Econ 440: Lecture 6 PDF

Econ 440: Lecture 6 Prof. Ragan Petrie Texas A&M University Sept 5, 2024 Prospect Theory Prospect Theory  Prospect Theory An Overview of Prospect Theory ▶ Prospect theory originally laid out by Kahneman and Tversky (1979) 1. Reference dependence:...

Econ 440: Lecture 6 Prof. Ragan Petrie Texas A&M University Sept 5, 2024 Prospect Theory Prospect Theory  Prospect Theory An Overview of Prospect Theory ▶ Prospect theory originally laid out by Kahneman and Tversky (1979) 1. Reference dependence: decision value determined by reference point 2. Loss aversion: losses loom larger than gains 3. Diminishing sensitivity: risk averse over gains, risk seeking over losses 4. Non-linear probability weighting ▶ We will talk about the first three pieces of the theory ▶ Probably the most well-known, well-cited contribution from behavioral economics  Prospect Theory Reference Dependence Reference Dependence  Prospect Theory Reference Dependence Motivating Example ▶ Consider the following decision problems: ▶ Problem 1: Would you rather win $900 for certain OR take a 90% chance of winning $1000? ▶ Problem 2: Would you rather lose $900 for certain OR take a 90% chance of losing $1000? Most people choose the certain option when only gains are possible but the risky option when only the losses are possible ▶ If you are always risk averse, expected utility theory says that you should choose certain option in both. Why?  Prospect Theory Reference Dependence Motivating Example, cont ▶ Another pairing: ▶ Problem 3: You have been given $1000. You are now asked to choose between these two options: 50% chance of winning another $1000 OR winning $500 for certain ▶ Problem 4: You have been given $2000. You are now asked to choose between these two options: 50% chance of losing $1000 OR losing $500 for certain ▶ According to expected utility theory, these are exactly the same problems. Why?  Prospect Theory Reference Dependence What is Reference Dependence? ▶ Reference dependence: when people evaluate alternatives by comparing them to a reference point ▶ Where could reference point come from? current wealth level; aspirational wealth level; expected outcome; social comparison ▶ So which one is reference point? ▶ Depends on context ▶ Theory is still weak here: determination of reference point gives an extra degree of freedom to the model another aspect to the model where you could have screwed up  Prospect Theory Reference Dependence Biological Roots of Reference Dependence “Our perceptual apparatus is attuned to the evaluation of changes or differences rather than the the evaluation of absolute magnitudes... The past and present context of experience defines an adaptation level, or reference point, and stimuli are perceived in relation to this reference point.” – Kahneman and Tversky (1979) ▶ Many perceptual systems in the brain evaluate differences rather than absolute values ▶ For example, the visual system ▶ Retinal cells respond to differences in light intensity  Prospect Theory Reference Dependence Reference-Dependent Utility ▶ Suppose consumption is evaluated relative to some reference point c r ▶ Then utility of consumption c depends on c r as well ▶ One useful formulation: utility depends on the difference between current consumption and reference level u(c|c r ) = v (c − c r ) ▶ In general, more complex formulations are possible Prospect Theory Loss Aversion Loss Aversion  Prospect Theory Loss Aversion Loss Aversion: Motivation ▶ Our motivating examples from earlier had another feature: “A salient characteristic of attitudes to changes in welfare is that losses loom larger than gains. The aggravation that one experiences in losing a sum of money appears to be greater than the pleasure associated with gaining the same amount.” – Kahneman and Tversky (1979) ▶ People attach more of a utility change to a decrease in consumption relative to the reference point than to an increase in consumption of the same magnitude ▶ Biological basis: Different brain regions are used to value losses and gains  Prospect Theory Loss Aversion Loss Aversion is Not Risk Aversion ▶ Thinking Fast and Slow is a bit imprecise about this point ▶ Turning down a positive expected value lottery is completely consistent with having risk-averse expected utility preferences ▶ Eg prefer not to take coin flip for +$150 or -$100 ▶ What is not consistent with classic expected utility is for the framing of the problem (and hence the reference point) to affect the apparent risk aversion  Prospect Theory Loss Aversion Loss Aversion: Field Evidence ▶ Suppose you are a cab driver in New York City ▶ It is an extremely cold day, so you make more per hour because demand for cabs is very high ▶ Should you work longer or shorter hours than you usually do? classic econ theory says work longer hours -the price of leisure time has gone up, so you should consume less leisure ▶ However, the data show that cab drivers’ hours are negatively correlated with hourly wages ▶ That is, they work long days when wages are low and go home early when wages are high ▶ One explanation: ▶ Cab drivers have reference or target income for the day ▶ Losses (ie not reaching income target) are very painful, so work longer on slow days to avoid missing target Source: Camerer et al (1999)  Prospect Theory Loss Aversion Incorporating Loss Aversion into the Theory ▶ We want losses to hurt more than gains of the same magnitude feel good ▶ One way to get this feature ▶ Recall u(c|c r ) = v (c − c r ) ▶ Let v (−x) = −λv (x) for some λ > 1 ▶ So then ( v (|c − c r |) c − c r > 0 u(c|c r ) = −λv (|c − c r |) c − c r < 0 if lambda is 2, losses hurt twice as much as gains feel good  Prospect Theory Diminishing Sensitivity Diminishing Sensitivity  Prospect Theory Diminishing Sensitivity Motivation ▶ In our examples of problem 1 and problem 2 earlier, we saw that people appear to be risk-seeking when they are in the loss domain (below the reference point) ▶ Psychological motivation: people become risk seeking in loss domain to increase likelihood of getting back to reference point ▶ However, tend to be risk-averse when gains are involved ▶ We call the combination of these features diminishing sensitivity because of the decreasing marginal impact of increasing a gain or loss farther from reference point ▶ Biological basis: Weber-Fechner law: The just-noticeable difference between two stimuli is proportional to the stimulus magnitude  Prospect Theory Diminishing Sensitivity Picture of Weber-Fechner  Prospect Theory Diminishing Sensitivity Incorporating This into the Theory ▶ Recall that risk-averse preferences require v (x) to be concave ▶ Conversely, risk-seeking preferences require v (x) to be convex ▶ One possible way to implement this: ▶ Let α ∈ [0, 1], β ∈ [0, 1] where α > β ▶ Utility is then ( r (|c − c r |)α c − cr > 0 u(c|c ) = −λ(|c − c r |)β c − cr < 0 ▶ This incorporatess all three features we’ve seen so far  Prospect Theory Diminishing Sensitivity Prospect Theory in One Picture Source: Kahneman and Tversky (1979)