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).
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).
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).
Additional Tests of Economic Theory
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.
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.
Additional Specification Tests
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.
Table 1: Variables
|YES||Response 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|
|COST||Increase in the total cost of taking bass fishing trips|
|CATCH||Response to: 'About how many bass did you catch during 1991?' includes those caught and released|
|INCOME||The variable is categorical and coded as the midpoint of the income category and divided by 1000: |
$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
|EMPLOY||Has a Job/Business=1, Not Employed=0|
|EDUCATIO||Years of completed schooling|
|MARRIED||Married=1, Not Married=0|
|AGE||Age of the respondent|
Table 2: Descriptive Statistics
|Valid N (listwise)||196|
Table 3: Logistic Regression Results
Dependent Variable = YES
|Model 1||Model 2||Model 3|
|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.
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.