Financing consumption of the elderly in the face of the projected increase in life expectancy is a key challenge for economic policy. Moreover, standard structural models with fully rational agents suggest that about 50-60 percent of old-age consumption is financed with voluntary savings, even in the presence of a fairly generous public pension system. This is clearly inconsistent with either the data, or the alarming simulations of old-age poverty in the years to come. Old-age saving (OAS) schemes are widely used policy instruments to address this challenge, but structural evaluations of such instruments remain rare. We develop a framework with incompletely rational agents: lacking financial literacy and experiencing commitment difficulties. We study a broad selection of OAS schemes and find that they raise welfare of financially illiterate agents and to a lesser extent improve welfare of agents with a high degree of time inconsistency. They also reduce the incidence of poverty at old age. Unfortunately, these instruments are fiscally costly, induce considerable crowd-out and direct fiscal transfers mostly to those agents, who need it the least.

1. Stimulating old-age savings
under incomplete rationality
Krzysztof Makarski (FAME|GRAPE, and WSE)
Artur Rutkowski (FAME|GRAPE, and UW)
Joanna Tyrowicz (FAME|GRAPE, UW, and IZA)
IAAEU
Trier, February, 2020
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2. Motivation
With rational agents,
• gov’nt-subsidized old-age savings (OAS) schemes end up in crowd-out
• second order GE effects negligible.
Come incomplete rationality:
• crowd-out no longer has to be complete, potential for welfare gains
• small fraction of people “react” to reforms as homo oeconomicus would
Chetty 2013, Myck and Lachowska 2019, ...
• who benefits from particiption
(−→ how optimal is non-participation?)
• are government-subsidized OAS schemes good for the economy?
(−→ all? which?)
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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
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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4. 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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5. Puzzle – extreme share of own-financed consumption in old-age
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6. Our contribution: the case of Germany
• Study the mechanics behind incomplete rationality in OLG
1. Behavioral heterogeneity
2. Voluntary participation in government-subsidized old-age saving 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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7. Results - preview
1. OAS laissez-faire public PAYG
2. Poverty declines
BUT
3. Large scope for crowd-out
4. Fiscal incentives have perverse effects
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8. Table of contents
Model
Policy reforms
Calibration
Results
Good news
Not so good news
Conclusions
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9. Model

10. 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: defined benefit (DB) with the point system
• Economy fully annuitized (abstract from annuity value)
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11. 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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12. Households belong to a type κ
• present bias: βκ
• financial literacy: saving technology vs storing technology
Present bias (time inconsistency) for financially literate agents
uc,j
uc,j+1
·
1
βκδ
·
πj
πj+1
= µj+1 + (1 − τk
)¯rj+1
Present 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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13. Policy reforms

14. Policy reforms: longevity ↑
Stable replacement rate → ↑ in contribution rate
How much to ↑ τ to maintain b
Stable contribution rate → ↓ in pensions
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?
• TTE + flat subsidy - flat subsidy is calibrated so that its fiscal cost is the
same as of EET
Fiscal rule: consumption tax balances the budget (in FSS)
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15. Calibration

16. German economy
Demography
• Eurostat forecast: longevity ↑
• 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
• 50% of financially literate
• 50% of illiterate agents.
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17. 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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18. 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)
+ a proxy for saving regret
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19. Saving regret
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20. Results

21. Good news

22. Agents like the instruments
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23. Saving regret declines – EET
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24. Agents like the instruments – TTE
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25. Agents like the instruments – TTE flat
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26. And (consumption) poverty declines
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27. And (consumption) poverty declines
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28. And (consumption) poverty declines
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29. And (consumption) poverty declines
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30. Not so good news

31. Transfers go to those who need it the least
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32. Macroeconomy
ISS FSS
raise τ reduce ρ E-E-T T-T-E T-T-E flat
(1) (2) (3) (4) (5) (6)
pensions (replacement) 1.00 1.00 0.74 0.74 0.74 0.74
contributions rate (%) 14.32 19.39 14.32 14.32 14.32 14.32
OAS contribution rate (%) - - - 5.07 5.07 5.07
consumption tax (%) 15.00 14.94 13.42 16.81 17.31 17.75
OAS transfers per worker - - - 0.0296 0.0293 0.0292
labor 100% 107.1% 108.1% 109.7% 109.6% 108.3%
aggregate product 100% 109.6% 112.9% 118.7% 116.8% 115.4%
wages 100% 102.3% 104.4% 108.1% 106.6% 106.6%
aggregate capital 100% 114.6% 123.3% 139.2% 133.0% 131.5%
of which
voluntary 100% 114.6% 123.3% 51.3% 56.9% 56.3%
in OAS scheme - - - 87.9% 76.2% 75.2%
interest rate (%) 5.18 4.66 4.18 3.44 3.74 3.74
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33. Macroeconomy
ISS FSS
raise τ reduce ρ E-E-T T-T-E T-T-E flat
(1) (2) (3) (4) (5) (6)
pensions (replacement) 1.00 1.00 0.74 0.74 0.74 0.74
contributions rate (%) 14.32 19.39 14.32 14.32 14.32 14.32
OAS contribution rate (%) - - - 5.07 5.07 5.07
consumption tax (%) 15.00 14.94 13.42 16.81 17.31 17.75
OAS transfers per worker - - - 0.0296 0.0293 0.0292
labor 100% 107.1% 108.1% 109.7% 109.6% 108.3%
aggregate product 100% 109.6% 112.9% 118.7% 116.8% 115.4%
wages 100% 102.3% 104.4% 108.1% 106.6% 106.6%
income tax revenues 100% 109.6% 112.9% 102.9% 116.8% 115.4%
pension tax revenue 100% 148.3% 112.8% 118.6% 116.7% 115.3%
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34. Macroeconomy
ISS FSS
raise τ reduce ρ E-E-T T-T-E T-T-E flat
(1) (2) (3) (4) (5) (6)
pensions (replacement) 1.00 1.00 0.74 0.74 0.74 0.74
contributions rate (%) 14.32 19.39 14.32 14.32 14.32 14.32
OAS contribution rate (%) - - - 5.07 5.07 5.07
consumption tax (%) 15.00 14.94 13.42 16.81 17.31 17.75
OAS transfers per worker - - - 0.0296 0.0293 0.0292
labor 100% 107.1% 108.1% 109.7% 109.6% 108.3%
aggregate capital 100% 114.6% 123.3% 139.2% 133% 131.5%
of which
voluntary 100% 114.6% 123.3% 51.3% 56.9% 56.3%
in OAS scheme - - - 87.9% 76.2% 75.2%
interest rate (%) 5.18 4.66 4.18 3.44 3.74 3.74
capital tax revenues 100% 103.1% 99.5% 34.1% 96.1% 94.9%
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35. Macroeconomy
ISS FSS
raise τ reduce ρ E-E-T T-T-E T-T-E flat
(1) (2) (3) (4) (5) (6)
pensions (replacement) 1.00 1.00 0.74 0.74 0.74 0.74
contributions rate (%) 14.32 19.39 14.32 14.32 14.32 14.32
OAS contribution rate (%) - - - 5.07 5.07 5.07
consumption tax (%) 15.00 14.94 13.42 16.81 17.31 17.75
OAS transfers per worker - - - 0.0296 0.0293 0.0292
labor 100% 107.1% 108.1% 109.7% 109.6% 108.3%
aggregate gross consumption 100% 107.0% 107.5% 116.0% 115.8% 114.6%
consumption tax revenues 100% 106.6% 96.1% 130.0% 133.5% 135.5%
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36. Little inter-generational redistribution
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37. Complete participation: PE vs GE
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38. Results are robust
1. Higher productivity growth
2. Lower labor share
3. Shares of IR agents in the economy
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39. Conclusions

40. Conclusions
1. Government subsidies to old-age savings instruments:
• reduce old-age poverty
• do not raise assets too much even under incomplete rationality
• fiscally costly −→ which problem is solved?
2. Redistribution from more conscientious to less conscientious agents
3. With sufficient share of IR agents political support for fiscal incentives
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41. 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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