20(40)
5
Empirical strategy
In the following, I discuss the empirical strategy and how the effect of
competition on prices is identified.
Suppose that the relationship between prices and competition could be
described by the following simple model:
(1)
Where
is the log price charged by clinic
, in area
,in time period
and
is log competition. The parameter of interest is
, capturing
the effect of competition on prices. Simply estimating (1) by running a
regression is not sufficient to establish a causal relationship. The
identification problems can be illustrated by decomposing the error term
into three parts;
. The term
captures overall demand
in area
. It is correlated with
if there, for example, are more clinics in
areas with higher incomes.
24
The term
captures demand for both types
of services facing clinic
, and changes in demand over time. Given that
high demand is reflected by high prices,
is correlated with
if clinics
choose to establish where prices historically have been high. The potential
relationship can be expressed as
. The implication is that
is not strictly exogeneous. The last part of the error term,
is an
idiosyncratic error. Estimating (1) with OLS will yield biased estimates
of
.
25
Since
and
are unobservable parts of the error, they cannot
fully be "controlled away". However, I can use that
in (1) differs across
services as discussed in section 3.
Consider two kinds of services
, where
represents the first-
stage service and
represents the follow-on service. We can write:
(2)
(3)
Where the outcome variables,
, is the mean log price of treatment
at clinic
, in area
, in year
.
captures the average price for services
of type
. With a log-log specification,
captures the average elasticity
of prices for services of type
with respect to competition. Because of the
differences in consumers’ price sensitivity it is assumed that
,
reflecting that the average effect of competition on prices is larger for the
24
This is the case if the income elasticity is positive. Tentative results suggests a
positive income elasticity for dental care (Grönqvist, 2012; Holtmann and Olsen Jr,
1976; Manning and Phelps, 1979).
25
This is because and
and we get:
̂