Benefit Estimates 



Three alternative measures of willingness to pay are presented 

 for the deer data. The mathematical expectation (mean) of 

 maximum willingness to pay is first presented and is labeled 

 MEAN-LOGIT. The bivariate forms of the estimated equations 

 (showing the probability of a "yes" response as a function of the 

 bid amount) can be graphed with the probability of acceptance on 

 the vertical axis and the bid amount on the horizontal axis. 

 This graphing shows a high probability of acceptance at low bid 

 amounts. This probability declines and asymptotically approaches 

 zero at high bid amounts. The MEAN-LOGIT is obtained by 

 integrating the logit function from a bid level of zero to some 

 upper limit. The mean of the logit corresponds to the area under 

 the two dimensional curve and thus it can be intuitively 

 interpreted as the probability of a "yes" times the bid amount. 

 In this study the models were estimated using a bivariate 

 specification and the MEAN-LOGIT calculation was based upon this 

 bivariate form (the bivariate specifications of all models used 

 in this study are shown in Appendix B) . The upper limit of 

 integration to be used in the MEAN-LOGIT calculation is the 

 uppermost bid level asked, or $2000. While there is no clear 

 basis for choosing an upper limit of integration it is 

 inappropriate on statistical grounds to extrapolate beyond the 

 range of the sample data (in this case $2000). 



The second measure of willingness to pay presented here is the 

 median of the distribution (labeled MEDIAN) . The median is 

 simply the point where the probability of acceptance equals .5. 

 Solving the bivariate estimates of the equations for P=.5 yields 

 a median which is equal to the antilog of the calculated 

 intercept over the slope coefficient on bids. 



A final measure of willingness to pay is calculated using a 

 nonparametric estimation technique suggested by Duffield and 

 Patterson (1990) . As stated before, the mean of the logit can be 

 intuitively interpreted as the probability of a "yes" times the 

 bid amount. The nonparametric technique explicitly calculates 

 this mean from the bid levels and the responses to those levels. 

 The use of this nonparametric technique sidesteps a constraint of 

 the logit mean by allowing the calculation of a sample variance 

 and hence the construction of confidence intervals around the 

 calculated mean. 



Table 12 shows willingness to pay for each of the three measures 

 (MEAN-LOGIT, MEDIAN, and NONPARAMETRIC) for the current 

 conditions question. These statistics are reported for the 

 entire sample as well as for each of the four hunter subgroups. 

 Although there are significant differences between hunter 

 subgroups, it appears that the surveyed trips are relatively 

 valuable to all hunters. It is interesting to note that the 

 estimated MEAN-LOGIT and the calculated NONPARAMETRIC mean are 



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