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

found these to yield no significant improvements to the model fit.⁶

In the random parameters logit model, we allow for taste heterogeneity - even
after controlling for the effects of the interaction variables contained in z — by
treating the coefficients of cost and ∆Q as random. Alternative distributions
can be availed for capturing heterogeneity, the most common of which are the
normal and log-normal. The latter, being bounded on the left by zero, is par-
ticularly useful when theory suggests that the coefficient has the same sign for
every decision-maker, as is the case here for the expected negative and positive
coefficients of cost and ∆Q. The drawback of the lognormal - shared with the
normal - is that its long tail can produce unreasonably large coefficients for some
share of the observations. We consequently follow Revelt and Train (2000) and
Hensher and Greene (2003) in specifying β₁ and β₂ as triangular distributed.
The triangular distribution has the form of a tent, peaking in the center at the
mean and dropping off linearly on both sides of the center to form a density. It
is possible to restrict the triangular distribution to yield coefficients of the same
sign for all observations, but this restriction was found to be unnecessary with
the present data.

As conditional and error component logit both have closed form solutions,
they can be estimated using maximum likelihood. The random parameters logit,
by contrast, requires that the integral in equation (7) be approximated by means
of simulation using random draws from the mixing distribution (Train 2003). To
this end, we employ a Halton sequence to draw realizations from the population
triangular distribution. We tested the sensitivity of the parameter estimates with
different numbers of Halton draws per observation and found the results to be
stable with as few as 100 draws.

⁶As noted by Hensher, Jones, and Greene (2007), specific alternatives can appear with
different subsets of alternatives, making it possible to build overlapping error components that,
in the present case, include both grimy and prestigious alternatives.

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