Prospect-Theory's Diminishing Sensitivity versus Economic's Intrinsic Utility of Money: How the Introduction of the Euro Can Be Used to Disentangle the Two Empirically September 1, 2004, 3rd Tilburg Symposium on Psychology and Economics: Games and DecisionsPeter P. Wakker(& Veronika Köbberling, Christiane Schwieren) Topic: An empirical test of the different views on utility of psychologists and economists.
Utility of $ $ 2 Classical economic assumption:diminishing marginalutility. Very natural assumption: 1st $ spent on most valuable thing. 2nd $ on second-most valuable thing. Etc. It is concave (= accelerated downward). Under expected utility: gives risk aversion.
3 Different assumption in prospect theory. Diminishing sensitivity. Outcomes are changes wrt reference point (denoted 0). For gains: U($20) – U($10) > U($120) – U($110), as economists have it. For losses: U(–$10) – U(–$20) > U(–$110) – U(–$120),opposite to economists’ views.
4 Views so diametrically opposed: How can this be? Answer: Because they concern different aspects. Economics: Intrinsic value of money. Prospect theory: perception of quantity (Kahneman 2003, Thaler 1985). Thaler: “… captures the basic psychophysics of quantity. The difference between $10 and $20 seems greater than the difference between $110 and $120, irrespective of the signs of the amounts in question” (p. 201).
5 Synthesis: Both aspects together in utility as observed (Fennema & van Assen 1999; Myagkov & Plott 1997; Shafir, Diamond, & Tversky 1997). For gains: Reinforce each other. “Overly” concave. For losses: Neutralize each other. Close to linear. Our hypothesis, iso reflection hypothesis, is Partial Reflection: For gains, utility is concave. For losses, utility is mildly convex, and closer to linear than for gains. Literature search confirmed it:
6 Supporting evidence for partial reflection: Abdellaoui (2000, p. 1506), Abdellaoui, Vossmann, & Weber (2003), Currim & Sarin (1989, p. 30), Davies & Satchell (2003), Fennema & van Assen (1999), Galanter & Pliner (1974, Power 0.45 for gains, 0.39 for losses), Laury & Holt (2000), and Loehman (1998). In line with this, stronger risk aversion for gains than risk seeking for losses: Battalio, Kagel, & Jiranyakul (1990, p. 32), Battalio, Kagel, & MacDonald (1985), Budescu & Weiss (1987, p. 193), Camerer (1989, Table 5), González-Vallejo, Reid, & Schiltz (2003, Fig. 1 and Table 2), Harless & Camerer (1994 p. 1281), Hershey & Schoemaker (1980, Table 3 and p. 409), Kühberger, Schulte-Mecklenbeck, & Perner (1999, pp. 216-217), Lopes & Oden (1999), Schneider & Lopes (1986), Smith et al. (2002, Figure 2), Wakker, Timmermans, & Machielse (2003), Weber & Bottom (1989, Exhibit 8). Unclear/balanced evidence: Hogarth & Einhorn (1990, Tables 2 and 4), Kahneman & Tversky (1979), Tversky & Kahneman (1992). Counterevidence: Fishburn & Kochenberger (1979, p. 511). In line with this, weaker risk aversion for gains than risk seeking for losses: Cohen, Jaffray, & Said (1987, Table 3), Levin, Irwin & Hart (2003).
7 • Purpose of our research: • Empirically disentangle in utility of $: • Economic intrinsic value; • Psych. numerical sensitivity ("money illusion"). What’s this got to do with the price of beans? For rational decisions: Take out numerical sensitivity! It’s irrational (we think). For empirical work: Numerical sensitivity - important for one-shot everyday decisions; - less important for learning/careful decisions (markets). P.s.: Myagkov & Plott (1997) / Kahneman & Tversky (1986) agree more than they think.
Arrow: in direction of increasing RRA intrinsic value common finding intrinsic-value effects and/or numerical effects? nominal value 8 How separate the two factors? Hard because they covary. €40x €x
9 Might try to compare different currencies: BF2000 vs Dfl.100, and BF2000 vs Dfl.2000? Cultural/economic differences, different people not in identical positions ... 2002 euro-conversion gave a unique opportunity. We considered Belgium francs in Dec. 2001 versus Euro's in May 2002 in Belgium. We chose Belgium, because: - Conversion factor (BF40 = €1) round, - and big. Lucky thing:€ best accepted in Belgium (Eurobarometer)
€40x intrinsic value intrinsic value effect under constant numbers common finding €x numerical effect under constant intrinsic value nominal value 10 BF € can separate effects as follows: BF40x Question. Why ascribe effects beyond intrinsic value to nominal value? Aren’t there many other effects!?
11 Other effects of Euro-change: linguistic changes, changes of coins and notes, loss of the national identity, arithmetic requirements, domestic versus joint currency, fear for nickle in the 1- and 2-Euro coins, etc. All affect absolute levels of utility; not, as far as we can see, relative risk aversion (RRA), the dependent variable of our study. Hypothesis that numerical perception of increased numbers enhances RRA:- Fetherstonhaugh et al. (1997)- Quattrone & Tversky (1988, p. 727, the "ratio- difference principle").
12 Our exact empirical hypotheses: explained later. Better to first describe stimuli. Then our hypothesis.Then (rest) of experimental plan.Then … etc. (results, conclusion).
13 Example of choice for BF, small stakes: Lottery: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Proba-bility 15 5 20 20 Gain 600 BF 0 Sure Amount : 400 BF
€ € € 14 matching numerically: Example of choice for BF, small stakes: Lottery: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Proba-bility 15 5 20 20 Gain 600 BF 0 Sure Amount : 400 BF
€ € € 15 matching in value: Example of choice for BF, small stakes: Lottery: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Proba-bility 15 5 20 20 Gain 600 BF 0 15 Sure Amount : 400 BF 10
16 Now, having explained shape of stimuli, let’s go to our research plan in concrete terms.
numerical effect under constant intrinsic value; intrinsic value intrinsic value effect under con- stant numbers commonly observed effect commonly observed effect numerical effect under constant intrinsic value; nominal value Common finding: RRA increases with (Laury&Holt’02, Harri- son et al’03,’04). 17 H€ (€x) HBF (BF40x) L€ (€/40) LBF (BFx) Traditional economists: increase due to ; not to . s: it is also (Fetherstonhaugh et al. 1997; Quattrone & Tversky 1988) We can distinguish! Our hypothesis: Both and amplify RRA.
18 BF, small stakes: large Lottery: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Proba-bility 15 5 20 20 Gain 600 BF 0 24000 BF Sure Amount: 400 BF 16000 BF
19 Experimental Procedures Inter-individual design; n = 45 for each treatment. Subjects recruited during breaks in meeting area of University of Diepenbeek. Interview took about 10 minutes pp. About 50% male; age 18-24; except 3, all Flamish. In total we paid about €900. Average pp. for low-payment: €2. Average pp. for high-payment: €8. Max €2000. Much for 10 minutes!
Instructions to Students (Flamish language corrected by Myriam Welkenhuysen) 20 Investigation of Opinions about Uncertain Payments In this investigation, we are interested in opinions of people about uncertain payments. We will present seven choice situations to you. In each you can choose between the certain receipt of an amount of money or the playing of a lottery. When playing the lottery you may win, with a certain probability, an amount of money, and you gain nothing otherwise. You can only gain money, and you will never lose money. There are no right or wrong answers for these questions, and they only concern your own preferences. Your preferences are what we are interested in! ·On each of the following seven pages there is an amount of money that you can gain with certainty and a lottery for money. You are asked each time what you would prefer most: receiving the sure amount of money or playing the lottery. Cross out your preference each time. It is next determined whether one of your choices will be played for real. For this purpose, you will be asked to guess whether an odd or even number shows up when you throw a 20-sided die. [For this purpose, you will be asked to guess which number will come up when you throw a 20-sided die.] ·If you guessed wrong, the experiment is over and you, unfortunately, did not gain anything. If you guessed right, then one of the choices that you crossed out will be played for real. ·You then draw one of seven numbered cards to determine from which page the choice you made will be played out for real. ·From the selected page you receive the sure amount of money if that is what you crossed out, and we play the lottery if that is what you crossed out. As said before, there are no right or wrong answers, and we are interested in your own preferences. It is also favorable for yourself to cross out your preferred option at each page. After all, if that page is selected, then we really carry out what you crossed out there.
Cross out a choice on 7 pages Guess odd/ even, (or nr. 20) pagenr. chosen through drawing of card 21 Implementation of real incentives We use a 20-sided die. guessed wrong gues-sed wrong receive nothing chose pros-pect receive nothing choose numbers20 throw die throw die receive big prize gues-sed right Receive sure amount gues-sed right chose sure amount implementation of real incentives
22 All stimuli
numerical effect; H€ HBF common observation; t91 = 1.74,p = 0.05; * intrinsic value common observation; intrinsic v. effect common observation; L€ LBF numerical effect; S = 42.4% nominal value *: significant at 0.05; **: significant at 0.01; ***: significant at 0.001. S: % of safe choices; 23 Results numerical effect; t88=0.79, p=0.22 S = 57.4% S = 60.8% t86 = 2.95, p = 0.002;** t86 = 3.67;p < 0.001;*** S = 49.2% t89 = –1.32, p = 0.90 ANOVA confirmed everything, and showed no interaction between high/low intrinsic value versus BF/€.
24 Discussion: Intrinsic value affected RRA (relative risk aversion). Numerical effect maybe didn't. (We may have lost some power because people were not yet used to €.) Conclusion: Good news for classical economics: This study is the first to confirm increasing RRA while avoiding numerical effect (“money illusion”).