compare pre- and post-treatment periods (where the “treatment” is a change in price) and control
for any time trend as well as any permanent average difference between the treatment and
control group (e.g., whether a firm offers coverage at all). Difference-in-difference estimation
assumes that a parallel trend would have occurred for the treatment and control groups in the
absence of the treatment, all else being equal. It yields a biased estimate of demand elasticity if
this assumption fails.
Observational studies—those that rely on secondary data from household or employer
surveys—typically suffer most from endogeneity. Most observational studies capture price
variation based on existing differences in plans or coverage, making it very difficult to establish
how price changes may have affected demand. Researchers have developed complex statistical
models to deal with endogeneity, many relying on instrumental variables. An instrumental
variable must be correlated with the endogeneous variable itself (in this case, price), but
uncorrelated with the outcome variable (i.e., demand), except through the endogeneous variable.
A variable that would meet both criteria is extremely hard to find.
C. OMITTED VARIABLES
Many statistical models, using a variety of data sources, have been developed to control for
factors other than price or income in estimating demand elasticity. Nevertheless, the likelihood
that an estimation model would miss some determinants of demand—and that the resulting
elasticity estimate is biased—is very high. However, the number of potential omitted variables
probably has declined, as data and information about health insurance and health care markets
have improved. Many variables that were unavailable in earlier studies now are often available
and widely used—for example, individual health status, plan benefit design, and whether
coverage is obtained through a spouse or other source.