Modelling household behaviour with the data from dichotomous choice contingent valuation (DCCV) surveys is often complicated by zero willingness to pay (WTP) responses in the sample. To deal with the zero responses, a two-equation model is considered, which incorporates a two-level decision structure, a decision on whether to participate in having WTP and a decision on the WTP amount conditional on deciding to participate, and two separate stochastic processes that determine the probability and conditional level of WTP are featured. The model is empirically applied to household survey data, in which the DCCV questions concerned the benefits of air quality improvement in Korea. To put the issue of the two-equation model in perspective, this paper also experiments with economic and econometric specifications: utility theoretic restriction and heteroscedasticity. It is shown how failure to allow for the restriction distorts aggregate benefit estimates and the existence of heteroscedasticity in error term is found.