use value is positive, individuals will be observed
participating in recreation.
The probability of participation is equal to the
probability that the mean valuation function with
mean zero random error is greater than zero
(7) π1 = π [/(p1*, pi, m; τ) + ɛ > 0 ]
πι = π [/(p1*, pl, m; τ) > -ɛ ]
where π1 is π(xι > 1). The probability of participa-
tion can be estimated with one of several discrete
choice econometric models (Amemiya). The logis-
tic regression model has been recommended for
recreation economic applications and is used here
(Stynes and Peterson 1984). The logit equation
specifies the log odds of recreation participation to
depend on a linear spécification of the index variable
in equation (6) as:2
(8) In
TTlj
1 - πlj
√
= α + βpιj + γ ' Zj
where π1j is the probability of participation by indi-
vidual j at site 1, α and β are coefficients, γis a
coefficient vector, and z is a vector of independent
variables to account for individual differences, in-
cluding income. From the theoretical valuation
function, trip costs and income are required in esti-
mation of the participation equation. Taste and pref-
erence indicator variables should also be included in
the regression. No restrictions on functional form is
suggested by theory.
Once the maximum likelihood coefficients are
found for equation (8), the logit equation can be
solved for the unobserved probability of participa-
tion for each individual in the sample
(9) πlj =----------ʌ----.----∙
1 +exp{ - [α+ βpij + γ'zj]}
Ex-ante, each individual has a nonzero probability
of choosing to participate. An individual is expected
to participate (not participate) if the estimated prob-
ability is > (<) .50. Exploiting this information al-
lows estimation of the latent use value. First, the
probability of participation for each individual is set
to .50 to solve for the maximum trip cost that would
be tolerated by the individual
fY + V , 7∙
(10) pij(πlj = .5) =---I-K
β
The maximum trip cost is the maximum willing-
ness to pay per trip. A property of maximum will-
ingness to pay per trip is that if the recreation
probability is greater (less) than .50, maximum will-
ingness to pay per trip will be greater (less) than the
observed trip cost.
Next, the difference between the estimated maxi-
mum willingness to pay and the observed trip cost
for each individual (pŋ - pŋ) can be calculated. This
value is positive for expected recreation participants.
The difference in the maximum willingness-to-pay
per trip and the observed trip cost is the use value per
trip (UVij / Ху). Use value per year is equal to use
value per trip multiplied by the number of trips taken
during the past year. For expected recreation non-
participants, use value per trip is negative. But,
because the actual trip cost is observationally equal
to the reservation price for expected recreation non-
participants, the expected number of trips and use
value must be equal to zero for this group. Therefore,
use values for expected nonusers are set equal to
zero.
EMPIRICAL ESTIMATES OF USE VALUE
The Study Area
In the western Kentucky coalfield along the lower
Ohio River, surface coal mining is a competing use
of wetlands that contributes to the conversion of
wetland acreage. These wetlands provide functions
such as fish and wildlife habitat, water quality im-
provement, flood control, and outdoor recreation.
Surface coal mining directly reduces wetland func-
tions by converting wetlands to mined areas and
indirectly reduces wetland functions by its negative
effect on the water quality of downstream wetlands.
Within the western Kentucky coalfield a three
county recreation region was identified from maps
of the area (Mitsch et al. 1983)?
Within the three-county region, the Kentucky De-
partment of Fish and Wildlife Resources (KDFWR)
manages public hunting areas, and private coal com-
panies, in cooperation with the KDFWR, manage
reclaimed surface coal mines as wildlife areas, rec-
reation areas, and waterfowl refuges. The region is
a popular deer hunting area (Shadowen et al. 1984;
2The standard conceptual model of recreation participation utilizes the household production function approach (Deyak and
Smith 1978). The valuation function approach used in this paper results in identical empirical specifications of the participation
decision.
3The counties were Hopkins, Muhlenberg, and Ohio.
115