An analysis of the goodness of fit statistics for the 9 estimated 

 models show that all but 2 of the logistic models fit the data 

 well. This indicates that the choice of the double log 

 functional form shown in Equation 2 is generally consistent with 

 the distribution of the sample data. Goodness of fit statistics 

 for all models are reported in Tables 10-13. 



Benefit Estimation 



Two measures of benefit per trip were calculated from the 

 bivariate logit models and are presented in Tables 14-16. They 

 are the median and the truncated mean. The truncation point used 

 for the truncated mean was the maximum bid — $500 for all 

 aggregation levels. The truncated mean was calculated by 

 numerical evaluation of the integral shown in Equation 3 since 

 this integral cannot be evaluated analytically for the model with 

 log (bid) as the independent variable. 



Truncated Mean = f (1 - Fix)) dx (3) 



Jo 



Where: Fix) is the probability density function of the 

 willingness to pay distribution. 



It should be noted that use of the truncated mean represents a 

 conservative estimate of the true (hypothetical) mean willingness 

 to pay because all individuals having willingness to pay greater 

 than T are included at the value T. 



The second welfare measure presented in Tables 14-16 is the 

 median of the willingness to pay distribution. The median is 

 defined as the point where 50% of the sample would say "Yes" to 

 the bid. The median is analytically defined as: 



Median = exp|--g-| ^^^ 



Both truncated mean and median are reported as there is currently 

 a debate in the economics literature as to which measure is most 

 appropriate, Duf field and Patterson (1991) argue that the 

 truncated mean is best used since it, unlike the median, can be 

 aggregated over the whole population. 



24 



