Modeling industrial location decisions in U.S. counties

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). ε_ij_k 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

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 p_j/_k.

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
zj_k 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

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