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

terms are not independent, as is the case when there are subsets of alternatives for
which unobserved shocks have concomitant effects. For example, those renovation
alternatives involving roof and facade insulation may be associated with high
levels of noise and dirt, thereby having a common adverse effect on utility. On
the other hand, these same alternatives and possibly others may positively affect
utility by contributing to social standing. Hence, each retrofit option may belong
to several sets of alternatives that have a common effect on utility. Following
Brownstone and Train (1998), one can account for such groupings of similar sets
of alternatives - and thereby relax the IIA assumption - by imposing a particular
correlation structure on the utility of the alternatives via the addition of an error
component:

Uij = Vij ^{+ l}ψ^lj ^{+ e}ij = Vij ⁺ ηij^,

where ψ is a normally distributed random parameter with zero mean, and μj
is a dummy variable which equals one if a certain latent effect is present in the
utility of alternative j . Hence, the random quantity ψ only enters the utility of
alternatives that share this effect.² Although the iid assumption for the e’s still
holds, the utility of the respective alternatives are correlated via the unobserved
portion of utility η :

(5)      E ( ηjj ,ηik ) = E ( ψμj + eij ,ψμ∣_s + eik ) = E ( ψ,ψ ) = σψ,  j = k.

Incorporating this latent effect into Equation (3) yields the error-component logit
model:

²For the sake of simplicity, we restrict our attention here only to the case where one such
effect is present, although much more complex correlation structures can be imposed with
additional error components.

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