FISHERY BULLETIN: VOL. 87, NO. 1 



(e.g., see Kealy and Bishop 1986), our focus on mar- 

 ginal success valuations (i.e., 3P/3S) makes Equa- 

 tion (4) more appropriate since no parameter trans- 

 formations are necessary.' 



Equations (3) and (4) were estimated first by or- 

 dinary least squares (OLS). Because the data are 

 cross sectional on individual marine anglers, large 

 variations in travel frequencies and cost exist which 

 could lead to errors with unequal distributions. Vari- 



'Two statistical issues are relevant in the context of choice of 

 dependent the variable: 1 ) The choice of dependent variable (e.g. , 

 In Q or In P) affects the regression slope unless the correlation (e.g., 

 between In Q and In P) is perfect. Thus, estimating the In Q rela- 

 tionship and solving for In P generally yields a different estimate 

 for 3 In P/3 In Q than estimating the In P relationship directly. 

 For a clear treatment of this point, see Wonnacott and Wonna- 

 cott (1979). 2) In addition, we note that parameter unbiasedness 

 generally does not hold under nonlinear transformation although 

 consistency does. Thus, partial effects on P using Equation (4) are 

 potentially both unbiased and consistent whereas when using Equa- 

 tion (3) unbiasedness is lost for partial effects on P. 



ous tests for heteroscedasticity were performed on 

 the OLS residuals including Park, Glejser, and 

 Bruesch-Pagan tests. The results were mixed with 

 some tests indicating insignificant heteroscedas- 

 ticity and some indicating significant (0.05 level, 

 two-tailed) relationships between OLS residuals and 

 travel cost (In P) or travel frequency (In Q) in Equa- 

 tions (3) and (4) respectively. Since the Glejser tests 

 indicated the strongest relationship between the ab- 

 solute OLS residual and the square root of In P or 

 In Q in Equations (3) and (4) respectively, weighted 

 least squares (WLS) was performed using l/\/X 

 (i.e., where X is In P or In Q in Equations (3) and 

 (4) respectively). 



The results are found in Tables 2 and 3 for both 

 OLS and WLS applied to the demand frequency (Q 

 endogenous) and demand price (P endogenous 

 models). The variables trip frequency (Q), trip cost 

 (P), fishing success (S), and income (I) were defined 



Table 2. — Log-linear demand frequency regressions (Equation 3). OLS = ordinary least 

 squares; WLS = weighted least squares. 



^Computed from the formula (Afl^) {n-k-1)/(1 - R^) (r) where r, R^, and (n-k-1) represent the number 

 of restrictions, coefficient of determination, and degrees of freedom of the unrestricted model in hier- 

 archial order (1), (2). and (3) respectively See Wonnacott and Wonnacott 1979 



228 



