Andrew M. Jones 609health throughout the period and are also in employment in the first two years.
The outcome is employment status in the third year. In addition to matching on
pre-treatment outcomes, PSM is used to make the treated and controls comparable
in terms of their observed characteristics. Four methods of matching are com-
pared: nearest neighbor matching on the propensity score; kernel matching on
the propensity score; matching of the four nearest neighbors on a set of explana-
tory variables; and simple matching on the four nearest neighbors according to the
propensity score.
Other studies that use matching are summarized in Table 12.2.
12.7.2 Regression discontinuity
The regression discontinuity (RD) design exploits situations where the assignment
to treatment changes discontinuously with respect to a threshold value of one or
more exogenous variables. The contrast between individuals on either side of the
discontinuity is used to identify the treatment effect. In a sharp regression dis-
continuity design, passing the threshold completely determines the allocation of
treatment. In a fuzzy design, which is more likely in practice, the allocation of
treatment is stochastic and the threshold creates a discontinuity in the probabil-
ity of treatment. The discontinuity design relies on a comparison of observations
“before and after” the threshold and does not have a separate control group. For
this reason, applications typically use a narrowly defined neighborhood around
the discontinuity to try and ensure that the treated and untreated observations are
comparable in other respects. Studies that use a discontinuity design were described
in section 12.2 above (Almond, 2006; Lleras-Muney, 2005; Pop-Eleches, 2006).
12.7.3 Difference-in-differences
The difference-in-differences, or diff-in-diff (DD) approach to evaluation with non-
experimental data has been applied extensively in the health economics literature.
The method is based on a before and after (pre–post) design with a control group.
It can be used with both panel data and repeated cross-sections and requires
treatment and control groups to be specified.
The basic form of the DD estimator of the average treatment effect compares
mean outcomes for the treated (1) and controls (0) before (B) and after (A) the
treatment:
ATEDD=(y ̄^1 A−y ̄^1 B)−(y ̄^0 A−y ̄^0 B). (12.39)
With individual panel data, the DD estimator can be computed using a two-way
fixed effects specification:
yit=γ(TiPt)+x′itβ+νt+ui+εit. (12.40)The treatment effect is identified by the parameter (γ) on the interaction term
between the indicator for whether the individual is in the treated group (T)and
the indicator for the post-treatment period (P).^4 The observed regressors (x)control
for any observable differences between the treated and controls and the individual
effects (u)control for any time invariant unobservable differences that may be