Valuing Access to our Public Lands: A Unique Public Good Pricing Experiment

subsample includes every household that received an initial bid of $65 and was unaware of the GEP.⁸
Protest households (i.e., those that refuse the pass for free) are excluded from the analysis.

The underlying economic model is similar to (3) but modified to incorporate hypothetical bias

WTPi = exp(X'β + δ ∙ SPi + ε_i ) = exp(δ ∙ SPi ) exp(X'_iβ + ε_i ),                                (9)

where WTPi is unobserved willingness to pay for either the GEP or the NRP, SPi is a dummy variable
equal to one for the stated preference subsample and zero for the revealed preference subsample, and δ is
the hypothetical bias coefficient. We form the probability (Pi) that the i^th household purchases the pass at
price of $65:

Pi = Pr(WTPi ≥ $65) = Φ(-1 (X'β + δ ∙ SPi- ln($65))) .                                     (10)

σ

Let yi = 1 indicate the household purchased the pass (either hypothetical or real), and let yi = 0 indicate
they did not purchase the pass. This is a probit model with (log) likelihood function

ln L(β, δ | y, X) = ∑i=_ι [y, ln(P_i ) + (1 - y ) ln(1 - P )].                                  (11)

The coefficients β and δ are only identifiable up to the scale factor (1∕σ). That is, because β and δ
only show up in the likelihood function as a ratio with σ (i.e., (β^) and (δ^)) and the price is fixed at
$65, it is impossible to disentangle the ratios and obtain individual estimates of β, δ and σ. However, the
marginal effects, which measure the change in probability for a one unit change in the explanatory

⁷ The design for estimating the degree of hypothetical bias follows Aadland and Caplan (2003).

⁸ We also excluded 61 and 336 revealed-preference households in the RDD and NPF samples who were aware of the
policy that allows receipts from recent entrance fees to federal recreation sites to be applied toward the cost of the

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