In contingent valuation surveys the category of zero bidders refers to individuals that are not willing to pay anything for the programme under analysis. Specific questions can help to identify true zero values, coming from people that are indifferent to the programme, separately from protest responses: the latter are generally excluded from the analysis. This paper introduces a mixture-sample selection model that takes into account both zero values and protest responses in the estimates. The model is applied to the valuation of a traffic calming scheme aimed at reducing risks for residents in three villages in the north-east of England.

The sample selection model is based upon a bivariate or a multivariate structure, and distributional assumptions are in this context more severe than in univariate settings, due to the limited availability of tractable multivariate distributions. While the standard FIML estimation of the selectivity model assumes normality of the joint distribution, alternative approaches require less stringent distributional hypotheses. As shown by Smith (2003), copulas allow great flexibility also in FIML models. The copula model is very useful in situations where the applied researcher has a prior on the distributional form of the margins, since it allows separating their modelling from that of the dependence structure. In the present paper the copula approach to sample selection is first compared to the semiparametric approach and to the standard FIML, bivariate normal model, in an illustrative application on female work data. Then its performance is analysed more thoroughly in an application to Contingent Valuation data on recreational values of forests.

The dichotomous choice contingent valuation method can be used either in the single or double bound formulation. The former is easier to implement, while the latter is known to be more efficient. We analyse 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. The greater efficiency of the double bound is confirmed, although differences tend to reduce by increasing the sample size. Provided that a reliable pretest is conducted, and the sample size is large, use of the single rather than the double bound model is warranted.