NAREA Workshop 2009 @ Burlington, VT June 10, 2009 Yohei Mitani 1 Yohei Mitani Institute of Behavioral Science University of Colorado, Boulder Nicholas.

NAREA Workshop 2009 @ Burlington, VT June 10, 2009 Yohei Mitani

1

Yohei Mitani Institute of Behavioral Science

University of Colorado, Boulder

Nicholas Flores Department of Economics & IBS University of Colorado, Boulder

A New Explanation of Hypothetical Bias: Subjective Beliefs about

Payment and Provision Uncertainties


Hypothetical Bias

• Hypothetical Bias & Induced-values

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Financial Incentives often reduce variance but usually have no effect on mean performance.

Carmerer & Hogarth (1999) J Risk Uncrtain

ExperimentExperiment

$ Actual Payment

QuestionnaireQuestionnaire

$ Hypo. Payment

Hypo. Bias

Control Incentives No IncentivesTrue Value

$

Need to understand the relationship to True Value

Background Model 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.

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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.

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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.

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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.

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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.

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Probability Space

• Probability Space– Define subjective beliefs as a joint distribution

of payment & provision.

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Four Outcomesnot only: {Pay, Provide}; {Not Pay, Not Provide} but also: {Pay, Not Provide}; {Not Pay, Provide}



Model Specification

• Expected Utility (if project passes: Σj cj > PP)

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Risk-neutral Case

{Pay, Pro} {Pay, Not Pro}

{Not Pay, Pro} {Not Pay, Not Pro}



Theoretical Predictions

• Upper Bound of a Subject’s Contribution– Option Price (ex ante WTP for project)

• Effect of Subjective Probability

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Risk-neutral case



• Under our Experimental Setting– Standard constant relative risk-aversion utility function

Upper Bound Numerical Prediction 11

Risk-neutral (r=0)

PurelyReal

PurelyHypothetical

Effect of ProvisionEffect of

Payment

With Equal Probabilities



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.

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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.

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Aggregate Level Results

• Average Observed Contributions

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Our BenchmarkReal Contribution

Positive Effect on Contributions

Negative Effect on Contributions



Individual Level Analysis

• Econometric Analysis

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Significant NegativeEffects

Significant PositiveEffects



With Equal Probabilites

• A Case of Ppay = Ppro

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Observations are consistent with contributions made by risk-averse subjects in our theoretical predictions.



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.

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Real Decision

HypotheticalDecision

Provision-sideUncertainty

Payment-sideUncertainty



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.

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Real Decision

HypotheticalDecision

Provision-sideUncertainty

Payment-sideUncertainty



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.

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Thank you for your attention.

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Yohei Mitani

Contact Information Email: [email protected] Web: http://homepage3.nifty.com/ymitani/


• Risk-averse Case (r = 0.9)

Upper Bound Numerical Prediction 21


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.

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Experimental Design

• Provision Rule– Two-stage Provision Rule was employed.

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NAREA Workshop 2009 @ Burlington, VT June 10, 2009 Yohei Mitani 1 Yohei Mitani Institute of Behavioral Science University of Colorado, Boulder Nicholas.

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