EC989 Behavioural Economics
Sketch solutions for Class 2
Neel Sagar
(adapted from solutions by Andis Sofianos)
February 17, 2016
1 Prospect Theory
1. Illustrate the way individuals usually weight the probability of a state of the world and how
to react to losses in Prospect Theory.
Expected utility theory states that if certain axioms are satisfied (Completeness, Transitivity, Continuity, Independence) then we can compute expected utility as the sum of probability multiplied by
the respective utility in that particular state of the world:
EU =
∑
pi u(xi )
(1)
i
However, the axioms (Independence in particular) tend to be violated in practice. From experimental evidence, it has been found that:
• Individuals do not seem to apply linear weights when evaluating lotteries. People have difficulty
comprehending extreme events and so might treat uncertain but highly likely events as certain
and highly unlikely events as impossible. People also generally tend to overweight unlikely events
and underweight highly likely events (see S-shaped weighting function in Cumulative Prospect
Theory).
• Individuals reason in terms of gains and losses rather than in terms of absolute levels
1
• Losses hurt more than gains are enjoyed – loss aversion, endowment effect
• Context and framing affects choices
Kahneman and Tversky developed Prospect Theory to address these issues. They proposed the
following value function:



x α
v(x) =
if x ≥ 0


−λ(−x)β
(2)
if x < 0
Here, the origin represents a reference point, rather than 0 as an absolute. Usually, individuals are found
to be risk averse in gains, but risk seeking in losses. From data, λ tends to be larger than 1 (around
2.2 according to K & T), meaning that losses are perceived as twice the magnitude of an equivalent
gain. To reflect the overweighting of low probabilities and underweighting of high probabilities, they
proposed a weighting function of the form (for gains and losses respectively):
w+ (p) =
pδ
pγ
−
,
w
(p)
=
[pγ + (1 − p)γ ]1/γ
[pδ + (1 − p)δ ]1/δ
(3)
Therefore, calculating the value of risky prospects takes the form:
V =
∑
w(pi )v(xi )
(4)
i
2. Why is the decision to work more on sunny days not consistent with traditional theory?
Dynamic models of labour supply predict that work hours should be responding positively to
transitory positive wage changes. That is, when wages go up should be working more and when wages
are low enjoy more leisure and work less – since the opportunity cost (forgone wage) is lower.
This prediction in theory makes sense but it’s proven difficult to confirm as in the literature estimated elasticities of intertemporal substitution have in general been low and insignificant or even
in some cases negative. Problem with past data is lack of authentically transitory wage changes; cab
drivers paper helps with this as cab drivers face correlated within day wages (weather, subway break2
downs, day-of-the-week effects, conventions etc.) but uncorrelated across days. Additional advantage
is that cab drivers choose number of hours to work hence giving endogenously decided working hours.
In the paper they estimate negative intertermporal elasticities which is in contradiction to what
traditional labour supply models predict. That is, individuals should be working until their marginal
productivity equalises their marginal effort. Since sunny days are days where their productivity is lower
(given the lower demand for cab services) they should be working less hours and more during rainy
days. What they find instead indicates that drivers tend to quit early on high wage days and drive
longer on low wage days.
Possible explanations offered in the paper for this contradicting evidence:
• Target setting – one day at a time ie. narrow bracketing of decisions
• Loss aversion – fear of falling behind their usual targets motivates more working hours on low
wage days
3. How does Odean (1998) test the disposition effect? And what does it find?
The disposition effect is the tendency to hold losing investments too long and sell winning investments too soon. The effect is a direct implication of prospect theory.
Odean uses data from a nationwide discount brokerage house on 10,000 randomly selected accounts from Jan 1987 to Dec 1993. He tests whether investors sell their winners too soon and hold
their losers too long. Study also investigates any tax-motivated trading in December.
Recall example explaining realised gains, realised losses, paper gains and losses in the lecture slides.
In the paper, Proportion of Gains Realized (PGR) and Proportion of Losses Realized (PLR) are compared
Main hypothesis is that investors sell their winners and hold their losers. This would imply that
PGR > PLR for the year. Secondary hypothesis is that in December, investors are more willing to sell
losers and less willing to sell winners than during the rest of the year due to the fact that taxes on gains
are calculated at the end of the year.
Result: PGR for the entire year is found to be 0.148 while the PLR for the entire year is 0.098,
confirming the main hypothesis that the disposition effect in trading behaviour exists. PLR > PGR in
3
December, confirming the secondary hypothesis.
4. In Odean 1998, why is it not sufficient to look at the number of securities sold for gains
versus the number sold for losses?
When trying to test the disposition effect it is not enough to simply look at the number of securities
sold for gains versus the number sold for losses. It might depend on the general situation in market.
Suppose investors are indifferent to selling winners or losers. Then in an upward-moving market they
will have more winners in their portfolios and will tend to sell more winners than losers even though
they had no preference for doing so. To test whether investors are disposed to selling winners and
holding losers, need to look at the frequency with which they sell winners and losers relative to their
opportunities to sell each.
2 Social Preferences
1. Briefly describe the main features of the experiment by DellaVigna et al on charitable giving,
and its main results.
Experiment by DellaVigna et al. (2012) tries to disentangle reasons for charitable giving. According to standard theory, charitable giving would not make sense if utility did not incorporate the
preferences of others. Two broad classes of motivation for charitable giving have been offered:
1. Warm Glow - Individuals enjoy giving (see Andreoni, 1990)
2. Social Pressure (see Akerlof and Kranton, 2000)
The experiment involved door-to-door campaign to gather charitable offers for two charities. The
two charities (La Rabida Children’s Hospital, and East Carolina Hazard Center) were chosen so that
most households in their sample would clearly prefer one (La Rabida) to the other (ECU). They verified
this using a survey where they asked residents to rank five charities: La Rabida was first and ECU was
ranked 5th.
Treatments:
4
• Treatment without flyer: canvassers knock on the door or ring the bell, if they reach a person,
inform household about one of the two charities and whether they would be willing to donate.
• Flyer treatment: A different canvasser leaves a flyer the day before informing of the visit the next
day.
• Opt-out treatment: The flyer has a box to be checked if they do not want to be disturbed. If
checked, canvassers did not knock.
Difference between flyer and no flyer treatment allows to identify the added motivation of social
pressure on charitable giving. A warm glow effect would be signified by an increased % of givers. A
social pressure effect would be indicated by a reduction in giving.
An additional, but less important treatment was the survey treatment: the canvasser enquires
whether the household member would like to respond to a survey and informs them about duration and of payment ($10, $5, or nothing).
2. Briefly summarize the main conclusions one can derive from the experiment of DellaVigna
et al.
In the flyer treatment, there was no change in giving, but a 9% decrease in people who opened
the door. This effect was stronger in the opt-out treatment, with a 23% decrease in door openers, and
either a 28% or 40% reduction in donations (depending on the charity).
Giving is not reduced in the flyer treatment; this is consistent both with altruism and social pressure. The advance notice increases the presence of altruistic givers and lowers the presence of those
who give due to social pressure, as long as these two forces are about the same size one would expect
no overall impact.
Giving is significantly reduced with the opt-out treatment, which supports the view that social
pressure is dominating in this context. By not answering the door, people are escaping the guilt which
would force them to donate. If giving was primarily due to altruism the opt-out treatment should not
affect giving rates or levels relative to the flyer treatment. The reduction in donation amount in the
opt-out treatment is mainly due to a reduction in small donations (below $10).
They conclude that allowing people to opt-out should increase social welfare, by giving people the
5
option to avoid unpleasant social pressure.
3. Briefly describe the experiment of Kube et al, 2012 and its main results.
The experimental design involved recruiting workers from the university campus for a real job that
was advertised as a one-off opportunity. Advertisement called for a 3 hour job paying 12 Euros per
hour. Each participant was asked to enter a book’s author, title, publisher, year and ISBN number into
an electronic database. The software recorded the time for each log so authors could calculate the rate
of character input.
All subjects received the same hourly wage. Additional payments and benefits were the only differences across treatments. These were announced before the participants started their task. There were
6 total treatments:
1. Baseline Treatment: workers received the hourly wage with no additional benefits.
2. Money Treatment: wages were unexpectedly raised by roughly 20% by giving them an additional
fixed amount of 7 Euros.
3. Thermos Treatment: workers received a thermos bottle worth 7 Euros, wrapped in transparent
gift wrap.
4. Price Tag Treatment: same as Thermos treatment, only the flask’s market price was explicitly
mentioned and marked with a price tag.
5. Choice Treatment: workers were given the choice between receiving the 7 Euros or the Thermos.
The Thermos was presented as in price tag treatment.
6. Origami Treatment: same as money treatment, only the cash was folded into an origami shape.
In the Thermos treatment, the flask was offered immediately with the announcement, while in the
money treatment the 7 Euro bonus was given together with the rest of the earned wage. To control for
potential timing confounding, had an additional Money Upfront treatment and found no significant
performance difference between Money and Money Upfront treatments.
Main results:
6
• Money treatment increases productivity by 5% on average, but effect is not statistically significant
• The Thermos treatment increases productivity significantly by 25%
• Price-tag treatment has similar results as Thermos treatment thus showing how uncertainty on
market price of gift does not account for the treatment effects
• In choice treatment more than 80% chose the cash gift indicating that the gift in kind is unlikely
to be in line with their preferences.
• Output was 25% higher in choice treatment than in baseline treatment; also substantially higher
than in money treatment despite most workers opting for the cash gift. This shows that simply
giving people the option of a gift can trigger reciprocation, even if they do not actually want
that gift!
• Origami treatment resulted in 30% higher productivity, showing that people are reciprocating
the effort of making the origami, rather than the cash itself.
4. Why did they add the “Origami” treatment?
This allowed them to compare two gifts with exactly the same objective value, where the only difference is clearly due to effort/positive intentions. Individuals seem to reciprocate intention, thought,
or effort behind a gift, rather than the gift itself.
7