EC989 Behavioural Economics. Sketch solutions for Class 2

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1 EC989 Behavioural Economics Sketch solutions for Class 2 Neel Ocean (adapted from solutions by Andis Sofianos) February 15, 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 = i p i u(x i ) (1) 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

2 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 if x 0 v(x) = λ( x) β if x < 0 (2) 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) = p γ [p γ + (1 p) γ ] 1/γ, w (p) = p δ [p δ + (1 p) δ ] 1/δ (3) Therefore, calculating the value of risky prospects takes the form: V = i w(p i )v(x i ) (4) 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 positively related to wage increases. That is, when wages go up in future relative to today, you should reduce your working hours today and instead work those hours in future. This would maximise your overall income. In formal terms, this means the elasticity of intertemporal substitution is positive. 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. Us- 2

3 ing NYC taxi drivers helps with this as cab drivers face correlated wages within a day (weather, subway breakdowns, day-of-the-week effects, conventions etc.) but uncorrelated wages across days. Taxi drivers are free to choose the number of hours to work. In the paper they estimate the EIS to be around -1, which contradicts predictions generated by traditional labour supply models. 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 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. 3

4 Result: PGR for the entire year is found to be 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 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 Utility and Subjective Well-being 1. How would you argue that indices of SWB contain useful information for economics? Indices of SWB have been found to correlate with objective measures like for example heartbeat, income, sociability, self-reported health, sleep quality, personality, and physical evidence of affect like smiling or laughing. 2. According to Benjamin et al., to what extent would you say that SWB and Utility coincide? In Benjamin et al (2012) they directly try to examine the presence of discrepancy between SWB and preferences. To do so they devised 13 hypothetical scenarios in which they ask participants which of two options would provide higher SWB, and which they would actually choose, given the option. There were three different forms of SWB that were elicited: Life satisfaction: Between these two options, which do you think would make you more satisfied with life, all things considered? 4

5 Happiness with life as a whole: Between these two options, taking all things together, which do you think would give you a happier life as a whole? Between these two options, during a typical week, which do you think would make you feel happier? On average, 83% of choices matched what people thought would give them higher SWB. A common violation of this was observed when income was higher, but some qualitative factor was lower, in one of the options. People tend to choose the higher income option, but feel it would give less SWB than the other option. When SWB is controlled for, the other main factors that influence choice are: 1. Family happiness 2. Social status 3. Purpose 4. Control over life Overall, the paper finds that SWB is the strongest explanatory factor for choice by far. Hence, it is a good proxy for choice utility. 3. Can you argue why adaptation and sensitivity to relative income are problematic when one wants to consider SWB as a proxy for utility? Hedonic adaptation is the finding that people s levels of well-being seem to revert back to some sort of baseline level over time, after some large shock occurs. Started with Brickman et al (1978), but subsequent studies have confirmed some level of adaptation does occur. Full adaptation would render well-being measures meaningless as a proxy for utility, but generally this does not seem to be the case. Blanchflower and Oswald (2004) have found that relative income can actually explain as much or more of the variation in happiness data than absolute income. Size of effect depends on which group you compare your income to (bigger when you consider those in the top quintile). The classic notion of utility in economics prescribes that context should not affect your valuation for something, 5

6 and that this valuation should not change over time. If relative comparisons are important, then this complicates matters when attempting to relate utility to SWB. 6