EC989 Behavioural Economics
Sketch solutions for Class 1
Neel Sagar
(adapted from solutions by Andis Sofianos)
February 17, 2016
1. Illustrate the concept of Hyperbolic discounting, showing how the traditional problem of
Intertemporal Choice faced by individuals should be modified, and its implications.
The idea of hyperbolic discounting is to incorporate how decisions about now and later are qualitatively different. That is, individuals seem to have a bias towards the present. Recall the example from
lecture: £110 in 31 days is preferred to 100 in 30, but £100 today is preferred to £110 tomorrow.
This is an example of time inconsistency, and is incompatible with models that assume a constant
intertemporal discount factor δ between time periods (exponential discounting).
Hyperbolic discounting has instead a declining discount factor. The decline is very rapid between
now and the near future, but much slower between delays that are further into the future. This helps
to explain many of the preference reversals observed in choice experiments.
One such formulation of hyperbolic discounting is (β, δ) discounting, as used in O’Donoghue
and Rabin’s 1999 paper:
Ut = δ t u t + β
T
∑
δ τ uτ
(1)
τ =t+1
where δ ≤ 1 and β > 0. Here, δ is the standard discount factor found in exponential discounting.
Individuals exhibit present-bias when β < 1.
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2. When is an individual naive, and when is she sophisticated with respect to her intertemporal
preferences (you can use an example if you prefer)?
The aforementioned ODR paper splits (β, δ) discounters into two types: Naifs, and Sophisticates.
Both are present-biased. The key difference is that Sophisticates are aware of their susceptibility to
present bias in the future. Naifs, on the other hand, believe (incorrectly) that they will behave like a
time consistent (TC) individual in future periods.
One example from the ODR paper involves choosing when to do a report out of 4 possible weeks.
The reward v is fixed, but the costs c increase over time:
δ = 1, β = 1/2, v = (v̄, v̄, v̄, v̄), c = (3, 5, 8, 13)
(2)
We solve the problem by backwards induction. Table 1 shows the decision at each time period
by each type of individual (I have omitted the v̄ from the utilities to save space). TC’s do it immediately, Sophisticates do it in week 2, and Naifs procrastinate until week 4 and incur the maximum cost.
TC
Naif
Sophisticate
t
4
3
2
1
4
3
2
1
4
3
2
1
U from doing report
-13
-8
-5
-3
-13
-8
-5
-3
-13
-8
-5
-3
(Exp) U from waiting
-13
-8
-5
-6.5
-4
-2.5
-6.5
-6.5
-2.5
Do report now?
Yes
Yes
Yes
Yes
Yes
No
No
No
Yes
No
Yes
No
Table 1: Example of procrastination for naifs and sophisticates from ODR 1999.
3. Using the evidence provided by Ariely and Wertenbroch, discuss whether individuals have
preferences for commitments.
(see lecture slides)
The students impose costly deadlines upon themselves, which is an indication that they have a
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preference for commitment devices. They could potentially have set far looser public deadlines (i.e. all
at the end) and impose intrinsic private deadlines to themselves.
4. Using the evidence provided by Ariely and Wertenbroch, discuss whether students set deadlines optimally.
Students that set their own deadlines in the free-choice condition performed on average worse
than their classmates that were in the no-choice (but evenly spaced) condition. Recall that the mean
grade in the no-choice condition was 88.76 while in the free-choice condition it was 85.67 and the
two values are statistically different (p-value=0.003). Therefore, the deadlines were not set optimally
in the free-choice condition.
5. Can you mention and briefly describe other field experiments aimed to test individual’s
preferences for commitments?
See the end of the lecture slides. Examples include:
• DellaVigna and Malmendier 2006 - paying monthly subscriptions for the gym, even though the
frequency of visits does not justify the cost
• Ashraf et al 2005 - people commit to costly restrictions on their savings accounts
• Gine et al 2010 - smokers willing to put money in holding (and potentially forfeit it) to help
them quit
• Royer et al 2015 - offering costly commitment contracts to incentivise exercise at a company
All of these behaviours violate predictions based on exponential discounting. TC’s would be able
to choose their optimal course of action without falling into any present-bias traps, and so incurring a
commitment cost would only have a negative effect on utility.
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