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CHAPTER 3. MEDIGAP 134
3.6.2 Causal Impact on Costs
Table 3.7 presents estimates of the third stage cost model. Columns 1 through 3
show simple OLS estimates of log total costs on a Medigap indicator and controls;
columns 4 through 6 show estimates with predicted values from the multinomial logit
model for Medigap choice used as instruments. The models are estimated with block
bootstrap standard errors clustered by individual for consistency (?). In Appendix
Table 3.12, we show 3SLS estimates of the cost equation using the linear probability
model for Medigap choice.
The OLS estimates (columns 1 to 3) suggest that Medigap coverage increases total
medical utilization by about 40 percent. With the full set of controls, a 95 percent
confidence interval allows us to reject any effect outside of 16 to 65 percent. The
instrumental variables estimates are about 40 percent larger than the OLS estimate
across the different sets of controls. With demographic controls (columns 5 and 6), the
point estimates suggest that Medigap coverage causally increases medical utilization
by 57 to 61 percent for individuals local to the instrument. (The 3SLS estimates,
shown in Appendix Table 3.12 indicate effects of 59 to 63 percent.) In the logit
specification with the full set of controls, a 95 percent confidence interval allows us
to reject any effect outside of 30 to 84 percent.
We find it sensible that the instrumental variables estimates are larger than those
estimated by OLS (57 versus 41 percent). As we have discussed elsewhere, Fang et
al. (2009) find strong evidence of advantageous selection on a set of health variables
that increase the R-squared of their baseline model from 7 to 21 percent. Yet even
these controls leave 79 percent of the variation unexplained. If there is some selection
on information contained in this remaining variation, and this selection continues to
be advantageous, then we would expect an approach that overcomes this selection
problem to yield larger estimates than a simple OLS approach.
A second reason for why our baseline estimates may be larger than the OLS
estimates is because we are measuring the moral hazard effect for individuals on the
margin of selecting into Medigap. The OLS estimates are best interpreted as an
average moral hazard effect that may be biased due to selection. In contrast, our
baseline logit estimates capture the moral hazard effect for individuals on the margin