Transcript PPT

Optimal Defaults
David Laibson
Harvard University
July, 2008
Outline:
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Normative Economics
Revealed preferences
Mechanism Design
Optimal policies for procrastinators
Active decision empirical implementation
Normative economics
• Normative preferences are preferences that society (or you)
should optimize
• Normative preferences are philosophical constructs.
• Normative debates are settled with empirical evidence and
philosophical arguments
• Positive preferences are preferences that predict my choices
• Positive preferences need not coincide with normative
preferences. What I do and what I should do are different
things (though they do have some similarities)
• For example: I have a heroin kit in my room and I shoot up
after every dinner. Just because I shoot heroin (and
understand the consequences) does not mean that it is
necessarily normatively optimal
The limits to “revealed preferences”
Behavioral economists are particularly skeptical of the claim
that positive and normative preferences are identical.
Why?
• Agents may make cognitive mistakes
– I hold all of my retirement wealth in employer stock, but that does
not mean that I am risk seeking; rather it really means that I
mistakenly believe that employer stock is less risky than a mutual
fund (see survey evidence).
• Agents may have dynamically inconsistent preferences
(there is no single set of preferences that can be
measured).
• But in both cases, we can still use behavior to infer
something about normative preferences.
Positive Preferences ≠ Normative Preferences
But…
Positive Preferences ≈ Normative Preferences
Identifying normative preferences? (No single answer.)
• Empirically estimated structural models that include
both true preferences and behavioral mistakes (Laibson
et al, MSM lifecycle estimation paper, 2005)
• Asymptotic (empirical) choices (Choi et al, AER, 2003)
• Active (empirical) choices (Choi et al “Active Decision”
2004)
• Survey questions about ideal behavior (Choi et al 2002)
• Expert choice (Kotlikoff’s ESPlanner; Sharpe’s
Financial Engines)
• Educated choice
• Philosophy, ethics
Example: Normative economics with
present-biased preferences
Possible welfare criteria:
• Pareto criterion treating each self as a separate agent
(this does not identify a unique optimum)
• Self 0’s preferences: basically exponential δ discounting
• Exponential discounting: θt (θ=δ?)
• Unit weight on all periods
• One analytic forward-looking brain and every affective myopic brain
• Other suggestions?
Mechanism Design
How should a good default be chosen when true
preferences (and rationality) are heterogeneous?
• Maximize a social welfare function
– Need true preferences (which may be
heterogeneous).
– Need to model endogenous responses of behavioral
actors
• Often this implies that you should heavily weight the
preferences of the most behavioral subpopulations.
• Assymmetric/cautious paternalism (Camerer et al 2003)
• Libertarian paternalism (Sunstein and Thaler 2005)
Optimal policies for procrastinators
Carroll, Choi, Laibson, Madrian and Metrick (2004).
• It is costly to opt out of a default
• Opportunity cost (transaction costs) are time-varying
– Creates option value for waiting to opt out
• Actors may be present-biased
– Creates tendency to procrastinate
Preview of model
• Individual decision problem (game theoretic)
• Socially optimal mechanism design (enrollment regime)
• Active decision regime is optimal when consumers are:
– Well-informed
– Present-biased
– Heterogeneous
Model setup
• Infinite horizon discrete time model
• Agent decides when to opt out of default sD and move to
time-invariant optimum s*
• Agent pays stochastic (iid) cost of opting out: c
• Until opt-out, the agent suffers a flow loss
L(sD, s*)  0
• Agents have quasi-hyperbolic discount function:
1, bd, bd2, . . . where b ≤ 1
• For tractability, we set δ = 1:
1, b, b, . . .
Model timing
s≠s*
L
v(c)
c~uniform w(c)
Period begins:
delay cost L
Draw transaction cost
Cost functions
Incur cost c and move
to personal optimum s*
(game over)
Do nothing and start
over again, so
continuation cost
function is given by:
β[L+Ev(c+1)].
Decision node
Agent’s action
Equilibrium solves the following system:
w(ct
, s *, s
D)
=
v(ct , s *, sD ) =
c*
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Action threshold and loss function
c+
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Threshold is increasing in b , increasing in L, and
decreasing in the support of the cost distribution
(holding mean fixed).
Ev(×=
)
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- L+
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b 2 - b øö÷÷÷
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if 0 < L < c + c + c
2
b
ot herwise
Graph of expected loss function: Ev(c)
Case of b = 1
Ev(c)
1.2
1
0.8
0.6
c + c
Ev ()  c
L=
0.4
c
2
0.2
0
0
1
2
3
L : loss per period of inaction
Key point: loss function is monotonic in cost of waiting, L
c = 0.5, c = 1.5
4
Graph of loss function: Ev(c)
Ev(c)
1.2
b = 0.67
1
Ev (×) =
c
b
b=1
0.8
0.6
Ev ()  c
L=
0.4
c
b
c + c
2
0.2
0
0
1
2
3
4
L : loss per period of inaction
Key point: loss function is not monotonic for quasi-hyperbolics.
c = 0.5, c = 1.5
Why is the loss function non-monotonic
when b < 1?
• Because the cutoff c* *is a function of L, we can write the
loss function as Ev(c (L ), L )
• By the chain rule,
dEv
¶ Ev ¶ c
¶ Ev
=
+
< 0
*
dL c * ( L )= c
¶c ¶L
¶L
*
-
+
0
• Intuition: pushing the current self to act is good for the
individual, since the agent has a bias against acting.
When acting is very likely, this benefit is not offset by the
cost of higher L.
Model predictions
• In a default regime, early opt-outs will show the largest
changes from the default
• Participation rates under standard enrollment will be lower
than participation rates under active decision
• Participation rates under active decision will be lower than
participation rates under automatic enrollment
Model predictions
People who move away from defaults sooner are, on average, those whose
optima are furthest away from the default
Average contribution
rate upon enrollment
Standard enrollment regime
9
8
7
6
5
4
0
10
20
30
40
Tenure in months at first participation
50
Model predictions
People who move away from defaults sooner are, on average, those whose
optima are furthest away from the default
Average change from
default
Automatic enrollment company
5
4.5
4
3.5
3
2.5
2
0
10
20
30
Tenure in months at opt-out
40
The benevolent planner’s problem
• A benevolent planner picks the default sD to minimize the
social loss function:
ò
s
s
*
*
=s
E t v (ct , s , s D )dF (s
*
)
• We adopt a quadratic loss function:
2
L (s , s ) = k (s - s )
*
D
*
D
• To illustrate the properties of this problem, we assume s*
is distributed uniformly.
Loss function in s*-sD space
1
0
-2
-1
0
s*-sD
1
2
Lemma:
The individual loss at each boundary of the
support of s* must be equal at an optimal default.
¶
¶ sD
ò
s
s
s
¶
*
*
Ev(s , s D )dF (s ) =
Ev
(
s
s
)
ds
D
¶ s D òs
s - sD
¶
=
Ev(x )dx
ò
¶ s D s - sD
= Ev(s - s D ) - Ev(s - s D )
*
*
= Ev(s, s D ) - Ev(s , s D )
= 0
Proposition:
There are three defaults that satisfy Lemma 1 and the
second-order condition.
Center
Offset
0 .8
0 .8
0 .7
0 .7
0 .6
0 .6
0 .5
0 .5
0 .4
0 .4
0 .3
0 .3
0 .2
0 .2
0 .1
0 .1
0
-2
-1
0
0
1
2
-2
-1
0
Active decision
0 .8
0 .7
0 .6
0 .5
0 .4
0 .3
0 .2
0 .1
0
-2
-1
0
1
2
1
2
Proposition:
Active decisions are optimal when:
• Present-bias is large --- small b.
• Average transaction cost is large.
• Support of transaction cost is small.
• Support of savings distribution is large.
• Flow cost of deviating from optimal savings rate is
large (for small b).
s - s
High Heterogeneity
30%
Offset
Default
Low Heterogeneity
Active Decision
Center
Default
0%
0
Beta
1
Naives:
Proposition: For a given calibration, if the optimal
mechanism for sophisticated agents is an active
decision rule, then the optimal mechanism for naïve
agents is also an active decision rule.
Mechanism Design: Summary
• Model of standard defaults and active decisions
– The cost of opting out is time-varying
– Agents may be present-biased
• Active decision is socially optimal when…
 b is small
– Support of savings distribution is large
Active decisions: empirical implementation
Choi, Laibson, Madrian, Metrick (2004)
Active decision mechanisms require employees to make an
active choice about 401(k) participation.
• Welcome to the company
• You are required to submit this form within 30 days of
hire, regardless of your 401(k) participation choice
• If you don’t want to participate, indicate that decision
• If you want to participate, indicate your contribution rate
and asset allocation
• Being passive is not an option
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A 97
pr
M - 97
ay
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8
Participation Rate in
3rd Month of Tenure
Rate of Participation in the 401(k)
plan by month of hire
80%
70%
60%
50%
40%
30%
20%
10%
0%
Month of hire
Ju
ly
ne
Ju
M
ay
A
pr
il
ch
M
ar
ry
br
ua
Fe
ua
ry
80%
70%
60%
50%
40%
30%
20%
10%
0%
Ja
n
Participation Rate in 3rd
Month of Tenure
Hire Date and 401(k) Participation
Month of Hire
Active decision
Standard enrollment
401(k) participation increases under active decisions
Fraction of employees ever
participated
401(k) participation by tenure: Company E
100%
80%
60%
40%
20%
0%
0
6
12
18
24
30
36
42
Tenure at company (months)
Active decision cohort
Standard enrollment cohort
48
54
FIGURE 4. The Likelihood of Opting Out of
401(k) Plan Participation by Tenure
Fraction Of Ever
Participants Not Currently
in the 401(k) Plan
8%
7%
6%
5%
4%
3%
2%
1%
0%
0
6
12
18
24
30
36
42
Tenure (months)
Active Decision Cohort
Standard Enrollment Cohort
48
54
Active decisions
• Active decision raises 401(k) participation.
• Active decision raises average savings rate by 50 percent.
• Active decision doesn’t induce choice clustering.
• Under active decision, employees choose savings rates
that they otherwise would have taken three years to
achieve. (Average level as well as the entire multivariate
covariance structure.)
Challenge to revealed preferences
• We should no longer rely on the classical theory of
revealed preferences to answer the fundamental
question of what is in society's interest.
• Context determines revealed preferences.
• Revealed preferences are not (always) normative
preferences.
Conclusions
• It’s easy to dramatically change savings behavior
– Defaults, Active Decisions
• It’s harder to know how to identify socially optimal
institutions.
– How can we impute people’s true preferences?
– What if they are dynamically inconsistent?
– What set of preferences are the right ones?
– How do we design mechanisms that implement
those preferences when agents are
psychologically complex.
– Who can be trusted to design these
mecdhanisms?