Car Ownership? Evidence from the Copenhagen Metropolitan Area

∑ ∑ ∑
,,
, which implies that the choice probabilities are given by the multinomial logit
model (MNL). 9
We are interested in what the model can tell us about the decision to own a car and the
impact public transport has on that decision. The consumer will own a car if the maximum utility
of the alternatives in which a car is owned exceeds the maximum utility of the alternatives in
which no car is owned. The former maximum utility, which we denote as ,, |
1 is:
ln∑ ∑
,,
. (3)
For the utility U
of not having a car we have:
ln∑ ∑
,,
. (4)
The first terms on the right-hand side of (3) and (4) are known as the logsums. The random terms
and are independent and Extreme Value Type I distributed. The choice whether or not
to own a car can therefore be described as a binomial logit model in which the logsums are the
deterministic parts of the utilities. Denoting the probability of car ownership as we thus
have:
∑ ∑ ,,
∑ ∑ ,,
∑ ∑ ,,
(5)
It should be noted that this model differs from one in which we estimate car ownership
conditional on the choice of a residential area and housing type, as is the case in the literature on
the impact of urban form on car ownership cited in the introduction. In that literature binomial
models of the type:
|,
,,
,,
(6)
,,
9
That is: ,,
,,
∑ ∑ ∑
,,
.
10