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

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)

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)

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

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

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 )

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

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

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

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

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

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

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

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

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

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

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

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%

How I Learned to Stop Worrying and Love Leakage

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

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