instead—that is, a model that first estimates whether firms will offer coverage at all, and then
how much they offer (measured as the price of coverage). As a result, many researchers now use
a Heckman two-stage procedure (first estimating the probability of firms offering coverage and
then the price) to impute the unobserved price offered to those who decline coverage (Feldman et
al. 1997, Hadley and Reschovsky 2002). However, the selection of explanatory variables to
include in the imputation of unobserved price is critical (see the discussion of omitted variables
below). Moreover, based on observation of premiums for both takers and decliners, Blumberg et
al. (2001) demonstrated that using imputed versus actual offered premiums for group coverage
resulted in larger elasticity estimates with respect to employees’ take up of coverage.
To obtain unbiased estimates of price or income elasticity, both price and income must be
uncorrelated with any variable that affects the purchase decision but for which the model does
not control. To the extent that there are no such omitted variables, then price or income are
exogenous to the estimation, and estimates of elasticity are unbiased.
The HIE is still considered to be the most reliable source of estimates for the price elasticity
of demand for insured services, because it largely (but not entirely) avoided adverse selection
(and, therefore, the problem of endogeneity) by randomly assigning families to health insurance
plans. Individuals with unobserved high health care needs did not have the opportunity to
systematically select greater coverage that would bias their sensitivity to a change in the price of
health care services.
In contrast, studies that have used a natural experimental design usually face little risk of
endogeneity. This risk may be mitigated, if elasticity estimates can be estimated using panel
data—that is, data on experience over a period of time for both the “treatment” group and the
“control” group. With panel data, researchers can use a difference-in-difference method to