560 Panel Data Methods
If unobserved factors (u)influence whether an individual is selected into the
treatment group or how they respond to the treatment, this will lead to biased esti-
mates of the treatment effect. A randomized experimental design may achieve
the desired orthogonality of measured covariates (x,d)and unobservables (u).
However, econometric studies typically rely on observational data gathered in a
non-experimental setting. One strategy is to rely on selection on observables: find-
ing a sufficiently rich set of observable characteristics so that unobservables can be
assumed to have no systematic influence on treatments. This approach includes
matching estimators and inverse probability weighted estimators. In contrast, the
selection on unobservables strategy looks for factors that predict treatment, but
have no direct effect on outcomes and which can therefore be used to mimic
random assignment of treatment. This approach includes using within-individual
variation to allow for time invariant individual heterogeneity in panel data mod-
els (fixed effects) as well as conventional instrumental variables (IVs) estimators. It
also includes multiple equation models in which equations for the treatment and
outcome are estimated jointly by full information maximum likelihood (FIML).
“Natural experiments” often lead to the use of difference-in-differences estimators,
which combine selection on observables (by includingxin the regression models)
with selection on unobservables (by using differencing to control for time invariant
heterogeneity).
Natural experiments are often also linked to IV estimation, which relies on instru-
ments (z)that predict the assignment of treatment, but do not have a direct effect
on the outcome. When there is heterogeneity in the response to treatment the IV
estimator identifies a local average treatment effect, or LATE (Imbens and Angrist,
1994; McClellanet al.,1994). This is the average treatment effect over the sub-group
of the population that are induced to participate in the treatment by variation in
the instrument. The fact that IV estimates only identify the LATE and that the
results are therefore contingent on the set of instruments explains why different
empirical studies can produce quite different estimates, even though they examine
the same outcomes and treatments. Heterogeneity in treatment effects is likely to
be widespread: for example, Auld (2006a) finds considerable heterogeneity in the
treatment effect of local HIV infection prevalence on risky sexual behavior among
gay men in the San Francisco Men’s Health Study (SFMHS), with HIV prevalence
having less impact among those at high risk.
Recent work by Heckman and Vytlacil has extended the analysis of local treat-
ment effects by specifying a model for the assignment of treatment and using
it to identify those individuals who are indifferent between treatments, givenx
andz(see, e.g., Heckman and Vitlacyl, 1999, 2007; see Basuet al.,2007, for
an application to health data). This approach defines the marginal treatment
effect (MTE): the treatment effect among those individuals at the margin. The
MTE provides a building block for the LATE, ATET and ATE. It can be identi-
fied using local instrumental variables (LIVs) methods or by specifying multiple
equation models with a common factor structure (see, e.g., Aakviket al.,2005; Basu
et al.,2007).