Modeling industrial location decisions in U.S. counties

probability of an investor selecting location j can be expressed as,

_   exp(θ0 yj + β⁰Zjk + Yj )

P^j/kY   PJ=1 e^χp(θ⁰yj + ^β0zjk + Yj )

The above formulation may be interpreted as a variant of the mixed logit
model, where the attributes of the characteristics which are not explic-
itly modeled are assumed to reside in the error terms.¹¹ On the other
hand, in light of their relation between the CLM and the Poisson regres-
sion, one can estimate the model above by means of a Poisson model with
random effects.¹² If we assume that exp(Y _j) follows an i.i.d. gamma dis-
tribution with (δ^-1 , δ^-1) parameters and consequently that E (exp(Y _j )) = 1
and V (exp(Y _j)) = δ, then, as shown by Hausman, Hall & Griliches (1984),
the resulting Poisson model with gamma distributed random effects has
an analytically tractable log-likelihood. In the pure cross-section case, this
later model collapses to a standard negative binomial regression [Cameron
& Trivedi (1998)]. Thus, if our specification does not include sectorial effects
(i.e. zj_k variables) one can estimate (6) by applying the negative binomial
model. More recently, there have been studies using the negative binomial
regression to model location decisions [Wu (1999)and Coughlin & Segev
(2000)] but the authors failed to note the compatibility of their approach
with the Random Utility Maximization framework.

The CLM with random effects relies on the assumption that the alter-
native specific effects are uncorrelated with the explanatory variables. This
is a questionable assumption for dealing with the IIA problem in location
studies. Omitted factors which are supposedly accounted for by the random

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