0.7379 (16.1) 0.7584 (17.7) 0.5295 (7.2) 0.6052 (9.7)
Regression for the Hypothetical Adoptors Only - SNP CONTILL -
SMTST 0.6120 (9.7) 0.6722(12.1) 0.7906 (14.8) 0.7749(17.4)
Next, given that the restricted correlation model is not accepted (i.e., the BMP adoption decisions are not independent across BMPs), we turn to an evaluation of how the unrestricted MVN results can be used for analysis of bundling. The basic value of the multivariate analysis is it allows us to calculate the joint probabilities as a function of the incentive payments.
Figures 5.1 through 5.4 provide examples of how the joint probability changes as a function of the incentive payment offers for four of the five BMPs analyzed here, i.e., the curves represent dGC (Ci,..., Cj)/dCj calculated across a wide range of cost share offers. For example, Figure 5.1 plots the probability of non-acceptance of the conservation tillage cost share as a function of the cost share offer amount, given the value of the cost share offers for the other four BMPs. In Figure 5.1, four scenarios (numbers 2 through 5) with different fixed offers for BMPs other than CONTILL are presented. For comparison, scenario 1 is the predicted probability for the standard univariate normal density function that does not explicitly account for the other bid offers.
Given the estimates of the CDFs generated from the analysis of discrete responses in the figures, the question may arise of how to summarize these distributions of WTA for practical purposes. In the discrete choice contingent valuation (CV) literature, the most common summary statistic is the mean of
the estimated WTP or WTA distribution. Given the estimated coefficients from the multivariate probit model, it is possible to calculate measures of conditional mean WTA. Hanemann (1984) notes that in the case where the benefit measure CR is restricted to the non-negative range, its mean value can be found using the following formula for the mean of a random variable:
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