Labels and choice Directory UMM :Data Elmu:jurnal:E:Ecological Economics:Vol32.Issue2.Feb2000:
One way of circumventing the IIA property is to allow for correlations among the error terms
within different subsets or classes of alternatives by estimating a nested logit model McFadden,
1978; Daganzo and Kusnic, 1993. In a two-level nested logit model, the probability of an individ-
ual choosing the hth alternative in the rth branch P
hr
is represented as: P
hr
= PhrPr
5 where Phr is the probability of an individual
choosing the hth alternative conditional on choos- ing the rth class of outcome, located in the rth
branch of the tree. Pr is the probability that the individual chooses the rth branch. Following
Kling and Thomson 1996:
Phr = exp[V
hr
a
r
] exp[I
r
] 6
P = exp[a
r
I
r
]
R k = 1
exp[a
k
I
k
] 7
where I
r
= log
H
r
i = 1
expV
ir
a
r
n
8 is referred to as the inclusive value. This is a
measure of the expected maximum utility from the alternatives associated with the rth class of
alternatives. H
r
is the number of alternatives in branch r, and V
hr
is the utility of the hth alterna- tive in the rth branch. The coefficient of the
inclusive value,
a
r
, measures
substitutability across
alternatives. When
substitutability is
greater within rather than between alternatives, 0 B a
r
B 1. In this case, respondents will shift to
other alternatives in the branch more readily than they will shift to other branches Train et al.,
1987. The popularity of the nested logit model is in part due to the way in which nested decision
structures
lend themselves
to behavioural
interpretations. Welfare estimates are obtained in CM studies
using the following general formula described by Hanemann 1984:
W = − 1
m ln
i C
e
V
i 0
− ln
i C
e
V
i 1
n
9 where m is the marginal utility of income, V
i0
and V
i1
represent the indirect observable utility before and after the change under consideration, and C
is the choice set. In CM, the absolute value of the coefficient of the monetary attribute in the choice
model is taken as an estimate of m. Changes in V
i0
or V
i1
can arise from changes in the attributes of alternatives or the removal or addition of alter-
natives altogether. For example, in recreational site studies where alternatives are substitutes in
consumption, the removal of an alternative from the choice set might correspond to a site closure,
which one would expect to result in a welfare loss. When alternatives are substitutes in ‘production’,
such as when a single solution has to be chosen from a set of feasible solutions, the removal of
alternatives can be used to estimate selection probabilities and welfare implications based on
different choice sets.
When the choice set includes a single before and after policy option, Eq. 9 reduces to:
W = − 1
m [lne
V
i 0
− lne
V
i 1
] = − 1
m [V
i0
− V
i1
] 10
In the case of changes in a single attribute, this further reduces to − b
j
m when a linear in
parameters utility function is employed. This is equivalent to calculating the ratio of marginal
utilities for the attribute in question and the mon- etary attribute, or the marginal rate of substitu-
tion MRS Hensher and Johnson, 1981. Kling and Thomson 1996, Herriges and Kling 1997,
Choi and Moon 1997 consider the application of Eq. 9 in the nested logit case.