APPENDIX A
To simplify matters, let us admit that the probability of locating in a
particular site is only a function of area characteristics (yj), as in Bartik
(1985), Woodward (1992)and Levinson (1996). Replacing the j index by an
index for state, s, and for county, c, we obtain,
_ exp(αs + θ0ysc)
(9)
p'c^ PS=1 PC= 1 ”. + θy ,
where C. is the number of counties in state s. Thus, the log-likelihood
for the discrete choice problem is:
S Cs
log L = n.c log p.c .
.=1 c=1
If we compute the first order condition with respect to any one of the state
”dummy variables” we get,
Cs
n. - n p.c =0,
c=1
and thus,
exp(α.) =
ns PS=1 PC= 1 exP(αs + θ0 y sc)
n PC= 1 exP(θ0ysc)
If we now plug this back into the log-likelihood function we obtain the
21
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