184 July 1989
Western Journal of Agricultural Economics
that part of the day that pertains to the primary
activity, e.g., the four hours devoted to fishing
each day.
Willingness to pay for a constant unit of rec-
reation use of an existing site should be ap-
proximately the same since both methods yield
similar though not identical demand curves.
The TCM estimates an ordinary Marshallian
demand curve while the CVM estimates a
Hicksian compensated demand curve. Both
approaches specify that benefit is a function of
the number of trips to a recreation site which
is separable in consumption and subject to a
budget constraint. If the specification of quan-
tity and other variables can be controlled, the-
ory suggests that there should be little or no
difference between values obtained by the two
methods.
A variable indicating location of the study
sites in Forest Regions is included as a proxy
for socioeconomic characteristics of the user
population. Since the regression model con-
trols for site quality and substitutes, the other
important effect of location is the distribution
of income and other socioeconomic charac-
teristics of the population in the relevant mar-
ket for the study site. While extensive data on
household demographics and equipment own-
ership are available for outdoor recreation ac-
tivities from national and state samples, sim-
ilar information is available only for a small
fraction of the studies reviewed here. Thus,
this important feature of variation in benefits
would have to be ignored without an effective
proxy variable.
Statistical Results
With the increased output of empirical studies
in recent years, there is enough data to begin
understanding the variables which explain the
observed differences in benefit estimates. Ta-
ble 3 includes three functions showing the sta-
tistical relationship of recreation benefits to
some important explanatory variables. These
are for the total sample of 287 benefit esti-
mates, 156 TCM and related estimates, 129
CVM estimates (and two hedonic price esti-
mates). The number of observations is suffi-
cient for statistically significant analysis. The
R2, adjusted for degrees of freedom, indicates
that 36% to 44% of the total variation in the
reported values is explained by the variables
included in the functions. The overall equa-
tions are significant at the .01 level. The /-sta-
tistics shown in parentheses beneath the coef-
ficients indicate that about two-thirds of the
variables (27 of 42) are significant at the .10
level or above. Omission of the coefficient for
a variable (—) indicates that it is not statisti-
cally related to benefits.
The panel nature of the data render the usual
statistical tests of the model an approximation
rather than a precise estimate. Although the
residuals are close to normally distributed, het-
Croskedasticity is likely to be present in any
study with parameters drawn from different
data sets. Even though review of the correla-
tion matrixes indicates mostly low levels, mul-
ticollinearity is likely to result from inclusion
of more than one benefit estimate from some
studies. The Cstatistics somewhat over- or un-
derestimate variable significance based on a
Smith and Kaoru comparison of OLS esti-
mates with the Newey and West variation of
the White consistent covariance estimates of
standard errors used in calculating /-statistics.
Of primary interest here are the variables
estimating the effect of the three adjustments
in benefit by Sorg and Loomis, namely, for
omission of travel time cost, use of the indi-
vidual observation approach, and for in-state
samples at sites with out-of-state users. The
increase in reported values by 30% for omis-
sion of travel time cost seems to be about right.
The statistically significant coefficient indi-
cates that TCM benefits are about 34% less for
the 30 studies omitting travel time cost, other
variables in the equation held constant. (The
13.333 coefficient for travel time cost is 34%
of TCM mean value of $39.) On the other
hand, the decrease in reported benefits by 15%
for use of the individual observation approach
seems quite conservative. The significant coef-
ficient indicates that benefits are 46% greater
for the 52 TCM studies using individual ob-
servations. The increase of both TCM and
CVM values by 15% for omission of out-of-
state users appears to be about right for the
total sample where the coefficient shows a 20%
increase, although not statistically significant.
The 15% adjustment seems conservative for
TCM studies where the significant coefficient
indicates the correct adjustment would be an
increase of about 30%. Thus, while the three
adjustments appear about right or to err on the
low side, their overall effect is reasonably cor-
rect. The regression for the total sample (table
3) indicates that when variations in site qual-