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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


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