WATER RESOURCES RESEARCH, VOL. 31, NO. 7, PAGES 1781-1787, JULY 1995
Influence of choice set considerations in modeling the benefits
from improved water quality
T. Peters and W. L. Adamowicz
Department of Rural Economy, University of Alberta, Edmonton, Canada
P. C. Boxall
Northern Forestry Centre, Canadian Forest Service, Edmonton, Alberta
Abstract.
Random utility models have become popular tools for the measurement of
economic benefits from environmental quality changes. These models, however, require
assumptions about the choice sets held by the individuals in the sample. Typically,
researchers specify the choice set and assume that individuals are aware of all elements of
this set. This paper compares the standard approach with an alternative that uses an
estimate of each sampled individual's specific choice set. The latter approach produces
model parameters and welfare estimates that are quite different from those using standard
assumptions.
Introduction
Random utility models have become very popular for mea­
suring the benefits of water-based recreation [e.g., Bockstael et
ai., 1991]. These models are popular because they readily ac­
commodate quality attributes, they provide theoretically cor­
rect measures of welfare change, and they address some "cor­
ner solution" problems. (Corner solutions arise when zero
quantities of certain "goods" within the model are demanded
by the individual. Continuous demand systems, like the tradi­
tional travel cost model, do not address this issue well. Ran­
dom utility models address the 0/1 corner well but do not
address issues of the number of trips (e.g., three versus four)
[see Smith, 1989; Fletcher et al., 1990]. A number of problems
with these discrete choice models, typically multinomial logit
models, have been assessed in the literature. The issue of
independence of irrelevant alternatives and the use of nested
models have been examined by Carson et at. [1989] and Bock­
stael et al. [1989]. The issue of nonparticipation has been ex­
amined by Morey et al. [1991]. Issues of specification and dy­
namics have also been explored [see Morey et al., 1993;
Adamowicz, 1994]. However, one issue which has received little
attention is the determination of the choice set.
Random utility models require specification of the choice set
an individual is choosing from. These choice sets may be dif­
ferent for each individual, but the choice set must be deter­
mined before the analysis begins. The issue examined in this
paper is, What is the impact of alternative assumptions about
the choice set on model parameters and welfare measures?
Evidence in the transportation literature shows that parameter
estimates will change with alternative choice set definitions
[Swait and Ben-Akiva, 1987]. Furthermore, given a certain pa­
rameter vector, welfare measures will be affected by the choice
set assumption. Compensating variation calculations in ran­
dom utility models are based on choice probabilities over a set
of alternatives, the choice set. Thus the size and composition of
the choice set will affect welfare measures.
The alternative choice set constructs considered are (1) the
set of all sites known to the researcher, (2) an individual spe­
cific choice set constructed from a survey question designed to
identify the choice set, and (3) estimation of the model using
randomly generated choice sets. The last approach is a tech­
nique developed by McFadden [1978] and employed by Parsons
and Kealy [1992] to estimate multinomial logit models when
choice sets are very large.
Using data collected from a survey of recreational anglers,
individually defined choice sets are constructed and compared
to choice sets defined by the researchers in random utility
models. The results show that parameter estimates and welfare
measures from models with individual specific choice sets are
different than those using researcher-defined choice sets. We
argue that the former provides a more consistent behavioral
model since recreationists are unlikely to visit sites not in their
choice set.
Random Utility Model
Discrete choice models utilize dependent variables that are
discrete values [Maddala, 1983], for example, the site visited on
a single fishing trip. In a random utility framework the angler
is faced with a choice set, denoted Cn• By definition, all alter­
natives within this set are assumed to be mutually exclusive.
Each choice, i, in the set has associated with it a conditional
indirect utility function:
Ui
fCY
-
T;, Qi' S),
(1)
where the utility associated with a visit to each site is a function
of income (y), travel cost to the site (Tj), environmental
quality of the site (Q;), and other socioeconomic variables
(S).
If site i is chosen, we assume that the utility associated with
visiting site i is higher than for any other site j, i.e.,
Ui> Uj V j E Cn•
Copyright 1995 by the American Geophysical Union.
Paper number 95WROO975.
0043-1397/95/95WR-00975$05.00
=
(2)
The underlying indirect utility function is composed of a sys­
tematic component, Vi' and a random component, 8j:
1781
PETERS ET AL.: CHOICE SETS IN RANDOM UTILITY MODELS
1782
Ui
=
Vi + 8i·
(3)
The systematic component includes attributes of the sites as
well as characteristics of the decision maker. The random com­
ponent accounts for incomplete information, unexplained
changes in consumer tastes, and researcher error.
Examining this choice process in a statistical context, the
probability that an angler will choose to visit site i is
Pr( i)
=
Pr( Ui> U)
=
Pr(Vi
=
+
8 i> Vi + 8)
Pr(Vi - Vi> 8i - 8;).
If the 8 values are type 1 extreme value (Weibull) distributed,
then the probability of visiting site i can be denoted as
Pr(i )
e Vi
=
'V
L.J
e
v·,
J
(5)
jECn
where the denominator is the sum of the exponential of the
conditional indirect utilities over all the alternatives in the
choice set.
To date, many of the random utility models presented in the
literature have been estimated based on the assumption of
perfect information regarding sites available, across individu­
als. In other words, Cn is assumed to be identical for all
individuals and equal to the full set of sites observed by the
researcher. In this paper we focus on the impact of changing
Cn to represent the choice set reported by the angler. We
examine the influence of the choice set in a simple conditional
logit model. One could examine choice set influences in nested
logit models [see Morey et at., 1993]. Also, one could consider
choice sets as alternative nesting structures. However, even
with a relatively small number of alternatives, the number of
combinations of alternatives that are possible choice sets be­
comes large (the power set of all alternatives), making the
analysis intractable. We address whether the individual's
awareness of the available choice opportunities enhances the
understanding and prediction of the patterns of spatial behav­
ior [Perdue, 1987].
Welfare Theory
Hanemann [1982] derives the compensating variation mea­
sure of the change in consumer's welfare (under the assump­
tion of no income effects) associated with some change in
utility as
where ViO and Vi 1 represent the utility before and after the
change and J.t is the marginal utility of income. Hanemann
[1982] shows that J.t is the negative of the coefficient on the
travel cost parameter estimated in the random utility models.
In the model described above, changes in utility can arise from
changes in environmental quality (changes in the attributes in
(1», changes in prices, or changes in the number of alterna­
tives available (site closures or the creation of new sites). When
measuring the welfare impact of a site closure, the site is
removed from the choice set Cn (for all individuals) in the
expression for utility after the change.
The issue of choice set assumptions discussed above will
have some influence over welfare estimation. Because welfare
estimates for a quality change are summed over all sites in an
anglers' choice set, the size and composition of that choice set
will have an impact on the magnitude of the welfare estimate
(see the appendix). Just as the number of good substitutes (or
the degree of substitution) will have an effect on demand
curves and welfare measures in traditional demand analysis,
the structure of the choice set, and implicitly the structure of
substitutes, will affect welfare measurement in discrete choice
models.
Recreation Choice Sets
Determination of the underlying choice set (Cn) of the
random utility model is a fundamental component of the rec­
reation demand modeling process. The elements contained in
this set represent those sites the recreationist is choosing from
when making decisions. When determining the structure of the
choice set in the model, researchers are faced with either using
their own judgment to design the choice sets or using infor­
mation from the recreationists. The key issue then becomes,
Which approach results in a behaviorally correct model?
Researchers must find a method to elicit information about
the nature of the choice set recreationists use to base trip
decisions on. There are a variety of ways to do this, such as the
use of spatial limits [e.g., Smith and Kopp, 1980] or other
criteria. The method used in this study was direct elicitation of
the choice set by means of a survey question asking individuals
to identify the set of sites they consider or are aware of when
making fishing trip decisions. This was done by presenting the
individuals with a map and a list of all potential fishing sites in
a region. The set of sites identified by the respondents was
considered to be their choice set, or the set of sites they are
choosing from when making trip decisions.
Choice sets will probably be related to distance (sites further
away from home will be less likely to be in one's choice set) and
will depend on the individual's years of experience. Because
knowledge, experience, habits, and residence location play a
role in defining a choice set, individuals living in the same town
may not have the same choice set. Furthermore, given limited
information on sites, and limited time to explore sites, it is
unlikely that individual choice sets will be "large" relative to
the total number of possible recreation sites. Below, we ex­
plore these issues empirically.
Data
The primary source of data for this research project was the
Southern Alberta Sportfishing survey administered in 1991.
The main objective of the survey was to elicit information on
fishing preferences, values, and attitudes and, further, to ob­
tain information on recreational sportfishing trips taken during
the 1990 fishing season. The survey was based on a geograph­
ical distribution which was expected to account for approxi­
mately 95% of the fishing trips taken to sites in southern
Alberta. The survey was divided into four main subcompo­
nents: attitudes and opinions about fishing, awareness of rec­
reational fishing sites in southern Alberta, trip information,
and demographics. A summary of the results of the survey can
be found in the work by Adamowicz et al. [1992]. A random
sample of 5000 names, obtained from copies of fishing licenses
sold in the southern or central regions of Alberta in 1990, was
1783
PETERS ET AL.: CHOICE SETS IN RANDOM UTILITY MODELS
generated for the survey. Overall, the effective response rate
for the survey was 48% (2115 responses). This response rate is
reasonable given the complexity and length of the survey. For
more details regarding survey design, mail-out procedure, and
response rates, see Adamowicz et al. [1992].
Defining Choice Sets
Sixty-seven fishing sites were used as the base choice set for
the economic analysis. This set was chosen because it ac­
counted for over 95% of all fishing activity in the region and
thus captures most of the "market" for trips. This set was
identified by Alberta Fish and Wildlife Division pers6nnel.
Each survey respondent was shown a list and a map of the sites
and asked to indicate "which of these sites they had visited in
the past or would consider when choosing a site to go fishing"
(quotation marks indicate the actual text of the question). (See
Adamowicz et at. [1992] for the actual question structure.) The
data obtained from this question were used to identify the
angler's awareness set, or choice set. This type of data is similar
to "consideration sets" employed in the marketing literature
[Horowitz and Louviere, 1990]. The anglers were also asked to
provide information on their 1990 fishing trips, using the sites
described in the map and list. The survey originally considered
77 sites which were supposed to capture all of the fishing
activity in the region. However, 10 sites were deleted due to the
unavailability of environmental quality attributes for these
sites, the fact that few individuals visited these sites (less than
1% of all trips), and the fact that very few individuals indicated
that they were aware of these sites. We expect that exclusion of
these 10 sites will have little impact on the models.
Complete trip information was available for 3465 trips made
to the sites in the southern region. On average, anglers were
aware of 33 sites (of a maximum of 67 sites). Few respondents
were aware of more than 45 sites. A simple ordinary least
squares (OLS) model explaining the number of sites an angler
was aware of was estimated. This model suggests that the
number of sites an angler is aware of increases with years of
angling experience and fishing expenditures. This conforms
with the expectation that awareness is related to learning and
information.
Quality Attribute Data
Data on quality attributes of the 67 sites were obtained from
fisheries managers employed by the Alberta Department of
Environmental Protection (for further details on the environ­
mental quality attributes, see Adamowicz et al. [1992]). The
quality attributes are indicators of overall environmental qual­
ity and reflect those site characteristics related to recreational
fishing that anglers deem most important. Table 1 summarizes
the main quality aspects used in the econometric analysis. The
main environmental quality indicators used in the modeling
are water quality (WATQUAL), pristine wilderness lake
(PRISTINE), how easy it is to catch a large fish (SIZECOT),
and whether the site was treed (TREES). The biological as­
pects encompassed in the quality variables are catch rates for
general fishing and trout fishing, respectively (CATCHRT and
TROUTCR), and whether a lake is stocked annually with trout
(STOCK). The other quality variables are representative of a
cross section of quality factors that are hypothesized to influ­
ence an angler's site choice; these variables manifest them­
selves as the physical attributes of a particular site. Distances
between fishing sites and anglers' residences (DISTANCE)
Description of Site Attributes Used in Estimation
of the Models
Table 1.
Variable
DISTANCE
CAMP
CATCHRT
WATQUAL
PRISTINE
DEVELOP
SIZECOT
Description
distance from home to
fishing site
campground
catch rate (general)
water quality
pristine wilderness lake
level of development
TREES
INAPARK
AREAWAT
LENGTH
RESERV
STABLE
index of ease of catching
a large fish
forested or treed
in a designated park
area of water body
length of stream
reservoir
stability of water flow
TROUTCR
STOCK
catch rate (trout)
stocked with trout
Rating
miles
o= absent, 1 = present
number caught per hour
1 = poor, 10= excellent
0= no, 1 = yes
1= no development,
10 = full development
1= difficult, 10= easy
0= no, 1= yes
0= no, 1= yes
hectares
kilometers
0= no, 1= yes
1 = very stable,
10 = fluctuations
number caught per hour
0= no, 1= yes
were measured using a measuring wheel on maps of the region
[Watson et aI., 1993].
Model Estimation
Three random utility models of angler site choice were es­
timated using maximum likelihood. In each model the utility
associated with site i (utility conditional on choosing site i),
Vi' was modeled as
15
Vi
=
L f3kXki
(7)
k=1
where each k represents one of the 15 independent variables
described above and in Table 1 (DISTANCE, CAMP,
CATCHRT, WATQUAL, ... STOCK), 13k represents the pa­
rameter to be estimated, and, Xik represents the value of each
independent variable at site i. Note that this utility function
corresponds to one site and that utilities for all sites in the
choice set must be used to construct the site choice probabil­
ities described in (5). Note also that the estimated parameters
apply to all sites in the choice set (i.e., the parameters do not
vary over sites in the choice set). Welfare analysis using (6)
proceeds by calculating the base utility (Vi evaluated at base
attribute levels) and comparing this with the utility following
the environmental change (Vi evaluated at the changed at­
tribute levels). Table 2 summarizes the parameter estimation
results.
RUM 1: Basic Random Utility Model
In this model, each site is modeled as a bundle of objective
quality attributes and travel cost. The choice set is composed of
all 67 southern region sites. Examination of the "RUM 1"
column in Table 2 shows all parameters to be statistically
significant and the signs are as expected, with one notable
exception. The sign on the coefficient INAPARK is negative. It
is suspected that the variable INAPARK is capturing the fact
that sites within park areas tend to be more developed and
congested than sites outside of parks.
PETERS ET AL.: CHOICE SETS IN RANDOM UTILITY MODELS
1784
Table 2.
Coefficient Estimates From the Random Utility
Models
Variable
DISTANCE
CAMP
CATCHRT
WATQUAL
PRISTINE
DEVELOP
SIZECOT
TREES
INAPARK
AREAWAT
LENGTH
RESERV
STABLE
TROUTCR
STOCK
p2
RUM 1
RUM 2
RUM 3
-0.045
(0.00083)
0.726
(0.064)
0.307
(0.090)
0.0530
(0.018)
0.217
(0.110)
-0.0680
(0.011)
0.166
(0.014)
0.808
(0.056)
-0.178
(0.056)
0.0002
(0.000014)
0.00403
(0.00066)
0.802
(0.076)
-0.0329
(0.0096)
1.09
(0.125)
0.132
(0.049)
0.19
-0.043
(0.0011)
0.765
(0.081)
0.357
(0.110)
0.0428
(0.022)
0.0477*
(0.130)
-0.0666
(0.016)
0.131
(0.018)
0.797
(0.072)
-0.225
(0.076)
0.0002
(0.00002)
0.00380
(0.00086)
0.656
(0.096)
-0.0487
(0.012)
0.878
(0.160)
0.0191*
(0.064)
0.34
-0.025
(0.00088)
0.217
(0.066)
0.221
(0.089)
0.0954
(0.018)
-0.134*
{O.flO)
-0.116
(0.013)
0.149
(0.015)
0.393
(0.061)
0.0852*
(0.059)
0.000784
(0.000014)
0.00405
(0.00072)
0.497
(0.078)
-0.0508
(0.0097)
0.398
(0.130)
0.0106*
(0.051)
0.08
Standard errors in parentheses.
*Insignificant at the 95% level.
RUM 2: A Modification of the Standard RUM
It has been suggested in the literature [Parsons and Kealy,
1992] that when the choice set is large, estimation may become
burdensome. Hence it is postulated that a randomly generated
choice set drawn from the full set of sites can provide a valid
representation of the true behavioral patterns of the angler.
The approach taken with the second random utility model is
to estimate the model using a randomly drawn choice set of
five of the 67 southern Alberta fishing sites. The random draw
works as follows: four randomly generated sites are chosen; to
that set is added the site actually visited, bringing the total size
of the choice set to five. A unique random choice set is gen­
erated for each of the 3465 trips taken to sites in the southern
region.
It is hypothesized that the signs of the coefficients will re­
main the same as in the standard random utility model de­
scribed above. The column labeled "RUM 2" in Table 2 sum­
marizes the results of the model. Note that the variables
PRISTINE and STOCK become statistically insignificant. Un­
der the constructs of a randomly generated choice set of five
sites, it is likely that there is not enough variability in these
attributes to have significant influence over site choice.
These results are not surprising in light of the premise that
a randomly generated choice set will approximate behavior
when the actual choice set is large. Comparing this model with
the standard random utility model previously estimated, two
things become evident: First, all coefficients are of the ex­
pected sign, and second, the model remains relatively robust.
However, upon closer examination of both models estimated,
it is seen that in all cases there is a relative increase in the
standard errors of the coefficients for RUM 2. Parsons and
Kealy [1992] suggest that using information on individuals'
perceived choice sets may yield some promising results. The
next random utility model examines this approach.
RUM 3: Restricted Choice Set Model
The final model estimated is based on the actual (as stated
in the survey) choice set of each respondent. Hence the choice
set varies from one angler to the next. The column labeled
"RUM 3" in Table 2 summarizes the results of this model. As
in RUM 2 the variables PRISTINE and STOCK are statisti­
cally insignificant, but INAPARK is also insignificant. The
signs on the coefficients remain consistent with the previous
model and a priori expectations. However, an examination of
the estimated coefficients reveals significant changes in their
magnitude.
There are notable declines in the coefficients on DIS­
TANCE, CAMP, CATCHRT, TREES, RESERV, and
TROUTCR and increases in WATQUAL, DEVELOP,
AREAWAT, and STABLE, and the coefficients on SIZECOT
and LENGTH remain relatively robust. Intuitively, the re­
searcher may expect a decline in magnitude of the distance
parameter and CAMP. Typically, anglers will be more aware of
sites relatively close to home. Hence the relative influence that
these variables have on the probability of choice is smaller.
Economic Welfare Analysis
Welfare analysis was carried out using the three model spec­
ifications. The distance measure was transformed into travel
cost using $0.48 per mile ($0.30 per km) as the cost of oper­
ating a vehicle in Alberta in 1990 (cost data provided by the
Alberta Motor Association). The welfare effects of four site
closures will be examined. The sites selected are McGregor
Reservoir, Chain Lake, Reesor Lake, and Beavermines Lake.
These sites were selected because they were the four most
popular sites among survey respondents, with 31.0%, 23.6%,
20.9%, and 17.3%, respectively, of respondents visiting these
sites during the 1990 fishing season. Also, the benefits from
planting trees at selected sites will be measured. The tree­
planting policy changes the TREES attribute in the random
utility models (the "after change" expression in (6) includes a
1 in the trees attribute expression for these sites). Finally, a
trout-stocking policy at Reesor Lake is examined. The vari­
ables affected in the random utility model are STOCK,
CATCHRT, and TROUTCR (each factor is adjusted in the
"after change" expression in (6». It is assumed that this trout
stocking policy will increase catch rates (both general and
trout) by 10%. All coefficients on the affected quality attributes
are positive; hence it is speculated that there will be a welfare
gain from implementation of this management action.
Per-trip welfare estimates of the above noted management
proposals were calculated for all three random utility models.
(There is some controversy regarding the use of per-trip wel­
fare measures [e.g., Morey, 1994]. However, that issue is be­
yond the scope of this paper.) Table 3 summarizes the per-trip
welfare measures. The table also presents the minimum, max­
imum, and coefficient of variation over the sample for each
estimate. The estimates are in dollars per trip. Since our model
assumes that the total number of trips is constant, total benefits
can be obtained by multiplying per-trip benefits by the number
of trips. A more complete analysis, however, would also exam-
PETERS ET AL.: CHOICE SETS IN RANDOM UTILITY MODELS
Table 3.
1785
Per-Trip Welfare Measures for Alternative Quality Changes
Management Policy
Close McGregor
Reservoir
Mean
Standard deviation
Coefficient of variation
Minimum/maximum
Close Chain Lake
Mean
Standard deviation
Coefficient of variation
Minimum/maximum
Close Reesor Lake
Mean
Standard deviation
Coefficient of variation
Minimum/maximum
Close Beavermines Lake
Mean
Standard deviation
Coefficient of variation
Minimum/maximum
Plant Trees at Crowsnest
Site
Mean
Standard deviation
Coefficient of variation
Minimum/maximum
Trout Stocking
Mean
Standard deviation
Coefficient of variation
Minimum/maximum
RUM 1
RUM 2
RUM 3
- 1.89
2.06
-1.09
-12.74/-0.009
-1.80
1.92
-1.07
- 1 1.91/-0.01
-6.62
8.28
- 1.25
-40.7/0.00
-0.80
0.91
-1.14
-2.93/-0.004
-0.63
0.70
-1. 1 1
-2.23/-0.0005
-0.20
0.29
- 1.45
-2.1l/0.00
-0.59
1.02
-1.73
-7.04/-0.003
-0.58
0.99
-1.71
-6.77/-0.003
-0.13
0.32
-2.57
-3.49/0.00
-0.93
0.92
-0.98
-4.16/-0.02
-0.76
0.70
-0.92
-3.21/-0.02
-0.43
0.76
-1.75
-5.49/0.00
0.62
0.51
0.82
0.01/2.50
0.63
0.49
0.77
0.02/2.35
0.10
0.20
1.83
0.00/1.35
0.10
0.17
1.70
0.004/1.07
0.03
0.05
1.67
0.00/0.30
0.004
0.009
2.50
0.00/0.09
.:
"
ine how the number of trips changes as quality attributes
change [Morey, 1994].
RUM 1 and RUM 2 Welfare Estimates
Examining the results for the standard random utility model
(RUM 1), all welfare changes are in accordance with a priori
expectations: There is a welfare loss associated with the site
closures and a welfare gain from the tree-planting and trout­
stocking management actions. Comparing the welfare mea­
sures of the RUM 1 model with those of RUM 2, it is seen that
with a few exceptions, the two closely reflect one another.
Closing McGregor Reservoir and Reesor Lake, and planting
trees in the Crowsnest region, result in welfare measures of
approximately equal magnitude between models. These results
are expected because a randomly generated choice set of five
sites should approximate behavior when the angler is faced
with a large choice set.
There are, however, some changes in welfare estimates for
four management proposals between RUM 1 and RUM 2.
First, there are relatively large differences in the welfare loss
associated with closing Beavermines and Chain Lakes, going
from -$0.93 to -$0.76 and -$0.80 to -$0.63, respectively.
Second, welfare estimates for the trout-stocking policy change
by $0.07 between RUM 1 and RUM 2. A reexamination of
Table 2 leads to the conclusion that the difference in magni­
tude of the estimated coefficients in the random utility models
is resulting in notable welfare differences.
RUM 3 Welfare Estimates
Freeman [1979] suggested that if an individual is unaware of
a site, then a quality change at that site will have no impact on
the individual's welfare. Hence it is expected that there will be
some difference in welfare estimates between RUM 3 and the
other two models. In terms of the direction of change for these
welfare estimates, it is not clear whether these impacts will be
smaller or larger than those from the full choice set models. If
a site the angler is unaware of is affected by a quality change,
there will be no impact on the angler's welfare. However, if the
site affected is in the angler's choice set, the impact may be
large, relative to the full choice set predictions, because the
reduced choice set model contains fewer substitutes. There­
fore, while little can be said about the absolute difference
between the welfare measures, it is expected that there will be
larger variation in welfare impacts from RUM 3 because of the
different composition of each individual choice set.
Examining the RUM 3 column of Table 3, the welfare esti­
mates from the awareness model are markedly different from
the standard random utility models. The only case where the
welfare impact is greater in absolute value in RUM 3 is closing
McGregor Reservoir. This result is not surprising. McGregor
Reservoir is the most popular site visited, and 58% of respon­
dents are aware of it. Hence closing this site may result in a
large welfare loss. Generally, though, the welfare estimates
from RUM 3 are smaller than those from models RUM 1 and
RUM 2.
In examining the minimum and maximum values of the
welfare estimates from RUM 3, two interesting details arise:
First, in all policy proposals, zero is the minimum (or maxi­
mum for a reduction in welfare) welfare measure. The pres­
ence of these structural zeros validates the speculation that for
some anglers, there will be no welfare impact due to the
PETERS ET AL.: CHOICE SETS IN RANDOM UTILITY MODELS
1786
change in quality attributes. Further, the coefficient of varia­
tion for all quality changes is higher in
RUM 3 than
1
- - [In
IL
the other
two models. This confirms the hypothesis that there is greater
variation in welfare estimates across respondents when site
choice decisions are made from their own choice set.
As
k
I
(eV,o
+
k)
- In
I
(eVil
+
k)]
increases (additional sites in the choice set), the welfare
impact associated with the change at site
1
will become small.
The derivative of the expression above with respect to
Discussion
1
The analysis described above shows that choice set assump­
- Ii
tions may have a significant impact on recreational value esti­
mates. In the estimates provided here the mean values of
quality impacts between full choice sets and reduced choice
sets are often significantly different. Also, the variabiJity of
welfare estimates is larger when using the anglers' own re­
ported choice sets in the estimation. The procedure employed
by Parsons and Kealy
[1992], while not exactly mirroring the full
choice analysis, does provide measures that are very similar to
(9)
(
1
evio + k
-
1
evI,
+
k
)
k
is
(10)
which illustrates that for site improvements (welfare increases)
the change in welfare as
k
increases is negative. As
proaches infinity, the welfare effect at site
1
k
ap­
approaches zero.
However, this exposition is based on constant parameters over
different choice sets. As explained in the text, parameters will
also be affected by choice sets.
the full choice set analysis.
Both the full choice set method and the Parsons and Kealy
method can be considered a form of "long run" analysis under
the assumption that eventually anglers will be aware of all sites
available to them. The reduced choice set model corresponds
to a "short run" analysis, using only those sites that the angler
considers part of hislher current choice set. This raises the
issue of choice set formation and dynamic choice set analysis.
If quality attributes change, one would expect anglers to po­
Acknowledgments. The authors would like to thank two anony­
mous referees, the associate editor, F. Bishop, M. Needelman, G.
Parsons, and D. Watson for helpful comments on this paper. Respon­
sibility for errors and omissions remains with the authors. Funding
support from the Alberta Environmental Protection Fisheries Man­
agement Enhancement Fund and the Science and Technology Oppor­
tunities Fund of the Canadian Forest Service is gratefully acknowl­
edged.
tentially seek out new sites. Also, anglers are constantly search­
ing for information on new sites and are probably constantly
expanding their choice sets. Therefore a more complete anal­
ysis would consider choice set formation and site choice as
simultaneous processes. Such an analysis has been suggested
by
Horowitz and Louviere [1990].
They state that models of
choice set formation and models of selection from the choice
set may share attributes and have correlated error processes.
For example, in our case, improving the quality at a set of sites
may lead to an expansion of choice sets by anglers (as they are
influenced by the increase in overall fishing quality, or as anglers
who were previously unaware of these sites become aware of
them). The welfare impact of the quality change will be different
depending on how quality changes affect choice set structures. In
our analysis we assume that quality changes have no effect on
choice set structures. We have insufficient information to examine
this aspect of choice set dynamics; however, these aspects of
discrete choice models are certainly worthy of further research.
The results presented here suggest that an important element
of benefit measurement should be the collection of recreationists'
choice sets, or at least some idea of the sites individuals are aware
of. We have shown that the model parameters and welfare mea­
sures are quite different when these individual specific choice sets
are used. In terms of the use of values in benefit-cost analysis, the
incorporation of individual choice sets may affect the aggregate
benefit estimates. Also, these estimates will likely reveal a very
different pattern of the distribution of benefits than will values
estimated from a full choice set model.
Appendix
Compensating variation is based on the expression:
(8)
Suppose we are interested in valuing changes at only site
(VI).
1
Let utility over all other sites in the expression above be
represented by
k.
The expression then becomes
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(Received January 27, 1994; revised March 17, 1995;
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