When any element of z
ij
is constant across alternatives and the corresponding element of g
j
is also constant, the effect of that element on choice
is not identifiable. H owever, a constant element of z
ij
may interact with other non-constant elements requiring its inclusion in an interactive, or varying
coefficients model G riffiths et al., 1993. F or example, while income remains constant across
choices, the effect of environmental quality im- provements on choice may depend on income.
The inclusion of h
ij
in Eq. 7 allows for fixed effects over individuals and alternatives. There
may be a threshold of utility increase before an individual selects an alternative to the status quo.
Letting j = 0 represent the status quo, h
i1
− h
i0
= h
i
\ 0. A more complex possibility of a fixed effect
arises from potential experimental design and elic- itation procedures. F or example, if respondents
act as if the ‘right’ response is to choose the alternative to the status quo, h
i
\ 0. A fixed effect
could also be present if respondents have a desire for change h
i
\ 0 or no change h
i
B 0. The
procedure for introducing fixed effects into the binary choice model has been developed by
Chamberlain 1980, 1984 and Baltagi 1995. The procedure requires a panel data set, as in the
present study, and conditions the likelihood func- tion on the summed 0, 1 responses across each
individual’s revealed choices. F or example, the present study asked each respondent to make a
choice in five different scenarios; the maximum conditioning value is then five.
4. Specific forms for estimation of shadow values
Let z
ij
represent a vector of attributes of alter- native j presented to individual i, where z
ij
= w
ij
, q
ij
. Therefore, z represents a combination of monetary payments and quality scenarios. Let p
ij
, c
ij
and I
ij
be defined as above and assume they are constant for each individual across alternatives. A
first-order approximation to V in Eq. 3 is: V
ij
= z
ij
a + c
ij
g + uI
ij
+ p
ij
d + h
ij
10 where a = a
w
, a
q
and h
ij
is a fixed effect. F rom Eq. 10:
DV
i
V
ij
− V
ik
= Dz
i
a + Dc
i
g + u DI
i
+ Dp
i
’d +
Dh
i
11 where
Dz
i
= z
ij
− z
ik
, etc. The experimental design in this study holds p, c and I constant across
alternatives, so estimating Eq. 8 becomes: y
i
= Dz
i
a + Dh
i
+ o
i
12 where
Dz
i
a = Dw
i
a
w
+ Dq
i
a
q
. This formulation al- lows for choice between alternatives j and k to
depend upon the characteristics of those alterna- tives, w and q, as well as a fixed effect.
While p, c and I are constant across alternatives in the experimental design, they can potentially
interact with alternatives to affect choice. This may be the case for income and distance from
sites variables. D istance from an individual’s resi- dence to a site in the choice set, D, is a proxy for
price of user access to the site. It may also reflect psychological distance from a site for non-users.
While D may have a direct effect on V , it will not have a direct effect on
DV . However, it may interact with q, the environmental quality variable
in the choice setting, to affect choice; for example, individuals further distant from a site whose qual-
ity is improved would be less likely to value an improvement alternative than a person closer to
the site. These interaction effects can be incorpo- rated by assuming:
a
q
= a¦
q
+ a
D
D + a
I
I 13
This formulation allows individual characteris- tics to interact with alternatives in determining
choice. The resulting estimating equation is: y
i
= Dw
i
a
w
+ Dq
i
a +
Dq
i
a
D
D + Dq
i
a
I
I + Dh
i
+ o
i
14 The shadow value of a qualitative change,
Dq, can be obtained from the first-order approxima-
tion to DV
i
: DV
i
V
i
w Dw
i
+ V
i
q Dq
i
15 Setting
DV
i
= 0: Dw
i
Dq
i
− V
i
q V
i
w 16
Estimation of Eq. 14 results in:
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