John Beshears James J. Choi Christopher Clayton Christopher Harris David Laibson Brigitte C. Madrian May 30, 2015

Many savings vehicles with varying degrees of liquidity  Social Security  Home equity  Defined benefit pensions  Annuities  Defined contribution accounts –IRA’s (Individual Retirement Accounts)  CD’s  Brokerage accounts  Checking/savings 2

Assumptions for illustrative lifecycle simulation  6.5% guaranteed return  2% inflation rate  6% DC saving rate  100% employer match  No leakage  Start working at age 22  First job: $35,000  Start saving at age 22  1% real wage growth  50% Soc Sec replacement  “4% rule” in retirement 3 At retirement: 103% replacement ratio $719,275 DC assets (+ house + Social Security) Laibson (2011)

The U.S. has been trending toward a more liquid financial system since the 1970’s  Collateralized borrowing against house –Smaller down-payments –Cash-out refinancing  Uncollateralized consumer debt  Defined benefit pensions vanishing  Those with DB pensions take lump-sum payments  Defined contributions systems –Non-compulsory contributions –401(k) loans –Early withdrawals 4

Retirement Plan Leakage Source: GAO , 2009

Households <55 make $0.40 of taxable withdrawals from retirement accounts for every $1 of contributions (Argento, Bryant, and Sabelhaus 2014) 6 Billions

For every two dollars that go into the retirement system almost one dollar simultaneously leaks out (before retirement) 7

8

“Leakage” (excluding loans) among households ≤ 55 years old For every $2 that flows into US retirement savings system $1 leaks out (Argento, Bryant, and Sabelhaus 2014) 9

ReplacementDC RatioAssets Original scenario1.03 $ 719, % balance leakage0.78 $ 380,584 40% don’t have access0.68 $ 249,283 Match rate is $ 192,195 Net return is 5.5%0.61 $ 152,672 20% with access don’t participate0.59 $ 125,463 Start saving at age $ 103,644 Soc Sec replacement rate lower0.53 $ 103,644 A little more realism 10

Married households age (medians; 2008) Financial assets: $ 27,800 Home equity: $170,000 Personal retirement accounts: $ 35,000 Defined benefit pension$ 0 Social Security (SS): $284,000 Net worth including SS: $769,100 Real per capita annuity value$ 15,382 Real annuity value$ 16,577 Pre-retirement income$ 30,651 Source: Health and Retirement Study; Venti, Poterba, and Wise 2013

Single-person households age (medians; 2008) Financial assets: $ 5,000 Home equity: $ 60,000 Personal retirement accounts: $ 0 Defined benefit pension$ 0 Social Security (SS): $136,700 Net worth including SS: $295,800 Real per capita annuity value$ 11,832 Real annuity value$ 16,577 Pre-retirement income$ 30,651 Source: Health and Retirement Study; Venti, Poterba, and Wise 2013

13 Net National Savings Rate: Table 5.1, NIPA, BEA

14 Net National Savings Rate: Table 5.1, NIPA, BEA

15

16 What is the socially optimal level of household liquidity? This question has been largely ignored in the development of the US retirement savings system.

The Senate and the House of Representatives had different views on optimal liquidity in the 1970’s  The Senate wanted a 30% early withdrawal penalty for the precursor account to the modern 401(k)/IRA.  The House wanted a 10% penalty.  These issues have been barely debated at any point in the development of the US retirement savings system. 17

US Anti-Leakage Strategy Defined Contribution Pension Schemes e.g., 401(k) and IRA o 10% penalty for early withdrawals o Allow in-service loans without penalty  10% penalty if not repaid o Special categories of penalty-free withdrawals  Education  Large health expenditures  First home purchase Unintended liquidity: IRA tax arbitrage

International comparison of employer-based DC accounts Beshears, Choi, Hurwitz, Laibson, Madrian (forthcoming) o United States: liquidity (10% penalty or no penalty) o Canada, Australia: no liquidity, unless long-term unemployed o Germany, Singapore, UK: no liquidity

What is the socially optimal level of household liquidity? 1.Legitimate unanticipated/uninsurable spending needs 2.Illegitimate overspending –self-control problems –other types of “mistakes” 3.Externalties (penalties = government revenue) 4.Heterogeneity in preferences (self-control problems) 20

Total leakage in the US (for non-retired workers) About 2.5% of $10 trillion = $250 billion per year For comparison, flows into US retirement accounts: $500 billion

Is a 10% penalty a good idea? More generally, how much liquidity (and of what type) should one have in a retirement savings system? Classical answer: liquidity raises welfare and households should prefer more liquidity to less. Behavioral answer: flexibility is a two-edged sword.

Socially optimal savings: Behavioral mechanism design

How Are Preferences Revealed? Beshears, Choi, Laibson, Madrian (2008)  Revealed preferences  decision utility  Normative preferences  experienced utility 24

25 Behavioral mechanism design 1. Specify a positive theory of consumer behavior consumers may or may not behave optimally 2. Specify a normative social welfare function not necessarily based on revealed preference 3. Solve for the institutions that maximize the social welfare function, conditional on the theory of consumer behavior. Caveats when we’ve worked through 1-3.

26 Behavioral mechanism design 1. Specify a positive theory of consumer behavior: Quasi-hyperbolic (present-biased) consumers Discount function: 1, βδ, βδ 2 2. Specify a normative social welfare function Exponential discounting Discount function: 1, δ, δ 2 3. Solve for the institutions that maximize the social welfare function, conditional on the theory of consumer behavior.

27 Behavioral mechanism design 1. Specify a positive theory of consumer behavior: Quasi-hyperbolic (present-biased) consumers Discount function: 1, βδ, βδ 2 2. Specify a normative social welfare function Exponential discounting Discount function: 1, δ, δ 2 3. Solve for the institutions that maximize the social welfare function, conditional on the theory of consumer behavior.

Present-biased discounting Strotz (1958), Phelps and Pollak (1968), Elster (1989), Akerlof (1992), Laibson (1997), O’Donoghue and Rabin (1999) Current utils weighted fully Future utils weighted βδ t u t + βδ u t+1 + βδ 2 u t+2 + βδ 3 u t+3 + βδ 4 u t+4 + … u t + β[ δ u t+1 + δ 2 u t+2 + δ 3 u t+3 + δ 4 u t+4 + … ] u t + ½ [ u t+1 + u t+2 + u t+3 + u t+4 + … ]

Present-biased discounting Strotz (1958), Phelps and Pollak (1968), Elster (1989), Akerlof (1992), Laibson (1997), O’Donoghue and Rabin (1999) Current utils weighted fully Future utils weighted 1/2

Present-biased discounting Strotz (1958), Phelps and Pollak (1968), Elster (1989), Akerlof (1992), Laibson (1997), O’Donoghue and Rabin (1999) Assume β = ½ and δ = 1 Assume that exercise has current effort cost 6 and delayed health benefits of 8 Will you exercise today? -6 + ½ [ 8 ] = -2 Will you exercise tomorrow? 0 + ½ [-6 + 8] = +1 Won’t exercise without commitment.

Start with Amador, Werning and Angeletos (2006), hereafter AWA: 1. Present-biased preferences 2. Short-run taste shocks 3. A general non-linear budget set ◦ commitment mechanism

Timing Period 0. An initial period in which a commitment mechanism is set up by self 0 or by the planner. Period 1. A taste shock is realized and privately observed. Consumption ( c₁ ) occurs. Period 2. Another taste shock is realized and privately observed. Final consumption ( c₂ ) occurs.

U₀=βδ θ 1 u₁(c₁) + βδ²θ 2 u₂(c₂) U₁= θ 1 u₁(c₁) + βδ θ 2 u₂(c₂) U₂= θ 2 u₂(c₂) Taste shocks, with CDF F(θ)

U₀= θ 1 u₁(c₁) + θ 2 u₂(c₂) U₁= θ 1 u₁(c₁) + β θ 2 u₂(c₂) U₂= θ 2 u₂(c₂)

A1-A3 admit most commonly used densities. For example, we sampled all 18 densities in two leading statistics textbooks: Beta, Burr, Cauchy, Chi-squared, Exponential, Extreme Value, F, Gamma, Gompertz, Log- Gamma, Log-Normal, Maxwell, Normal, Pareto, Rayleigh, t, Uniform and Weibull distributions. A1-A3 admits all of these densities except some special cases of the Log-Gamma. A1-A3 also exclude some special cases of generalizations of the Beta, Cauchy, and Pareto, which did not appear in these textbooks.

c2c2 c1c1 Self 0 hands self 1 a budget set (subset of blue region) Budget set y y

c2c2 c1c1 Self 0 hands self 1 a budget set (subset of blue region) Budget set y y

c2c2 c1c1 Two-part budget set

c2c2 c1c1

c2c2 c1c1 Self 0 hands self 1 a budget set (subset of blue region) Budget set y y

c2c2 c1c1 Self 0, or the planner, gives self 1 a budget set (subset of blue region) Budget set y y

c2c2 c1c1 Two-part budget set

c2c2 c1c1 Three-part budget set

Theorem 1 Assume:  CRRA utility.  Early consumption penalty bounded above by π. Then, self 0 will set up two accounts:  Fully liquid account  Illiquid account with penalty π.

Theorem 1 (AWA): Assume self 0 is sophisticated and can choose any feasible budget set. Assume self 0 doesn’t care about revenue externality from penalties. Then self 0 will choose a two-part budget set:  fully liquid account  fully illiquid account (no withdrawals in period 1)

c2c2 c1c1 Two-part budget set with a perfectly illiquid account

Assume there are three accounts:  one liquid  one with an intermediate withdrawal penalty  one completely illiquid Then self 0 will allocate all assets to the liquid account and the completely illiquid account.

 Give subjects $100  Ask them to divide it among three accounts  All accounts offer a 22% rate of interest 1.One account is perfectly illiquid 2.One account has a 10% penalty for early withdrawal 3.One account is perfectly liquid  For the first two accounts, set a goal date  Maximum holding period: 1 year

When three accounts are offered Freedom Account Completely illiquid 33.9% 49.9% 16.2% 10% penalty

 Give subjects $100  Ask them to divide it among two accounts  Both accounts offer a 22% rate of interest 1.One account has a 10% penalty for early withdrawal 2.One account is perfectly liquid  For the illiquid account, set a goal date  Maximum holding period: 1 year

Goal account usage Freedom Account Freedom Account Freedom Account Goal Account 10% penalty Goal account 20% penalty Goal account No withdrawal 35% 65% 43% 57% 56% 44%

 Descriptive theory of consumer behavior.  Theoretical predictions that match experimental data

55 1. Specify a positive theory of consumer behavior: ◦ Quasi-hyperbolic (present-biased) consumers ◦ Discount function: 1, βδ, βδ 2 2. Specify a normative social welfare function ◦ Exponential discounting ◦ Discount function: 1, δ, δ 2 3. Solve for the institutions that maximize the social welfare function, conditional on the theory of consumer behavior.

 This is the preference of all past selves for today.  This is the long-run perspective.  This is the restriction that eliminates present bias.  For large T, the resulting behavior dominates the unconstrained equilibrium path (Caliendo and Findley 2015)  However, this is a normative assumption.  The rest of the paper is only an ‘if, then’ analysis.  If the planner has a social welfare function with β=1, then the following policies are socially optimal.

U₀= δ θ 1 u₁(c₁) + δ²θ 2 u₂(c₂) U₁= θ 1 u₁(c₁) + δ θ 2 u₂(c₂) U₂= θ 2 u₂(c₂) Planner preferences: β=1. These are dynamically consistent preferences.

58 1. Specify a positive theory of consumer behavior: ◦ Quasi-hyperbolic (present-biased) consumers ◦ Discount function: 1, βδ, βδ 2 2. Specify a normative social welfare function ◦ Exponential discounting ◦ Discount function: 1, δ, δ 2 3. Solve for the institutions that maximize the social welfare function, conditional on the theory of consumer behavior.

1. Need to incorporate externalities: when I pay a penalty, the government can use my penalty to increase the consumption of other agents. 2. Heterogeneity in present-bias, β.

 If a household spends less than its endowment, the unused resources are given to other households.  All “penalties” are collected by the government and used for general revenue.  This introduces an externality, but only when penalties are paid in equilibrium.  Now the two-account system with complete illiquidity is no longer socially optimal.

1. Corollary: 2-account optimum (one perfectly liquid and one perfectly illiquid) does not generalize when interpersonal transfers are allowed. 2. Proof relies on interpersonal transfers. Without them, the perturbation in the proof is welfare reducing.

β Unconstraining penalty on first penalty account Adding a second penalty account

≈ 1- β

CRRA = 2 CRRA = 1 Present bias parameter: β

Expected Utility (β=0.7) Penalty for Early Withdrawal

Account Allocations and Expected Penalties (β=0.7) Penalty for Early Withdrawal

Expected Utility (β=0.1) Penalty for Early Withdrawal

Account Allocations and Expected Penalties (β=0.1) Penalty for Early Withdrawal

Expected Utility Given A Fixed Penalty Level Penalty for Early Withdrawal 100 β=1.0 β=0.9 β=0.8 β=0.7 β=0.6 β=0.5 β=0.4 β=0.3 β=0.2 β=0.1

Once you start thinking about low β households, nothing else matters.

1. You only need one illiquid account to achieve the (second best) social optimum 2. That illiquid account should be completely illiquid These properties won’t hold exactly, as we relax the extreme distributional assumption on β. But the properties will continue to hold as a good approximation (with heterogeneous β).

0.02% wealth

See Camerer, Issacharoff, Loewenstein, O’Donoghue & Rabin (2003). “Assymetric Paternalism”

Expected Utility For Each β Type Penalty for Early Withdrawal β=1.0 β=0.9 β=0.8 β=0.7 β=0.6 β=0.5 β=0.4 β=0.3 β=0.2 β=0.1

Optimal Account Allocations Penalty for Early Withdrawal

Expected Penalties Paid For Each β Type Penalty for Early Withdrawal

Expected Utility For Each β Type Penalty for Early Withdrawal β=1.0 β=0.9 β=0.8 β=0.7 β=0.6 β=0.5 β=0.4 β=0.3 β=0.2 β=0.1

Expected Utility For Total Population Penalty for Early Withdrawal

 Who is helped by paternalism? ◦ Low β types.  Who is hurt by paternalism? ◦ High β types, but their welfare is barely affected.  An example of asymmetric paternalism: ◦ Camerer, Issacharoff, Loewenstein, O’Donoghue & Rabin 2003.

Regulation for Conservatives: Behavioral Economics and the Case for “Asymmetric Paternalism” Colin Camerer, Samuel Issacharoff, George Loewenstein, Ted O’Donoghue & Matthew Rabin "Regulation for Conservatives: Behavioral Economics and the Case for “Asymmetric Paternalism”. 151 University of Pennsylvania Law Review 101: 1211–

Robustness illustration 110 Baseline Low σ(θ) High σ(θ) CRRA = 0.5 CRRA = 2 High E(β) Low E(β) Standard Deviation of θ = σ(θ) Standard Deviation of β = σ(β) Mean of β Welfare Gain From 1 st z Account x z=1-x % Penalty on 2 nd z Account Welfare Gain From 2 nd z Account x z(1)z(1) z(2)z(2) Leakage (%) % Illiquid Wealth in 2 nd z Account

Robustness illustrations 111 Baseline Low σ(θ) High σ(θ) CRRA = 0.5 CRRA = 2 High E(β) Low E(β) σ(θ) σ(β) E(β) Penalty (%) Leakage (%) (k)/[SS+401(k)]

A family of tent densities on the β parameter indexed by their mode

123 Mode of the density on β Socially optimal penalty (%) on partially illiquid account

 “Number” of accounts: 2 vs. N  CRRA  Distribution of β values  Distribution of taste shocks  Functional form of taste shock: θu(c) vs. u(c-θ)  Number of periods: 3 vs. T  Individualization: pooling vs. separation ◦ See Galperti (2014)  Individualization: is income correlated with β?  And everything else that we did to simplify the problem. Why do people dislike penalty-based schemes?

 The calibrated model (with heterogeneous β) implies that the 10% penalty account isn’t important for welfare  Explaining why we don’t see such accounts outside U.S.  Partially illiquid accounts are a two-edged sword with both edges almost equally sharp.

 We tried to write a normative paper. ◦ “What is the socially optimal retirement savings system?”  We ended up with a positive paper. ◦ “The U.S. system is what you would predict a perfectly rational planner to do.”* *According to the stripped down model presented today.