

Preferences
• Preference for leisure (φ) matches participation rate of 56.8%
• Female child rearing time (ϕκ) according to Time Use Survey 2013, approx.
0.231 for κ = 1, 0.236 for κ = 2 and 0.257 for κ = 3
• Consumption scaling factor ( ) and child consumption scaling factor (ϑκ)
matches OECD equivalence scale

Demographic assumptions
• no mortality until children are raised (j < 41)
• historical data on fertility and mortality 1964-2014
• AWG projections until 2080, and stable afterwards
• completed fertility data from household structure for 2006-2014

Data match
• completed fertility

Data match
• mortality

Data match – calibrating to path
Data Model
Completed fertility 1.38-1.52 1.44
Share of cohorts at j < 21 0.23 0.23
Share of cohorts at 20 < j < 41 0.31 0.30
Share of cohorts at j ≥ ¯J 0.18 0.19
Life expectancy at j = 1 73.47 73.83
Life expectancy at j = ¯J 15.41 15.42
Shares of childless women 0.36 0.35
s1 : s2 : s3+ 0.16 : 0.28 : 0.2 0.16 : 0.29 : 0.2
Note: Completed fertility measured as realized fertility for women aged 45 years, data averaged over 2006-
2014. Shares of age groups based on population structure data, averaged over 2006-2014. Data from
Eurostat.

Generating fertility scenarios
1. Pick target (completed) fertility rate
target = reach that rate in 35 years, gradually
We test target fertilities of 1.5, 1.85 and 2.1
2. For intensive scenarios (families have more kids)
2.1 Keep childless ratio constant
2.2 Randomly generate N=100 paths yielding given fertility, from compositions of 1,
2 and 3+ kids per household
2.3 Number of paths can be any
3. For extensive scenarios (more families has kids)
3.1 Keep ratio of 1, 2 and 3+ families constant
3.2 Randomly simulate N=100 paths yielding given fertility, from varying the share of
households without kids and adjusting remaining shares (with a ﬁxed ratio)

Evaluating welfare and economic effects of raised fertility

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