The Agglomeration-Differentiation Tradeoff in ... - Yale University

the researcher, varying the size will have only a miniscule effect on our inferences about firms’
strategies (See discussion in Seim (2006)).
Next, note that for a given θ and
m
N , we can get estimates of price and revenue when
firms’ locations are set to be identical to the observed spatial configuration of stores in the data.
We can compare these estimates with our price and revenue data and thus obtain the price and
pr r
revenue shocks, ( obv , obv )
ω θ ω θ , for the set of chosen locations that correspond to the observed
spatial configuration of stores in the data. These price and revenue shocks are included in the
likelihood function:
L
( )
Θ =
M
∏
m=
1
l ⎧ F m
I ( fl)
⎫
m m pr 2
r
⎨∏∏( ψ fl ( N , P ; θ) ) ⎬*
∏φ( ωobv θ,0, σ pr ) * ∏φ( ωobv θ,0,
Σ)
⎩ f = 1 l=
1
⎭
Price Data
Revenue Data
⎡ ⎤
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎢ Location Choice
⎥
⎢ ⎥
⎢
m 2 * φξ ( ; µσ , ) ⎥
⎢ ⎥
⎢⎣ Entry Choice ⎥⎦
( θ) ( θ)
m m m m
s.t. P N ; =Ψ N , P ; , ∀ m
(28)
( )
2
where, Θ is the set of all model parameters { θ , µσ , }
Θ= , and I( fl ) is an indicator that
equals one if location l is chosen by a f-format firm, and is zero otherwise. φ is the pdf of a
normal distribution whereas φ has been used to indicate the pdf of the marginal distribution of
revenue shocks.
2.2 Estimation Strategy
2.2.1. Simplifying Restrictions
20