While the rst-dierence setup in equation (1) eliminates permanent unobserved household
heterogeneity, the estimated parameter 0 may still be biased because of unobserved dierences in
the changes in outcomes across dierent types of households. What are examples of situations that
would violate my identifying assumption? Changes in aggregate resources, such as the supply of
health care and local economic conditions, may aect the health shock and changes in outcomes.
However, the inclusion of county-year xed eects already controls for unobserved dierences across
counties and over time. Household mobility is restricted, which limits the extent of self-selection
into areas with better health services through regional mobility. Perhaps a more plausible source
of bias is unobserved shocks to household resources which induce the health shock. For instance,
previous job displacement may simultaneously aect current health (and hence a change in health
since displacement) and changes in outcomes (Black, Devereux, and Salvanes, 2012). In Section
5.5, I show that there is little correlation between past income shocks and the current health shock,
indicating that this potential source of bias may be less of a concern in my sample. Note that even
if the eect of the health shock is contaminated by the eect of other types of shocks to household
resources, the estimated coecient 1 will be unbiased as long as the omitted variable bias on the
coecient of 4hijt does not change with the reform.11 This is more of a concern if the reform
aects the unobserved composition of households reporting any illness. In Section 5.5, I provide
some evidence that the reform is unlikely to aect the distribution of illness across households.