Post on 31-May-2020
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)
Choi, Laibson, Madrian, and Metrick (2006)
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?
Choi, Laibson, Madrian, and Metrick (2004)
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?
Choi, Laibson, Madrian, and Metrick (2004)
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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
Explanatory variablesFemale dummy
Married dummy
log(Base pay)
Age bucket dummies
Active decision dummy
Interactions between active decision dummy and demographic variables
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
Contribution rate tobit (selected coefficients)
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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)
Active decision cohort × (30 ≤ Age < 40) ‐0.577
(3.552)
Active decision cohort × (40 ≤ Age < 50) 0.004
(3.578)
Active decision cohort × (50 ≤ Age < 60) ‐0.103
(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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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)
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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
Carroll, Choi, Laibson, Madrian, and Metrick (2009)
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
Choi, Laibson, and Madrian (2009)
$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
Choi, Laibson, and Madrian (2009)
$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?
Choi, Laibson, and Madrian (2009)
Financial education seminarsCurriculum
Setting savings goals
Asset allocation
Managing credit and debt
Insurance against financial risks
Choi, Laibson, Madrian, and Metrick (2001)
14%7%
100%
Planning to
enroll
Actually
enrolling
Actually
enrolling
Employees not yet enrolled in 401(k)
Attended seminar Didn’t attend seminar
Choi, Laibson, Madrian, and Metrick (2001)
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
Choi, Laibson, and Madrian (2007)
Choi, Laibson, and Madrian (2007)
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
Choi, Laibson, and Madrian (2007)
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.