including the number of fish caught as well as kept. 

 These numbers were available in total as well as by 

 species. Since the total number of fish kept con- 

 sistently provided the best statistical fit, we report 

 these results only.'" 



Our findings on income are mixed and appear to 

 depend on the equation specification. While an im- 

 portant theoretical variable in most demand func- 

 tions, we find that income is a significant positive 

 determinant of travel cost but not travel frequen- 

 cy. Thus anglers with higher incomes travel greater 

 distances but do not fish with greater frequency. 

 This result is perhaps not surprising given the higher 

 time opportunity cost for anglers with higher in- 

 come. Our results for the lack of significant income 

 effects on demand frequency are similar to findings 

 in other studies (e.g., Vaughan and Russell 1982). 



The coefficients for travel cost (P), frequency (Q), 

 and success (S) in Tables 2 and 3 provide the basis 

 for valuing fishing success. The valuation algorithm 

 is outlined below using the instantaneous (marginal) 

 approach discussed in the paper. Of particular in- 

 terest is the measurement of the marginal value of 

 fishing success (3P/3S) shown as (P, - Pi) in Fig- 

 ure 1)." We illustrate these calculations for sum- 

 mer flounder using the WLS model (3) results from 

 Table 3. Since the regression slope coefficients 

 reflect log derivatives (sometimes referred to as 

 elasticities or price flexibilities), we begin by noting 

 that 



3 In P 



3 In S 



3 P S 

 3 S P' 



(5) 



Solving this equation for 3 P/3 S provides a basis for 

 valuing fishing success (S) using a log-linear model. 



3P 



as 



3 In P 



3 In S 



P 



S' 



(6) 



For summer flounder 3 In P/3 In S = (0.135 - 

 0.056) = 0.079 which reflects the combination of the 

 fish kept (S) term and the flounder and fish kepi (FS) 

 interaction term. Evaluating P and S at their sam- 



'»The design of the survey may in part be responsible for the 

 better fit with fish kept versus fish caught. Fishermen were asl<ed 

 to recall the number of fish landed, whereas the number kept were 

 actually inspected by the interviewer (see Table 1, questions 29 

 and 30). 



'^We also note that by utilizing the marginal trip valuation algo- 

 rithm outlined earlier rather than a consumer surplus integration 

 calculation intercept estimates can be ignored. Thus, since only 

 slopes are relevant there is not need to transform parameters by 

 the factor exp(o'/2) in order to obtain unbiased mean rather me- 

 dian estimates (where o~ is the error variance; see Stynes et al. 

 1986). 



FISHERY BULLETIN: VOL. 87. NO. 1 



pie means of $50.61 and 1.94 respectively we obtain 



3P 



3S 



= 0.079 ($50.61/1.94) = $2.06. 



This number reflects the extra travel cost that a 

 typical or representative fisherman is willing to 

 incur in order to keep an additional fish per trip. In 

 reality, since fishermen incur varying travel costs 

 and experience a variety of success levels, the value 

 of success is not unique. 



Given that S in the calculation above was set at 

 its mean for the entire sample, we refer to 3P/3S 

 in this case as the marginal value of success for the 

 typical fisherman (i.e., mean value). Alternatively, 

 S can be set at different levels to obtain valuations 

 other than at the mean since in a logarithmic model 

 elasticities are constant but derivatives are not. For 

 example, setting S = 1 we obtain a marginal value 

 for the first fish kept of $4.00, which is predictably 

 higher than the marginal value of success evaluated 

 at the mean ($2.06). Since many fishermen catch one 

 fish or even no fish, setting S = 1, although less 

 reliable, does not reflect a large extrapolation. The 

 logarithmic model allows us to observe the behavior 

 of the value gradient for success across species and 

 models. 



In Table 4, marginal success valuations for all 

 three species using various models (demand fre- 

 quency and price) and statistical methods (OLS and 

 WLS) are presented. The demand frequency results 

 are based on the regression estimates from Table 

 2, models OLS (1) and WLS (1) since species pool- 

 ing is appropriate. For the demand frequency 

 results, different valuations are solely a reflection 

 of alternative mean values of P and S across anglers 

 preferring the various species. The combined valu- 

 ation results reflect the weighted means of P and 

 S across all anglers. The demand price results are 

 based on the regression estimates from Table 3, 

 models OLS (3) and WLS (3) because species pool- 

 ing was not appropriate. Different valuations thus 

 reflect both differences in regression coefficients as 

 well as mean values of P and S. For comparison pur- 

 poses with the demand frequency model, combined 

 valuations in the case of the demand price model are 

 based on the regression results of OLS (1) and WLS 

 (1) in Table 3. 



Although the absolute dollar values in Table 4 are 

 subject to qualification, they do provide managers 

 with numbers which can be compared across species 

 as well as with market-determined commercial 

 values. With the exception of the demand price 

 models for weakfish where the combination of the 



230 



