Modeling industrial location decisions in U.S. counties

If we plug the γ_js back into the expression for pj/_k, we obtain,

_    exp(Yj) exp(β0zjk)

pj/k " PJ=1 exp(β⁰Zjk + Yj )

_ __________nj__exp(β⁰Zjt)

PK=1 ^exp(^βzjk + Ik) PJ=1 ^exP(^αj + ^βzjk)

_     exp(β⁰Zjk + Ik )

^P_t^T₌₁ exp(β⁰zjk + Ik)

and the concentrated log-likelihood is that of a logit model where the choices
are now the sectors with an alternative specific constant added to the model.
This log-likelihood is equivalent to that of a Poisson regression with fixed-
effects (see, for example, Cameron & Trivedi (1998)].

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