- The document discusses evaluating the long-term macroeconomic and welfare effects of raising fertility rates through policy interventions. - It develops an overlapping generations model with household structure and heterogeneity to analyze different fertility increase scenarios on extensive and intensive margins. - The results show that only large increases in completed fertility lead to long-term fiscal advantages, while the costs and benefits depend on the policy pathway and who bears the costs of raising children.

1. Motivation Model Demographics Results
Evaluating welfare and economic effects
of raised fertility
Magda Malec
(with Krzysztof Makarski and Joanna Tyrowicz)
FAME|GRAPE & University of Warsaw & Warsaw School of Economics
MKE 20017
23th September, Poznan
1 / 29

2. Motivation Model Demographics Results
Motivation
substantial decline in population due to lowering fertility and longevity in most
of advanced and middle income economies
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3. Motivation Model Demographics Results
Motivation
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
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4. Motivation Model Demographics Results
Motivation
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
introduction a variety of costly pro-natalistic policies and instruments
2 / 29

5. Motivation Model Demographics Results
Motivation
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
introduction a variety of costly pro-natalistic policies and instruments
vast empirical literature evaluating previous policy interventions =⇒ negligible
effects, ”too soon to tell”, methodological issues
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6. Motivation Model Demographics Results
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)
evaluation within OLG framework
Fehr et al. (2017), Georges and Seekin (2016), Mamota (2016), Hock and Weil (2012)
endogenous fertility
Liao (2011), Ludwig et al. (2012), Hock and Weil (2012)
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7. Motivation Model Demographics Results
Remaining questions
1 What are long-term macroeconomic and welfare effects of fertility changes?
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8. Motivation Model Demographics Results
Remaining questions
1 What are long-term macroeconomic and welfare effects of fertility changes?
2 Assumming effectiveness of policies, how much can be spent to achieve certain
fertility targets and maintain long-term aggregate welfare unharmed?
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9. Motivation Model Demographics Results
Remaining questions
1 What are long-term macroeconomic and welfare effects of fertility changes?
2 Assumming effectiveness of policies, how much can be spent to achieve certain
fertility targets and maintain long-term aggregate welfare unharmed?
3 Is there a differenece between intensive (families with chilldren have more kids)
and extensive (more families have children) margin adjustments?
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10. Motivation Model Demographics Results
Outline
1 Motivation
2 Model
3 Demographics
4 Results
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11. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
Things we really care for:
Model Calibration Demography
6 / 29

12. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
Things we really care for:
family structure – households with κ = 0, 1, 2, 3+ children
Model Calibration Demography
6 / 29

13. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
Things we really care for:
family structure – households with κ = 0, 1, 2, 3+ children
heterogeneity – two types of agents within a household
Model Calibration Demography
6 / 29

14. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
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
Model Calibration Demography
6 / 29

15. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
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 intesive margin adjustments
Model Calibration Demography
6 / 29

16. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
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 intesive margin adjustments
calibrating the model closely to the data
Model Calibration Demography
6 / 29

17. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
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 intesive margin adjustments
calibrating the model closely to the data
Things we simplify:
Model Calibration Demography
6 / 29

18. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
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 intesive margin adjustments
calibrating the model closely to the data
Things we simplify:
policies are successful
Model Calibration Demography
6 / 29

19. Motivation Model Demographics Results
What do we do?
We develop large OLG model with family structure.
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 intesive margin adjustments
calibrating the model closely to the data
Things we simplify:
policies are successful
no direct utility from having children
Model Calibration Demography
6 / 29

20. Motivation Model Demographics Results
Outline
1 Motivation
2 Model
3 Demographics
4 Results
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21. Motivation Model Demographics Results
Fertility scenarios
What is baseline?
constant completed fertility 1.44 (data avereged for 2006-2014)
data on household structure
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22. Motivation Model Demographics Results
Fertility scenarios
What is baseline?
constant completed fertility 1.44 (data avereged for 2006-2014)
data on household structure
What is fertility change scenario?
1.44 −→ 2.2
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23. Motivation Model Demographics Results
Fertility scenarios
What is baseline?
constant completed fertility 1.44 (data avereged for 2006-2014)
data on household structure
What is fertility change scenario?
1.44 −→ 2.2
How many combinations of household structure can generate a fertility increase
path?
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24. Motivation Model Demographics Results
Fertility scenarios
What is baseline?
constant completed fertility 1.44 (data avereged for 2006-2014)
data on household structure
What is fertility change scenario?
1.44 −→ 2.2
How many combinations of household structure can generate a fertility increase
path? Countless.
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25. Motivation Model Demographics Results
Fertility scenarios
What is baseline?
constant completed fertility 1.44 (data avereged for 2006-2014)
data on household structure
What is fertility change scenario?
1.44 −→ 2.2
How many combinations of household structure can generate a fertility increase
path? Countless.
Does it matter?
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26. Motivation Model Demographics Results
Fertility scenarios
What is baseline?
constant completed fertility 1.44 (data avereged for 2006-2014)
data on household structure
What is fertility change scenario?
1.44 −→ 2.2
How many combinations of household structure can generate a fertility increase
path? Countless.
Does it matter? Yes.
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27. Motivation Model Demographics Results
Outline
1 Motivation
2 Model
3 Demographics
4 Results
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28. Motivation Model Demographics Results
Measuring fiscal effects
fiscal advantages only after large
increase of completed fertility
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29. Motivation Model Demographics Results
Measuring fiscal effects
fiscal advantages only after large
increase of completed fertility
intensive and extensive margin do
matter
⇐= labor market effects
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30. Motivation Model Demographics Results
Measuring fiscal effects
fiscal advantages only after large
increase of completed fertility
intensive and extensive margin do
matter
⇐= labor market effects
immediate costs or delayed gains
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31. Motivation Model Demographics Results
Measuring fiscal effects
fiscal advantages only after large
increase of completed fertility
intensive and extensive margin do
matter
⇐= labor market effects
immediate costs or delayed gains
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32. Motivation Model Demographics Results
Measuring fiscal effects
completed fertility = 1.69
completed fertility = 2.09
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33. Motivation Model Demographics Results
Measuring fiscal effects
How much can we spend every year, assuming
completed fertility = 1.69
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34. Motivation Model Demographics Results
Measuring fiscal effects
How much can we spend every year, assuming
completed fertility = 1.69 completed fertility = 2.09
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35. Motivation Model Demographics Results
Measuring welfare effects
consumption equivalent
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36. Motivation Model Demographics Results
Measuring welfare effects
consumption equivalent
larger population is welfare
improving, but...
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37. Motivation Model Demographics Results
Measuring welfare effects
consumption equivalent
larger population is welfare
improving, but someone has to bear
the costs of children
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38. Motivation Model Demographics Results
Measuring welfare effects
consumption equivalent
larger population is welfare
improving, but someone has to bear
the costs of children
expected welfare
transition 0 → 1+ type of
household the most harmful
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39. Motivation Model Demographics Results
Measuring welfare effects
consumption equivalent
larger population is welfare
improving, but someone has to bear
the costs of children
expected welfare
transition 0 → 1+ type of
household the most harmful
lower consumption and wages
or higher pensions and tax base
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40. Motivation Model Demographics Results
Measuring welfare effects
larger population is welfare
improving, but someone has to bear
the costs of children
expected welfare
transition 0 → 1+ type of
household the most harmful
lower consumption and wages
or higher pensions and tax base
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41. Motivation Model Demographics Results
Measuring welfare effects
Consumption equivalent distribution for
completed fertility = 1.69
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42. Motivation Model Demographics Results
Measuring welfare effects
Consumption equivalent distribution for
completed fertility = 1.69 completed fertility = 2.09
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43. Motivation Model Demographics Results
Summary
1 FISCAL: net surplus in government budget, but far less than costs of most
implemented policies
fiscal gains realization only after substantial fertility increase, > 1.6
for central path 0.1% GDP
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44. Motivation Model Demographics Results
Summary
1 FISCAL: net surplus in government budget, but far less than costs of most
implemented policies
fiscal gains realization only after substantial fertility increase, > 1.6
for central path 0.1% GDP
2 WELFARE: negative welfare effect
completed fertility↑ −→ welfare↓
intensive and extensive margin greatly matter, but extensive margin can be
unrealistic (no trend in data)
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45. Motivation Model Demographics Results
Questions or suggestions?
m.malec@grape.org.pl
Thank you!
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46. Producers
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
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47. 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
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48. 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 hosuehold they were born in
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49. 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 hosuehold they were born in
reaching adulthood j = 21 they form their own household and observe the
realization of the fertility
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50. Households
consist of men and women (the latter denoted by *)
differ by the number of children κ = 0, 1, 2, 3+
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51. 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 ]
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52. 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 scalling factor,
consumption scalling factor, Ξκ scale effect
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53. Households II
during child rearing female labor supply is reduced according to ϕκ
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54. Households II
during child rearing female labor supply is reduced according to ϕκ
utility functions in a household:
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
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55. Households II
during child rearing female labor supply is reduced according to ϕκ
utility functions in a household:
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 the following budget constraint
(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)
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56. Government
collects taxes
Tt = τl(1 − τ)wtLt + τlBt + τcCt + τkrtSt + Υt
Lt, Ct, St, Bt denote labor, consumption, savings and benefits
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57. Government
collects taxes
Tt = τl(1 − τ)wtLt + τlBt + τcCt + τkrtSt + Υt
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
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58. DC pension system
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
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59. DC pension system
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
1 + rI
t = γt
Lt+1
Lt
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60. Calibration to replicate 2014 Polish economy
Discounting rate (δ) matches interest rate of 6.5%
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61. Calibration to replicate 2014 Polish economy
Discounting rate (δ) matches interest rate of 6.5%
Depreciation rate (d) matches investment rate of 21%
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62. 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%
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63. 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
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64. 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
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65. Preferences
Preference for leisure (φ) matches participation rate of 56.8%
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66. 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, 0.236 and 0.257 depending on κ
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67. 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, 0.236 and 0.257 depending on κ
Consumption scalling factor ( ) and child consumption scalling factor (ϑκ)
matches OECD equivalence scale of 0.5, 0.65, 0.62 and 0.6 depending on κ
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68. Demographic assumptions
no mortality until children are raised (j < 41)
historical data on fertility and mortality 1964-2014
Central Statistical Office projections until 2060, at the same level afterwards
completed fertility from household structure for 2006-2014
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69. Data match
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
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70. Data match
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
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71. Data match
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
Shares of women with one child 0.16 0.16
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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