Measuring and Estimating Risk Preferences
February 21, 2013
Younjun Kim
Outline
• Measuring risk preferences
– Rankings of risk preferences: rough vs. exact
– Who is called risk-averse?
– Elicitation methods
• Estimating risk preferences
– Interval regression
– Discrete (binary) choice estimation
• Utility Models
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Expected Utility Model
Rank-Dependent Utility Model
Cumulative Prospect Theory
Stochastic reference-dependent utility Model (Koszegi and Rabin, 2006)
Application: bias in Multiple Price List elicitation
• My know-how about paper-and-pencil survey
• References
Rankings of risk preferences: rough vs. exact
• If you want rough rankings of subjects’ risk preferences, even a
simple risk preference question is okay.
– eg. health-related behaviors (smoking, drinking, vaccination and BMI) and risk
preferences
– External validation
• If you want exact rankings of subjects’ risk preferences, you need
to ask more questions or use more complicated elicitation
method.
– Eg. group differences of risk preferences (eg. gender and age)
– In this case, individual risk preference can be assumed to be a function of
gender and age.
Who is called risk-averse?
• Q1) Which payment do you prefer?
– Payment A: $8 if a flipped coin is a head, and $2 if the coin is a tail
– Payment B: $10 if a flipped coin is a head, and $0 if the coin is a tail
• Suppose that person A has chosen payment A, and that person B
has chosen payment B. Who is more risk-averse?
• Q2) Which payment do you prefer?
– Payment A: $8 if a flipped coin is a head, and $2 if the coin is a tail
– Payment B: $10 if a flipped coin is a head, and $1 if the coin is a tail
– Payment C: $12 if a flipped coin is a head, and $0 if the coin is a tail
• Suppose that person A has chosen payment A, and that person B
has chosen payment B. Who is more risk-averse?
Who is called risk-averse? (Con’d)
• Q3) At least how much would you accept in exchange for the
following lottery ticket?
– Lottery ticket: $8 if a flipped coin is a head, and $2 if the coin is a tail
• Suppose that person A says $2, and that person B says $3. Who
is more risk-averse?
• Can you believe subjects’ responses?
Who is called risk-averse? (Con’d)
• To get truthful responses, you can use BDM (Becker-DeGrootMarschak) method or Multiple Price List design.
• Subjects may not understand how the BDM method works.
Who is called risk-averse? (Con’d)
Source: Cason and Plott (Working
paper, 2012)
Who is called risk-averse? (Con’d)
• Multiple price list design is easier to understand than the BDM
method, but you need to ask many questions.
Source: Sprenger (Working paper, 2010)
Elicitation methods
• Multiple Price List design
– Certainty equivalent, probability equivalent, and Holt and Laury (2002)
• Random Lottery Pair design
• Ordered Lottery Selection design: Question 2
• BDM (Becker-DeGroot-Marschak, 1964) designs
Elicitation methods (Con’d)
• Elicitation in Holt and Laury (2002) is commonly used in many
studies, which is somewhat more complicated than the ordered
lottery selection design.
Estimating risk preferences: Interval regression
• A dependent variable is an interval at an option where a subject
switches from option A to option B.
Source: Holt and Laury (2002)
Discrete choice estimation with Expected Utility Model
• Expected utility of lottery i is defined as following:
• Choice probability is defined as below (here we use Probit):
• Log-likelihood function is:
• For STATA code, refer to Appendix F in Harrison and Rutstrom
(2008).
Rank-dependent Utility Model
• Rank-dependent Utility of lottery i is defined as following:
Source: Harrison and Rutstrom (2008)
Rank-dependent Utility Model (Con’d)
Source: Wakker (2010)
Rank-dependent Utility Model (Con’d)
Source: Wakker (2010)
Rank-dependent Utility Model (Con’d)
Source: Wakker (2010)
Rank-dependent Utility Model (Con’d)
Source: Wakker (2010)
Rank-dependent Utility Model (Con’d)
Source: Wakker (2010)
Cumulative Prospect Theory
Source: Wakker (2010)
Cumulative Prospect Theory (Con’d)
Source: Wakker (2010)
Cumulative Prospect Theory (Con’d)
• Cumulative Prospect Theory utility (Tversky and Kahneman, 1992)
of lottery i is defined as:
Source: Harrison and Rutstrom (2010)
Koszegi and Rabin (2006) Model
• This model is useful when a reference point is stochastic.
Source: Sprenger (working paper, 2010)
Application: Bias in Multiple Price List Elicitation
Payment A:
50% chance of
winning $10, and
50% chance of
winning $0
Payment B:
$3
Payment A:
50% chance of
winning $10, and
50% chance of
winning $0
Payment B:
$1
Payment A:
50% chance of
winning $10, and
50% chance of
winning $0
Payment B:
$2
Payment A:
50% chance of
winning $10, and
50% chance of
winning $0
Payment B:
$3
First Certainty Equivalent MPL: CE1
Q. Which payment do you prefer below?
- Payment A: $10 if the flipped coin is a head, and $0 if the flipped coin is a tail
- Payment B: $3
I definitely prefer payment
A
I think I prefer payment A but I
am not sure.
I think I prefer payment B but I
am not sure.
I definitely prefer payment
B
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Q.
1
2
3
4
5
6
7
8
9
10
If the flipp
ed coin is..
.
Payment A
You rec and If the flipp
eive...
ed coin is..
.
You recei
ve…
Head
Head
Head
Head
Head
Head
Head
Head
Head
Head
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Tail
Tail
Tail
Tail
Tail
Tail
Tail
Tail
Tail
Tail
Payment B
Certain amo
unt
$1
$2
$3
$4
$5
$6
$7
$8
$9
$10
Check one box
I definite I think I prefer
ly prefer payment A bu
payment t I am not sur
A
e.
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for each row
I think I pr I definitel
efer payme y prefer p
nt B but I a ayment B
m not sure.
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Note that the table is based on Andreoni and Sprenger (AER, Forthcoming), and that the four
response options come form Butler and Loomes (AER, 2007)
Second Certainty Equivalent MPL: CE2
Q. Which payment do you prefer below?
- Payment A: $8 if the flipped coin is a head, and $0 if the flipped coin is a tail
- Payment B: $4
I definitely prefer payment
A
I think I prefer payment A but I
am not sure.
I think I prefer payment B but I
am not sure.
I definitely prefer payment
B
□
□
□
□
Q.
1
2
3
4
5
6
7
8
If the flipp
ed coin is..
.
Payment A
You rec and If the flipp
eive...
ed coin is..
.
You recei
ve…
Head
Head
Head
Head
Head
Head
Head
Head
$8
$8
$8
$8
$8
$8
$8
$8
$0
$0
$0
$0
$0
$0
$0
$0
Tail
Tail
Tail
Tail
Tail
Tail
Tail
Tail
Payment B
Certain amou
nt
$1
$2
$3
$4
$5
$6
$7
$8
Check one box for each row
I definitel I think I pr I think I pr I definitel
y prefer p efer payme efer payme y prefer p
ayment A nt A but I nt B but I a ayment B
am not sur m not sure.
e.
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Certainty Equivalent MPLs and Single Question
CE1: 36 subjects in wave 1
CE2: 38 subjects in wave 1
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
$1 $2 $3 $4 $5 $6 $7 $8 $9 $10
$1
$2
$3
$4
$5
$6
$7
$8
Note: Proportions of lottery choices in each decision in MPL (Diamond) and in the
selected single question (Square)
P-values of Wilcoxon Signed-ranks test
Wave
CE1
CE2
1
0.008
<0.001
2
0.006
0.004
3
0.058
0.133
Know-how about paper-and-pencil survey
• Pretesting
– Missing responses
– Fine-tuning of questions
– Pre-analysis
• Recruitment and compensation
References
•
•
Becker, G. M.; M. H. DeGroot and J. Marschak. 1964. "Measuring Utility by a
Single-Response Sequential Method." Behavioral Science, 9(3), 226-32.
Butler, David J. and Graham C. Loomes. 2007. "Imprecision as an Account of the
Preference Reversal Phenomenon." The American Economic Review, 97(1),
277-97.
•
•
•
•
•
•
Cason, Timothy N and Charles Plott. 2012. "Misconceptions and Game Form
Recognition of the Bdm Method: Challenges to Theories of Revealed
Preference and Framing." Available at SSRN 2151661.
Harrison, Glenn W and E Elisabet Rutström. 2008. "Risk Aversion in the
Laboratory," J. C. Cox and G. W. Harrison, Research in Experimental
Economics. Bingley: Emerald Group Publishing Limited,
Holt, Charles A. and Susan K. Laury. 2002. "Risk Aversion and Incentive Effects."
The American Economic Review, 92(5), 1644-55.
Kőszegi, Botond and Matthew Rabin. 2006. "A Model of Reference-Dependent
Preferences." The Quarterly Journal of Economics, 121(4), 1133-65.
Sprenger, Charles. 2010. "An Endowment Effect for Risk: Experimental Tests of
Stochastic Reference Points," working paper,
Tversky, Amos and Daniel Kahneman. 1992. "Advances in Prospect Theory:
Cumulative Representation of Uncertainty." Journal of Risk and Uncertainty,
5(4), 297-323.
•
Wakker, Peter P. 2010. Prospect Theory: For Risk and Ambiguity. New York:
Cambridge University Press.