Dw
i
Dq
i
= − a
+ a
D
D
i
+ a
I
I
i
a
w
17 the individual’s marginal valuation of a change in
environmental quality, Dq.
5. Results
The Binary Choice BC estimation results for the R U M are shown in Table 1. While the exper-
imental design allowed individuals to state an intensity of preferences for or against the alterna-
tive to the status quo, the dependent variable used in BC estimates is coded 1 yes if the individual
designates they would ‘probably yes’ or ‘definitely yes’ prefer the alternative to the status quo, and 0
no otherwise. The 0 response then includes ‘defin- itely not,’ ‘probably not’ and ‘maybe yes – maybe
no’ responses. All estimations were performed using LIM D EP™ procedures.
The simplest BC model is shown in column 1 of Table 1. All signs are theoretically correct and
highly significant in most cases. The implied mar- ginal valuation of an improvement in Stream A
from M oderately Polluted to U npolluted A: M U is
DwDq
1
= 0.2891 − 0.0076 = 38.04. G iven the phrasing of the choice question, this represents
the respondent household’s willingness to pay each year for 5 years for this improvement. The corre-
sponding value for improving Stream B from Severely to M oderately Polluted B: S M is
52.30 per household for each of 5 years; and the value for B: S U is 90.01. These marginal
valuations are shown in Table 3, column 1, along with the S.E. of the calculated values.
The set of choice alternatives was designed to permit testing of interaction effects of Streams A
and B quality changes on each other; for example, to allow testing of whether an improvement in
Stream B from S to M would depend upon whether Stream A was improved from M to U, or vice versa.
U nfortunately, there was too much collinearity when these stream quality change interaction ef-
fects were added to the basic model, and the LIM D EP statistical procedure would not converge.
H owever, if Streams A and B, being in the same region, are strong substitutes, the valuation for B:
S U 90.01 should equal the sum of valuations of B: S M 52.30 and A: M U 38.04. This
is nearly true in the sample. The inability to assess stream quality interaction effects in the dataset
means that we cannot confidently infer the value of one stream quality improvement independently of
the quality conditions of the other stream.
The BC model for income interacting with the stream quality change variable is shown in Table
1, column 2. All signs are correct; higher incomes increase the likelihood of accepting a quality im-
provement. A likelihood ratio test shows that the increase in Log L with this specification is signifi-
cant. Table 3, column 2, shows that this specifica- tion reduces marginal valuations only slightly when
evaluated at sample mean incomes. A simple ver- sion of the fixed effects BC model, which takes
advantage of the panel-type data set, is shown in
Table 1 Estimation results for binary choice BC logit random utility
models
a
Coefficient for Interactive
F ixed effect Basic
3 variable
2 1
Constant − 0.4156
−0.3959 na
0.02 0.03
0.2891 Dq
1
, A: M U
b
0.0953 0.4476
0.02 0.60
0.03 Dq
2
, B: S M
b
0.6034 0.0311
0.3979 0.01
0.89 0.02
Dq
3
, B: S U
b
0.6848 0.2436
1.2712 0.00
0.00 0.26
−0.0168 −0.0077
Dw − 0.0076
0.00 0.00
0.00 Dq
1
·I na
0.0437 na
0.17 Dq
2
·I na
0.0854 na
0.02 Dq
3
·I na
0.1043 na
0.00 −1016.3
−1001.1 Log L
−202.7
a
Probability values in parentheses; N = 362.
b
The symbolism, A: M U, represents the hypothetical qualitative change in Stream A Loyalhanna from M oderately
Polluted to U npolluted; S for Stream B represents Severely Polluted.
Table 2 Estimation results for inclusion of distance variables in user BC and IP logit random utility models
a
Coefficient for variable Conemaugh R iver
Loyalhanna Creek IP
BC BC
IP 2
3 4
1 1.4745
−0.2083 1.5110
− 0.2278 Constant
0.31 0.00
0.35 0.00
0.3932 Dq
1
, A: M U 0.5903
0.0066 0.2328
0.17 0.01
0.98 0.22
0.2084 0.6275
Dq
2
, B: S M 0.7368
0.1857 0.52
0.36 0.08
0.01 0.4103
1.1036 1.0660
0.4904 Dq
3
, B: S U 0.08
0.07 0.00
0.00 Dw
− 0.0078 −0.0063
−0.0079 −0.0064
0.00 0.00
0.00 0.00
0.0807 0.0211
0.0261 Dq
1
·I 0.0830
0.05 0.42
0.05 0.51
Dq
2
·I 0.0541
0.0758 0.0602
0.0702 0.11
0.13 0.09
0.13 0.0877
0.0978 Dq
3
·I 0.0967
0.0862 0.06
0.01 0.03
0.01 Dq
1
·D
L
−0.0169 −0.0161
na na
0.02 0.00
na −0.0197
na −0.0234
Dq
2
·D
C
0.04 0.00
na −0.0280
na −0.0291
Dq
3
·D
C
0.00 0.00
m
2
1.0303 na
na 1.0414
0.00 0.00
1.7727 na
1.7920 na
m
3
0.00 0.00
na m
4
2.9216 na
2.9525 0.00
0.00 − 1621.2
−618.4 −622.53
−1612.7 Log L
a
Probability values in parentheses; N = 217.
Table 1, column 3. The fixed effects model cre- ates a dummy-like variable for eachperson, repre-
senting the sum of instances in
which the
individual selected rejected the status quo. A likelihood ratio test, with degrees of freedom be-
ing the number of individuals in the estimating sample, can be used to test the superiority of the
fixed effects model. Such a test shows the fixed effects model to be a statistical improvement over
either of the BC models. Table 3, column 3, shows that the estimated marginal valuations di-
minish substantially for the fixed effects model compared to the other models. The purpose of
estimating a fixed effects model was to account for the possibility that some respondents may
approve of all changes, regardless of price and quality. If this behavior existed in the sample, not
controlling for it would result in overestimates of marginal valuations for each type of quality
change. This expectation is supported by the fact that the fixed effects valuation estimates are lower
than the others. Addition of the income interac- tion terms to the fixed effects model did not
significantly increase Log L , so these estimates are not shown.
The S.E. of the estimates for marginal valuations are shown in Table 3. The
valuation estimates using the Basic and Interac- tive BC models are similar, and within 1 S.E. of
each other. H owever, the estimated marginal val- uations using the F ixed Effects model, are nearly
1 S.E. lower than the other two BC model esti- mates. The estimated marginal valuations in
columns 1 – 3, Table 3, all possess the property that the sum of the valuations for B: S M and
A: M U roughly equals the valuation for B: S U, which would be expected if streams A and
B are close substitutes.
The estimates for the IP models are not shown but are available from the authors. All coefficients
are correctly signed and, except for the interactive model, were highly significant. Table 3 shows the
IP marginal valuations to be higher than their BC counterparts. Apparently compressing the prefer-
ence scale into two YesN o categories reduces valuation estimates. F or example, the marginal
valuation for A: M U in the basic IP model, column 4, is 50.02 per household for each of 5
years, compared to 38.04 in the BC model. The valuation estimates from the IP model are typi-
cally at least 1 S.D . higher than the BC estimates. The F ixed Effects model continues to show lower
valuation estimates than the Basic and Interactive models.
5
.
1
. N on-user 6alues The total value of water quality improvement is
the sum of non-use and use valuations. One means of operationalizing non-use values is to
define valuations by persons who do not use the streams for any active or passive use as non-use
values. This definition would implicitly include option values held by non-users. N on-use values
held by users would not be estimated through this operationalization. We selected the subsample of
households whose members did not use either of the two streams for any active or passive use
during the year prior to the survey; they may or may not have used them prior to that time. The
BC and IP models were estimated for this sub- sample of non-users.
R oughly 25 of the sampled households did not make any visit to either of the two streams in
the study. The estimated marginal valuations for the three types of quality improvements are
shown by estimation model in Table 4 for the 70 non-user households. The estimated models are
not presented in this paper, but are available from the authors. Table 4 suggests considerably lower
valuations than those presented above for the total sample. In fact, none of the estimated valua-
tions shown in this table are statistically signifi- cant, as shown by the large S.E. Valuations for
stream A improvements, A: M U, ranged from 3.05 to 15.45 per household per year for 5
years, depending upon the estimating model. Stream B improvements from severely to moder-
ately polluted ranged from 1.39 to 48.36, de- pending on the estimating model. While the
estimated valuations for the largest stream im-
Table 3 Estimated marginal valuations of stream improvements using the various R U M s
a
Stream improvement BC
IP Basic
Interactive
b
F ixed effects Basic
Interactive
b
F ixed effects 5
6 4
3 2
1 38.04
38.59 A: M U
51.35 51.02
26.63 35.76
15.80 15.89
12.07 17.17
17.20 9.27
B: S M 52.30
49.62 35.90
66.70 67.64
55.46 21.40
15.55 22.85
22.82 21.40
11.97 90.01
B: S U 87.43
75.63 109.92
112.44 92.76
21.78 16.12
23.10 21.80
23.13 11.90
Table 1, col. 2 Source
R egressions available from author Table 1, col. 3
Table 1, col. 1
a
Values represent household willingness to pay for each of 5 years; S.E. of DwDq in parentheses; N =362.
b
Evaluated at sample mean household income.
Table 4 N on-user estimated marginal valuations of stream improvements using the various R U M s
a
Stream improvement IP
BC Interactive
b
F ixed effects Basic
Basic Interactive
b
F ixed effects 1
2 3
4 5
6 A: M U
3.05 5.95
15.45 13.13
12.55 5.17
35.65 32.10
48.67 35.22
48.02 22.95
5.50 B: S M
1.39 10.01
48.36 47.61
28.50 49.45
49.92 42.83
65.20 64.33
30.40 38.87
45.51 54.26
42.20 54.22
B: S U 29.15
49.41 49.59
43.62 64.19
63.42 28.95
a
Values represent household willingness to pay for each of 5 years; S.E. of DwDq in parentheses; N =70. Source: regressions not
shown in paper, but are available from authors.
b
Evaluated at sample mean household income.
provement, B: S U, ranging from 29.15 to 54.22, are greater than for the other improve-
ments, they are not statistically significant.
5
.
2
. Use 6alues M odels were estimated separately for the 217
households that claimed to have members who used either of the two streams during the year
prior to the survey. The marginal value estimates of users are shown in Table 5. The regressions
that are the basis for these estimates are available from the authors. These estimated marginal valu-
ations are highly significant, as the S.E. show. The BC models result in lower valuation estimates
than the IP models. The fixed effects models result in lower values than the basic and interactive
models. U ser values range from 23.09 to 53.56 per household per year for 5 years for the A:
M U change; from 39.93 to 70.63 for the B: S M change; and from 81.42 to 125.25 for the
B: S U change. U ser valuations in Table 5 are generally higher than those in Table 3, the latter
representing the total sample including non-users.
5
.
3
. Distance effects on user and non-user 6aluations
D istance from an individual’s residence to stream sites would be correlated with the prices of
use of those sites as well as psychological distance. Since distance remains constant across alterna-
tives in the choice set, a direct distance effect on choice cannot be identified. H owever, distance
may have an interactive effect on choice insofar as it may diminish the desirability of stream im-
provements. This would obviously be true of users of streams. But it also may be true for non-users,
who may place existence or option values on stream quality improvements; a ‘sense of place’
may motivate individuals to value nearby quality improvements
more highly
in their
‘neighborhoods.’ A difficulty with testing distance hypotheses in
this study is that the two streams under consider- ation are in close proximity, so any distances from
a residence to each stream will be highly corre- lated. This limits the ability to analyze distance
effects. D istance was measured using a G eo- graphic Information System which calculated
straight line distances from the center of each respondent’s zip code to the nearest point of each
stream.
The introduction of distance from residence to either stream provided no significant improve-
ment to the non-user subsample estimation mod- els, and these models are not presented in this
paper. Combined with the results noted above for non-users, this suggests that not only do non-
users place low and statistically insignificant val- ues on stream improvements, but those values are
unrelated to distance from the streams. This dis- tance result is consistent with a ‘purist’ interpreta-
tion
of non-use values which suggests that
non-use values have to be independent of space, otherwise they are use values in some form.
The distance effect should be more substantial for use values. Table 2 presents the model estima-
tion results for the subsample of users. D istance to each stream is analyzed separately due to the
high correlations of distances to the two streams. Columns 1 and 2 include the BC and IP estimates
with the distance to Loyalhanna Creek. D istance has a significant negative effect when interacted
with the quality change for that stream. M arginal valuation estimates for improvements to this
stream are shown in Table 6. F or example, the BC estimate, evaluated at the subsample mean
income and distance, is 45.36 per household per year for 5 years, which is comparable to the BC
estimate for users in Table 5. Table 6 also shows a distance gradient for the BC estimate implying a
decrease in marginal valuation of 2.15 per mile from this stream. The extent of the ‘market’ is
defined as the distance at which the marginal valuation is zero, and is estimated to be 44.29
miles for this stream improvement. The IP model increases marginal valuations and the gradient.
Table 2 shows the estimation models including distance to the Conemaugh R iver interaction
terms. The distance interaction effects are signifi- cant and negative. Table 6 shows the resulting
marginal valuations for the two possible quality improvements for this river. The BC estimates are
60.05 per household per year for 5 years for the B: S M improvement; and 106.90 for the B:
S U improvement. The gradients are − 2.49 and − 3.54 per mile, respectively; and the ex-
tents of the ‘market’ are 48.26 and 54.40 miles, respectively. It makes sense for the more substan-
tial quality improvement to have a larger ‘mar- ket.’ The IP model estimates result in higher
marginal valuations and gradients as well as smaller ‘market’ areas.
6. Conclusions
