Transcript document

An experiment on the
influence of individual
risk attitudes
by
Hermann Trenkel
Department for Food and Resource Economics
University of Bonn
FUR XII
25.06.2006
Measurement of
individual risk attitude
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• 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
Measurement of
individual risk attitude
Hartog,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.
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1:
Hartog et al. (2000): On a simple measure of individual
risk aversion, tinbergen institute discussion paper TI2000-074/3
Measurement of
individual risk attitude
•
•
•
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•
In 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
Measurement of
individual risk attitude
•
•
•
•
•
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•
Even though they didn´t give monetary
incentives or use any method like the BDMmethod to elicit real reservation prices the
results showed
risk aversion is significantly lower for the selfemployed
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
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
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• Conducting an adjacent game the
hypothesis „individual risk aversion has
a predictable influence on decisions in
an uncertain context“ will be tested
The game - participants
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• 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
The experimental
game
Price distribution
production costs
25%
20%
15%
10%
5%
0%
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contract price
• 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
1• 2
4
5 have
6 27choices:
8
9 10 11
The 3students
Price P(x)for
in €
– they can produce
the random market
price
– they can sell their production (or parts of it)
at a fixed contract price
The experimental game
• Afterwards the „market price“ was
choosen by drawing a card from a deck
of cards reflecting the distribution
2
x
4x
6x
8x 10x
8x
6x 4x
• The game included 3 rounds
• On 3 days 127 students took part
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2x
Theleftexperiment
–
1.
skewed price distribution
25 repetition
Contract price
%
20
15
10
5
=production costs
• the distribution now was leftskewed
• The game lasted 4 rounds
• On 2 occasions 164 students took
part
0
2
3
4
5
6
€uro
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7
8
9
10
The experiment – test
for consistency
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• 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
The experiment –
reservation prices
800
lottery
reservation price
700
n
600
500
5/1000
400
E(x) = 200
300
10/1000
200
E(x) = 100
100
10/5000
0
0
E(x) = 500
2000
100/1000
E(x) = 10
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100/1Mio
E(x) = 10T
2004
2005
all
female
male
63
113
176
110
66
43,8
64,1
56,9
45,3
76,3
20,1
30,2
26,6
22,1
34,1
63,0
102
90,3
63,4
135,2
4000
6000
8000
10000
12000
3,5
E(x)
5,2
4,6
3,9
5,7
499
686
619
359
1053
The experiment –
reservation price coefficient
By dividing the reservation prices for the
lotteries by the expected values of the
lotteries a Reservation Price Coefficient
RPcoeff was calculated
 5 reservation _ price i 
 
 : 5  RPcoeff
 i 1 Expected _ valuei 
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For risk neutrality RPcoeff = 1, with
increasing risk aversion it moves
towards 0.
The experiment –
reservation price coefficient
Reservation Price coefficient
frequency (n = 176)
90
80
70
60
50
40
30
20
10
0
0,0- 0,1- 0,2- 0,3- 0,4- 0,5- 0,6- 0,7- 0,8- 0,9- >
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,0
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RPcoeff (m ean = 0,25)
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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RPcoeff.
The experiment –
results
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
→no evidence for any relation
between the answers to the
lotteries and the performance in
the game
0
20
40
60
contract %
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80
100
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
Are You someone who accepts risks or do You avoid risk?
Avoid risk



0
1
2

3

4

5

6
willing to take risk




7
8
9
10
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1:
FALK et al. (2000): Individual Risk Attitudes: New Evidence from a Large,
Representative, Experimentally-Validated Survey
The experiment with
monetary rewards
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• 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
The monetary experiment
- results
• Only 30 consistent participants
Reservation Price Coefficient
Average
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monetary
(n = 30)
previous
(n = 176)
0,2511
0,2504
Female
Male
0,2063
n = 11
0,2007
n = 110
0,2782
n = 19
0,3332
n = 66
The monetary experiment
- results
frequencies n = 30
RPcoeff.
12
10
8
6
4
2
0
0,0- 0,1- 0,2- 0,3- 0,4- 0,5- 0,6- 0,7- 0,8- 0,9- >
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,0
RPcoeff (mean = 0,25)
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The monetary experiment
- results
risk attitude self estimation
Percent
40
30
20
10
0
1
2
3
4
5
female (mean = 4,73)
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6
7
8
9
10
male (mean = 5,05)
The monetary experiment
- results
1
RP coeff
0,8
0,6
0,4
0,2
0
0
1
2
3
4
5
self estimation
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female
male
6
7
8
The monetary experiment
- results
1.round
2.round
3.round
4.round
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
market price
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• Production costs = 72.000
• Expected value = 84.000
The monetary experiment
- results
selling price
101000
96000
91000
86000
81000
76000
71000
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
RP coeff
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1.round
2.round
3.round
4.round
0,9
elicited selling price
The monetary experiment
- results
101000
96000
91000
86000
81000
76000
71000
0
2
4
6
risk attitude self estimation
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25.06.2006
1.round
2.round
3.round
4.round
8
The monetary experiment
- results
RPcoeff
market
RPcoeff
contract
Self est.
market
Self est.
contract
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25.06.2006
1.round
2.round
3.round
4.round
0,27
0,25
0,30*
0,29
0,21
0,26
0,13*
0,14
4,77
4,67
5,14
5,00
5,22
5,40
4,33
4,63
The monetary experiment
- results
selling price
100000
96000
92000
88000
84000
80000
76000
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
RP coeff
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25.06.2006
best contract
3.round
0,8
0,9
Conclusions
FUR XII
25.06.2006
• 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
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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25.06.2006