Interval bidding in a distribution elicitation format

ABSTRACT

Interval bidding allows people to report a range of values for a non-market good. Herein, we allow people to choose their distribution over this range endogenously. We consider a multiplicative error model explaining the willingness to pay (WTP) which is estimated using a feasible generalized least squares estimator. We apply our framework to a representative sample of the French population who were asked about the valuation of a bear conservation programme. We find that most participants prefer stating their WTP as a range rather than a point, but the shape of the distribution greatly varies across people. Our results support the use of the interval bidding with endogenous distribution approach in valuation studies.

KEYWORDS:

• Contingent valuation
• uncertainty
• distribution format
• bears
• feasible generalized least squares

JEL CLASSIFICATION:

• C5
• Q51

Acknowledgements

We are indebted to one anonymous reviewer for very helpful comments on a previous draft. We thank participants at the congress of the French Association of Environmental and Resource Economists (FAERE) and the second edition of the workshop on non-market valuation (WONV) held in Marseille a well as seminar participants at Lille Catholic University. Any remaining errors are ours.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Recent work in behavioural economics has rediscovered and relabelled this preference uncertainty phenomenon as coherent arbitrariness: A person has a range of values and might select one value within this range arbitrarily given some unknown or unexpected cue (Ariely, Loewenstein, and Prelec 2003).

² Ranneby and Yu (2011) consider an additive measurement error model based on the idea that respondents opting for a range do not know their true WTP, with four probability density functions (PDFs) for the measurement error: left triangular, symmetric triangular, right triangular and uniform.

³ Rowe, Schulze, and Breffle (1996) argue that the width of the range might be proportional to WTP. Håkansson (2007) find some empirical support for this hypothesis in a study dealing with a Baltic river in Sweden that allowed for point or range responses. In the marketing literature, Dost (2012) claims that the width of the WTP range might be proportional to WTP. Furthermore, it has been shown that consumers tend to evaluate differences in price levels in relative terms rather than in absolute terms (Kahneman and Tversky 1979; Janiszewski and Lichtenstein 1999).

⁴ A similar approach can be employed for the stochastic payment card. Each of the amounts in the payment ladder is multiplied by the associated likelihood that the individual would agree to pay.

⁵ Given the logarithm transformation of the dependent variable, a simple transformation to account for the case of respondents reporting a zero value is to consider $ln\left(W_i^{\ast }+1\right)$. Such transformation is common in the WTP literature (Basu 2013).

⁶ Comparing the FGLS and OLS with robust SEs, Lewis and Linzer (2005) show that FGLS ought to be used when reliable information about ${\omega }_i^2$ is available.

⁷ The original sample size is 1004 respondents. We removed 81 questionnaires due to protest responses (like ‘I would need more time’; ‘government should pay’, ‘I do not trust NGO’) or implausible high WTP. Protest answers were detected by means of the open-ended follow-up question that was asked to those refusing to pay.

⁸ The survey aimed at valuing changes in the risk of non-fatal road injuries.

⁹ Participants may feel it easier to choose a distribution when the stated range is wide.

¹⁰ In (b), the variable WTP is highly significant, and the adjusted R² goes 0.021 to 0.304.