162 



Fishery Bulletin 105(2) 



multiple purposes. Because focus is strictly on single 

 day trips, it would be incorrect to include sites in an 

 angler's choice set if those sites are "too far" for the 

 angler to consider when choosing a site for a single day 

 trip. Second, a large number of sites in each individual's 

 choice set can be computationally costly, particularly 

 when a nested choice structure is appropriate, and in- 

 crease the time it takes to bring policy analyses to the 

 table. This problem may indicate that there is a tradeoff 

 between computational efficiency and angler behavior in 

 reality; a balance that will be examined here. 



There is literature on the specification of choice sets 

 based on many factors including distance. Parsons and 

 Hauber (1998) estimated a freshwater recreational an- 

 gler site choice model and found that there is little 

 difference in the magnitude of welfare effects as one 

 reduces the spatial scope of choice sets until a threshold 

 of 1.6 hours one-way travel time is reached. This spa- 

 tial scope translates into 32 mile and 80 mile distance 

 thresholds, if one assumes a 20 mile per hour (mph) 

 urban travel speed and a 50 mph highway travel speed, 

 respectively. Below that threshold, welfare estimates 

 inflate as the constraint tightens. Whitehead and Haab 

 (1999) estimated a site choice model using a range of 

 choice sets constructed with distance and site-quality 

 metrics. They found that there is very little difference 

 in the trip cost coefficients across distance-based choice 

 sets that eliminate between 13% and 82% of the avail- 

 able sites. Hicks and Strand (2000) found that because 

 the probability of choosing a site depends on the choice 

 set, the likelihood function is also dependent on the 

 choice set. If the choice set is incorrect, biased param- 

 eter estimates could be a consequence. The welfare es- 

 timates derived in the "Materials and methods" section 

 below explicitly include the choice set and demonstrate 

 this interaction. 



This analysis will examine the sensitivity of wel- 

 fare estimates in a RUM model of recreational demand 

 across six distance-based definitions of site choice. This 

 analysis will focus on a single species, striped bass 

 (Morone saxatalis), from a single mode (the private 

 rental boat mode) to avoid a nested choice structure. A 

 simulation approach will be used to derive confidence 

 intervals around these estimates in order to examine 

 the significance of any differences found and to ex- 

 pand the literature that has previously been focused 

 on only on the magnitude of the differences in welfare 

 estimates. 



Materials and methods 



An angler chooses a fishing site from the set of all alter- 

 native sites if the utility of visiting that site is greater 

 than the utility of visiting any other site in the global 

 choice set. Denoting the set of all alternatives faced by 

 any angler by S = 11, . . . , A^^l as the choice set, the indi- 

 rect utility of visiting site 7 is 



where C/ = an individuals utility; 



V = the deterministic portion of utility; 

 y = income; 



p = the cost of angling at site j; 

 q = a. vector of characteristics of sitey; and 

 £ = the unobservable portion of indirect utility. 



In the RUM framework, an angler will choose site j 

 from S if 



V,(9,,y-p,) + £,>n(g„y-p,) + £„7eS,VAeS, (2) 



where the indirect utility of visiting site j is greater 

 than the indirect utility of visiting site k for all k in the 

 global choice set, S. 



The random portion of the random utility model stems 

 from the unobservable portion of indirect utility, cap- 

 tured here in the error term f^. If this error term is 

 assumed to be distributed in a type-I extreme value dis- 

 tribution, the above site choice framework can be mod- 

 eled with the conditional logit model. Maddala (1983) 

 has provided a complete derivation of the conditional 

 logit model. Within this framework, the probability that 

 i visits site 7 is given by 



P,(j)^P(j\jeS) 



,v/i,-y-pj> 



s... 



Vj,(<j,v-pt) 



(3) 



Up to this point it has been assumed that each angler 

 faces the same choice set, S. This is not a necessary 

 assumption and can be generalized to represent the 

 possibility that i faces a choice set S, that is a subset of 

 the global choice set S. In this case the indirect utility 

 comparison becomes 



V/<7,,y-p,) + f, > V^(<?t,y-PA.) 

 +ei^JeSyK&S,,S,czS 



(4) 



and the probability that angler i chooses sitej becomes 



P,U) = 



V/Qj.y-p,) 



I. 



Vk<<i.y-Pk> 



(5) 



Because the goal of the present study is to examine the 

 sensitivity of welfare estimates of a quality change to 

 the specification of choice sets, it is necessary to show 

 how the choice set enters the calculation of compensating 

 variation (CV), or the level of income required to keep 

 the angler at the same level of expected utility after the 

 quality change. The following expression for CV is taken 

 from the work of Bockstael et al. (1991), who examined 

 the value of quality improvements in the demand for 

 recreation, where j3^, is the travel cost parameter. 



Uj(.qj,y-Pj,£j) = Vj(qj,y-Pj) + ej, 



(1) 



CV 



ln(l..,^'"^-1-l"l"(l..,^"""" 



(6) 



