2030 Final Exam
Behavioral Economics (spring 2015)
Please write legibly.
Instructor: David Laibson
Problem 1 of 2 (45 minutes): Consider a present-biased household with
• 0<β<1
• δ=1
• Per period loss from delay L > 0 (paid at the beginning of each period,
if action has not yet been taken by the end of the prior period).
• Stochastic action cost ct drawn from a uniform distribution on the
interval [0, 1].
• When the agent does the action, the agent stops experiencing flow
losses.
a. (20 minutes) Assuming the agent is sophisticated, derive the threshold
rule for taking action (assume a stationary equilibrium rule as we did
on the problem set).
Solution. The (stationary) equilibrium takes form: act if ct ≤ c∗ , wait
otherwise. Therefore, we need only determine c∗ . Since the agent must
be indifferent between waiting and acting given cost c∗ ,
c∗ = β[L + EV ]
where EV is the continuation value. Moreover,
Z c∗
Z 1
EV =
cdc +
[L + EV ]dc
0
c∗
1 ∗
1 − c∗
1 ∗ 2
∗
L
= (c ) + (1 − c )(L + EV ) = (c ) +
2
2
c∗
using ct ∼ U [0, 1]. Plugging this back into (2) reveals
1 − c∗
1 ∗
∗
c = β L + (c ) +
L
2
c∗
β
∗ 2
0 = (c )
− 1 + βL
2
s
s
βL
2βL
c∗ =
=
β
2−β
1− 2
1
(1)
b. (25 minutes) Assume that the agent has not chosen to act at time zero.
How many utils would the agent be willing to give up at time zero to
create a commitment device that compels the agent to make optimal
choices in all future periods? You can assume that this commitment
device takes the following form: act when ct ≤ c† and do not act when
ct > c† . To solve for the willingness to pay, you’ll need to solve for the
optimal commitment threshold c† .
Solution. The exponential agent perceives the same continuation
value, but solves for indifference condition
c† = [L + EV ]
(2)
Thus,
1 − c†
1
L
c = L + (c† ) +
2
c†
1
† 2
0 = (c )
−1 +L
2
s
√
L
†
c =
2L
=
1 − 21
†
So the availability of a commitment device decreases the expected time
of completion by
s s
r
2−β
1
1 1−β
−
=
2βL
2L
L
β
periods in expectation.
Problem 2 of 2 (45 minutes): True/False/Uncertain. Evaluate the following eight statements by judging them to be either true, false, or uncertain.
You will be graded on the strength of your explanation.
1. (5 minutes) Genetic variation does not strongly predict economic
behavior.
Solution. Uncertain. If genetic variation is taken to mean measured
SNPs, then (given our current state of knowledge) the maximum predictive power that one can get from a polygenic score that aggregates
all the SNPs into a single predictor is of the order R2 = 2 − 3%.
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2. (7 minutes) Partially naive agents are more likely to procrastinate
than fully naive agents.
Solution. False. Consider the earliest time τn at which the (full) naif
believes that he will take an action, if he waits in the current period.
This time has to be weakly later than the earliest time τp at which the
partial naif believes that he will take an action, since if action is optimal
for the agent with present bias β = 1, it will also be optimal for the
agent with present bias β < 1. Assuming that costs are increasing in
time to completion, the naif has weakly greater incentive to wait than
the partial naif.
3. (5 minutes) To analyze genetic data, one needs more subjects than
single nucleotide polymorphisms.
Solution. False. The statement would be correct if it were the case
that the only way to analyze genetic data was to regress the outcome of
interest on all SNPs measured simultaneously. This regression would
violate the rank order condition if the number of SNPs exceeds the
number of observations. But in practice, SNPs are analyzed one at
a time. (For example, Rietveld et al. (2013) tested approximately 2
million SNPs for association in a subject pool of approximately 100,000
individuals.)
4. (5 minutes) The CARD Act worked because of the effects of improved
disclosures.
Solution. Uncertain. Improved disclosures had a positive effect, but
the larger positive effect came through the new regulations on fees.
5. (6 minutes) Dellavigna and Malmendier’s gym study showed that
people use gym memberships as a commitment device.
Solution. Uncertain. It’s possible that agents engage in costly commitment to increase their number of attendances, but this doesn’t seem
to be the most convincing explanation of their results. These agents
don’t succeed in going to the gym much despite the commitment (on
average 4 visits per month), and this theory also doesn’t explain why
agents who buy the monthly subscription are less likely to cancel.
6. (7 minutes) Active choice is socially optimal when β is large (in a
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present-biased model) and agents have highly heterogeneous preferences.
Solution. False. Heterogeneous preferences indeed increase the attractiveness of active choice (intuition: the greater the heterogeneity
in preference, the worse a “one size fit all” default), but higher β decreases the attractiveness of active choice, which is primarily a tool to
help present-biased agents. (In the extreme case β = 1, agents will
choose the optimal time to make a decision, so forcing a decision in
time 0 is suboptimal.)
7. (5 minutes) Self-regulation is associated with neural activation in the
dopamine reward system.
Solution. True. See e.g. McClure, Ericson, Laibson, Lowenstein, and
Cohen (2007). The dopamine reward system rewards immediacy, which
makes self regulation more difficult.
8. (5 minutes) Asymmetric paternalism is paternalism that hurts some
people and helps other people.
Solution. Essentially true. Asymmetric paternalism is paternalism
that mildly hurts some people (fully rational individuals) while greatly
helping others (behavioral agents).
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