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 U_ij
of household i for alternative j ∈ C comprises a deterministic and a stochastic
component:

Uij = Vij ^{+ e}ij^,

with V_ij = αj + X_ijβ as representative utility, determined by the alternative
specific constant αj and the matrix X_ij , 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 e_ij.

Household i chooses alternative j if and only if U_ij >U_ik for all k = j, with
j, k ∈C. The probability P_i(j) of selecting j from the set of alternatives is thus
dependent on e_ij and is equal to:

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:

(3)                                Pi(j) =

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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