Fully rational agents respond to old-age savings incentives with complete crowing out, hence any effects of such incentives stem from second order general equilibrium adjustments. However, agents facing constraints in obtaining optimal savings profiles experience also first order effects, i.e. substantial changes to the lifetime profiles of assets accumulation. We develop a fully-fledged overlapping generations model with intra-cohort heterogeneity. In addition to fully rational agents, each generation has also agents with other types of preferences. In this economy we introduce a variety of tax incentivized old-age savings schemes with endogenous participation. We analyze macroeconomic and welfare effects of such instruments.

1. Stimulating old-age savings
under incomplete rationality
Krzysztof Makarski (FAME|GRAPE, and WSE)
Patrick Puhani (Hannover University, and IZA)
Artur Rutkowski (FAME|GRAPE)
Joanna Tyrowicz (FAME|GRAPE, IAAEU, UW, and IZA)
RCEA
Waterloo, September, 2019
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2. Motivation
With rational agents,
• government-subsidized old-age savings schemes end up in crowd-out
• second order GE effects small
401k debate in the US: Engen et al vs Hubbard et al; recently Gelber 2011
Come incomplete rationality:
• small fraction of people “react” to reforms as homo oeconomicus would
Chetty 2013, Myck and Lachowska 2019, ...
• how optimal is non-participation?
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3. Literature
General macro context
• hand-to-mouth
Weil 1992, Kaplan et al. 2014, Heathcote and Perri 2018, House et al 2018
• rule-of-thumb agents
Attanasio and Wakefield 2008, Attanasio and Weber 2010, Kaplan and Violante 2014
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4. Literature
General macro context
• hand-to-mouth
Weil 1992, Kaplan et al. 2014, Heathcote and Perri 2018, House et al 2018
• rule-of-thumb agents
Attanasio and Wakefield 2008, Attanasio and Weber 2010, Kaplan and Violante 2014
Surprisingly little OLG models with incomplete rationality
• time-inconsistency
Imrohoroglu et al. 2003, Fehr et al. 2008, Caliendo 2011, Andersen and Bhattacharya
2011, Moser and de Souza e Silva, 2019
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5. Literature
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6. Literature
Absent in macro, but well documented
• financial (il)literacy
Lusardi and Mitchell 2014 and more empirical literature in this spirit
• slow update of expectations
Evans and Honkapohja 2003, 2012, Elliott et al. 2008, Mackowiak 2009, Coibion and
Gorodnichenko 2012, Armantier et al. 2016
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7. Our contribution
• Study the mechanics behind incomplete rationality in OLG
1. Behavioral heterogeneity
2. Voluntary old-age savings schemes
• Study the instruments
1. Voluntary vs compulsory
2. Market completeness vs actual government intervention (e.g. subsidy)
3. Distortionary vs non-distortionary interventions
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8. Our contribution
• Study the mechanics behind incomplete rationality in OLG
1. Behavioral heterogeneity
2. Voluntary old-age savings schemes
• Study the instruments
1. Voluntary vs compulsory
2. Market completeness vs actual government intervention (e.g. subsidy)
3. Distortionary vs non-distortionary interventions
The big question
Private vs public pensions: which one?
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9. Results - preview
1. Private voluntary savings preferred to public PAYG
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10. Results - preview
1. Private voluntary savings preferred to public PAYG
2. Consumption is better smoothened
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11. Results - preview
1. Private voluntary savings preferred to public PAYG
2. Consumption is better smoothened
3. Poverty declines
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12. Results - preview
1. Private voluntary savings preferred to public PAYG
2. Consumption is better smoothened
3. Poverty declines
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13. Results - preview
1. Private voluntary savings preferred to public PAYG
2. Consumption is better smoothened
3. Poverty declines
BUT
4. Asset do not actually increase
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14. Results - preview
1. Private voluntary savings preferred to public PAYG
2. Consumption is better smoothened
3. Poverty declines
BUT
4. Asset do not actually increase
5. Fiscal incentives have perverse effects
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15. Table of contents
Model
Policy reforms
Calibration
Results
Good news
Not so good news
Conclusions
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16. Model

17. Model: overlapping generations
• Firms are perfectly competitive with Cobb Douglas production
Y = AKα
L1−α
• Government: taxes to finance G, deficit in the pensions + services debt.
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18. Model: overlapping generations
• Firms are perfectly competitive with Cobb Douglas production
Y = AKα
L1−α
• Government: taxes to finance G, deficit in the pensions + services debt.
• Pension system: Bismarckian defined benefit (DB)
• Economy fully annuitized
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19. Households
• Born at j = 21 and live up to 100 years
• Face survival probability πj,t (where t = ISS, FSS)
• Choose labor supply l and consumption c endogenously
• Pay taxes (labor, consumption, capital gains) & contribute to pensions
• Have time preference of δ
• Have leisure preference φ (and hump-shaped age specific productivity, ωj )
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20. Households
• Born at j = 21 and live up to 100 years
• Face survival probability πj,t (where t = ISS, FSS)
• Choose labor supply l and consumption c endogenously
• Pay taxes (labor, consumption, capital gains) & contribute to pensions
• Have time preference of δ
• Have leisure preference φ (and hump-shaped age specific productivity, ωj )
• Have instantaneous utility function:
uκ(cj,κ, lj,κ) = φ ln cj,κ + (1 − φ) ln(1 − lj,κ)
and maximize lifetime utility:
Uκ = Uκ,j=1 + βκ
j=J
j=2
δj
Uκ,j
subject to a sequence of j budget constraints.
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21. Households belong to a type κ
• presence bias: βκ
• financial literacy: saving technology vs storing technology
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22. Households belong to a type κ
• presence bias: βκ
• financial literacy: saving technology vs storing technology
Presence bias (time inconsistency) for financially literate agents
uc,j
uc,j+1
·
1
βκδ
·
πj
πj+1
= µj+1 + (1 − τk
)¯rj+1
Presence bias (time inconsistency) for financially il - literate agents
uc,j
uc,j+1
·
1
βκδ
·
πj
πj+1
= 1
with ¯rj = µj · rt where rt = f (k) and µj = Nj−1/Nj
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23. Policy reforms

24. Policy reforms: longevity ↑
Rollout: stable replacement rate → ↑ in contribution rate
How much to ↑ τ to maintain b
Baseline: stable contribution rate → ↓ in b
Consequences of mandatory PAYG b decline
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25. Policy reforms: longevity ↑
Rollout: stable replacement rate → ↑ in contribution rate
How much to ↑ τ to maintain b
Baseline: stable contribution rate → ↓ in b
Consequences of mandatory PAYG b decline
Government-subsidized voluntary old-age saving scheme
→ funding replaces the rise in mandatory PAYG + voluntary participation
• EET (full exempt)
• TTE (matching EET in terms of fiscal cost) → tax incentives?
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26. Policy reforms: longevity ↑
Rollout: stable replacement rate → ↑ in contribution rate
How much to ↑ τ to maintain b
Baseline: stable contribution rate → ↓ in b
Consequences of mandatory PAYG b decline
Government-subsidized voluntary old-age saving scheme
→ funding replaces the rise in mandatory PAYG + voluntary participation
• EET (full exempt)
• TTE (matching EET in terms of fiscal cost) → tax incentives?
Fiscal rule τc balances the budget (in FSS)
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27. Calibration

28. German economy
Demography
• Eurostat forecast
• longevity ↑
• fertility ↓
• age-specific productivity (following Fehr et al, 2013)
Heterogeneity
• present bias βκ 10 values: βκ ∈ {0.5, 0.55, ..., 0.95}
βκ subcohorts are equinumerous
• financial literacy within each βκ subcohort there is
• 70% of financially literate
• 30% of illiterate agents.
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29. German economy
Financial market and firms
• interest rate r = 6%
• deprecation d → investment rate 20%
• capital share in GDP α = 0.33
• technological progress ISS: 1.00%, FSS 1.54% (AWG)
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30. German economy
Financial market and firms
• interest rate r = 6%
• deprecation d → investment rate 20%
• capital share in GDP α = 0.33
• technological progress ISS: 1.00%, FSS 1.54% (AWG)
Fiscal side
• taxation: τl , τk , τc (following Mendoza et al, 1986)
• debt do GDP D/Y = 70% (the average for years 1996-2016, OECD)
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31. German economy
Financial market and firms
• interest rate r = 6%
• deprecation d → investment rate 20%
• capital share in GDP α = 0.33
• technological progress ISS: 1.00%, FSS 1.54% (AWG)
Fiscal side
• taxation: τl , τk , τc (following Mendoza et al, 1986)
• debt do GDP D/Y = 70% (the average for years 1996-2016, OECD)
Pension system
• replacement rate ρ → share of benefits in GDP: 9.5%
calibrated ρ = 0.385 against replacement in the data = 0.38
• contribution τ → pensions system deficit in ISS: τISS = 0.128
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32. How to measure welfare effects
Our agents have TI preferences (internally inconsistent):
1. ex ante: use Uj=1, so βκ between j = 1 & j = 2, and no TI henceforth
2. ex post: omitt βκ (true utility rather than decision utility)
3. Imrohorouglu et al (2003): weighted average from each j (with π)
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33. Results

34. Good news

35. Agents like the instruments – EET
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36. Agents like the instruments – TTE
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37. And instruments are better than mandatory PAYG
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38. And instruments are better than mandatory PAYG
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39. And instruments are better than mandatory PAYG
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40. And (consumption) poverty declines
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41. Not so good news

42. Assets for financially illiterate (very) TI agents
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43. Assets for financially literate (very) TI agents
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44. Assets for financially illiterate (not so) TI agents
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45. Assets for financially literate (not so) TI agents
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46. Macroeconomy
Table 1: Model results (relative to ISS)
Variable FSS (rollout) FSS (pensions decline) FSS EET FSS TTE
capital (%) 99.8% 103.1% 111.8% 110.1%
interest rate (p.p.) 0.0% -0.3% -0.9% -0.8%
labor (%) 104.7% 106.7% 103.4% 102.5%
wages (%) 99.9% 101.0% 103.8% 103.2%
instrument (p.p.) 0.0% 0.0% 3.7% 3.7%
pensions decline 0.0% 25.9% 25.9% 25.9%
change in τc (p.p.) 1.6% 0.6% 3.9% 8.8%
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47. Conclusions

48. Conclusions
1. Government subsidies to old-age savings instruments:
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49. Conclusions
1. Government subsidies to old-age savings instruments:
• help smoothening consumption and leisure
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50. Conclusions
1. Government subsidies to old-age savings instruments:
• help smoothening consumption and leisure
• do not actually raise assets too much
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51. Conclusions
1. Government subsidies to old-age savings instruments:
• help smoothening consumption and leisure
• do not actually raise assets too much
• even if universal participation is individually
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52. Conclusions
1. Government subsidies to old-age savings instruments:
• help smoothening consumption and leisure
• do not actually raise assets too much
• even if universal participation is individually
2. With sufficient share of incompletely rational agents political support
for fiscal incentives.
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53. Conclusions
1. Government subsidies to old-age savings instruments:
• help smoothening consumption and leisure
• do not actually raise assets too much
• even if universal participation is individually
2. With sufficient share of incompletely rational agents political support
for fiscal incentives.
3. Even though it is essentially an instrument of redistribution: from more
conscientious to less conscientious agents
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54. Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
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