where γ , θ and β are vectors of unknown parameters, xk is a vector of sector
specific variables (e.g. entry barriers or concentration ratios), yj is a vector
of location specific variables (such as agglomeration economies, land costs
or local taxes), and zjk is a vector of explanatory variables that change
simultaneously with the region and the sector (e.g. wages or localization
economies). εijk is an identically and independently distributed random
term assumed to have an Extreme Value Type I distribution. This random
term reflects the idiosyncrasies specific to each investor, as well as unob-
served attributes of the choices. Based on McFadden (1974)we can show
that if investor i is profit oriented then his probability of selecting location
j, conditional on his choice of sector k, equals,9
exp(θ0 yj + β0zjk )
pj/k PJ=1 exp(θ0yj + βZjk )
(2)
This expresses the familiar CLM formulation. Let us denote by njk the
number of investments in region j and sector k. Then, we can estimate the
parameters of the above equation by maximizing the following log-likelihood:
KJ
log Lcl = ΣΣnjk log pj/k.
(3)
k=1 j=1
As shown in Guimaraes, Figueiredo & Woodward (2002)the above log-
likelihood function is equivalent to that of a Poisson model which takes as
a dependent variable njk and includes as explanatory variables the yj and
zjk vectors plus a set of dummy variables for each sector. That is, we will
obtain the same results if we admit that njk follows a Poisson distribution