WEAI/AERE 2009 - Individual Paper Abstract
Title: More Trouble with Turnbull: Calculating Confidence Intervals for WTP When Using Estimators with Monotonicity Constraints
Author(s): Craig Mohn, Cascade Econometrics, craigmohn@earthlink.net; Barbara Kanninen
Abstract:
Economists frequently use simulated referendum techniques such as single-, double-, or one-and-one-half-bounded contingent valuation to measure the total value to consumers of goods for which adequate markets do not exist. This often arises in the context of publicly-owned natural resources which provide recreational, habitat, and other services to a large number of potential beneficiaries. Data from these surveys is often used in planning situations where there are winners and losers from any policy change. This means that there is often a constituency which seeks to have the public good assigned a lower valuation, which in turn causes practitioners to rely on estimators which produce defendably conservative valuations.
Parametric analysis of the results of these surveys easily provide valuation estimates which offer insight into the differences in worth as a function of respondents' attributes, but these results are inevitably driven by the distributional assumptions behind the model. A popular alternative is to use nonparametric estimators such as the Turnbull to generate an empirical distribution of willingness-to-pay (WTP) which satisfies certain economic restrictions, such as requiring the probability of saying yes to a bid to be monotonically nonincreasing in the amount of the bid. Turnbull-like estimators easily provide lower bounds to the median and mean WTP.
These point estimates of valuation are useful, but it is generally important to get confidence intervals for these estimates. The lower bound to the mean WTP which the Turnbull Estimator supplies is a simple function of the estimated parameters of the model. The usual method of deriving confidence intervals for this quantity would be to use the delta-method and the covariance matrix of the parameter estimate. However, the fact that a monotonicity constraint is imposed on the coefficients in Turnbull-like models means that some regions in the multivariate-normal distribution of parameters described by the asymptotic covariance matrix do not correspond to viable parameter estimates, and the delta-method may yield confidence intervals which are too small or too large, depending on the data and the underlying preferences of consumers.
We examine the effect of using the correct distribution of WTP in contrast to the computationally-simpler delta-method technique using three contingent valuation datasets which measure the value of the preservation of Mono Lake in Northern California, the protection of wildlife and wetland habitat in the San Joaquin Valley, and the value to the public of clean beaches on the Southern California coast.