Modeling industrial location decisions in U.S. counties

APPENDIX B

The log-likelihood for this conditional logit problem is,

log Lcl = ΣΣnjk log p_j/_k.

k=1 j=1

From the first order condition for maximization with respect to one of the
fixed effects we obtain,

∂ log L_cl

_d.---= > n ∣ⁿjk ^- Pj∕kⁿk∖ = 0

^γ^j k=1

Solving the first order condition with respect to γ_j we arrive at,

j =exp(γ_j)

k=1

exp(β⁰zjk)

---J------------n---------ⁿk
_j^J₌₁ exp(β⁰zjk + γ_j)

Now, if we let,

Ik = log fp⁷----Z 4- )

_j₌₁exp(β⁰zjk+γ_j)

we can express the γ_j sas,

exp(γ_j)=

____n____

PK=1 ^exp(^β0 zjk + Ik )