Dealing with censored data from contingent valuation surveys: symmetrically-trimmed least squares estimation.

• Author: Kwak, Seung-Jun

1. Introduction

   The purpose of this paper is to explore the use of a consistent and robust estimator when estimating a willingness to pay (WTP) equation using the censored data collected by a contingent valuation survey.(1)

   Mitchell and Carson's payment card format [11; 12] strongly encourages the respondent to give a WTP value that is zero or greater, because payment cards do not normally include any negative values. But some respondents who answer with a zero WTP may in fact have negative WTP. As a simple example, if people are asked about improving a salt water pond's water quality to the point that shellfish taken from it would be edible, there may be individuals in the sample who use the pond for other recreational activities that would be hindered by the presence of people shellfishing. In addition, anyone who enjoys quietness around and on the pond also might want to be paid a certain amount to allow the ponds to be made shellfishable. In brief, not every "public effect" on net is a good to every affected person, but anticipating the varieties of reasons for negative valuation is at least difficult if not impossible. This was true in our research aimed at estimating the willingness to pay for improving the level of security of tap water quality in Seoul, Korea, as we discuss in section II.

   This censoring of the WTP responses becomes problematic when one seeks to estimate a willingness to pay equation as a check on internal consistency of the study results and potentially as a basis for total benefit projection. Thus, with WTP censored at zero, OLS parameter estimates will be inconsistent. One popular method that has been used in such cases is the Tobit model [1; 17]. However, there are two possible pitfalls to this approach. First, the Tobit estimator becomes inconsistent when heteroskedasticity occurs in the errors [2; 9]. Moreover, when the normality assumption on the distribution of the error term is not satisfied, it is again inconsistent [2]. We have tested the hypothesis of an i.i.d. censored normality by employing the test procedure of Nelson [13]. We can reject the hypothesis at the 1% level. The assumptions required to use the Tobit model are, therefore, too strong to be satisfied.

   As an alternative to the Tobit estimation, we consider here the symmetrically trimmed (censored) least squares estimation (STLS) method proposed by Powell [16]. This method is based on symmetric censoring of the upper tail of the distribution of the dependent variable. This semi-parametric estimator is consistent and asymptotically normal for a wide class of distributions of the error term and is robust to unknown heteroskedasticity.

   In this paper, we apply the STLS method to estimating a WTP equation and compare the results with those from OLS and the Tobit estimation. As noted, this estimator is robust under quite general conditions, so differences between coefficients estimated in STLS compared to OLS or Tobit can be interpreted as evidence of problems of inappropriate clustering at zero, or violation of assumption of homoskedasticity and normality. The paper proceeds as follows. Section II describes the WTP model to be estimated. Section III explains the estimation method. A discussion of results appears in section IV. Conclusions will be found in the final section.

2. A Model of WTP and the Censoring Problem

   Our theoretical model for explaining individuals' WTP comes from the income compensating function [18]. When we take WTP as the desired benefit measure, the income compensating function is referred to as the WTP function, and we hypothesize that the arguments are elements of a vector of the respondent's tastes or personal characteristics as well as variables representing both the respondent's environmental and economic situations. Thus:

   WTP([q.sub.1], [q.sub.0]) = f([P.sub.0], [q.sub.1], [q.sub.0], [Q.sub.0], [Y.sub.0], T), (1)

   where [P.sub.0] is the price level of private goods, the [q.sub.i] are tap water "quality" descriptions, [Q.sub.0] is other environmental goods, [Y.sub.0] is income, and T is a vector of the respondents' tastes or characteristics.

   In our study, [q.sub.0] was the current situation as related to the security of Seoul's tap water quality, while [q.sub.1] represented the improvement goal described in the survey. Both the current situation and the policy goal were described to respondents by relating them to incidents that occurred in a large river south of Seoul in 1991, less than a year before our survey. These incidents were two accidental industrial spills of phenolic compounds that went undiscovered until they had contaminated the water supply of a major city that used the river (the Nak-dong) as its raw water source. Routine chlorination made the effect worse in one sense because the water gave off an even worse smell after treatment, but it is possible that the terrible smell was a major cause of so little reported health damage.

   The base condition, [q.sub.0], described to our Seoul respondents was vulnerability to a Nak-dong-like spill incident. We let respondents in effect define their own subjective probabilities of such an event occurring.(2) The goal, [q.sub.1], ascribed to the government was...