Modeling industrial location decisions in U.S. counties

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)

^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,

ns PS=1 PC= 1 ^exP(^αs ^{+ θ}0 y sc)
ⁿ      PC= 1 ^exP(^θ0ysc)

If we now plug this back into the log-likelihood function we obtain the

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