What determines consumption growth and asset allocations? · · 2019-08-14Automatic enrollment in...

Household finance and libertarian paternalism

James J. Choi

Yale Summer School in Behavioral Finance 2009

What determines consumption growth and asset allocations?The classic Euler equation

With CRRA utility where γ is RRA, log‐linearize to get

11

'( )1

'( )t

t tt

u cE R

u cβ +

+

⎡ ⎤= ⎢ ⎥

⎣ ⎦

( )1

21 , 1 ln

1 1ln ln

2 tt t t f t cE c E R β γσγ ++ + ΔΔ = − +

What do households say?At one large U.S. food corporation

Choi, Laibson, Madrian, and Metrick (2002)

Assessment of own savings rate

68%

31%

1%0%

20%

40%

60%

80%

100%

Too low About right Too high

The old routine when you joined a company with a 401(k) planWelcome to the company

Here is information on your 401(k) plan

If you’d like to join, call this toll‐free number or visit the benefits website

Automatic enrollment in the 401(k)Welcome to the company

Here is information on your 401(k) plan

If you don’t do anything, you will be automatically enrolled at this contribution rate and asset allocation

If you’d like to opt out, call this toll‐free number or visit the benefits website

Automatic enrollment effect

0%

20%

40%

60%

80%

100%

0 6 12 18 24 30 36 42

Tenure (months)

Fraction enrolled in 401(k)

Hired and observed before automatic enrollment

Hired under automatic enrollment (3% contribution default)

Hired under automatic enrollment (6% contribution default)

Beshears, Choi, Laibson, and Madrian (2008)

Defaults and herding

7 10 10

37

2016

2

70

3

137 63

13

4

66

6 7

0

10

20

30

40

50

60

70

80

1‐2% 3% 4‐5% 6% 7‐10% 11‐15%

Contribution Rate

Fraction of Participants

Hired before automatic enrollmentHired during automatic enrollment (3% default)Hired during automatic enrollment (6% default)


Defaults and herding

16%

3%

81%75%

18%

7%

Stocks

Stocks

BondsBonds

Money Market

Money Market

After Automatic EnrollmentMoney Market Default Fund

Madrian and Shea (2001)

BeforeAutomatic Enrollment

How sticky are defaults?


0%

20%

40%

60%

80%

100%

0 6 12 18 24 30 36

Tenure (months)

Fraction of participants

Hired before AE: Default rate and fund Hired after AE: Default rate and fund

Hired before AE: Default rate (3%) Hired after AE: Default rate (3%)

Hired before AE: 100% in default fund Hired after AE: 100% in default fund

How sticky are defaults?


0%

20%

40%

60%

80%

0 6 12 18 24 30 36 42 48 54 60

Tenure (months)

Fraction of participants

Hired before AE: Default rate and fund Hired after AE: Default rate and fund

Hired before AE: Default rate (2%) Hired after AE: Default rate (2%)

Hired before AE: 100% in default fund Hired after AE: 100% in default fund

Is this a welfare-neutral change?401(k) is an illiquid, tax‐advantaged savings vehicle

This company matches contributions dollar‐for‐dollar up to 6% of employee’s salary

Is this a welfare-neutral change?In national sample:

Fraction agreeing with statement, “You are glad your company offers automatic enrollment”

98% of those who were automatically enrolled and didn’t opt out

79% of those who opted out of automatic enrollment

Harris Interactive, 2007. “Retirement Made Simpler.”http://www.retirementmadesimpler.org/Library/FINAL%20RMS%20Topline%20Report%2011‐5‐07.pdf.

Inertia: An application to corporate financeIn a stock‐for‐stock merger

80% of individuals passively keep acquirer shares they receive

30% of institutions passively keep acquirer shares they receive

Optimal corporate response if demand curve for its stock is downward‐sloping:

Use stock‐for‐stock mergers instead of SEOsto raise equity capital

Baker, Coval, and Stein (2007)

Dynamic defaults:Save More Tomorrow

401(k) contribution rate rises automatically in the future

Rise may coincide with pay raises

Thaler and Benartzi (2004)

Thaler and Benartzi (2004)

0%

2%

4%

6%

8%

10%

12%

14%

16%

Before Pay

raise 1

Pay

raise 2

Pay

raise 3

Pay

raise 4

Contribution rate

Accepted advice to save more now Joined SMT

0%

20%

40%

60%

80%

100%

‐Q4 ‐Q3 ‐Q2 ‐Q1 +Q1 +Q2 +Q3 +Q4

Time relative to auto‐enroll into SMT

SMT participation rate

Benartzi, Peleg, and Thaler (2008)

Practical impact of defaults researchAutomatic enrollment in savings plans promoted by legislation

– Pension Protection Act of 2006

– New Zealand Kiwisaver

– U.K. Pensions Act of 2008

Automatic enrollment adopted by

41% of 401(k) plans with >5,000 participants

31% of plans with 1,000‐4,999 participants

31% of plans with 200‐999 participantshttp://www.retirementmadesimpler.org/WhoWeAre/Automatic401(k)FactSheet.shtml

Libertarian paternalism (Thaler and Sunstein, 2003)

Nudging people to an outcome without restricting choice

Helps irrational types

Imposes minimal costs on rational types

Active decisionWelcome to the company

You have 30 days to tell us whether you want to be in the 401(k) plan

Not stating a preference is not an option

Carroll, Choi, Laibson, Madrian, and Metrick (2009)

Active decision participation effect


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 5 10 15 20 25 30 35 40 45 50 55

Tenure at company (months)

Fraction enrolled in 401(k)

Active decision cohort Standard enrollment cohort

Active decision contribution rate effect


0%

1%

2%

3%

4%

5%

6%

0 5 10 15 20 25 30 35 40 45 50 55

Tenure at company (months)

Average 401(k) contribution

rate (non‐participants included)

Active decision cohort Standard enrollment cohort

Contribution rate chosen under active decisionRegression dependent variable

If hired under active decision, contribution rate 3 months after hire

If hired under standard enrollment, contribution rate 30 months after hire


Explanatory variablesFemale dummy

Married dummy

log(Base pay)

Age bucket dummies

Active decision dummy

Interactions between active decision dummy and demographic variables


Contribution rate tobit (selected coefficients)


Active decision cohort 0.086

(0.247)

Active decision cohort × Female ‐1.989**

(0.547)

Active decision cohort × Married ‐0.528

(0.503)

Active decision cohort × Log(Base pay) ‐1.930

(1.053)

Active decision cohort × (0 ≤ Age < 30) ‐0.584

(3.553)


(3.552)

Active decision cohort × (40 ≤ Age < 50) 0.004

(3.578)


(3.659)

A model of default and active decision effects1. It is costly to opt out of a default

2. Opt‐out costs are time‐varying → Creates option value for waiting

3. Actors may be procrastinators


Hyperbolic discounting

Today Tomorrow 2 days from

now

3 days from

now

Value

of 1 util

1

βδ βδ 2 βδ 3

Phelps and Pollack (1968), Laibson (1997)

Immediate cost of opting out: 6

Delayed benefit of opting out: 8

Short‐run discount factor β = 0.5

Long‐run discount factor δ = 1

Payoff from opting out today:

‐6 + 0.5 × 8 = ‐2

Payoff from opting out tomorrow:

0 + 0.5 × (‐6 + 8) = 1

Model setupInfinite horizon

Agent decides when to opt out of default sD and move to optimum s*

s* is time‐invariant and treated as if known by agent

Agent pays stochastic i.i.d. cost of opting out c

Agent observes c before making her decision

Until opt‐out, agent suffers flow loss L(sD, s*) ≥ 0

Agents have hyperbolic discount function

For analytical tractability, we set δ = 1

Agent’s solutionOpt out if draw an action cost c < threshold c*

Threshold increasing in flow loss L

Threshold increasing in β

Model predictionActive decision causes agents to immediately move to the savings rate they would have eventually chosen in a default regime

Faster opt‐outs by those who move the furthest from the default upon opting out

Opt‐out delay from a 0% contribution default

0

50

100

150

200

250

300

350

400

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Contribution rate chosen upon enrollment (% of salary)

Mean time to enrollment

(days)


Evaluating welfare under default policiesNormative well‐being evaluated using exponential discounting, i.e. β = 1

One justification for this welfare criterionSuppose changes in the default policy are always implemented with a lag

Then every incarnation of the agent would vote to use this welfare criterion

Welfare loss function

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

Initial flow loss L

Total discounted loss

β = 1

β = 0.67

Candidate optimal defaultsProposition 2

If β < 1, L = κ(s* – d)2, s* is uniformly distributed from s to s, then the optimal default is one of the following three types:

1. Center default (mean s*)

2. Offset default (to one side of the distribution)

3. Active decisions


Optimal defaults as a function of s* heterogeneity and time inconsistencyProposition 3

s–

s

active decisions

offset default

center default0.05

0.1

0.15

0.2

0.25

0.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1β

s–

ss

–s

active decisions

offset default

center default0.05

0.1

0.15

0.2

0.25

0.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1β


Classifying libertarian paternalistic interventions1. Change default, d

(Active decision is mathematicallyequivalent to an infinitely unappealingdefault that induces immediate action)

2. Change action cost, c

3. Change perceived optimum, s*

Quick Enrollment: Making action cognitively easier“Here is a pre‐selected contribution rate and asset allocation.

“Check this box and mail in this card if you’d like to enroll at the pre‐selects.”

Quick Enrollment effect

Beshears, Choi, Laibson, and Madrian (2006)

Gentle reminders1,503 unenrolled employees at one company

received survey

9% response rate

Among survey questions:1. How much are you actually saving for

retirement?2. How much should you ideally be saving

for retirement?3. When (if ever) are you planning on

enrolling in your 401(k)?Carroll, Choi, Laibson, Madrian, and Metrick (2009)

401(k) enrollment in 4 months after survey

3.3% 3.7%

0%

20%

40%

60%

80%

100%

Survey responders Survey non‐responders


Norm salienceU = –(1 – s)(x – x0) – s(x – xNorm)

where

x is action taken

x0 is optimum in absence of norm

xNorm is action prescribed by norm

s is salience of norm

Benjamin, Choi, and Strickland (2008)

8.8%

2.2%

0%

2%

4%

6%

8%

10%

12%

14%

Asian identity not salient Asian identity salient

Median reservation interest rate for delayingreceipt of $4 for one week

Benjamin, Choi, and Strickland (2008)

Targeted information provisionTask

Allocate $10,000 among four S&P 500 index funds

Subject pool

Wharton MBAs

Harvard undergrads

Harvard staff

Choi, Laibson, and Madrian (2009)

Fees information treatment

Mutual fund Symbol Front-end load Front-end load fee if

you purchase $10,000 worth of shares

Expense ratio

Approximate annual ongoing fee if your average balance is

$10,000

Allegiant S&P 500 Index Fund - Class A

AEXAX 2.50% $250 0.60% $60

Morgan Stanley S&P 500 Index Fund

- Class A SPIAX 5.25% $525 0.64% $64

Phoenix Insight Index Fund - Class A

HIDAX 5.75% $575 0.73% $73

UBS S&P 500 Index Fund - Class A

PSPIX 2.50% $250 0.70% $70


$456$421 $431$432

$366$410

$255$309 $309

$0

$100

$200

$300

$400

$500

Staff MBAs College

Control Fees info Min possible

Mean fees paid


$456

$389 $395

$513

$409$435

$519

$424$453

$0

$100

$200

$300

$400

$500

$600

Staff MBAs College

Mean fee paid

Not at all likely Somewhat likely Very likely

How likely is it that you would change your decisionif you consulted a professional investment advisor?


Financial education seminarsCurriculum

Setting savings goals

Asset allocation

Managing credit and debt

Insurance against financial risks


14%7%

100%

Planning to

enroll

Actually

enrolling

Actually

enrolling

Employees not yet enrolled in 401(k)

Attended seminar Didn’t attend seminar


8% 5%

28%

Planning to

increase

contribution rate

Actually

increased

Actually

increased

Employees already enrolled in 401(k)

Attended seminar Didn’t attend seminar

Subsidizing “good” behaviors: 401(k) matchInstantaneous, riskless return on 401(k) investment

If you are over 59½ years old, can withdraw 401(k) money without penalty

→ Lost arbitrage profits if match is unexploited



Fraction of >59½ employees with arbitrage

losses

0%

20%

40%

60%

80%

100%

A B C D E F G

Average arbitrage loss (if loss > 0)

$0

$200

$400

$600

$800

A B C D E F G


ReferencesBaker, Malcom, Joshua Coval, and Jeremy C. Stein, 2007. “Corporate Financing Decisions When Investors Take the Path of Least Resistance.” Journal of Financial Economics.

Benartzi, Shlomo, Ehud Peleg, and Richard H. Thaler, 2008. “Choice Architecture and Retirement Saving Plans.” UCLA mimeo.

Benjamin, Daniel J., James J. Choi, and A. Joshua Strickland, 2008. “Social Identity and Preferences.”NBER Working Paper 13309.

Beshears, John, James J. Choi, David Laibson, and Brigitte C. Madrian, 2008. “The Importance of Default Options for Retirement Saving Outcomes: Evidence from the United States.” In Lessons from Pension Reform in the Americas, Stephen J. Kay and Tapen Sinha, editors.

Beshears, John, James J. Choi, David Laibson, and Brigitte C. Madrian, 2006. “Simplification and Saving.”NBER Working Paper 12659.

Carroll, Gabriel D., Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2009. “Optimal Defaults and Active Decisions.” Quarterly Journal of Economics.

Choi, James J., David Laibson, and Brigitte C. Madrian, 2007. “$100 Bills on the Sidewalk: Suboptimal Investment in 401(k) Plans.” NBER Working Paper 11554.

Choi, James J., David Laibson, and Brigitte C. Madrian, 2009. “Why Does the Law of One Price Fail? An Experiment on Index Mutual Funds.” Review of Financial Studies, forthcoming.

Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2002. “Defined Contribution Pensions: Plan Rules, Participant Decisions, and the Path of Least Resistance.” In Tax Policy and the Economy 16, James Poterba, editor.

Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2004. “For Better or For Worse: Default Effects and 401(k) Savings Behavior.” In Perspectives in the Economics of Aging, David A. Wise, editor.

Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2006. “Saving for Retirement on the Path of Least Resistance.” In Behavioral Public Finance: Toward a New Agenda, Ed McCaffrey and Joel Slemrod, editors.

Laibson, David, 1997. “Golden Eggs and Hyperbolic Discounting.” Quarterly Journal of Economics.

Madrian, Brigitte C., and Dennis Shea, 2001. “The Power of Suggestion: Inertia in 401(k) Participation and Savings Behavior.” Quarterly Journal of Economics.

Phelps, Edmund S., and Robert A. Pollak, 1968. “On Second‐Best National Savings and Game‐Equilibrium Growth.” Review of Economic Studies.

Sunstein, Cass R., and Richard H. Thaler, 2003. “Libertarian Paternalism.” American Economic Review.

Thaler, Richard H., and Shlomo Benartzi, 2004. “Save More Tomorrow: Using Behavioral Economics to Increase Employee Savings.” Journal of Political Economy.

What determines consumption growth and asset allocations? · · 2019-08-14Automatic enrollment in...

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