Seminarium Uniwersytet Ekonomiczny w Krakowie i Fisher Black Institute In the context of the second demographic transition, many countries consider rising fertility through pro-family polices as a potentially viable solution to the fiscal pressure stemming from longevity. However, an increased number of births implies private and immediate costs, whereas the gains are not likely to surface until later and appear via internalizing the public benefits of younger and larger population. Hence, quantification of the net effects remains a challenge. We propose using an overlapping generations model with a rich family structure to quantify the effects of increased birth rates. We analyze the overall macroeconomic and welfare effects as well as the distribution of these effects across cohorts and study the sensitivity of the final effects to the assumed target value and path of increased fertility. We find that fiscal effects are positive but, even in the case of relatively large fertility increase, they are small. The sign and the size of both welfare and fiscal effects depend substantially on the patterns of increased fertility: if increased fertility occurs via lower childlessness, the fiscal effects are smaller and welfare effects are more likely to be negative than in the case of the intensive margin adjustments.

1. Evaluating welfare and economic effects of raised fertility
Magda Malec
with Krzysztof Makarski and Joanna Tyrowicz
28th of May 2018
Cracow University of Economics and Fisher Black Institute
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 1

2. Motivation

3. 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
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4. 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)
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5. 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
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6. Model

7. 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
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8. Demographic scenarios

9. 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
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10. Results

11. 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)
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12. 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
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13. Measuring fiscal effects
How much can we spend every year, assuming increase of fertility?
target fertility 1.50 target fertility1.85
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14. Measuring fiscal effects
Distribution of the fiscal effects over time
target fertility 1.50 target fertility1.85
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15. 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
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16. Measuring welfare effects
Does intensive and extensive margin matter?
target fertility 1.50 target fertility1.85
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17. Fiscal effect
Fertility rate prior to the simulated increase
1.20 1.70
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18. Welfare effect
Fertility rate prior to the simulated increase
1.20 1.70
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19. Summary

20. 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
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21. Thank you for your attention!
w: grape.org.pl
t: grape_org
f: grape.org
e: m.malec@grape.org.pl
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22. Producers – very standard
• Perfectly competitive representative firm
• Standard Cobb-Douglas production function
Yt = Kα
t (ztLt)1−α
,
• Profit maximization implies
wt = (1 − α)Kα
t zt(ztLt)−α
rt = αKα−1
(ztLt)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

23. 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
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

24. 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)ϖ
cκ,j,t = Ξκcκ,j,t
ϑ child consumption scaling factor,
ϖ consumption scaling factor, Ξκ scale effect
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

25. 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,tlκ,j,t + (1 − τ − τl)wj,tl
∗
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)
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

26. Government
• collects taxes
Tt = τl(1 − τ)wtLt + τlBt + τcCt + τkrtSt + Υt
where Lt, Ct, St, Bt denote labor, consumption, savings and benefits
• finances spending on public goods and service Gt = gtYt,
• 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
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FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

27. Calibration

28. 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
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

29. 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 (ϖ) and child consumption scaling factor (ϑκ)
matches OECD equivalence scale
FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

30. 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
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31. Data match
• completed fertility
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32. Data match
• mortality
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33. 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.
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FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics

34. 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)
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FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics