Heterogeneous visitors and the spatial limits of the travel cost model.

Introduction Accurately modeling heterogeneous visitors in recreation demand models is a complex issue that has received much attention. Recently, Randall (1994) listed a number of difficulties that afflict travel cost models and are also inherent in random utility models. These complications all arise from the researcher's inability to observe the prices of recreation site visitation, since these prices are likely to be endogenous. The allocation of joint costs, the price of substitute goods, and the value of time are somewhat unobservable to the researcher. For visitors traveling long distances these difficulties are particularly problematic. Indeed, the inaccurate observation of prices may be the source of the spatial parameter instability demonstrated by Smith and Kopp (1980). Recently, however, a series of papers (Bell & Leeworthy, 1990; Shaw, 1991; Hof & King, 1992; McConnell, 1992; Larson, 1993) have attempted to accommodate the diversity of visitors by focusing on differences in the distance they travel. Some of these authors separate monetary outlays for recreation into two categories: on-site costs and long distance travel costs. We refer to these models as on-site cost models. The visitor is assumed to choose both the number of long distance trips to the site, as well as the number of days spent on-site. One of the major motivations (Bell & Leeworthy, 1990; Hof & King, 1992) behind these on-site cost models is as a solution to the spatial limits of the standard travel cost model identified by Smith and Kopp (1980)., This paper empirically examines if the on-site cost model, with its unidimensional focus on distance traveled as a measure of visitor heterogeneity, effectively deals with the spatial limits identified by Smith and Kopp. Our findings indicate that serious spatial limits still may exist in the on-site cost model. As a feasible remedy, we propose a classification of diverse visitors based upon their total travel itinerary, rather than simply on distance traveled. Econometric implementation of this classification scheme suggests that for our application the approach alleviates the spatial limits of the on-site cost approach. There are five remaining sections. The next section concisely presents the on-site travel cost model. In Section 3, we briefly discuss the GVE data and report the results of parameter stability tests. Section 4 contains our alternative classification of fishermen. The empirical implementation of this scheme is discussed in Section 5. We conclude in the last section. In equation (5) if P^sub D^ is large enough to drive D^sup *^ to zero, then the optimal number of long distance trips, R^sup *^, will also be zero. If this is the case, the weak complementarity condition required to obtain welfare estimates using the on-site cost model is satisfied. Separating travel costs into categories that break out costs incurred onsite provides several potential advantages. 1. Breaking survey questions regarding recreationists' expenditures into disaggregated categories will aid visitor recall and elicit more accurate answers about expenditures as a whole. 2. Days on-site can be used as a dependent variable in recreation demand equations, rather than number of trips. This avoids the common assumption of standard travel cost models that trips of different lengths have the same price (Hof & King, 1992). 3. Empirical evidence suggests that recreationists react differently to changes in on-site costs than to changes in long distance costs (Gibbs, 1974; Gibbs & Conner, 1973, Bell & Leeworthy, 1990). Finally, allowing separate price effects may eliminate the parameter instability found by Smith and Kopp (1980). Although these potential advantages are appealing, their realization hinges upon the stability of parameter estimates. Parameter stability cannot be determined theoretically; rather empirical verification is required. …