Angler survey and estimation equations

level of crowding the angler expects; t is a vector of attributes of the available sites, including the costs of traveling to them and other attributes that may be influenced by management tools; and x is a vector of the anglers’ relevant socio-eco- nomic characteristics. The choice of which site to visit on any given day is a discrete one. Let the available sites be denoted S j for j = 1,..., J. D enote the probability that a particular site will be visited on any given day as ProbS j

c, t, x, where c is a vector of

site-specific crowding measures. The total visits to the jth site TV j by an angler to a specific site during the season is given by the product, ProbS j ·R ·. The marginal effects of changes in exogenous variables, c, say, at the ith site on TV j , in elasticity terms, are given by the gradient [{d[ProbS j ]dc i }[R ]+ [P S j ]{dR dc i }·] c i TV j i, j = 1, J 1 The elements of c will include variables that can be influenced by management tools and levels of crowding. To evaluate the efficacy and implica- tions of various management tools and self-regu- lation, we focus on estimating the signs and magnitudes of these changes. F or the visitation length decision, we use a travel cost model from Bell and Leeworthy 1990 and H of and K ing 1992. F or the site selection decision, we use a discrete choice, mixed logit model Caulkins et al., 1986; Siderelis et al., 1995. Economic theory suggests that increases in the costs associated with a given site lead to decreases in visitation to the site. Similarly, improvements in attributes considered desirable undesirable will lead to increases decreases in visitation. The effect of increased crowding, however, is less clear-cut. Jacob and Schreyer 1980 were among the first to discuss the normative dimensions of crowding and suggested that peoples’ perceptions of crowding are relative. The idea of social norms for crowding has important implications for re- source managers. Social norms are norms that individuals believe are held by the group and dictate appropriate behavior in specific settings Schwartz, 1977. In recreational fishing, social norms may induce self-regulation by anglers. If anglers disperse over a widening area as crowding increases and, if the norm regarding the distance between anglers is such that resource impacts are minimal, then self-regulation will help control hu- man impacts. N orms for appropriate distance may be influ- enced by recreational activity style, the resource intensity required for the activity and tolerance for diversity Jacob and Schreyer, 1980. This suggests that visitors’ responses to crowding will vary with a multitude of factors. Yet, after a quarter century of research, no consistent, clear impact of crowding on behavior has emerged Brown and M endelson, 1984; M cConnell, 1988; K uss et al., 1990; Berrens et al., 1993. These mixed findings are possibly explained by Schneider and H ammitt 1995 suggested three possible responses to crowding: product shift, ra- tionalization and displacement. Product shift means that the recreationist changes her concep- tion of what the experience should be in response to unexpected conditions. R ationalization occurs when crowding forces the visitor to examine the recreation experience, yet after examination the visitor decides that crowding has no impact on the quality of the activity. The visitor views the recre- ation experience as the same even though greater congestion is present. D isplacement occurs when the visitor’s response to crowding is to leave. Only displacement reduces crowding at a site. Shelby et al. 1988 suggest that rationalization operates strongly for recreation activities that re- quire large expenditures of time or money. If this is the case, major destination fisheries such as the G YE may be poor candidates for displacement by self-regulation.

3. Angler survey and estimation equations

3 . 1 . GY E angler sur6ey D uring the summer of 1993, we distributed 1100 questionnaires to trout anglers at five G YE sites. These sites are among the best known in this world-famous, blue ribbon trout fishery that in- cludes the headwaters of the M issouri, Yellow- stone and Snake R ivers. To many serious fly Table 1 D escriptive statistics travel cost data S.D . Variable M ean LN D AYS natural log of the number of days spent in G YE during season 2.14 1.05 OSC on-site costs, in dollars 81.29 86.36 459.19 LD TC long-distance travel cost, in dollars 443.89 0.94 PR IM P 1 if fishing is primary purpose of trip, 0 otherwise 0.23 43.76 AG E Age in years 14.43 0.98 CATCH R ATE number of fish caught per hour during day of fishing 1.18 SK ILL angler’s self-assessed fishing skill, Likert scale, 1,...,10, 10, most skilled 7.04 2.09 18.16 Crowding number of anglers encountered during the day’s fishing 15.72 K ID S number of angler’s children 1.52 1.57 0.68 M AR R IED 1 if married, 0 if not 0.47 1555.6 1382.10 OR EXP annual expenditures on outdoor recreation, in dollars 0.93 G EN D ER 1 if male, 0 if female 0.25 5.07 ED U Likert scale, 1,...,6; 1 if grade school graduation, 6 if angler holds graduate degree 1.26 .012 0.32 G ALLITAN 1 if angler intercepted at G allitan R iver, 0 otherwise 0.22 SLID E IN N 1 if angler intercepted at Slide Inn of M adison river 0.41 0.32 0.41 YELLOWSTON E 1 if angler intercepted at Yellowstone R iver in YN P 0.05 0.22 CABIN CR EEK 1 if angler intercepted at Cabin Creek of M adison R iver anglers, few if any good substitutes exist for these waters. Surveys were either handed to an- glers on or near the rivers or left on the wind- shields of cars at parking lots popular with anglers. In either case, a letter with an Oregon State U niversity letterhead asked anglers to com- plete and return the surveys in a pre-addressed, stamped envelope. Surveying was done at two different locations on the M adison R iver in M on- tana, known locally as Cabin Creek and Slide Inn, as well as at three different sites within YN P: Slough Creek, the G allitan R iver and the Yellow- stone R iver. Anglers returned 386 35 of the surveys. Al- though this response is somewhat low, the re- sponses are much the same as those we received in personal interviews with anglers conducted in the G YE 2 years later. 4 As a possible check for low response biases, we tested if individual responses on key variables such as income and catch rate were related to returning the survey late. 5 We rejected the hypothesis that late returned re- sponses were different from non-late responses a 5 0.01, 2-tailed test. In addition, the propor- tions of anglers at the surveyed sites within YN P closely mimic the proportions reported by the N PS F ranke, 1997. The survey contained three parts. All anglers were asked to complete Part 1, which collected information on fishing quality, angler’s demo- graphic variables, travel cost and on-site costs. Part 2 was completed by anglers spending multi- ple days in the G YE, but only visiting the G YE. Part 3 was completed by multiple day anglers who were also visiting destinations outside the G YE. Part 3 collected detailed information on the other destinations visited by the angler and, from this information, we constructed the additional mileage resulting from the G YE visit. Our sample consists of visitors arriving at the G YE by commercial plane 27, private cars 70, or motor homes 3. R espondents were overwhelmingly male 93, highly educated the mode response for level of education was ‘gradu- ate degree’ and predominately wealthy the mode response for income level using ten different cate- gories was ‘\ 100 000’. M ost anglers viewed themselves as skilled anglers; on a scale of 1 – 10 most skilled the mean response was 7.04. M ost 4 This latter survey was conducted by the H enry’s F ork F oundation on the H enry’s F ork of the Snake R iver, also in the G YE. 5 We distributed the surveys throughout the summer up to August 20. We classified late surveys as those returned with postmarks after Labor D ay. Table 2 D escriptive statistics site selection model COST TO SITE travel cost to site from location the previous night, in dollars 54.02 42.02 Variable S.D . M ean 42.83 COST TO SITE travel cost to site from location the previous night, in dollars 54.72 Crowding average number of other anglers encountered at the site 18.16 15.72 CATCH R ATE average catch rate at the site 0.98 1.18 K EEP 1, legal to keep any fish caught, 0, otherwise 0.20 0.40 CATCH AN D R ELEASE 1, illegal to keep any fish, 0, otherwise 0.40 0.20 H H Y1-H H Y4 annual income, 1 = 0, 10 = greater than 100 000 8.69 20.34 TYPE1-TYPE4 1, local residence, 0, otherwise 0.14 0.02 spent a considerable sum of money in outdoor recreation during the year average, 1382.10. The anglers surveyed averaged slightly over 11 days fishing in the G YE during the season. The average respondent encountered slightly over 18 other anglers each day on the stream. The data were used to estimate visitation length and site selection model. D escriptive statistics and short definitions for the variables used in estima- tion are given in Tables 1 and 2. 3 . 2 . V isitation length F irstly, consider the decision of how many days to visit the G YE. We separate travel costs into long-distance travel costs LD TC and on-site costs OSC Bell and Leeworthy, 1990; H of and K ing, 1992. This formulation says that, when traveling to a distant fishery, the angler decides how many long-distance trips to make to the fishery and the number of days to spend each trip. Together, these make up the anglers’ visitation length. The dependent variable used in modeling the number of days in the G YE is lnD AYS, the log e of the number of days the angler spends fishing in the G YE between October and M ay. The three categories of explanatory variables are travel costs, composites of G YE site attributes including congestion and demographic variables. 3 . 3 . V isitation length determinants We expect that LN D AYS will be inversely re- lated to the OCS of angling. H owever, the direc- tion of influence of LD TC is ambiguous. As LD TC increases, anglers will reduce the number of trips to the G YE, but may stay longer each trip. A substantial increase in trip duration could result in an increase in lnD AYS Bell and Leewor- thy, 1990. We separated LD TC from OSC differently for three different types of visitors: 1 Visitors mak- ing a single-day trip had all costs associated with their visit allocated to on-site costs and were assigned a LD TC equal to zero; 2 Anglers mak- ing multi-day trips to the G YE, but to no other sites, were assigned OSC costs equal to the sum of their single-day travel cost to the site, the cost of the prior night’s lodging and costs for fishing equipment purchased that day; 3 Anglers visit- ing the G YE in the course of a multiple destina- tion trip were asked if their total driving distance changed due to their stop in the G YE. If individ- uals were driving through the G YE on their way to another destination and indicated that their long distance travel plans would not have changed if they had not stopped in the area, we assigned them a LD TC of zero. If their total trip length did change because of coming to the G YE, we calculated their incremental increase in mileage traveled to visit the area and added the cost of this mileage to LD TC. Our sample consists of anglers who flew and rented a vehicle, drove their own vehicle, or drove a rental vehicle. Costs per mile for private vehicles were calculated at the costs of operating various types of vehicles, 0.47mile for cars and 0.54 mile for cars pulling trailers U S D epartment of Transportation, 1984, adjusted to June 1993 transportation prices U S D epartment of Labor, 1992. M otor home costs were obtained from local vendors of rental vehicles and included a base charge of 800, a rental fee of 0.16mile for any miles over 800, as well as gasoline costs of 0.12mile. M ileage was calculated from the R and M cN ally R oad Atlas. When there was more than one adult in the angler’s party, the calculated automobile costs were divided by the number of adults in the party. We used survey responses to identify anglers who flew to the G YE, but we did not obtain direct information on airfare. We approximated airfares by using a sample of actual air fares from 120 U S cities to Jackson, WY and Boze- man, M T, the two most likely airports used by G YE anglers. We estimated the following equa- tion for air fares t -statistics in parentheses: Airfare = 280.9 − 146.3 DUM + 0.14 M L 4.14 1.74 4.15 + 0.07 DUM M L 1.14 R 2 = 0.81; F = 76.33; N = 120 where DUM = 0 or 1 depending on whether the trip was \ B 1500 miles and M L is the one way mileage of the airplane trip. The vari- able DUM and its interaction with M L capture the effects of fixed costs and scale economies in the purchase of airline tickets. Predictions for airline costs were obtained by substituting mileage from the anglers’ origins into the above equation. A measure of the opportunity cost of time was also included in LD TC, but not OSC. We calculated this cost per hour as one-third of the anglers annual income divided by an estimate of the number of hours worked per year 1920. We estimated the hours of long-distance travel as distance from the angler’s origin to the G YE divided by 50 for automobile travelers and by 300 for airline travelers. 3 . 4 . Demographic 6ariables D emographic variables influencing visitation length include age AG E, a binary variable for gender G EN D ER ; 1, male, 0, female, marital status 1, M AR R IED , number of children K ID S, level of education ED U , annual ex- penditures for outdoor recreation OR EXP as a proxy for income Shaw, 1991, the angler’s per- ception of her fishing skill SK ILL. F inally, we include a binary variable, PR IM P = 1 if the pri- mary purpose of the visit was fishing and 0 oth- erwise. 3 . 5 . S ite attributes We include two site attributes that are likely to be important in anglers’ visitation length de- cision. CATCH R ATE is the number of fish caught per h by the angler and crowding is the number of other anglers encountered by the sur- vey respondent. The myriad unmeasured at- tributes of the five surveyed sites are proxied by four dummy variables. G ALLITAN , 1 for a G allitan R iver angler and 0 otherwise; CABIN CR EEK , 1 for an angler on the M adison river near Cabin Creek; SLID E IN N , 1 for the M adison R iver near Slide Inn; and YELLOW- STON E, 1 for the Yellowstone R iver near Buf- falo F ord inside YN P. Slough Creek, a tributary of the Lamar R iver in YN P, is the referent site. The visitation equation we estimate is LN D AYS = b + b 1 OSC + b 2 LD TC + b 3 PR IM P + b 4 AG E + b 5 CATCH R ATE + b 6 SK ILL + b 7 CR OWD IN G + b 8 K ID S + b 9 M AR + b 10 OR EXP + b 11 G EN D ER + b 12 ED U + b 13 G ALLITAN + b 14 CABIN CR EEK + b 15 SLID E IN N + b 16 YELLOWSTON E We expect b 1 B 0, b 5 \ 0. The signs of the other parameters, including b 2 and b 7, are not indicated by economic theory. 3 . 6 . S ite selection model We use a discrete choice, or random utility model to estimate the probability an individual visits a specific site based on a vector of congestion vari- ables at each site, c; a vector of other attributes of the sites, t and a vector of individual characteristics, x . On any given day in the G YE, the angler chooses the site that yields the highest level of utility. The mixed logit specification of the probability that an angler visits the j th site is ProbS i = e r c + b t + a x r c + b t + a x j = 1, 2, ....5, where a and b and r are vectors of parameters to be estimated. The 5 G YE sites are denoted: 1 = G allitan R iver, 2 = Slide Inn M adison R iver, 3 = Yellowstone R iver, 4 = Cabin creek M adison R iver. The refer- ent site is Slough creek. The means and S.D . of the variables used appear in Table 2. The first discrete choice site attribute is the site-specific COST TO SITE, the cost of travel from the place the angler stayed the previous night to the site. 6 We also included the average number of anglers that our respondents encountered at each site crowding, the average catch rate per angling hour at the site CATCH R ATE and two dummy variables indicating the type of fishing regulations at the site. The first of these, K EEP = 1 if it is legal to keep any of the fish caught and 0 otherwise. The second, CATCH AN D R ELEASE = 1 if all caught fish must be released and 0 otherwise. The referent sites have regulations such that some types of fish may be kept and others must be released. 7 M any individual characteristics were considered for inclusion in the discrete choice model. These included marital status, number of children, skill level and a dummy variable indicating if fishing was the primary purpose of the G YE visit. Based on likelihood ratio tests, two variables were retained in the estimates we report here. The first measures the respondent’s income, H H YJ , a ten-category scale from ‘0’ to ‘\ 100 000’, with : equal intervals. The second variable is TYPEJ = 1 if the angler resided in the local area and 0 otherwise. The J suffix on H H Y and TYPE indicates that a separate coefficient is estimated for each of the four non-referent sites. Slough creek S j = 5 is the referent site and is omitted. 8 The site choice specification we estimated is rc + bt + ax = r 1 CR OWD IN G + b 1 COST TO SITE + b 2 CATCH R ATE + b 3 K EEP + b CATCH AN D R ELEASE Table 3 Travel cost equation estimated coefficients a Absolute t -statistic Coefficient Variable Constant 0.747 1.690 OSC −0.001 2.034 LD TC 3.507 0.0004 PR IM P 0.996 3.986 AG E 2.501 0.012 0.126 2.435 CATCH R ATE SK ILL 0.089 2.988 −0.006 CR OWD IN G 1.598 K ID S −0.103 2.296 1.910 −0.282 M AR R IED 0.00005 OR EXP 1.209 G EN D ER −0.154 0.649 −0.105 2.177 ED U 0.067 G ALLITAN 0.332 0.313 CABIN CR EEK 1.141 0.648 YELLOWSTON E 0.102 −0.497 SLID E IN N 3.068 a R 2 , 0.294; Adjusted R 2 , 0.248; F 16 247, 6.42; N , 264. 6 R andall 1994 notes that the decisions such as lodging location on the previous night may be endogenous. The coeffi- cient for COST TO SITE should, therefore, be interpreted with caution. 7 On Slough Creek and the Yellowstone R iver all caught fish must be released. Only on the Cabin Creek section of the M adison can fish of any species and size be kept. 8 We also attempted to estimate separate intercepts for each of the non-referent sites and for locations in or out of YN P. H owever, we encountered convergence problems because of collinearity between these intercepts and K EEP and CATCH AN D R ELEASE. Consequently, the coefficients on these vari- ables may be picking up some of the effects of non-measured attributes. Table 4 Site selection model estimated coefficients a Absolute t -statistic Variable Coefficient COST TO SITE 10.41 −0.055 CR OWD IN G 3.02 −0.68 5.32 18.37 CATCH R ATE K EEP 6.23 3.88 9.41 3.34 CATCH AN D R ELEASE H H Y1 2.58 0.030 0.51 0.008 H H Y2 H H Y3 0.009 1.30 2.25 0.01 H H Y4 −1.04 TYPE1 1.16 TYPE2 0.98 −1.21 0.54 −0.34 TYPE3 1.27 TYPE4 −1.04 a LF , −285.1; R estricted LF , −429.72; x 2 significance level, 0.000002; n = 1335. cant at conventional levels. Site attributes have strong influences on visita- tion length. One would expect that catching more fish is viewed positively and we find that CATCH R ATE positively influences LN D AYS. Of the lo- cation dummy variables, SLID E IN N is negative and significant. This indicates that anglers who frequent the Slide Inn area of the M adison R iver tend to spend fewer days in the G YE than those who visit Slough Creek. The estimated crowding coefficient is negative, with a t -statistic of 1.60. This provides weak evidence anglers self-regulate in response to crowding. 4 . 2 . S ite selection estimation The site selection model estimates are in Table 4. Overall, the estimated equation has consider- able explanatory power and most of the coeffi- cients are statistically different from zero. We reject the null hypothesis that all of the slope coefficients are zero a 5 0.01. F irst consider the site attribute variables. The estimated coefficient for COST TO SITE is nega- tive as expected and statistically significant. Sites that are further away, therefore costing more to visit, are less likely to be visited by an angler who has arrived in the G YE. The estimated coefficient for crowding is negative and statistically signifi- cant a 5 0.01. The implication is that there is some angler self-regulation; anglers respond to increased crowding by moving to alternative sites. The large, positive and significant coefficient on CATCH R ATE indicates that anglers are very sensitive to the number of fish they catch, some even in the quality waters of the G YE. Increases in CATCH R ATE at a particular site lead to increases in the probability that a site is visited, ceterius paribus. The estimated coefficients associ- ated with K EEP and CATCH AN D R ELEASE are both positive and statistically different from zero a 5 0.01. Both catch-and-release manage- ment and regulations that allow any fish to be kept, encourage anglers to use a site. Complex regulations that target certain fish species or sizes for mandatory release seem to discourage visita- tion to a site. This may be due to anglers’ aver- sion to the complexities of the regulations and + a 1 H H Y1 + a 2 H H Y2 + a 3 H H Y3 + a 4 H H Y4 + a 5 TYPE 1 + a 6 TYPE 2 + a 7 TYPE 3 + a 8 TYPE 4

4. Estimation of anglers’ behavior