21(40)
first-stage services compared to the follow-on services. The error term,
can still be thought of as consisting of three parts. The idiosyncratic
error term
, is service-specific. However, overall demand
and changes
in overall demand,
, are common to both the first-stage service and the
follow-on service. Subtracting (2) from (3) gives:
(4)
where
and
.
is the relative elasticity of prices
with respect to competition, for first-stage services versus follow-on
services. By taking the difference over service types for given levels of
competition,
and
have been differenced away. Hence, the identifying
assumption is that the unobserved factors
and
are o
nly associated
with the level of competition. This assumption is consistent with clinics
establishing in areas where demand for first-stage services are high. Note
that the competition measure is general to all services as it captures the
number of clinics within a certain distance.
When
and
have been differenced away, we now only have the
idiosyncratic error terms,
. I can therefore estimate (4) with OLS,
adding a dummy
for the first-stage service:
(5)
Model (5) exploits variation in competition across clinics.
captures the
average association between
and price and
captures the average
association between competition and price. The parameter of interest is
capturing the difference across services in the average effect of competition
on prices (
interacted with competition. Following the reasoning in
the theoretical background,
is hypothesized to be negative, reflecting
that competition has a relatively larger effect on first-stage services
compared to follow-on services.
Apart from the identification issues discussed above, there may also be a
clinic specific component of the error,
. By further adding the year specific
effect
, we get:
(6)
The variation used in the estimation of model (6) is the within-clinic
variation in competition. The identifying assumption is that the evolution
of the price difference between services on the clinic level would have
been unchanged in the absence of a change in competition.
Given that the unobserved part of the error term is indeed associated with
the level of competition rather than clinic specific characteristics or some
year specific shock common to all clinics, models (5) and (6) should yield
quantitatively similar results. This is because the differencing across
services solves the fundamental market endogeneity problem and therefore
the cross-sectional variation in competition should be sufficient to identify
