Sensitivity of Willingness-to-Pay Estimates to Bid Design in Dichotomous Choice Valuation Models: Comment

Abstract

In their paper, Cooper and Loomis (1992) claim that willingness to pay (WTP) estimates derived using the dichotomous choice contingent valuation method (DC CVM) are very sensitive to the bid values specified, especially the bid values in the upper range of the WTP distribution. Their claim is supported using examples from ten WTP questions taken from three different surveys. Each of these WTP questions was a dichotomous choice question with 15-20 different bids offered, ranging from $2 to $1,200. They then show that when some of these bid values are dropped from the data sets, the WTP estimates resulting from logit estimation differ, sometimes substantially, from the estimates derived using the full data sets. They find particularly large variation in WTP estimates when the top bids are dropped, and claim that in these cases, WTP is substantially underestimated. Their results, they say, should as a note of warning for DC CVM Indeed, these results should serve as a warning for DC CVM researchers. The bid values in the tails of the distribution are highly influential points, not in a reliable way, as Cooper and Loomis suggest, but rather in a distorting way. Bid values in the tails increase the variances of the estimators of the parameters and, therefore, of WTP. Consider, for example, a bid value offered at the 1 percent right tail of the WTP distribution. In this case, we expect that 100 observations would have to be drawn at this point in order to get one positive response. It is easy to see that if more than one positive response occurred in this case, the tail, and therefore the entire distribution, would be thrown off. This strong influence of the tails is what increases the variance of the estimators, and in small samples, can cause bias. When Cooper and Loomis dropped the upper and lower bid values from their data, had they also compensated for the reduced sample size, they would have actually improved the efficiency of their estimators, provided their model specification was correct. The fact that the removal of the upper and lower bid values strongly influenced the resulting estimators is probably a result of the wrong model being fitted to the data. Cooper and Loomis assume WTP is distributed logistically. Many CVM studies have concluded that WTP is actually distributed asymmetrically, with a long right tail. The response rates in the upper tails that Cooper and Loomis report indicate that this is probably the case with their data. If their data actually were drawn from an underlying logistic distribution, the removal of particular bid values should not have influenced the estimation so much. This will be confirmed in our analysis below. The fact that these points are so influential indicates that either the model specified is incorrect, the responses in the tails are biased upward, or in all ten cases, the responses represent statistical anomalies. In this comment, we offer alternative analyses to those provided by Cooper and Loomis, and we suggest that the sensitivity they find in WTP estimates can be explained. In Section II, the influence of particular bid values is investigated using a data set from Kristr6m (1990a). It is shown that when particular bid values are dropped from the sample, the WTP estimates are not statistically different. In Section III,