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CHAPTER 3. MEDIGAP 131
levels in this area will reflect this propensity to travel.
A more subtle concern is that the marginal Medigap purchaser may be more
(or less) likely to travel than the average Medicare beneficiary. If this is the case,
then controlling for average local health care utilization is insufficient. Basically, the
concern is that although most people in Rural Town, USA don’t travel to Big City,
USA for care, the marginal Medigap purchaser might be the type of person who does.
A solution to this problem is to define markets broadly enough so that the closest Big
City, USA is included in the market. We believe this is exactly what we do by using
HRRs to define local markets as these regions are constructed explicitly to include
the major hospital where people travel for sophisticated treatment.
Therefore, given a measure of costs which accounts for travel and the conservative
definition of local areas, we think that the exclusion restriction is unlikely to be
violated. Nevertheless, if out-of-HRR costs did somehow directly impact costs, it
would downwardly bias the coefficient on Medgap, working against the direction of
our main finding. 19
Medicare Advantage
A final topic of discussion is our proxy for the price and availability of Medicare
Advantage coverage: a second order polynomial in the county-year specific MA pene-
tration rate. Controlling for the determinants of MA enrollment is important for the
explanatory power of the choice equation as Medigap and MA are typically viewed as
substitutes. For similar reasons, it is important to include MA enrollees in the sample
of analysis as MA coverage is the relevant alternative coverage to consider for changes
in the Medigap market. Yet for valid estimation, the variables used to predict MA
choice must satisfy the exclusion restriction of not directly impacting medical costs.
Below we make the case for their exclusion.
The main argument for the exogeneity of county-year specific MA penetration
rates is that much of the variation in this variable is driven by high-level federal
19 In this case, higher out-of-HRR costs would simultaneously shift individuals out of coverage
through the instrument and increase costs directly, creating a negative correlation between coverage
and unobserved costs and biasing downwards the coefficient on Medigap.