Willingness to Pay for Bass Fishing Trips in the Carolinas

by

May 1998

Introduction

The purpose of this paper is to estimate a model to determine the factors which influence bass fishing trips in North and South Carolina. The economic theory behind the analysis can be summarized by the following conceptual model:
Trips = f(cost, income, catch, demographics)
The willingness to take trips is expected to be inversely related with the cost of trips, positively related to the ability to pay for trips (income), and positively related to the quality of trips which is measured by the number of bass caught on all trips (catch).

Methods

The analysis is conducted with data (download SPSS data here) from the U.S. Fish and Wildlife Service of bass anglers from North and South Carolina. The variables used in the empirical analysis are described in Table 1. The descriptive statistics are presented in Table 2. A more complete description of the full data sets can be found in the appendix.

The dependent variable which measures the willingness to take fishing trips at different costs is YES. YES is equal to 1 if the respondent would still take fishing trips if the cost was \$[COST] higher, where COST is a randomly varied amount, and 0 otherwise. Since the dependent variable is discrete, the ordinary least squares regression can be used to fit a linear probability (LP) model. However, the linear probability model is heteroskedastic and may predict probability values beyond the (0,1) range, the logistic regression model is used to estimate the factors which influence trip-taking behavior (Stynes and Peterson, 1984; Greene, 1997).

Results

Logistic regression results are presented in Table 3 (SPSS output). Three models are presented, the dependent variable in each is whether the Carolina bass anglers would continue to take bass fishing trips if the costs of the trips were to increase (YES=1 if they would take more trips, 0 otherwise). Each model includes different blocks of independent variables.

A Test of Rational Choice Theory

The most parsimonious model inclues only the randomly assigned variable which specifies the higher trips costs (COST). The results from Model 1 indicate that anglers behave according to economic theory. As the costs of the trips increase, they are less likely to be willing to continue taking trips. The coefficient on the COST variable has a Wald statistic equal to 13.43 which is significant at the .01 level (99% confidence level) with a critical value of 6.635 [df=1]. The overall model is significant at the .01 level according to the model chi-square statistic. The model predicts 61% of the responses correctly. The McFadden's R2 is .053 (Amemiya, 1981).

Model 2 includes two additional theoretically important independent variables: INCOME and CATCH. According to the block chi-square statistic, Model 2 is superior to Model 1 in terms of overall model fit. The block chi-square statistic is significant at the .01 level (critical value = 9.21 [df=2]), the percentage of correct predictions increases by 6%, and the McFadden's-R2 value is almost 100% larger. The coefficient on the CATCH and INCOME variables are statistically significant at the .05 and .10 levels.

Including Demographics

Model 3 includes demographic variables to determine if social forces plays a role in the willingess to take trips. Males (SEX=1) and those who are EMPLOYED are more likely to take trips with higher costs. None of the other demographic variables are statistically significant according to the Wald test. The block chi-square statistic is significantly different from zero at the .05 level. The percentage correct predictions increases slightly while the McFadden's-R2 statistic increases by about 4%. According to statistical performance, Model 3 is slightly superior to Model 2.

The income coefficient becomes insignificant in Model 3. This is due to the correlation between income and the other demographic variables, especially employed. This does not suggest that ability to pay is not an important predictor of the willingness to take trips, ability to pay is now measured with the block of independent variables.

The "odds ratio" for the EMPLOYED coefficient is 3.96 with a 95% confidence interval of [1.23, 12.78]. This suggests that those who are employed are almost 4 times more likely to take trips than those who are unemployed (see Want, Eddy, and Fitzhugh, 1995). The "odds ratio" for the SEX coefficient is 2.67 with a 95% confidence interval of [1.05, 6.78]. This suggests that males are almost 2.67 times more likely to take trips than females. Since the other independent variables are either insignificantly different from zero or continuous, interpretation of there magnitude has little meaning in logistic regression.

Several other regression models were estimated to determine the sensitivity of our results to the geographic location and functional form of the regression model. First, splitting the sample into North and South Carolina residents we find no difference in the vector of coefficients for Model 3 according to the likelihood ratio test (chi-square=5.81[8 d.f.]). We also tried two alternative functional forms. The first is a log model where the increased cost, catch, and income variables are logged. The pseudo-R2 and model chi-square statistics both decrease with the log functional form indicating that the linear model is superior in terms of overall model fit. The second model includes a squared income term as an additional independent variable. The Wald statistics on both the income and squared income coefficients become insignificant indicating that this is an inferior specification.

Conclusions

The purpose of this paper was to estimate a model to determine the factors which influence bass fishing trips in North and South Carolina. The empirical results indicate economic theory is supported: anglers respond rationally to increases in fishing trip costs and their ability to pay. Also, the sex of the angler and their employment status has important effects on the willingness to take trips. Further research will be directed at estimating the economic value of these fishing trips for use in benefit-cost analysis (Loomis, 1989).

Table 1: Variables

VariableVariable Description
YESResponse to the question: 'Would you have taken any trips during 1991 ... if the total cost of all of your trips was \$[COST] more than the total cost amount you just reported?' Yes=1, No=0
COSTIncrease in the total cost of taking bass fishing trips
CATCHResponse to: 'About how many bass did you catch during 1991?' includes those caught and released
INCOMEThe variable is categorical and coded as the midpoint of the income category and divided by 1000:
\$5,000--Under \$10,000
\$22,500--Between \$10,000 and \$19,900
\$22,500--Between \$20,000 and \$24,900
\$27,500--Between \$25,000 and \$29,900
\$40,000--Between \$30,000 and \$49,900
\$62,500--Between \$50,000 and \$74,900
\$85,000--Over \$75,000
EDUCATIOYears of completed schooling
MARRIEDMarried=1, Not Married=0
SEXFemale=1, Male=0
AGEAge of the respondent
NCNC=1, SC=0

Table 2: Descriptive Statistics

N Minimum Maximum Mean Std. Deviation
AGE 196 18 86 37.39 13.16
CATCH 196 0 600 63.11 105.44
COST 196 6 924 414.68 298.00
EDUCATIO 196 4 20 12.56 2.94
EMPLOYED 196 0 1 .84 .37
INCOME 196 5.00 85.00 36.0714 18.5707
MARRIED 196 0 1 .74 .44
NC 196 0 1 .55 .50
SEX 196 0 1 .17 .38
YES 196 0 1 .55 .50
Valid N (listwise) 196

Table 3: Logistic Regression Results

Dependent Variable = YES

Model 1 Model 2 Model 3
Variable Coefficient t-stat Coefficient t-stat Coefficient t-stat
Constant 0.98* 13.91 0.10 0.06 -0.45 0.15
COST -0.0019* 13.43 -0.0020* 13.33 -0.0018* 10.01
INCOME .017* 3.77 .015 2.39
CATCH 0.057* 6.04 0.0059* 6.63
AGE -0.0045 0.082
EDUCATION -0.076 1.50
MARRIED 0.37 0.84
EMPLOYED 1.38* 5.31
SEX 0.98* 4.27
Model Chi-Square [df] 14.488 28.367 31.351
Block Chi-Square [df] 13.88 11.39
% Correct Predictions 60.71 67.35 68.37
Note: The Wald statistics are distributed chi-square with 1 degree of freedom.
*Indicates that the coefficient is statistically signficant at, at least, the .10 level.

References

Amemiya, T., "Qualitative Response Models: A Survey," Journal of Economic Literature, 19, pp. 481-536, 1981.

Greene, William H., Econometric Analysis, 3rd ed. Prentice Hall, 1997.

Loomis, John B., "Contingent Valuation Using Dichotomous Choice Models," Journal of Leisure Research, 20, pp. 46-56, 1988.

Stynes, Daniel J. and George L. Peterson, "A Review of Logit Models with Implications for Modeling Recreation Choices," Journal of Leisure Research, 16, pp. 295-310, 1984.

Want, MinQi, James M. Eddy, Eugene C. Fitzhugh, "Application of Odds Ratio and Logistic Models in Epidemiology and Health Research," Health Values, 19, pp. 59-62, 1995.