6. Estimated Revenue Functions
In this section, we describe the calibration processes and present the estimated NRP and gate revenue
functions. We calculate both parametric and non-parametric estimates of the revenue functions. The
parametric estimates of the revenue functions are based on the DBDC model and methods outlined in
Section 5. The non-parametric estimates of the revenue functions are based on the Turnbull distribution-
free estimator. These estimates are a direct reflection of households’ “YES” or “NO” responses to the
various bids presented in the CV analysis (see Haab and McConnell, 2002). For simplicity, we focus on
the non-parametric estimates and make the parametric estimates available upon request.9
6.1 Calibration
All the revenue functions are calibrated for awareness and hypothetical bias. Begin by considering
the adjustment for “pass awareness”. Approximately 50% of the RDD sample and 4% of the NPF sample
were unaware of both the NPP and GEP.10 Assuming the NRP is marketed in a similar manner, we
expect similar fractions of the respective populations will not purchase the NRP because they do not learn
of its existence. To account for this in our population revenue projections, we calculate NRP revenues in
the sample by summing NRP revenues only for those who were aware of either the NPP or the GEP and
have a maximum WTP that is higher than the proposed NRP price. We then scale that amount up to the
appropriate populations. Estimated gate revenues, include households who were unaware of either the
NPP or GEP, under the assumption such households will continue to visit federal recreation sites and pay
gate fees.
9 The primary difference between the estimates is that the non-parametric model has more success predicting the
smaller number of households that place themselves at the tails of the WTP distributions (see Greene (2003), page
685). Although the revenue functions tend to have a similar shape, the peak revenue occurs at a significantly lower
price for the parametric estimates.
10 The NPF sample consisted of telephone numbers that had belonged to households purchasing the NPP from one to
two years before the survey was conducted. Some of those telephone numbers may no longer have belonged to the
households that bought the pass, and respondents reached at those numbers might have been unaware of both the
NPP and the GEP.
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