Bias and Efficiency of Single vs Double Bound Models for Contingent Valuation Studies: a Monte Carlo Analysis

Abstract

The Dichotomous Choice Contingent Valuation Method (DC-CVM), both in the single and the double bound formulation, has been in the last years the most popular technique among practitioners of contingent valuation, due to its simplicity of use in data collection. The single bound procedure is easier to implement than the double bound, especially in data collection and estimation. On the other hand, it is well known that the double bound is more efficient than the single bound estimator. It remains to analyze the bias of the ML estimates produced by either model, and the gain in efficiency associated to the double bound model, in different experimental settings. We find that there are no relevant differences in point estimates given by the two models, even for small sample size, so that neither estimator can be said to be less biased than the other. The greater efficiency of the double bound is confirmed, although it can be seen that the differences tend to reduce by increasing the sample size, and are often negligible for medium size samples. Provided that a reliable pre-test is conducted, and the sample size is large, our results warrant the use of the single rather than the double bound model. * We would like to thank Rossella Diana for her helpful assistance in the early stage of this research. IntroductionThe Dichotomous Choice Contingent Valuation Method (DC-CVM) has been in the last years the most popular technique among practitioners of contingent valuation, due to its simplicity of use in data collection. When this elicitation method is used, the respondent is only required to answer YES or NO when asked if she/he is willing to pay a given amount (bid) for the public good. The single bound model comprises only one such question, while in the double bound model the first question is followed by another specifying a lower amount, if the answer to the first question was negative, and higher otherwise. This procedure is certainly easier for respondents than other methods requiring long adjustment processes, like the bidding game; or a precise assessment of the individual's own reservation price based on introspective analysis, as it happens in the open ended elicitation method. The price to pay for this is the limited information arising from DC-CVM data: the only information available to the researcher after the interview is an interval of values containing the true willingness to pay (wtp) of the individual.In the single bound model the interval is bounded by the bid and the limit of the wtp distribution (the upper limit if the answer was positive, the lower limit otherwise). In the double bound model the interval is enclosed within two bids, if one answer to the two questions was positive and the other negative (double bound); otherwise, the interval is bounded by the second bid and the limit of the wtp distribution. In order to gather more information about the support of the true wtp distribution, the initial bids are varied among individuals.Hanemann, Loomis and Kanninen (1991) proved that the ...

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