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

June 10, 2004, Conference on Measuring Risk and Time Preferences; Peter P. Wakker

(& Veronika Köbberling, Christiane Schwieren)

Topic: An empirical test of the different views on utility of psychologists and economists.

Make yellow comments invisible.

ALT-View-O

Make yellow comments invisible.

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Throughout talk, use “wealth” as equivalent to intrinsic value

Throughout talk, use “wealth” as equivalent to intrinsic value

Psychologists have diferent ways of looking at things than economists. In particular, they look differently at utility than economists do. We think that this is because they look at different components. I will explain to you what these components are, why they are interesting, how we could measure them thanks to the introduction of the euro, and, finally, what we found.

Psychologists have diferent ways of looking at things than economists. In particular, they look differently at utility than economists do. We think that this is because they look at different components. I will explain to you what these components are, why they are interesting, how we could measure them thanks to the introduction of the euro, and, finally, what we found.

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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.It is concave (= accelerated downward).

$

Utilityof $

Under expected utility: gives risk aversion.

Each new $ brings less than the one before.

Each new $ brings less than the one before.

Copenh: skipCopenh: skip

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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.

Even, if diminishing sensitivity were the only thing, then losses would exactly mirror gains (perfect reflection).Posited in 1979, but refuted and weakened later.

Even, if diminishing sensitivity were the only thing, then losses would exactly mirror gains (perfect reflection).Posited in 1979, but refuted and weakened later.

You are more sensitive to changes close to the reference point than to changes remote from the reference point.

You are more sensitive to changes close to the reference point than to changes remote from the reference point.

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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).

Purchasing power, or how much goodness it can do to you.

Purchasing power, or how much goodness it can do to you.

Copenh: don’t read citation, just say

Copenh: don’t read citation, just say

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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.

Partial Reflection: For gains, utility is concave. For losses, utility is mildly convex, and closer to linear than for gains.

Literature search confirmed it:

Overly: Rabin …Overly: Rabin …

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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), 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").In particular: Test relative risk aversion (RRA) while

avoiding numerical sensitivity.

Above disentanglement important: 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: increasing RRA

Figure does not seek to be proportional.

Figure does not seek to be proportional.

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.

Lucky thing:€ best accepted in Belgium (Eurobarometer)

Probably say, but maybe skip (because explained later).:

Same values, different nrs.

Probably say, but maybe skip (because explained later).:

Same values, different nrs.

Same nrs, different values.Same nrs, different values.Copenhagen: skip first para

Copenhagen: skip first para

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!?

Figure does not seek to be proportional.

Figure does not seek to be proportional.

After last question:

You may wonder: if €x to BF40x gives difference, it may indeed be due to numerical effects. But, it may as well be due to something else. This change brings about so many changes, why could not one of the other changes cause the difference? We can never prove that this is no so. We can do our best though. We studied the literature on effects of the change of euro. There are many such, and they do affect utility. To the best of our knowledge, though, they do not affect our research interest, RRA. Numerical effects do seem to affect RRA, and we can give references for that. So, we can’t prove our claim, but at least, we give the best evidence we can.

After last question:

You may wonder: if €x to BF40x gives difference, it may indeed be due to numerical effects. But, it may as well be due to something else. This change brings about so many changes, why could not one of the other changes cause the difference? We can never prove that this is no so. We can do our best though. We studied the literature on effects of the change of euro. There are many such, and they do affect utility. To the best of our knowledge, though, they do not affect our research interest, RRA. Numerical effects do seem to affect RRA, and we can give references for that. So, we can’t prove our claim, but at least, we give the best evidence we can.

After BF40x don’t explain effects immediately but first click to let effects appear.

After BF40x don’t explain effects immediately but first click to let effects appear.

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").

Tell them that details, such as what RRA is, will come later.

Tell them that details, such as what RRA is, will come later.

Half a year went by, they got older, winter versus spring. Fortunately (!), no world-shocking, or Belgium-shocking, events occurred.

Half a year went by, they got older, winter versus spring. Fortunately (!), no world-shocking, or Belgium-shocking, events occurred.

Copenh: say first part of page in one sentence, and two refs in one sentence.

Copenh: say first part of page in one sentence, and two refs in one sentence.

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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:

Don’t worry if at first click nothing changes: was transition to p. 14. Is signal to tell the following: this (= p. 13, previous page) was basic reference treatment. Now come other treatments that replace BF by Euros.

Don’t worry if at first click nothing changes: was transition to p. 14. Is signal to tell the following: this (= p. 13, previous page) was basic reference treatment. Now come other treatments that replace BF by Euros.

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

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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).

HBF: Say that examples of stimuli haven’t yet been shown.

HBF: Say that examples of stimuli haven’t yet been shown.

For , use term “increases in wealth.”

For , use term “increases in wealth.”

On this page explain RRA.

Why is this a test of RRA? Then explain prediction of constant RRA, etc.

On this page explain RRA.

Why is this a test of RRA? Then explain prediction of constant RRA, etc.

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 Copenhagen: skipCopenhagen: skip

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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!

Copenhagen: skipCopenhagen: skip

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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Copenhagen: skipCopenhagen: skip

Guess odd/ even, (or nr.

20)

choose numbers 20

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We use 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 incentivesCopenhagen: skipCopenhagen: skip

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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 Copenhagen: very fast

Copenhagen: very fast

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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”).