Environmental and Resource Economics 17: 89–108, 2000.© 2000 Kluwer Academic Publishers. Printed in the Netherlands.89Estimating Recreation Preferences Using HedonicTravel Cost and Random Utility ModelsLINWOOD PENDLETON1and ROBERT MENDELSOHN21The University of Southern California, Los Angeles, CA 90089-0253, USA;2Yale School ofForestry and Environmental Studies, 360 Prospect Street, New Haven, CT 06511, USAAccepted 3 September 1999Abstract. Over the last decade, several authors have questioned the validity of the hedonic travelcost model, arguing instead that the random utility model is a superior method for valuing recrea-tional site attributes. This paper demonstrates that the two methods emanate from a similar utilitytheoretic framework; yet in practice these methods differ in the assumptions made in their appli-cation. Constraining the underlying utility functions to be consistent, both models are applied to thevaluation of recreational site attributes in the Southeastern United States. The way in which eachmethod estimates preferences for site attributes is shown to depend critically on the method and thefunctional form of the underlying utility function.Key words: hedonic travel cost, RUM, recreation demandJEL classification: C25, Q23, Q261. IntroductionMicro-economic theory began as an attempt to describe, predict, and value thedemand and supply of consumption goods. Quality was largely ignored in initialtheoretical treatises; goods were assumed to be homogeneous. Over the last twodecades, however, economists have started to address quality within the theoryof demand. Environmental economists have extended the theory further to valuethe quality of recreational sites – an important component of land management.Two distinct approaches for incorporating quality into recreational analyses haveemerged: the hedonic travel cost method (HTC) and the discrete choice randomutility methods (RUM). The hedonic method views site attributes as though theywere individual goods which are bundled together in a single purchase. The randomutility model treats quality as an index which is estimated by examining a discretechoice of alternative sites facing a consumer.Because the mathematical derivations for the hedonic (Rosen 1974) and randomutility models (McFadden 1978) are quite different, many practitioners do notrecognize that both models are based on a common utility theoretic foundation.In the first section of this paper, we show how the hedonic and random utilitymethods are consistent with the same utility framework.90 LINWOOD PENDLETON AND ROBERT MENDELSOHNCuriously, practitioners of the two methods have often made different aprioriassumptions about utility when applying the methods. Many studies using theRUM method have assumed linear utility functions (see Morey et al. 1993, foran exception) while studies using the hedonic method frequently rely on quad-ratic utility functions (e.g. Brown and Mendelsohn 1984; Englin and Mendelsohn1991; Pendleton et al. 1998b). The choice of functional form imposes importantrestrictions on the way the researcher believes that consumers value site quality. InSection 2 of the paper, we examine linear and quadratic functional forms for utilityand show explicitly how these functional forms effect preferences.Although both methods are based on the same utility theoretic framework,assumptions made in the econometric estimation of the models differ significantly.Each method makes very different assuptions about (a) the nature of the errorterms in consumer decisions, (b) the smoothness of available attributes, and (c)the consumers’ choice sets. These econometric assumptions can significantly influ-ence the way the models estimate consumer preferences for site attributes. Sincethere may be little theoretical justification for certain underlying assumptions,it is important to consider how different assumptions influence the econometricperformance of the models. Of course, one could compare results. In Section 4 weestimate consumer preferences for wilderness attributes in the Southeastern UnitedStates. The two models also differ greatly in the assumptions in the calculation ofwelfare change. We leave a discussion of this matter for another paper.2. The Utility FrameworkIt is well known that the quantity of goods purchased are arguments in the utilityfunction of consumers. Although common utility theory glosses over quality, itis equally plausible that quality also is an argument in the utility function ofconsumers. Lancaster (1966) provides a rigorous framework for the role of charac-teristics as arguments in the utility function. Following Lancaster’s characteristics-based utility model, applied economists now value quality in terms of a good’sattributes. Two approaches have emerged to model the role of characteristics inconsumer utility and choice. The hedonic approach estimates the demand forattributes after first uncovering the implicit prices of attributes. The random utilityapproach treats quality as an attribute-based index to be attached to goods. In bothcases, the techniques attempt to place values on these attributes by observing howconsumers choose from amongst the packages of available goods. In this section,we demonstrate that the underlying theoretical foundation for both methods is thesame utility maximization subject to budget constraints. We argue that the theoret-ical foundations of both approaches are the same and consequently cannot be usedto argue for one rather than the other approach.HEDONIC AND RANDOM UTILITY MODELS 912.1. THE HEDONIC TRAVEL COST METHODThe theoretic derivation of the demand for goods from utility maximization subjectto a budget constraint is a well established part of basic micro-economic theory.Without loss of generality, we extend this derivation to include quality. We begin byconsidering a set of Hicksian demand functions for a vector of site attributes (quali-ties), Z, described by a vector of attribute prices, P, utility u, and an estimation errorterm, φ.Z = h(P,u,φ). (1)In the case of recreation demand, the price is not a market price, but an implicitprice. This implicit price is found by estimating the hedonic price function. Thehedonic price function is the empirical estimation of the hedonic price frontieracross visited sites. The cost of accessing any site on the frontier is a function ofthe attributes of that site. Formally, the hedonic price function1isC(site j) = fn(Zj) (2)and the vector of