Car Ownership? Evidence from the Copenhagen Metropolitan Area

area. Since it is difficult to choose for a particular nesting structure, the flexibility offered by the
cross-nested logit model (see Vovsha, 1997; Bierlaire, 2006) is attractive. In the model the three
types of correlation can be present simultaneously 23 and by estimating the model the data show
the relative importance of each of them. However, estimation of (cross-)nested logit models is
typically more involved than that of estimating a multinomial logit model. For instance, the
likelihood function is no longer necessarily concave and the ‘logsum parameters’ may be
difficult to estimate. A grid search over relevant values of these parameters may be a useful
strategy, although probably time consuming.
With respect to the instrument for the house price we noted some ambiguity with respect
to the use of exogenous characteristics of areas in the vicinity. It is not always clear that such
characteristics are excluded from the utility of a particular choice alternative. For instance,
amenities in contiguous areas may be easy to visit as those of one’s own residential area and
therefore contribute as much to the utility of living there. Bayer’s procedure for computing the
instrument for the price uses exogenous characteristics of all alternatives and therefore does not
rely solely on those of the neighbouring areas. But it does not exclude these characteristics from
the computation of the instrument which raises questions about its appropriateness. It may
therefore be useful to look for other ways to compute an instrument for the price. Reynaert and
Verboven (2014) have recently emphasized the importance of using approximations to the
optimal instruments. Their methodology appears to be flexible enough to avoid the use of
characteristics of neighbouring areas in the construction of the instrument. 24 We are currently
working on the incorporation of the nesting structures and the alternative procedures for finding
an instrument for the house price in models like that of the present paper.
23 The cross-nested logit may be formulated as a weighted average of the various nested logit models where the
weights are determined by some of the parameters to be estimated.
24 An alternative approach may be based on Belloni et al. (2012) who propose the use of Lasso methods.
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