Length-Biased Sampling in Contingent Valuation Studies
研究了在条件价值评估中，现场抽样因访问时长不同导致长度偏差的问题，并提出了已知抽样规则下的参数估计方法，对从事环境资源价值评估的研究者有用。
Contingent valuation is an often used method of valuing environmental commodities and other nontraded goods. A standard approach of contingent valuation is to design a questionnaire and conduct a bidding game over the phone or by personal interview. Consider the problem of trying to extract information from individuals who are using a particular site such as a fishing area, camping ground, or a sightseeing area located next to a scenic attraction. The purpose of the study is to estimate parameters associated with the utilization of the site over a specific interval of time. Variables of interest may include length of visit, willingness to pay, and total expenditures associated with a particular activity. If an on-site interview is conducted, one method commonly used to administer the questionnaire can be described as follows. Beginning at a predetermined point an interviewer follows a route and records data as individuals are encountered. Such an approach can cause individuals to be sampled with a probability proportional to length of their visit, i.e., sampling may be length biased (Cox 1969). If the parameters of interest are correlated with length of stay, their estimates will also be biased. This paper will address parameter estimation within the context of a sample design that results in length-biased sampling. The bias that results from using nonrandomly selected samples has been discussed by Heckman (1976,1979), and applications of sample selection bias have appeared most notably in wage comparison studies (Gronau 1974; Hausman 1980). Heckman developed regression techniques to estimate behavioral relationships free of selection bias when samples are nonrandom. He sugg sts examining the sample selection rule that results in the nonrandom sample and adjusting for the bias by taking into account the probability of an individual being included in the sample. This paper presents a special case where the sample selection rule that determines the availability of data is known. Because the sample selection rule is known, the regression techniques recommended by Heckman are not necessary in contingent valuation studie when samples are length biased. The problem of length-biased sampling has been addressed in the context of recreational surveys by Schreuder, Tyre, and James (1975), however applications have never appeared in he economics literature, and recent work (McDonald, Otis, and Becker 1986) has made the techniques more versatile and important for economists. The next section of the paper will outline the statistical techniques that have been developed to adjust the sampled, length-biased da a. In order to demonstrate the impact that adjusting the data can have, the final section will use a willingness-to-pay survey conducted in Yellowstone National Park in 1985.