Willingness-to-Pay for Energy Conservation and Free-Ridership on Subsidization – Evidence from Germany



2.1 Discrete Choice Models

Random utility theory provides a suitable framework for our analysis, as it pre-
dicts choices by comparing the utility associated with distinct retrofitting alter-
natives. Each household faces a choice set
C with K elements. The utility Uij
of household i for alternative j C comprises a deterministic and a stochastic
component:

(1)


Uij = Vij + eij,

with Vij = αj + Xijβ as representative utility, determined by the alternative
specific constant
αj and the matrix Xij , which captures alternative-specific at-
tributes (e.g. costs) as well as characteristics of the household (e.g. income). The
portion of utility that is unobservable to the researcher is represented by
eij.

Household i chooses alternative j if and only if Uij >Uik for all k = j, with
j, k C. The probability Pi(j) of selecting j from the set of alternatives is thus
dependent on
eij and is equal to:

(2)


Pi (j ) = Pr (Vij + eij > Vik + eik )


= Pr (eik - eij < Vij - Vik) , k = j


Assuming the error terms to be identically and independently (iid) distributed
as Gumbel (or Type I extreme value), the resulting probability model is logistic,
giving rise to the well-known conditional logit model (see e.g. Ben-Akiva and
Lerman 1985), with choice probabilities equal to:

eVij


(3)                                Pi(j) =

eVik


k

One drawback of this model is its imposition of the independence of irrelevant
alternatives (IIA) assumption, requiring that when one alternative is removed
from the choice set
C , the choice probabilities of the remaining alternatives rise
by the same proportion. This assumption is, in particular, violated when the error



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