Topic. Transition to the European Union, and conversion to the euro: a nice academic spin-off!

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 13, 2004, CERGE-EI, PraguePeter P. Wakker

(& Veronika Köbberling, Christiane Schwieren)

Topic. Transition to the European Union, and conversion to the euro: a nice academic spin-off!Allows for experimental test of differing views on the utility of money by psychologists and economists.

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Classical economic assumption: diminishing marginal utility.Very natural assumption:1st $ spent on most valuable thing.2nd $ on second-most valuable thing. Etc.Utility is concave (= accelerated downward).

$

Utilityof $

Under expected utility: gives risk aversion.

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Different assumption in prospect theory/psychology: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.

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Views so diametrically opposed: How can this be?

Answer: Because they focus on 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).

If only perception of quantity then reflection hypothesis: U for losses mirrors U for gains,

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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:

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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), Dickhaut et al (2003), 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).

7Purpose of our research:Empirically disentangle in utility of $:(a) Economic intrinsic value;(b) Psych. numerical sensitivity ("money illusion").

Importance of above disentanglement: 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.

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intr

insi

c va

lue

nominal value

€x

€40x

How separate the two factors?Hard because they covary.

intrin

sic-v

alue

effe

cts a

nd/o

r

num

erica

l effe

cts?

com

mon

findin

g

Arrow: in direction of increasing RRA

9Might try to compare different currencies: BF 2000 vs Dfl. 100, and BF 2000 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. 2001versusEuro's in May 2002 in Belgium.We chose Belgium, because: - Conversion factor (BF 40 = € 1) round, - and big.(Czech Republic: conversion factor 30 … !?!? )

Lucky thing:€ best accepted in Belgium (Eurobarometer)

10BF € can separate effects as follows:

BF40x

intrinsic value effect under constant numbers

numerical effect under constant intrinsic value

intr

insi

c va

lue

nominal value

€x

€40x

com

mon

findin

g

Question. Why ascribe effects beyond intrinsic value to nominal value? Aren’t there many other effects!?

11Other 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").

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Our exact empirical hypotheses: explained later.Better to first describe stimuli.Then our hypothesis.Then (rest) of experimental plan.Then … etc. (results, conclusion).

600 BF 0

Proba-bility

Gain

1 2 3 54 6 7 8 9 10 11 12 13 14 15 16 17 18 20 19

20

15

20

5

Lottery:

Sure Amount : 400 BF

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Example of choice for BF, small stakes:

600 BF 0

Proba-bility

Gain

1 2 3 54 6 7 8 9 10 11 12 13 14 15 16 17 18 20 19

20

15

20

5

Lottery:

Sure Amount : 400 BF

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Example of choice for BF, small stakes:€ matching numerically:

€

€

600 BF 0

Proba-bility

Gain

1 2 3 54 6 7 8 9 10 11 12 13 14 15 16 17 18 20 19

20

15

20

5

Lottery:

Sure Amount : 400 BF

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Example of choice for BF, small stakes:€ matching in value:

€

€

15

10

16

Now, having explained shape of stimuli, let’s go to our research plan in concrete terms.

LBF(BFx)

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numerical effect under constant intrinsic value;

in

trin

sic

valu

e

effe

ct u

nder

con

-

stan

t nu

mbe

rs

numerical effect under constant intrinsic value;

com

mon

ly

obse

rved

effe

ct

H€(€x) HBF

(BF40x)

nominal value

intr

insi

c va

lue

L€(€/40)

com

mon

ly

obse

rved

effe

ct

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.

Common finding: RRA increases with (Laury&Holt’02, Harri- son et al’03,’04).

600 BF 0

Proba-bility

Gain

1 2 3 54 6 7 8 9 10 11 12 13 14 15 16 17 18 20 19

20

15

20

5

Lottery:

Sure Amount: 400 BF

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BF, small stakes:

24000 BF

16000 BF

large

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Experimental Procedures

Between-subject 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!

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.

Instructions to Students (Flamish language corrected by Myriam Welkenhuysen)

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Guess odd/ even, (or nr.

20)

choose numbers 20

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We used a 20-sided die.

gues-sed wrongCross

out a choice on 7 pages

gues-sed right

receive nothing

pagenr. chosen through drawing of card chose

sure amount

Receive sure amount

guessed wrong

chose pros-pect

gues-sed right

receive nothing

receive big prize

throw die

throw die

implementation of real incentives

Implementation of real incentives

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TABLE 1. PERCENTAGES OF SAFE CHOICES

LBF HBF L€ H€ # risky

BF safe BF

% safe

risky BF

safe BF

%S risky €

safe €

%S risky €

safe €

%S

1 .50:300 20 14% .50:12000 800 09% .50:7.5 0.5 13% .50:300 20 16% 2 .05:220 200 100% .05:8800 8000 100% .05:5.5 5 100% .05:220 200 98% 3 .05:2000 120 60% .05:80000 4800 69% .05:50 3 65% .05:2000 120 62% 4 .25:800 200 70% .25:32000 8000 82% .25:20 5 73% .25:800 200 87% 5 .50:200 100 42% .50:8000 4000 80% .50:05 2.5 46% .50:200 100 58% 6 .75:600 400 30% .75:24000 16000 51% .75:15 10 40% .75:600 400 53% 7 .95:200 160 09% .95:8000 6400 20% .95:05 4 23% .95:200 160 27%

Total 46% 59% 51% 57% In the LBF treatment, the first choice was between BF 20 for sure (safe BF) and the lottery yielding BF 300 with probability 0.50 and nothing otherwise (risky BF). 14% chose the safe option (% safe); etc.

All stimuli

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S =

60.8%

S =

49.2%

S = 57.4%Results

S = 42.4%

S: % of safe choices; nominal value

intr

insi

c va

lue

intr

insi

c v.

eff

ect

numerical effect;

numerical effect;

com

mon

obse

rvat

ion;

com

mon

obse

rvat

ion;

LBF

H€ HBF

L€

t89 = –1.32, p = 0.90

numerical effect;

t88=0.79, p=0.22

t 86 =

3.6

7;

p <

0.00

1; ***

*: significant at 0.05; **: significant at

0.01; ***: significant at 0.001.

com

mon

obse

rvat

ion;

t 91 =

1.7

4,

p =

0.05

; *

t 86 =

2.9

5,

p

= 0

.002

; **

ANOVA confirmed everything, and showed no interaction between high/low intrinsic value versus BF/€.

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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”).