Specific forms for estimation of shadow values

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 = Žw 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 = Ža 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