5. The crowdout effect
The descriptive evidence summarized in the previous sections presents a strong circumstantial
case supporting the hypothesis that public assistance alters the terms of trade
between private health insurance and publicly provided health insurance. More precisely,
I have shown that health insurance coverage rates did not decline among immigrants who
potentially suffered the largest welfare cutbacks in the post-1996 period (i.e., non-citizens
living in less generous states). Instead, this group experienced an offsetting increase in
employer-sponsored insurance. I now examine the nature of this tradeoff. Consider the
regression model:
pij = Wijβ + δmij + ωij, (3)
where pij is the probability that person i living in state j is covered by employer-sponsored
insurance; Wij is a vector of socioeconomic characteristics defined below; and mij gives the
probability that the person is covered by Medicaid.
Two related obstacles prevent a straightforward estimation of the structural model in
Eq. (3). The first is that we do not observe the probability that a particular person receives
Medicaid or is covered by ESI. Instead, we simply observe the outcome of these probability
processes for a particular person. For example, the person is either covered by Medicaid or is not. This measurement problem can be easily addressed by changing the unit of
analysis from a particular person to a particular group, defined as persons who share a
particular immigration status, live in the same state, and are observed at the same point
in time. I can then calculate the probability of receiving Medicaid and of being covered
by employer-sponsored insurance for the “representative person” in each group, as well as
calculate the mean of the various socioeconomic characteristics.
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).
The structural parameter δ can be correctly estimated by using instrumental variables,
where the instruments are provided by the exogenous variation in eligibility rules introduced
by the immigrant provisions in the welfare reform legislation, as well as by the responses of
individual states to the changes in the federal safety net. In particular, consider a first-stage
regression model given by