A consistent method for calibrating contingent value survey data.

• Author: Mansfield, Carol

1. Introduction

   Contingent value (CV) surveys are used to estimate the economic value of nonmarket goods, especially environmental goods. A major concern with CV surveys is the potential for what have loosely been called hypothetical and strategic biases in the answers to CV questions. For a variety of reasons, often individual specific, a respondent's answer to a CV question may differ from his or her true value for the good. To address the potential problem of inaccurate bids, the initial version of the proposed rules for the Oil Pollution Act of 1990 called for all CV values to be divided in half.(1) The provision was intended as a challenge to practitioners to develop a method for calibrating the data from CV surveys.

   This paper outlines a statistical method for calibrating the data from CV surveys derived from the assumption that individuals make constrained utility maximizing decisions. The method allows us to determine the influence of individual characteristics on bias, as distinct from their influence on the preference parameters. To illustrate the logic of this approach, a specific functional form for individual preferences was used to derive closed-form analytical expressions for an individual's willingness-to-pay (WTP) and willingness-to-accept (WTA). These functions allow systematic deviations in individual responses to be explicitly modeled by providing a structural interpretation of the error term. The framework is appropriate for both open-ended and dichotomous choice data.

   The random utility model framework focuses attention on the error term, specifically on the possibility that there is an individual-specific, systematic component to the error term that is related to bias in CV responses. Evidence from experimental economics and psychology suggests that different respondents may react differently to the same survey question or laboratory experiment. Some elements of this reaction may be correlated with observable characteristics, such as education or age, while other elements will appear random to the researcher. Thus, it is important for calibration techniques to allow for the influence of individual characteristics on the existence and the size of any bias in CV responses.

   We illustrate this approach with three CV data sets using data from both open-ended and dichotomous choice responses. The particular applications were selected because comparable sets of laboratory or simulated market data exist for each of the three CV data sets. This allows a comparison between the results from the proposed calibration model and the laboratory or simulated market data. Ideally, the calibrated CV results should be compared to values from actual market transactions rather than the results from laboratory or simulated market experiments, which may also be biased. The calibration model proposed in this paper can be applied to simulated market data as easily as CV data, and for two of my data sets, I am actually able to estimate whether the simulated market data suffers from biased responses as well.

   The approach derived here does not require additional data beyond the CV survey itself to implement; thus, it can be used to calibrate data measuring use or nonuse values. Other calibration techniques for CV data require actual market data from weakly complementary goods or the identification of a surrogate market good for the nonmarket good valued in the CV survey.(2) But in many cases, especially where nonuse values are important, it may be impossible, if not contradictory, to define the appropriate set of weakly complementary market goods. Instead, we interpret the task of developing a calibration model for CV responses as a logical problem that considers whether there are sufficient model restrictions and sample information to identify the preference parameters and distinguish them from sources of bias in CV responses.

   While the choice of functional form for utility is an important maintained assumption conditioning the results derived from this approach to calibration, similar issues have been routinely addressed in modeling consumer demand. A great deal of work in demand analysis has focused on developing statistical models that can be used to test demand theory. In much of this work, researchers have been forced to make assumptions about the functional form for either the direct or the indirect utility functions. Even when the functional forms are restrictive, the resulting estimates can be informative and provide a foundation for future research (see Deaton [1986] for a review). Furthermore, failure to account for response bias when estimating bid functions for CV data will yield parameter estimates that are a composite of preference and response bias effects. Because response biases may be positive or negative, the parameter estimates will be difficult to interpret.

   This paper is organized as follows. Section 2 develops a model of CV bids and derives structural equations for WTP and WTA. The calibration model is applied to the three data sets in section 3, and the results are discussed in section 4. Section 5 contains ideas for further research.

2. A Model for Calibration

   A typical CV survey describes an environmental good and then proposes a change for better or worse in some feature of that good. The respondents are asked to decide how much they will pay for the improvement or how much compensation they require if the change is for the worse. Within this framework, assume that each respondent receives utility from two goods: the environmental good (E) that has two levels, [E.sub.high] and [E.sub.low], and a Hicksian composite good, represented by income (Y). In this framework, an individual's true maximum willingness-to-pay [wtp.sub.i], and minimum willingness-to-accept [wta.sub.i] satisfy the equalities

   U([Y.sub.i] - [wtp.sub.i], [E.sub.high]; [X.sub.i]) = U([Y.sub.i], [E.sub.low]; [X.sub.i]) (1)

   U([Y.sub.i] + [wta.sub.i], [E.sub.low]; [X.sub.i]) = U ([Y.sub.i], [E.sub.high]; [X.sub.i]), (2)

   where [X.sub.i] is a vector of individual characteristics and attitudes.

   For a given utility function with parameter vector [Beta], these equations can be solved explicitly for [wtp.sub.i] or [wta.sub.i] as

   [wtp.sub.i] = f([Y.sub.i], [E.sub.high], [E.sub.low], [Beta]([X.sub.i]); [X.sub.i]) (3)

   [wta.sub.i] = g([Y.sub.i], [E.sub.high], [E.sub.low], [Beta]([X.sub.i]); [X.sub.i]) (4)

   Most CV studies rely on bid functions assumed to be linear in observed characteristics.(3) By selecting a specific functional form for utility, explicit closed-form solutions for WTP and WTA can be derived. These structural equations will allow me to decompose the individual's bid into a preference-based component that is my estimate of WTP and WTA and a bias term that identifies systematic deviations from the assumptions of the model.

   I chose to estimate the equations based on a random utility model (RUM) where WTP (or WTA) is treated as a random variable. The random utility approach to analyzing CV data was popularized by Hanemann (1984). From Hanemann and Kanninen (in press), "one wants to formulate a statistical model for the CV responses that is consistent with an economic model of utility maximization" (p. 4). The calibration equations developed below exploit the link between the economic and statistical models that is the foundation of the RUM framework to identify deviations in CV bids from true WTP or WTA. My model uses the direct utility function rather than the indirect utility function (Hanemann 1984) or a variation function (McConnell 1990)(4) because the calibration method was developed in conjunction with efforts to estimate the parameters of utility functions associated with WTP and WTA responses (Mansfield, in press). However, one could develop similar, closed-form solutions for WTP and WTA from indirect utility functions.

   Two sources of error, systematic and random, may cause an individual's bid to differ from the amount he or she would actually pay for the good if a market existed. Systematic over- or understatement of WTP and WTA might occur due to factors such as the amount of time the individual has to answer the question, the wording of the survey, or the structure of the experiment. Hoehn and Randall (1987) and Crocker and Shogren (1991) develop theoretical models of CV bids that predict deliberate over- or understatement of WTP.(5) In addition, there is a large literature base on the incentive properties of various survey and experimental formats and the likelihood for strategic behavior.(6) For example, Bohm (1984) hypothesizes that individuals who favor the action proposed in the CV survey might purposely inflate their WTP if they did not believe the survey would actually be used to determine the amount they had to pay. Horowitz (1993) discusses the potential for misunderstandings between the analyst and the respondent to contribute to systematic bias in responses.

   Furthermore, whether and by how much individual bids differ from their true value will depend on the respondents' characteristics, attitudes, and interpretation of the survey. Evidence that individuals will react differently to identical incentive schemes can be found in experiments such as Andreoni (1995) on the provision of public goods. Herriges and Shogren (1996) found that local residents and recreationists exhibited different anchoring behavior in a survey valuing water quality improvements in an Iowa lake. Studies from the psychology literature, reviewed in Krosnick (1991), indicate that the response strategy an individual uses to answer a survey question may be a function of his or her personal characteristics.

   An ad hoc linear specification does not allow the analyst to distinguish the influence of a characteristic, such as education, on preferences from the influence of that characteristic on the propensity of respondents to systematically inflate or deflate their CV bids. Because individual characteristics and attitudes may...