A mixed approach to payment certainty calibration in discrete choice welfare estimation

Abstract

This article provides further empirical evidence of payment uncertainty in dichotomous choice (DC) Contingent Valuation (CV) and proposes an alternative way of certainty calibration, moving away from conventional recoding of uncertain responses. In an international CV application, the main sources of payment uncertainty are identified related to imperfect knowledge and information about the public good involved, future supply levels, income constraints, price levels and the survey instrument. Together these sources of uncertainty are responsible for a third of the error variance in the estimated discrete choice model. Accounting for the heterogeneity induced by payment uncertainty in the welfare estimation procedure with the help of a mixed probit model yields a significantly lower welfare measure albeit at the expense of estimation precision.

Acknowledgements

This study was conducted as part of the European Interreg IIIB NWE project Scaldit and funded by Rijkswaterstaat Zeeland. The survey work in France and Belgium was carried out by Arnaud Courtecuisse (French Water Agency Artois-Picardie), Ann Beckers and Lien van den Driessche (Flemish Environment Agency VMM), and Sandrine Dutrieux (Brussels Environment IBGE-BIM). A word of thanks goes to the International Scheldt Commission for its administrative support, Thijs Dekker, Marije Schaafsma and two anonymous reviewers for their useful comments on this article. The usual disclaimer applies.

Notes

¹ In turn, the more uncertainty in someone's preferences, the more expressed preferences will be subject to procedural and descriptive influences (e.g. Schkade and Payne, 1994; Ariely et al., 2003).

² Protest bidders typically object to the imposed market structure in a CV study (e.g. Meyerhoff and Liebe, 2006). A separate analysis was carried out using the nonparametric Mann-Whitney test to test differences between protest and non-protest bidders. Protest respondents are significantly higher educated and wealthier male respondents from slightly bigger households, with less trust and confidence in the description of the current situation and the feasibility of reaching the WFD objective of good ecological status for all water bodies in their region (test results are available from the author).

³ The model used here is a mixed binary probit model where random preference heterogeneity is picked up in the structure of the covariance matrix (Train, 2003) due to the expected clustering of responses across self-reported payment certainty levels (not to be confused with the panel data structure found in repeated choice experiments). A short model description is presented in Appendix 2.

⁴ In order to be able to compare the impact of the interaction term with that of the bid price, the original payment certainty classes were in this case recoded between 0 and 1.

⁵ The dummy has the value 1 if respondents never heard of the information before.

⁶ This variable was measured on a 5-point semantic differential scale ranging from ‘completely incredible’ to ‘completely credible’. Dummy variables were included for the two positive levels (somewhat and completely credible). No significant difference can be detected between the two dummy variables in any of the three models based on the Wald test (test results are available from the author).

⁷ Despite the lower number of observations underlying this estimate.

⁸ The variation coefficient is equal to the SE divided by mean WTP.

⁹ The payment certainty measurement scale is interpreted as an ordinal scale, justifying the use of an ordered probit model. This means that 100% is more certain than 50%, but 100% is not necessarily twice as certain as 50%. Nor is an increase in certainty from 50 to 60% the same as an increase in certainty from 90 to 100%. There are simply 11 categories with 10% being more certain than 0%, 20% more certain than 10%, etc.

¹⁰ The same explanatory factors are found to be statistically significant based on the original certainty categories and OLS regression based on these original categories, indicating that the estimated model is robust. The explanatory power of the estimated OLS models (adjusted R-square) is 35% for the yes responses and 37% for the no responses.

¹¹ Protest refers here to the underlying reason for payment certainty, not to the WTP question, hence the reason why the effect is significant for both yes and no responses.

¹² The Wald chi-square equals 3.21 (p < 0.073) for the pooled model, 5.21 (p < 0.022) for the yes responses and 0.08 (p < 0.776) for the no responses.

¹³ Based on Hausman and Wise (1978) and Train (2003).