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

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

Psychology's Diminishing Sensitivity versus Economic's Intrinsic Utility of Money: How the Introduction of the Euro Can Be Used to Disentangle the Two Empirically

May 7, 2004, Individual Decisions Conference; Peter P. Wakker(& Veronika Köbberling, Christiane Schwieren)

Make yellow comments invisible.

ALT-View-O

These two fields emphasize different aspects of utility. We now had a nice chance to isolate these two aspects, and so we did.

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

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).

Each new $ brings less than the one before.

Under expected utility: gives risk aversion.

Different assumption in prospect theory (= Luce’s rank- and sign-dependent utility).

Diminishing sensitivity.

Outcomes are changes wrt reference point.

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.

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

Even, if diminishing sensitivity were the only thing, then losses would exactly mirror gains (perfect reflection).

Posited in 1979, but refuted and weakened later.

How can these views be so diametrically opposed for losses?

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.

Synthesis: Both aspects together will determine utility as we observe it (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.

We replace the reflection hypothesis of prospect theory by the following hypothesis.

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

A literature search confirmed this hypothesis:

Overly: Rabin …

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).

- Purpose of our research:
- Empirically disentangle in utility of $:
- intrinsic value;
- numerical sensitivity ("money illusion").
- More precisely: Test relative risk aversion (RRA) while avoiding numerical sensitivity.

This disentanglement is important because:

For rational decisions: Take out numerical sensitivity! It’s irrational (we think).

For empirical work: Whereas numerical sensitivity may be important for one-shot everyday decisions, it becomes less so after learning and in markets that require careful decisions. On this point, Myagkov & Plott (1997) and Kahneman & Tversky (1986) may agree more than they seem to be aware of.

common finding

nominal value

8

How separate the two factors?

Hard because they covary.

Figure does not seek to be proportional.

€40x

intrinsic-value effects and/or numerical effects?

€x

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

Same values, different nrs.

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)

Same nrs, different values.

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:

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.

BF40x

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

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

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

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").

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

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

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

Now, having explained shape of stimuli, 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

(Holt & Laury 2002).

Common finding: RRA increases with

On this page explain RRA.

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

17

H€

(€x)

HBF

(BF40x)

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

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.

For , use term “increases in wealth.”

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

Experimental Procedures

Inter-individual design; n = 45 for each condition.

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.

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

All stimuli

H€

HBF

intrinsic value

common observation;

intrinsic v. effect

common observation;

L€

LBF

numerical effect;

nominal value

23

Results

numerical effect; t88=0.79, p=0.22

S = 57.4%

S = 60.8%

common observation; t91 = 1.74,p = 0.05; *

t86 = 2.95, p = 0.002;**

t86 = 3.67;p < 0.001;***

S = 49.2%

S = 42.4%

t89 = –1.32, p = 0.90

*: significant at 0.05; **: significant at 0.01; ***: significant at 0.001.

S: % of safe choices;

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

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, at least not bad, news for classical economics. This study is the first to have confirmed increasing RRA while avoiding/reducing the distortion due to numerical effect (“money illusion”).

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