start with our estimate of hypothetical bias, Δ, which is measured in terms of the increased probability the
NRP is purchased. This value is estimated using the method outlined in Section 5.2 and is represented by
the etched area in Figure 1. We then calculate the value of exp(δ) consistent with Δ assuming a normal
distribution with standard deviation σ. Finally, we use the resulting WTP scale factor, exp(δ), to form the
calibrated WTP estimates [WTPi / exp(δ)] that more accurately reflect actual purchasing decisions of
households.
We now turn our attention to the estimation results from the hypothetical bias model outlined above.
We estimate the hypothetical-bias model separately for the RDD and NPF samples. The first row of
Table 5 presents the estimates of (δ∕σ) under the coefficient heading and estimates of Δ under the
marginal effect (ME) heading. In both samples, the hypothetical bias coefficients are positive and
statistically significant. Furthermore, the ME estimates indicate that, all else equal, the average RDD and
NPF stated-preference households are 13.6 and 12.6 percentage points more likely to purchase a $65 pass
than similar revealed-preference households. The control variables include respondent and household
demographics such as age, gender, education, race and region of residence.
As discussed above, the estimates of Δ need to be translated from a probability into a WTP scale
factor (i.e., we need to map our estimates of Δ into estimates of exp(δ)) for the purpose of calibrating the
WTP estimates for hypothetical bias. To accomplish this, we use the baseline DBDC estimates reported
in Table 4. The estimated value for the hypothetical bias calibration factor, exp(δ), is approximately 1.4
and 1.3 for the RDD and NPF samples. Table 6 reports the details for this calculation. Put differently,
the RDD and NPF WTP values would need to be reduced by 40% and 30% to be consistent with the
observation that stated-preference households are 13.6 and 12.6 percentage points more likely than
revealed-preference households to purchase the pass at $65. The revenue functions reported below are
scaled by exp(δ) to more accurately reflect the actual purchasing decisions of households.
was not described to our survey respondents.
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