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 –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?

To get truthful responses, you can use BDM (Becker-DeGroot- Marschak) 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) Who is called risk-averse? (Con’d)

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)

Expected utility of lottery i is defined as following: Discrete choice estimation with Expected Utility Model 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 of lottery i is defined as following: Rank-dependent Utility Model 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 utility (Tversky and Kahneman, 1992) of lottery i is defined as: Cumulative Prospect Theory (Con’d) Source: Harrison and Rutstrom (2010)

This model is useful when a reference point is stochastic. Koszegi and Rabin (2006) Model 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: $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

First Certainty Equivalent MPL: CE1 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. 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 Q.Payment A Payment B Check one box for each row If the flippe d coin is... You rec eive... and If the flippe d coin is... You recei ve… Certain amou nt I definitel y prefer payment A I think I prefer payment A but I am not sure. I think I pref er payment B but I am not sure. I definitely prefer pay ment B 1Head$10 Tail$0$1 □□□□ 2Head$10 Tail$0$2 □□□□ 3Head$10 Tail$0$3 □□□□ 4Head$10 Tail$0$4 □□□□ 5Head$10 Tail$0$5 □□□□ 6Head$10 Tail$0$6 □□□□ 7Head$10 Tail$0$7 □□□□ 8Head$10 Tail$0$8 □□□□ 9Head$10 Tail$0$9 □□□□ 10Head$10 Tail$0$10 □□□□ 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 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. 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 Q.Payment A Payment B Check one box for each row If the flippe d coin is... You rec eive... and If the flippe d coin is... You recei ve… Certain amou nt I definitely prefer pay ment A I think I pref er payment A but I am not sure. I think I pref er payment B but I am not sure. I definitely prefer pay ment B 1Head$8 Tail$0$1 □□□□ 2Head $8 Tail$0$2 □□□□ 3Head $8 Tail$0$3 □□□□ 4 Head $8 Tail$0$4 □□□□ 5 Head $8 Tail$0$5 □□□□ 6 Head $8 Tail$0$6 □□□□ 7 Head $8 Tail$0$7 □□□□ 8 Head $8 Tail$0$8 □□□□

Certainty Equivalent MPLs and Single Question 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 WaveCE1CE < CE1: 36 subjects in wave 1CE2: 38 subjects in wave 1

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 "Measuring Utility by a Single-Response Sequential Method." Behavioral Science, 9(3), Butler, David J. and Graham C. Loomes "Imprecision as an Account of the Preference Reversal Phenomenon." The American Economic Review, 97(1), Cason, Timothy N and Charles Plott "Misconceptions and Game Form Recognition of the Bdm Method: Challenges to Theories of Revealed Preference and Framing." Available at SSRN Harrison, Glenn W and E Elisabet Rutström "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 "Risk Aversion and Incentive Effects." The American Economic Review, 92(5), Kőszegi, Botond and Matthew Rabin "A Model of Reference-Dependent Preferences." The Quarterly Journal of Economics, 121(4), Sprenger, Charles "An Endowment Effect for Risk: Experimental Tests of Stochastic Reference Points," working paper, Tversky, Amos and Daniel Kahneman "Advances in Prospect Theory: Cumulative Representation of Uncertainty." Journal of Risk and Uncertainty, 5(4), Wakker, Peter P Prospect Theory: For Risk and Ambiguity. New York: Cambridge University Press.