Of course, the OLS estimate of the parameter δ would be biased even if the regression
were estimated in these aggregate data. There is, after all, a spurious correlation between the
receipt of Medicaid and ESI coverage. Medicaid eligibility depends on many characteristics,
some of which are unobserved. Persons with favorable values of these characteristics (such
as higher assets) will not qualify and participate in the Medicaid program. Many of these
factors, however, are correlated with the probability that the person works and is covered
by ESI. An observed negative correlation between p and m, therefore, does not capture
the behavioral tradeoff between publicly and privately provided insurance, but is instead
contaminated by the correlation between the probability of receiving Medicaid and the error
term in Eq. (3).