REFERENDUM MODELS AND NEGATIVE WILLINGNESS-TO-PAY - ALTERNATIVE SOLUTIONS

Traditional referendum models of contingent valuation with linear util ity functions and additive errors have troubled researchers because th ey routinely predict negative willingness to pay. We explore solutions to this problem, including parametric models and the Turnbull empiric al distribution estimator of willingness to pay exploited by Carson et al. We show that there are closed form solutions for estimates of the empirical distribution function from the Turnbull likelihood maximiza tion problem which correspond to the self-consistency algorithm propos ed by Turnbull and the pooled adjacent violators algorithm (PAVA) desc ribed by Robertson, Wright, and Dykstra and implemented by Kristrom (L and Econom. 66, 135-139 (1990)). Further, a lower bound estimate of wi llingness to pay and the associated variance can be calculated by hand . The Turnbull estimator solves the problem of estimating negative wil lingness to pay without resorting to ad hoc distribution assumptions. It is shown that central tendency measures of willingness to pay from parametric models are sensitive to the assumed distribution, while the lower bound Turnbull estimate is robust across distributions. (C) 199 7 Academic Press.