An experiment on the influence of individual risk attitudes

byHermann Trenkel

Department for Food and Resource Economics

University of Bonn

FUR XII25.06.2006

Measurement of individual risk attitude• Lotteries are commonly

considered as a useful method to identify the risk attitude of individuals

• Subjects state their reservation price for a specified lottery

• Using the BDM-method monetary incentives are installed in a way which elicits real reservation prices if subjects act rational

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Measurement of individual risk attitudeHartog,Ferrer-i-Carbonell and

Jonker1 asked: “Among 10 people, 1000 guilders are disposed of by lottery. What is the most that you would be willing to pay for a ticket in this lottery?“ in two surveys with about 3600 paricipants.FUR XII

25.06.20061: Hartog et al. (2000): On a simple measure of individual risk aversion, tinbergen institute discussion paper TI2000-074/3

Measurement of individual risk attitudeIn a questionnaire in the Saturday

edition of Dutch newspapers, answered by 25.000 people, they included questions for lotteries with

• 1000 guilders are alloted among 5 people

• 5000 guilders are alloted among 10 people

• 1000 guilders are alloted among 100 people

• 1000.000 guilders are alloted among 100 people

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Measurement of individual risk attitudeEven though they didn´t give monetary

incentives or use any method like the BDM-method to elicit real reservation prices the results showed

• risk aversion is significantly lower for the self-employed

• risk aversion is falling with increasing income

• risk aversion is negatively related to wealth

• risk aversion is significantly reduced by schooling level

• Women have a substantially higher degree of risk aversion than men

• risk aversion increases with age

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Measurement of individual risk attitude• As they „…conclude that a simple

lottery question is a promising survey instrument to extract differences in risk attitudes among individuals“

• the lotteries questions are taken into my questionaire to extract risk attitudes– but we ask for € instead of guilders

• Conducting an adjacent game the hypothesis „individual risk aversion has a predictable influence on decisions in an uncertain context“ will be tested

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The game - participants• All participants are

students, most of them freshmen

• No monetary incentives are given

• Instead, questions and answers of last years exams were offered as award for participation

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The experimental game• In a paper and pencil game,

participants act as managers• Each round, they produce 10.000

items of a nonspecified good• The price for the good will be

randomly choosen from a known distribution

• The students have 2 choices:– they can produce for the random market price– they can sell their production (or parts of it) at a fixed contract price

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Price distribution

0%

5%

10%

15%

20%

25%

1 2 3 4 5 6 7 8 9 10 11

Price P(x) in €

contract priceproduction costs

The experimental game• Afterwards the „market price“ was

choosen by drawing a card from a deck of cards reflecting the distribution

• The game included 3 rounds• On 3 days 127 students took part

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2x

4x 6x 8x 10x 8x 6x 4x 2x

• the distribution now was left-skewed

• The game lasted 4 rounds• On 2 occasions 164 students

took part

The experiment – 1. repetition

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left skewed price distribution

0

5

10

15

20

25

2 3 4 5 6 7 8 9 10

€uro

%

Contract price =production costs

The experiment – test for consistency• As 3 lotteries offer the same prize

(1000 €) among different numbers of participants (5, 10 or 100), rationally the reservation price for a lottery with more participants cannot be higher as for a lottery with less participants

• Demanding the reservation price for lotterie 1 > lotterie 2 > lotterie 4 in the 2004 experiment only 63 (from 127) and in the 2005 experiment 113 (from 164) remain

• Most of the dropouts stated the same reservation price, i.e. 5 € for all lotteries

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The experiment – reservation prices

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lottery 2004 2005 all female

male

n 63 113 176 110 66

5/1000E(x) = 200

43,8 64,1 56,9 45,3 76,3

10/1000E(x) = 100

20,1 30,2 26,6 22,1 34,1

10/5000E(x) = 500

63,0 102 90,3 63,4 135,2

100/1000E(x) = 10

3,5 5,2 4,6 3,9 5,7

100/1MioE(x) = 10T

499 686 619 359 1053

0

100

200

300

400

500

600

700

800

0 2000 4000 6000 8000 10000 12000

E(x)

reserv

atio

n p

rice

The experiment – reservation price coefficientBy dividing the reservation prices for the lotteries by the expected values of the lotteries a Reservation Price Coefficient RPcoeff was calculated

For risk neutrality RPcoeff = 1, with increasing risk aversion it moves towards 0.

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RPcoeffvalueExpected

pricenreservatio

i i

i

5:_

_5

1

The experiment – reservation price coefficient

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Reservation Price coefficient

0

10

20

30

40

50

60

70

80

90

0,0-0,1

0,1-0,2

0,2-0,3

0,3-0,4

0,4-0,5

0,5-0,6

0,6-0,7

0,7-0,8

0,8-0,9

0,9-1,0

>1,0

RPcoeff (mean = 0,25)

freq

uen

cy (

n =

176

)

The experiment – core question and hypothesis• Is the RPcoeff as a measure

of individual risk aversion a predictor for actions in the game?

• Individuals with high risk aversion should contract a higher amount of their production

• individuals tending towards risk neutrality should sell on the free market

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The experiment – results

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00,20,40,60,8

11,21,41,61,8

0 20 40 60 80 100

contract %

RP

coef

f. →no evidence for any relation between the answers to the lotteries and the performance in the game

The experiment – new risk aversion measurement• A question to self-estimate

oneselfs risk-attitude was inserted

• It was used by FALK et al. (2005)1 with outstanding results

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Are You someone who accepts risks or do You avoid risk?

Avoid risk willing to take risk 0 1 2 3 4 5 6 7 8 9 10

1: FALK et al. (2000): Individual Risk Attitudes: New Evidence from a Large, Representative, Experimentally-Validated Survey

The experiment with monetary rewards• 4 training rounds, but now

contracts were only allowed for 100 % of the production each round

• 4 rounds with monetary rewards: 5 students would afterwards be randomly choosen and get their results payed out in 1/20 cents

• Instead of selling at a fixed contract price participants had to report their minimum price for selling the whole production

• Only the 30 % with the lowest offers would get a contract

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The monetary experiment - results

• Only 30 consistent participants

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Reservation Price Coefficient

Average Female Male

monetary (n = 30)

0,25110,2063 n = 11

0,2782 n = 19

previous (n = 176)

0,25040,2007n = 110

0,3332n = 66

The monetary experiment - results

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RPcoeff.

0

2

4

6

8

10

12

0,0-0,1

0,1-0,2

0,2-0,3

0,3-0,4

0,4-0,5

0,5-0,6

0,6-0,7

0,7-0,8

0,8-0,9

0,9-1,0

>1,0

RPcoeff (mean = 0,25)

freq

uen

cie

s n

= 3

0

The monetary experiment - results

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risk attitude self estimation

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10

Per

cen

t

female (mean = 4,73) male (mean = 5,05)

The monetary experiment - results

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0

0,2

0,4

0,6

0,8

1

0 1 2 3 4 5 6 7 8

self estimation

RP

co

eff

female male

The monetary experiment - results

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• Production costs = 72.000• Expected value = 84.000

1.round 2.round 3.round 4.round

market price 8 9 9 8

selling average

85349 85087 84890 82217

median 85000 84310 84000 81999

best contract 81999 82500 82000 81200

Minimum 72050 76000 79000 71000

Maximum 100000 99700 96000 95456

The monetary experiment - results

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71000

76000

81000

86000

91000

96000

101000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

RP coeff

sell

ing

pri

ce

1.round 2.round 3.round 4.round

The monetary experiment - results

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71000

76000

81000

86000

91000

96000

101000

0 2 4 6 8

risk attitude self estimation

elic

ited

sel

lin

g p

rice

1.round 2.round 3.round 4.round

The monetary experiment - results

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1.round 2.round 3.round 4.round

RPcoeff market

0,27 0,25 0,30* 0,29

RPcoeff contract

0,21 0,26 0,13* 0,14

Self est. market

4,77 4,67 5,14 5,00

Self est. contract

5,22 5,40 4,33 4,63

The monetary experiment - results

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76000

80000

84000

88000

92000

96000

100000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

RP coeff

sell

ing

pri

ce

best contract 3.round

Conclusions• Gender difference for risk aversion in

lotteries is confirmed • Predictive power of individual risk

aversion elicited from lottery reservation prices towards actions in a managerial game seems poor

• Instead of risk aversion it seems to be loss aversion: After the students accumulated money in 2 high priced rounds, they started to behave somewhat more consistent

• The only way to get a relation is to look the other way round: those, who act risk averse in the game are likely to be risk averse as well in the lottery questions

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Open questions

• Could different risk categories be a possible explanation?

• How to control for an effect of the term „contract“, as some of the students may have an attitude towards contracts?

• Is a game with several repetitions to complex?

• How to control for „terminal wealth“ effects?

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Thank You

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