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Traditionally, contingent valuation and travel cost models have been viewed primarily as substitute valuation techniques. Depending on the type of resource and the value to be estimated, one of the two methods would be chosen by the analyst and an appropriate survey instrument designed and undertaken. Sometimes analysts collect the requisite information to estimate both travel cost and contingent valuation models with the intention of comparing the resulting welfare estimates to examine internal consistency or validate one of the approaches. An incomplete list of such studies includes Bishop and Heberlein (1979), Sellar, Stoll, and Chavas (1985), Smith, Desvousges, and Fisher (1986), and Brookshire and Coursey (1987). However, since each approach is potentially subject to criticism, including data issues and a variety of possible biases, it is not clear that the validation strategy is very effective.(1)
In a significant departure from the conventional approach, Cameron (1992a) adopts a different view of the valuation problem: rather than treat CVM and travel cost as competing methods, she suggests and demonstrates that the two approaches can be successfully combined to estimate welfare measures. Thus, both sources of information on underlying preferences are used in estimating values.
Cameron's innovative suggestion has received little additional investigation and analysis. Larson (1990) provides a valuable refinement of Cameron's method by presenting a consistent treatment of the error term between the contingent valuation and travel cost components of the model, thereby providing a consistent, utility-theoretic model. Another example of combining direct and indirect methods in joint estimation is the well-known strawberry experiments of Dickie, Fisher, and Gerking (1987). Finally, a combined approach using contingent behavior methods and discrete choice models has been investigated by Adamowicz, Louviere, and Williams (1994). Their model employs the random utility framework of modeling the consumer's choice among one or several recreational trips. The Cameron and Larson applications employ a continuous demand function specification where there is a single recreational site, though the method could be extended to a system of sites.(2)
Both Cameron (1992a, 1992b) and Larson (1990) discuss potential benefits of combining contingent valuation and travel cost data for estimating welfare. Cameron focuses on the potential gains in producing "a more comprehensive picture of preferences" than what would be available from using either approach separately. Larson further notes that estimates from the combined model should result in more efficient parameter estimates as more information on the same set of underlying preferences is employed in constructing the estimates.
This paper contributes to this literature in two ways. First, the model of Cameron and Larson is extended to investigate a double-bounded version of the contingent valuation component. Many recent CVM applications present respondents with an initial bid and a follow-up bid. Double-bounded applications increase the efficiency of the welfare estimates (Hanemann, Kanninen, and Loomis 1991). It follows that there should be further gains in the combined model from employing a double-bounded CVM rather than a single-bounded model.
Second, potential gains in reduced bias or increased precision are investigated via simulation experiments. Simulated data is constructed based on a known set of parameters and error structure. A travel cost model (TCM), single-bounded contingent valuation model (CVMS), double-bounded contingent valuation (CVMD), combined single-bounded CVM and TCM (COMB-S), and combined double-bounded CVM and TCM (COMB-D) are estimated and the accuracy and precision of the welfare estimates are investigated. The focus of the simulation experiment is to identify the circumstances under which the gains from combining data are small, in some sense providing a lower bound to the likely gains. In that way, the conditions under which large gains may be expected will be highlighted thus possibly providing guidance to analysts in model identification and choice.
Since information from two sources are being combined to estimate a given set of parameters, the combined models should be estimated more precisely than the separate models. Likewise, the combined double-bounded model (COMB-D) should yield more precise estimates than the combined single-bounded model (COMB-S). Of interest then is the magnitude of increased precision an analyst can expect by employing a combined model relative to using one of the methods separately. Likewise, the increased precision due to the use of a combined model (COMB-S) and the increased precision from using double-bounded CVM both relative to single-bounded CVM is investigated.
Whether there are gains in reduced bias from combining methods is less clear than gains in precision as it is theoretically possible that the combined estimators might exhibit greater small sample bias than the separate models. The simulations examined below provide guidance on this question.
In the following sections, the combined single-bounded model is briefly outlined and the extension to a double-bounded model is presented. The design of the simulation experiments to investigate precision and possible accuracy gains from the combined models are described and results of the experiments follow. The last section offers final comments.
II. THE SINGLE-BOUNDED AND DOUBLE-BOUNDED COMBINED MODELS
Following Cameron (1992a), assume that the problem under investigation concerns the recreational value of a single good, such as visits to a fishing site or picnic area. The CVM component is of the referendum format; that is, respondents are offered either a single bid (CVMS) or an …