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

variables (X or SP), only depend on the identifiable ratios. For the average household, the marginal effect
for hypothetical bias is

Δ = Pr(y = 1| X, SP = 1) - Pr(y = 1| X, SP = 0)
= φ(X '(β / σ) + (δ / σ)) - φ(X '(β / σ))

This coefficient is defined in terms of increased (or decreased) probability of pass purchase. In the next
section, we describe how to translate Δ into a WTP scale factor using the baseline DBDC model.

5.3 Translating a Probability into a Dollar Measure of Hypothetical Bias

The coefficient of hypothetical bias Δ in expression (12) is measured in terms of probability the pass
is purchased. Although this provides evidence of hypothetical bias, it does not allow household WTP and
welfare measures to be directly adjusted to reflect revealed preferences. Furthermore, the probit model
shown in expression (10) does not identify a dollar amount of hypothetical bias because the bids are not
varied (i.e., the bid is fixed at $65). Fortunately, the DBDC model described in Section 5.1 uses the entire
bid vector and allows us to identify household WTP.

We use the normal distribution along with estimates of β and σ to back out the WTP hypothetical bias
scale factor consistent with Δ for the average household. This is accomplished by solving for δ (given
estimates of β, σ, and Δ) from the following equation:

Δ = Pr(WTPsp > $65) - Pr(WTpRP > $65) = Φ(-¹(X'β + δ - ln($65))) - Φ(-¹(X'β - ln($65))), (13)

σσ

where a bar over the variable represents its average value. Figure 1 illustrates the procedure for
identifying exp(δ), the WTP scale factor for hypothetical bias. The procedure is straightforward. We

NPP or GEP. This was done to level the playing field because the “receipt policy” may alter the value of a pass and

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