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On the Heterogeneity, Stability and Validity of Risk Preference Measures

On the Heterogeneity, Stability and Validity of Risk Preference Measures. ESA, July, 2007. Measuring Preferences: Key Questions. Are risk preferences stable across elicitation measures? Since Slovic (1964), considerable evidence they are not

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On the Heterogeneity, Stability and Validity of Risk Preference Measures

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  1. On the Heterogeneity, Stability and Validity of Risk Preference Measures ESA, July, 2007

  2. Measuring Preferences: Key Questions • Are risk preferences stable across elicitation measures? • Since Slovic (1964), considerable evidence they are not • Do risk preferences vary systematically by subject characteristics in the same way across measures? • (Gender, age, income) • Does math ability affect elicited preferences? • Ability: Low/Medium/High Math Literacy • Are risk preferences stable across time? • Two Datasets: Test Data vs. Re-Test Data

  3. Motivation • Lots of folks are working on heterogeneity in risk preferences • (many of them are here) • There are lots of elicitation tasks, depending on the purpose of the study • Our purpose: to develop a simple, easy to administer measure of individual risk preferences that can be used to “predict” or better understand individual choices. • Household decisions, human capital choices, technology adoption

  4. Motivation, cont’d • We compare two lottery choice methods (more on these soon) • Non-student data set (collected for another purpose) • Subjects complete both risk elicitation measures • Survey, math literacy measure • Subset of pre-selected subjects participated in a retest

  5. The CSL Study • Purpose: study barriers to post-secondary acquisition of human capital • Data: lab experiments with non-traditional subject pool • ~900 adult participants in Canada (recruited, volunteers) • 102 sessions • Ages 18-54 years • Urban and Non-Urban samples • 156 participate in retest 6 months later • Average earnings: CAD$165 • Subjects paid for one decision chosen at random • 100 decisions: 40 time pref; 32 risk and ambiguity; 28 financing for post-secondary education, max = $1000 grant, $5000 guaranteed loan

  6. The CLS Study (cont’d.) • Two experiments to elicit risk preferences: • Holt-Laury (2002) • 10 binary choices between more and less risky gambles • Eckel-Grossman (2002) • Choice of 1 from set of 6 50/50 gambles • Discrete binary response data • 0 = less risky choice • 1 = more risky choice

  7. Holt-Laury Task

  8. Eckel-Grossman Task x

  9. Short Detour • FAQ: How do you code Eckel-Grossman as a set of binary choices? • Notice the gambles are ordered • Increase linearly in risk and return as you go down the table • One choice implies binary ordering

  10. This person chooses Gamble 3 This implies 5 binary choices: 2 is preferred to 1 3 is preferred to 2 3 is preferred to 4 4 is preferred to 5 5 is preferred to 6

  11. Comparison of Eckel-Grossman and Holt-Laury • H-L: varying probabilities, constant payoffs • E-G: constant probability, varying payoffs, all 50-50 gambles

  12. The Numeracy Measure • Subcomponent of the Educational Testing Service’s Adult Literacy and Lifeskills Survey (ALLS) • 31 problems involving the use of mathematics in real-life situations. • Low numeracy ≤ 1 standard dev. below average • High numeracy ≥ 1 standard dev. above average

  13. Model and Estimation • Given a CRRA utility function for money (M) parameterized by r U(M|r) = M1-r/(1-r) • Can construct a likelihood function L(r,,|Y) where  measures ‘noise’ in binary risk choices (Y) • r and  can also be made a function of observed characteristics of subjects

  14. Results 1: Does the Elicitation Instrument Affect Estimates?

  15. Estimates of CRRA Utility Function r = Coefficient of relative risk aversion m = Logit error parameter Differences significant at p = 0.000, 2(1) = 52.62

  16. Estimates of CRRA Utility (cont’d.) • Eckel-Grossman and Holt-Laury give significantly different estimates of r • “Ruler” affects measure! • H-L has higher error parameter than E-G • Why?

  17. Results II: How do demographics and ability affect estimates ? IIA: Effect on preference parameters IIB: Effect on parameters and errors IIC: Are parameters stable across instruments?

  18. Effect on preference parameters

  19. Effect on Preference Parameters (cont’d.) • Income, Age and Math Literacy are significant determinants (correlates) of preferences • Low Income: more risk averse • Young: less risk averse • Low math score: appear more risk averse • Could this be due to greater errors?

  20. Effect on Parameters and Errors

  21. Effect on Parameters and Errors (cont’d)

  22. IIB. Parameters and Errors (cont’d.) • People who are consistent are more risk averse and have less noise (randomness) • Young have less noise • Lower numerical literacy increases randomness in risk parameters; appear more risk averse • Females are more risk averse and have lower noise

  23. IIIC: Parameter stability across measures • Is the impact of gender, age, income similar across measures? • Is the impact of math literacy similar across measures?

  24. Distribution of noise parameter

  25. How good are predictions? • Calculate index: • n is the number of decisions for the task (5 for Eckel-Grossman and 10 for Holt-Laury) • ‘fraction’ variables represent the true and the predicted fraction of safe choices for decision i across all individuals. • Holt-Laury task has indices of 0.79, 0.88 and 0.92 for low, medium and high math literacy subjects • Eckel-Grossman instrument has a precision index of 0.81.

  26. IIC: Comparison • Women are substantially more risk averse in E/G; lower noise in both • Young have lower noise in both • Low math literacy affects noise in H/L only • Noise parameter is similar to E/G for H/L high literacy, but higher for med and especially low literacy • “Precision” is equivalent for high literacy, not for Medium or Low.

  27. Results III: Are Preferences Stable Across Time? IIIA. Eckel-Grossman IIIB. Holt-Laury

  28. IIIA. Stability of Eckel-Grossman

  29. IIIB. Stability of Holt-Laury

  30. Concluding Remarks • Question # 1: Are preferences stable across measures used to elicit them? • Answer: A qualified No. Elicitation instruments do matter to an extent • Question # 2: Do preference estimates by subject characteristics vary across measures? • Answer for Demographics: Yes

  31. Concluding Remarks (cont’d.) • Question #3: Are preference measures sensitive to math literacy: • Answer: Yes, H/L only • Question # 4: Are preference measures stable across time? • Answer: Yes. But E-G does “better” than H-L • Question #A1: Internal v. external validity?

  32. Validity: Correlations of risk measures with “real” decisions.

  33. Measuring preferences • Need to develop instruments that are appropriate for population, purpose • Finer screen v. accessibility tradeoff • For literate population, no tradeoff • For medium and low literate population, there may be a serious tradeoff! • Considerable precision is lost with more complex instrument • Important to take care with design for low-literacy populations

  34. Ex: Next gen of instruments (risk)

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