Whitehead, John, O. Morgan, and William Huth. "Convergent validity of stated preference methods to estimate willingness-to-pay for seafood traceability: The case of Gulf of Mexico oysters." Economics Bulletin 38, no. 1 (2018): 326-335.

Abstract: In this study we compare willingness to pay for a seafood traceability system from contingent behavior demand and contingent valuation referendum vote models using data from a survey of Gulf of Mexico oyster consumers following the BP oil spill in 2010. We estimate a random effects model of oyster demand using contingent behavior data and find that a traceability program increases demand and consumer surplus. We estimate a referendum model for the seafood traceability program using contingent valuation data. We find that welfare estimates from the contingent behavior and contingent valuation methods are convergent valid under certain conditions.

URL: http://www.accessecon.com/Pubs/EB/2018/Volume38/EB-18-V38-I1-P31.pdf

For me, the most interesting part of the paper is our robustness checks on the contingent behavior and contingent valuation data. Here is what we say about the CVM data:

The traceability program increases consumer surplus per meal by $0.95 with a 95% confidence interval of $0.37 to $1.53. The consumer surplus estimates are robust to alternative econometric models such as random effects Poisson and random and fixed effects ordinary least squares models (these results are available upon request). ...

The conditional mean willingness-to-pay per meal ... constrains willingness-to-pay to be positive (Hanemann 1989). The 95% confidence interval is constructed using a bootstrapping procedure (Krinsky and Robb 1986). The willingness-to-pay per meal is $2.69 with a 95% confidence interval of 1.23 to 4.15. ...

We find that differences in the consumer surplus and mean willingness-to-pay estimates are not statistically significant since the 95% confidence intervals overlap. However, this obscures large differences in the point estimates. Mean willingness-to-pay is 183% higher than the consumer surplus estimate from the demand model.

When referendum data exhibits “fat tails” ... welfare measures will be less robust to alternative models relative to textbook data. The conditional mean welfare measure is not robust to alternatives such as the log-linear logit model (median WTP = $0.27 [-$0.03, $0.56] with the 95% confidence interval in brackets) and the Turnbull (Haab and McConnell 1997) nonparametric estimate (WTP = $1.47 [$1.20, $1.74]) which are not sensitive to the tail of the distribution. However, these two estimates also lead to the conclusion of convergent validity with the consumer surplus estimate.

On the other hand, the conditional mean willingness-to-pay estimate is robust to comparison with the Kriström (1990) nonparametric estimate (WTP = $2.65 [$2.23, $3.06]) (Boman, Bostedt, and Kriström 1999). But the confidence interval of the Kriström estimate does not overlap the confidence interval for the consumer surplus estimate. This lack of convergent validity is due to the narrow Kriström confidence interval which is partially an artifact of the smoothing of the data at the upper two bid amounts.

This sensitivity analysis was prompted by referee comments and my experience with two recent contingent valuation studies that, in my opinion, relied too heavily on the Turnbull estimator, especially with "smoothed" due to non-monotonicity (see Whitehead 2017a, 2017b). Smoothing data is equivalent recoding the dependent variable to fit the theory. Typically, recoding the dependent variable to fit the theory is a strong no-no. In the willingness-to-pay context it is OK in order to provide a lower bound willingness-to-pay estimate. But this estimate should not be used for hypothesis testing in the absence of other estimators. Here is the last line of Whitehead (2017b):

With what Haab and McConnell (2002) call “difficult data,” the entire range of nonparametric and parametric WTP estimates should be examined for validity testing and benefit-cost analysis.

References

Whitehead, John C., “Who Knows What Willingness to Pay Lurks in the Hearts of Men? A Rejoinder to Egan, Corrigan, and Dwyer,” Econ Journal Watch 14(3), 346-361, September 2017a. https://econjwatch.org/articles/who-knows-what-willingness-to-pay-lurks-in-the-hearts-of-men-a-rejoinder-to-egan-corrigan-and-dwyer?ref=articles

Whitehead, John C. "A replication of willingness-to-pay estimates in An adding up test on contingent valuations of river and lake quality’(Land Economics, 2015). Economics Discussion Papers, No 2017-55." Kiel Institute for the World Economy. http://www. economics-ejournal. org/economics/discussionpapers/2017-55 Page 2, no. 2 (2017b). http://www.economics-ejournal.org/economics/discussionpapers/2017-55/file