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

β = β κ ; β = β κ ; ...; β = β κ
f −f 2 f −f1 2 f −f 3 f −f1 3 f −fB f −f1
B
β = β κ ; β = β κ ; ...; β = β κ
(29.1)
f '−f 2 f '−f1 2 f '−f 3 f '−f1 3 f '−fB f '−f1 B
( # competition effect parameters = ( F*( F + 1) / 2 ) + ( B-1)
)
Similarly, the impact of market characteristics on cost ( γ fbx ) are allowed to be format-
specific but we assume a constant ratio between the impact of a variable at a particular distance
band to the impact in the first 0-1 mile distance band. The constant is specific to the variable and
the particular distance band. For instance, suppose for cost (Equation 14) the coefficients of
population and per capita income in different distance bands are denoted by γ 1fb and γ 2 fb ,
respectively; then the restriction implies:
γ1= γ1 λ ; γ1= γ1 λ ; ... ; γ1= γ1 λ
f 2 f 1 2 f 3 f 1 3 fB f 1 B
γ2= γ2 ζ ; γ2= γ2 ζ ; ... ; γ2= γ2ζ f 2 f 1 2 f 3 f 1 3 fB f 1 B
( # observable cost component parameters ∝ ( F + B)
)
22
(29.2)
Note that if we allow the ratios or the multipliers, κb, λb and ζ b to be format-specific
then that is equivalent to directly estimating the format-specific coefficients, such as β f − fb , γ 1fb and γ 2 fb . In our estimation, we do not impose any restrictions on the values that the multipliers
can take at different distance bands. If these multipliers turn out to be decreasing with distance
and less than one then that would imply that the impact of the variable weakens with distance. In
particular, weakening of the competitive effects at greater distances would indicate the benefits
of spatial differentiation.
2.2.2. Multiple Equilibria in the Model