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### lec19

Course: ECON 134A 62360, Spring 2012
School: UC Irvine
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Word Count: 686

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1 Prospect Question theory has the following features Loss aversion. v(-x) &lt; - v(x) where x&gt;0 diminishing sensitivity for gains and for losses. It implies risk aversion for gains and risk loving for losses. overweighing small probabilities and underweighing large probabilities. Thus explains lottery tickets and insurance. Answer: D Question 2 Objects of choice are (x, p; y, q) that deliver a...

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1 Prospect Question theory has the following features Loss aversion. v(-x) < - v(x) where x>0 diminishing sensitivity for gains and for losses. It implies risk aversion for gains and risk loving for losses. overweighing small probabilities and underweighing large probabilities. Thus explains lottery tickets and insurance. Answer: D Question 2 Objects of choice are (x, p; y, q) that deliver a gain x> 0 with probability p and a loss y<0 with probability q. With the remaining probability 1 p q, the prospect (x, p; y, q) delivers the status quo (zero gain). The utility of such prospect is V (x, p; y, q) = (p)v(x) + (q)v(y) where is the weighting function and v is the value function. Question 3 0.00005*v(10000) 0.99995*v(-1) < 0 Lottery ticket will not be bought. It would require a severe distortion of small probabilities. 0.001*v(-900) +0.999 v(0) = -0.6 > v(-9) = -6 Again, probabilities need to be distorted. 0.5*v(25) 0.5v(-16) = 2.5 4 < 0. Loss aversion. Answer: C Prospects Theory Value Function Value of outcome Reference Point Losses Gains Lottery outcome risk aversion when outcomes are framed as gains risk seeking when outcomes are framed as losses Prospects Theory Weighting Function (p) Decision Weight 1 Underweighting of high probabilities 0.5 Overweighting of small probabilities 0 0 0.5 Stated Probability: P 1 Critique The prospect theory has been criticized for being too arbitrary (lack of normative status) determination of reference points violations of monotonicity violations of transitivity framing and Dutch books Endogenous determination of the reference points Koszegi and Rabin (06) the reference point is modeled as an expectation of some equilibrium. For example, it explains the absence of the endowment effect among experienced traders. They expect to trade any item they receive, hence, their reference point is unaffected by the initial allocation of objects. Monotonicity violations Empirical evidence suggests that (p) + (1-p) < 1 Then (x, p; y, 1-p) can be worse than (z, 1) even if z< x and z< y. To avoid such problems, Kahneman and Tversky introduce the editing stage that captures some procedural rationality. Editing Stage Combination: Prospects are simplified by combining the probabilities associated with identical outcomes. For example, the prospect (100, 0.3; 0.3) 100, is reduced to (100, 0.6) Segregation: a riskless component can be segregated from the risky part. For example, (100, 0.7; 150, 0.3) can be segregated into a sure gain of 100 and a prospect (50, 0.3). Likewise, the prospect (-200, 0.8, -300, 0.2) can be segregated into a sure loss of -200 and a prospect (-100, 0.2). Editing Stage simplification: outcomes and probabilities are often rounded. The prospect (99, 0.51) can be identified with (100, 0.5). Outcomes that are extremely improbable can be sometimes ignored altogether. detection of dominance : to compare (100, 0.1; 110, 0.9) and (100, 0.5; 105, 0.5), one can notice that the first one dominates the other. Violations of transitivity Lack of transitivity can be explained by regret (Loomes and Sugden 82, 87) random preference (Loomes and Sugden 95) Empirical Evidence People are not good at probabilities, especially in areas where they do not have much experience. Some empirical anomalies: California lottery requires matching six numbers between 1 and 51 in order to win the main prize. The odds are about 1 to 18M. Kahneman, Tversky, Slovic (82): people overestimate the odds by 10 times on average. conditional probabilities are even harder. A rare disease (1 in 1000) There is a test that is positive for all cases of the decease, and is also false positive for 5% of cases without the decease. A patient has a positive test. How likely is he to be sick? Biases in Conditional Judgements the law of small numbers (Tversky and Kahneman 71) people exaggerate small samples. Overinference: the degree to which people invest in a stock strongly depends on the recent performance of the stock. Benartzi (2001) gamblers fallacy is the opposite: gamblers tend to bet less on the numbers that won recently (Clotfelter and Cook 93) Can explain some day trading patterns. belief perseverance and confirmatory bias. People dislike changing their hypothesis, and can be inattentive to new information contradicting their hypotheses. They can make opposite conclusions based on the same evidence. This effect is called polarization. Confirmatory Bias Economic behaviors that can be explained by confirmatory biases naivete: persistent overestimation of self-control and underestimation of future temptations (health clubs and credit cards) overinvesting in the stock of ones own firm excess trading
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