614 Panel Data Methods
estimators are refined using a PSM approach. The results show a significant reduc-
tion in deaths from infectious and parasitic diseases and suggest that privatization
helped to reduce health inequalities. Other studies that combine DD with match-
ing are Dano (2005), García-Gómez and López-Nicolás (2006), Girma and Paton
(2006) and Mariniet al.(2008).
Numerous studies in health economics use the DD strategy. Some of these are
summarized in Table 12.3.
12.7.4 Instrumental variables
The DD design is often applied in the context of natural experiments. Natural
experiments and natural controls also form the basis for the IV approach, which
is intended to capture “selection on unobservables” (see, e.g., Auld, 2006b). This
approach relies on the variation in treatment that can be attributed to variation
in an exogenous variable, or instrument; assigning individuals to treatments on
the basis that the instrument mimics the random assignment of an experimental
design. This approach is often hard to apply in practice as instruments should be
both powerful predictors of treatment and have no direct effect on outcomes. The
search for convincing instruments is therefore fraught with difficulty.
There are two broad estimation strategies. The FIML approach specifies a com-
plete system of equations for the outcomes and treatments and estimates them
jointly, allowing for common unobservable factors and identifying the model
through exclusion restrictions. Estimation can be by MLE, MSL, MCMC, DFM or
copulas, as described in section 12.6 above. The more commonly used approach is
the limited-information or single equation approach, using IV estimators, such
as 2SLS, GMM and 2SCML. Some studies that use instrumental variables were
described in section 12.2 above (Arendt, 2005; Auld and Sidhu, 2005; Evans and
Lien, 2005; Gardner and Oswald, 2007; Lakdawallaet al.,2006; Lindahl, 2005).
Other applications are too numerous to describe in detail here (some examples are
Cawleyet al.2006; Contoyanniset al.,2005; Dubayet al.,2001; Dusheikoet al.,
2004, 2007; Elliottet al.,2007; Guaraglia and Rossi 2004; Hadleyet al.,2003; Jewell
and Triunfo, 2006; Kessler and McClellan, 2002; Lindrooth and Weisbrod, 2007;
Meeret al.,2003; Sasso and Buchmueller, 2004; Schellhorn, 2001; Sloanet al.,
2001; Van Houtven and Norton, 2004; Yelowitz, 2000).
In section 12.1 it was emphasized that, when treatment effects are heteroge-
neous, the IV estimator identifies a local average treatment effect (LATE) and that
this estimate is conditional on the set of instruments that are used. In a recent
paper, Basuet al.(2007) apply Heckman and Vitlacyl’s (1999) LIV estimator which
identifies MTEs over the support of the propensity scorep(d= 1 |x,z). Computation
of the LIV estimator involves regressing the outcomeyon the observed regressors
xand on a flexible function of the propensity score, which is estimated usingxand
the instrumentsz. The model could be estimated semiparametrically, for example,
by using a partially linear model, or, as in Basuet al., by adding polynomial and
interaction terms betweenxandp(d= 1 |x,z). The LIV estimator of theMTE(x,ud)