equation is obviously complicated by the fact that we still cannot be sure what
share of the total costs is accounted for by hidden costs. If this share is large but
ignored in the calculation of total costs, our estimate of free-ridership would be
inflated. Although we are unable to assign a monetary value to the hidden costs,
we can rearrange the equation as (subscripts omitted):
(10) WTP - observed costs > hidden costs.
Starting with the special case of zero hidden cost, we designate the household
as a free-rider if the inequality in Equation (10) holds. If we subsequently allow
for increasingly higher hidden costs, a point will eventually be reached at which
the inequality in Equation (10) becomes an equality. From this point on, the
household would no longer be a free-rider, as its hidden costs are large enough
such that the total cost exceed its WTP.
With these mechanics in hand, we can explore the sensitivity of the estimated
free-rider share to different hypothetical levels of hidden costs for all alternatives.
Note that because the WTP estimates of households from eastern Germany are
likely to be inflated due to the urgency of renovation following reunification, we
consider in the following only the 2128 households located in western Germany.
We further restrict our attention to the western households that have a WTP
that exceed the observed cost, since this this is a necessary condition for potential
free-ridership.10 Depending on the respective retrofit option, roughly 50% of the
western households have a WTP ≥ observed cost, validating a similar result that
was observed by Banfi et al. (2008).
The abscissas of Figure 2 shows the hidden cost as a percent of the observed
cost for two commonly chosen retrofit combinations. To facilitate interpretation,
the hidden cost is expressed as a share of the observed cost, which for simplifica-
tion of the exposition is assumed to be equal across households. For each level of
10The remaining western households exhibit a WTP < observed cost, and hence can be
excluded as free-riders at the outset.
20