1. Optimal illiquidity John Beshears James J. Choi Christopher Clayton
Christopher Harris
David Laibson
Brigitte C. Madrian

2. U.S. is an outlier on DC account liquidity
10% penalty for most early withdrawals
0% penalty for loans and certain withdrawals
Canada, Australia
No liquidity unless long-term unemployed
Germany, Singapore, UK
No liquidity
Source: Beshears et al. (2015)

3. U.S. retirement savings leakage
Households < 55 withdraw $0.40 (not counting loans) from retirement accounts for every $1 contributed
Source: Argento, Bryant, and Sabelhaus (2014)

4. Questions Is this too much leakage? Is 10% the right penalty?
1970s Senate wanted 30% penalty
1970s House wanted 10% penalty

5. Why do we need to make savings illiquid?
Limited self-control
Creates need for illiquidity
But unpredictable, uninsurable legitimate spending needs exist
Creates need for flexibility

6. Model setup Households live for 2 periods
Period 1 = working life
Period 2 = retirement
Consumption in period 1, 𝑐1, produces utility 𝜃𝑢 𝑐1 =𝜃log⁡( 𝑐 1 )
𝜃 is random variable representing how valuable pre-retirement spending is
Lies between positive numbers 𝜃 and 𝜃
Consumption in period 2, 𝑐2, produces utility 𝑣 𝑐2 =log⁡( 𝑐 2 )

7. Benevolent social planner
Social planner’s preference over household’s consumption given by
𝜃 log (𝑐 1 ) +𝛿log⁡( 𝑐 2 )
𝛿 is discount factor representing how much less valuable future utility is
Lies between 0 and 1
𝜃 can’t be observed by planner, but planner knows population-wide distribution of 𝜃

8. Household preferences
Household’s preference over consumption given by
𝜃log⁡( 𝑐 1 )+𝜷𝛿 log ( 𝑐 2 )
Present bias term 𝛽 is between 0 and 1
Represents excessive impatience
Lower value = more excessive impatience

9. 𝜽 distribution
Normal distribution with mean 1, standard deviation 0.25, truncated at 1/3 and 5/3

10. Savings accounts Planner chooses for N accounts
How much to put in each account at period 1
Early withdrawal penalty

11. Optimal system with autarky and homogeneous 𝜷
Planner can’t redistribute early-withdrawal penalties collected
Penalties are “burned”
Everybody has same degree of self-control
Theorem: Optimal system has only 2 accounts: one completely liquid account and one completely illiquid account (Angeletos, Werning, and Amador, 2006)
Illiquid account like Social Security or DB pension

12. Optimal system with transfers and homogeneous 𝜷
Planner can redistribute early-withdrawal penalties collected
Everybody has same degree of self-control
Theorem: A system with one completely liquid account and one completely illiquid account is not optimal

13. Optimal penalty in illiquid account in two-account system
Empirical 𝛽 estimate ≈ 0.7
Optimal penalty ≈ 30%

14. Optimal system with transfers and heterogeneous 𝜷
Planner knows frequency of 𝛽 values but not each person’s 𝛽
Theorem: If all agents have 𝛽=0 or 1, then the optimal system has only 2 accounts: one completely liquid account and one completely illiquid account
Intuition:
Completely liquid system is a disaster for impatient types, who consume everything in period 1 and have nothing in period 2
Partially illiquid system increases period 2 inequality relative to completely illiquid system

15. Less extreme 𝜷 distribution
Average = 0.7
Modal agent has no self-control problem

16. Results from numerical simulations
Optimal 2-account system
1 completely liquid account
1 completely illiquid account
Welfare gain of 3.4% of income relative to system with only one completely liquid account
Optimal 3-account system
1 account with early withdrawal penalty = 9%
Welfare gain from third account is only 0.018% of income

17. Leakage
Planner puts 14% of partially and fully illiquid assets in partially illiquid account
Percent of personal retirement accounts + DB pension + Social Security in personal retirement account
Median married household in 2008: 12%
Median single household in 2008: 0%
74% of dollars in partially illiquid account leaks in period 1

18. Robustness to other parameterizations
Vary
Risk aversion
Shape of taste shocks 𝜃
Distribution of self-control parameter 𝛽
Optimal early withdrawal penalty: 6% to 13%
Leakage rate: 65% to 90%

19. How I Learned to Stop Worrying and Love Leakage

20. Takeaways U.S. retirement savings system might be close to optimal
Within highly simplified model
Completely illiquid layer like Social Security is optimal and achieves almost all possible welfare gains from policy
401(k)/IRA system adds only a little to welfare
10% withdrawal penalty from 401(k)/IRA system is about optimal
High leakage from 401(k)/IRA system is optimal
Some of that leakage is for legitimate purposes
Penalties paid by early withdrawers benefit the rest of us

21. Caveat Assumes that the optimal amount is deposited in each account
If current level of Social Security + DB benefits is inadequate, then system is not optimal
Would want to add an additional completely illiquid account to bring completely illiquid assets up to right level