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CHAPTER 3. MEDIGAP 128
We use bootstrap methods to calculate the standard errors, looping over the entire
set of equations for consistency.
3.5 Identifying Variation
3.5.1 The Instrument
The basic concept
The idea of the empirical model is to use plausibly exogenous variation in Medigap
premiums (equation 3.3) to shift individuals in and out of Medigap coverage (equation
3.2) and thereby identify the impact of Medigap on total medical spending (equation
3.1).
To isolate variation in premiums that is conditionally random, we leverage discon-
tinuities in Medigap premiums at state boundaries. As we discuss below, Medicare
costs, and thus the costs of supplemental Medigap insurance, exhibit considerable
within-state variation due to factors ranging from household incomes to local physi-
cian practice styles to the supply of medical resources (????). Yet despite this local
variation, within-state variation in Medigap premiums is highly limited (?). 17 This
means that otherwise identical individuals in otherwise identical localities can face
sharply different Medigap premiums solely due to Medicare costs in other parts of
their state.
We put this idea into practice by using state-level costs as an instrument while
simultaneously controlling for local costs in all the equations of our model. Controlling
for local costs is of course essential, as factors that influence costs in a local area almost
surely influence costs and enrollment decisions in our sample, even conditional on the
set of individual controls we include.
17 Although firms are allowed to vary premiums at the zip code level, ? find there is very little
within-state variation in the Medigap premiums for a given plan offered by given insurance company.
Maestas et al. cite state-level reporting requirements and regulations as a potential explanation.
Because plans must, for example, meet loss ratio requirements at state level, varying premiums
more locally may be administratively burdensome. We discuss a robustness check to this issue in
Section 3.6.