Yohei Mitani Institute of Behavioral Science University of Colorado, Boulder Nicholas Flores

1. A New Explanation of Hypothetical Bias: Subjective Beliefs about Payment and Provision Uncertainties Yohei Mitani Institute of Behavioral Science University of Colorado, Boulder Nicholas Flores Department of Economics & IBS University of Colorado, Boulder

2. BackgroundModel Design Results Implications $ Hypothetical Bias • Hypothetical Bias & Induced-values Hypo. Bias Questionnaire Experiment $Hypo. Payment $Actual Payment True Value Control Incentives No Incentives Financial Incentives often reduce variance but usually have no effect on mean performance. Carmerer & Hogarth (1999) J Risk Uncrtain Need to understand the relationship to True Value

3. BackgroundModel Design Results Implications Previous Findings • Meta-analysis by Murphy et al. (2005) ERE • Hypo. Payment > Real Payment • Note that these studies compare only b/w payments, do not compare them to true value. • Values of public goods are unobservable • Induced-value Test of Hypo. Bias • Induced-value experimental design allows us to observe/control true value. • No Evidence of Positive Hypo. Bias.

4. BackgroundModel Design Results Implications Motivation • No Systematic Explanation • Underling causes are not sufficiently understood. • Clarifying the causes is needed for mitigation. • This Paper Aims • To provide a systematic explanation for the results of hypo. bias.

5. BackgroundModel Design Results Implications Our Contributions • Payment and Provision Uncertainties • Introducing the probabilities of payment and provision to a threshold public goods game. • Investigate the Relative Probabilities • Providing a closer look at how the upper bound of a subject’s contribution changes depending on those probabilities. • Induced-value Experimental Test • Using a lab exp. design that varies the probabilities of payment and provision as treatments. • Finding • Relative probabilities explain the causes of hypo. bias.

6. Background Model Design Results Implications Discrete Public Project • Discrete Public Project • Voluntary contribution for a public project. • A threshold level of total contributions is required to provide the project. • Payoffs (PPM) • Provided: Income y – Contribution ci + Value vi • Not Provided: Income y • A threshold public goods experiment with continuous contribution, money back guarantee, no rebate and heterogeneous induced-values.

7. Background Model Design Results Implications Subjective Beliefs • Key Economic Issue: Payment & Provision • Hypothetical Natures in Stated Preference • Payment Uncertainty: whether payment is coercive • Provision Uncertainty: whether the project is provided • Subjective Beliefs • Respondents might form their subjective belief about payment & provision uncertainty when stating their values. • Decision-makings could be made based on their subjective beliefs.

8. Background Model Design Results Implications Probability Space • Probability Space • Define subjective beliefs as a joint distribution of payment & provision. Four Outcomes not only: {Pay, Provide}; {Not Pay, Not Provide} but also: {Pay, Not Provide}; {Not Pay, Provide}

9. Background Model Design Results Implications Model Specification • Expected Utility (if project passes: Σj cj > PP) {Pay, Pro} {Pay, Not Pro} {Not Pay, Pro} {Not Pay, Not Pro} Risk-neutral Case

10. Background Model Design Results Implications Theoretical Predictions • Upper Bound of a Subject’s Contribution • Option Price (ex ante WTP for project) • Effect of Subjective Probability Risk-neutral case

11. Background Model Design Results Implications Upper Bound Numerical Prediction • Under our Experimental Setting • Standard constant relative risk-aversion utility function With Equal Probabilities Effect of Provision Effect of Payment Purely Real Purely Hypothetical Risk-neutral (r=0)

12. Background Model Design Results Implications Experimental Design • Laboratory Designed for Economic Experiments • Subject Pool: 90 general public individuals • Induced-values • Induced-value was assigned to each subject. • Subjects were told the amount varies across individuals but not told the range & the frequency of values. • Subjects know only their own values. • Probabilities Pairs (experimental treatments) • A pair of two prob. was assigned to the group. • Two prob. were common knowledge. • 19 experiment treatments • 19 pairs were used from combinations of {0, .25, .5, .75, 1} • Within-subjects: Every subject participated in 11or14 choices.

13. Background Model Design Results Implications Experimental Design • Provision Rule • Two-stage Provision Rule was employed. • Stage 1: • A contribution decision like “how much would you contribute for a public project that provides you a value shown in your value card?” after the probabilities of payment and provision were announced to the group. If total contributions exceed the preannounced threshold, the project passes and Stage 2 comes. • Stage 2: • A computer decided whether subjects had to pay their contributions stated in stage 1 and whether subjects could receive their value, depending on the preannounced probability pair.

14. Background Model Design Results Implications Aggregate Level Results • Average Observed Contributions Negative Effect on Contributions Positive Effect on Contributions Our Benchmark Real Contribution

15. Background Model Design Results Implications Individual Level Analysis • Econometric Analysis Significant Negative Effects Significant Positive Effects

16. Background Model Design Results Implications With Equal Probabilites • A Case of Ppay = Ppro Observations are consistent with contributions made by risk-averse subjects in our theoretical predictions.

17. Background Model Design Results Implications Explanation of Hypo. Bias • Positive Hypothetical Bias occurs • if the relative probability satisfies that prob. of payment is greater than prob. of provision in the hypothetical payment decisions. • Many previous studies succeed to control whether payment is coercive; whereas, they often fail to control the provision-side uncertainty. Real Decision Provision-side Uncertainty Hypothetical Decision Payment-side Uncertainty

18. Background Model Design Results Implications Explanation of Hypo. Bias • No Hypothetical Bias occurs • if the relative probability satisfies that prob. of payment equals prob. of provision in the hypothetical payment decisions. • Well-controlled experiments like induced-value experiments wherein experimenters could control both payment & provision sides equally. Real Decision Provision-side Uncertainty Hypothetical Decision Payment-side Uncertainty

19. Background Model Design Results Implications Implications for Mitigation • Ex Ante Mitigation of Hypo. Bias • It will be important to control both payment & provision sides in the same way. • It should be designed so as not to have the worst & best outcomes. • Consequentiality is of course critical. • Ex Post Mitigation of Hypo. Bias • Measuring the subjective probabilities might allow us to calibrate ex-post hypothetical & real values.

20. Thank you for your attention. Yohei Mitani Contact Information Email:mitani@colorado.edu Web:http://homepage3.nifty.com/ymitani/

21. Upper Bound Numerical Prediction • Risk-averse Case (r = 0.9)

22. Background Model Design Results Implications Subjective Beliefs • Subjective Beliefs • Respondents might form their subjective belief about payment & provision uncertainty when stating their values. • Decision-makings could be made based on their subjective beliefs. • Probability Space • Define subjective beliefs as a joint distribution of payment & provision.

23. Background Model Design Results Implications Experimental Design • Provision Rule • Two-stage Provision Rule was employed.