APPENDIX B
The log-likelihood for this conditional logit problem is,
KJ
log Lcl = ΣΣnjk log pj/k.
k=1 j=1
From the first order condition for maximization with respect to one of the
fixed effects we obtain,
∂ log Lcl
d.---= > n ∣njk - Pj∕knk∖ = 0
γj k=1
Solving the first order condition with respect to γj we arrive at,
K
j =exp(γj)
k=1
exp(β0zjk)
---J------------n---------nk
jJ=1 exp(β0zjk + γj)
Now, if we let,
Ik = log fp7----Z 4- )
j=1exp(β0zjk+γj)
we can express the γj sas,
exp(γj)=
____n____
PK=1 exp(β0 zjk + Ik )
23
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