Pi4 = Pr(bl < WTPi < ,<) = Φ(-(X'β-ln(bH)))-Φ(-(Xβ-ln(bl))) (6.4)
σσ
Pi5 =--(Pi-+Pi2+Pi3+Pi4). (6.5)
The log likelihood function is then given by
lnL(β,σ)=∑iN=-∑5j=-wijlnPij(β,σ), (7)
where wij is a binary variable equal to one if household i chooses category j. We choose β and σ to
maximize the likelihood function. With estimates of β and σ in hand, we form WTP estimates for every
household in the sample, and in turn the NRP and gate revenue functions.
Table 4 presents the results from the DBDC model.5 Protest households (i.e., those who refuse the
pass for free) are excluded from the analysis, which is consistent with the original screening decision to
exclude households that have not visited any federal lands recently and are unlikely to participate in the
market for the NRP. As compared to the rest of the sample, protest households (N=67 for RDD; N=30
for NPF) tend to be older, less educated, lower income, less likely to be white, and more likely to reside in
the northeast (PA, NY and NJ) and great plains (IA, KS, MN, MO, ND, NE and SD) states.
We incorporate heteroscedasticity into the econometric model because the WTP bid intervals vary
across households. Recall that half of our follow-up bids are either half or twice the initial bid, so higher
initial bids tend to be associated with larger WTP intervals. We use the initial bid to proxy for interval
width and model the heteroscedasticity as
σi2 = exp(α0 +α-bi) . (8)
5 Although not explicitly modeled here, a potential source of explanatory power is the distance to all nearby federal
recreation sites. Measurement of this variable is difficult for various reasons: (i) many federal recreation sites have
multiple points of entry (e.g., national forests), (ii) the definition of ‘nearby’ is arbitrary, (iii) not all recreation sites
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