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Assessing the Effect of Conditional Cash Transfers in Children Chronic Stunting: The Human Development Bonus in Ecuador
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Analiti a, Revista de análisis estadístico, Vol. 13 (1), 2017
Z
= 1(
x
i
≤
c
)
Here
Z
is a binary instrument
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that takes the value 1 if the household has a score at least
as lower as the value of the cutoff, and 0 otherwise. Importantly, the units under analysis
are those very near to the threshold, to resemble an as-if random assignment. Taking into
account the non-deterministic association between the index and the probability of the treat-
ment, and following Imbens and Lemieux (2008), and Hahn et al. (2001), the identification
result can be written as:
α
FRDD
=
E
[
Y
1
−
Y
0
|
X
=
c
and unit
i
is a complier]
=
lim
x
↓
c
E
[
Y
|
X
=
c
]
−
lim
x
↑
c
E
[
Y
|
X
=
c
]
lim
x
↓
c
E
[
D
|
X
=
c
]
−
lim
x
↑
c
E
[
D
|
X
=
c
]
=
E
[
Y
|
Z
= 1]
−
E
[
Y
|
Z
= 0]
E
[
D
|
Z
= 1]
−
E
[
D
|
Z
= 0]
(3)
Here
Y
1
,
0
represent the observed outcome (height-for-age z-scores) for either treatment or
control groups. The association between the index and HAZ is possible though it is assumed
to be smooth, therefore a discontinuity in the conditional expectation is defined as a causal
effect. The ratio in (3) is the variation in the outcome discontinuity to the variation on
the treatment discontinuity. This non-parametric ratio represents the estimand, which is
the local average treatment effect (LATE) and as Angrist and Pischke (2008) stated, it is
local not only because is estimated for the compliers, but also because is for those around a
specific vicinity. The implementation strategy follows two approaches, one parametric and
one non-parametric. For the first, a 2SLS IV regression analysis was implemented. I defined
10,
±
1 vicinities around the threshold; then, with these bandwidths, I run different versions
of the specification:
Y
=
β
0
+
β
1
X
+
β
2
X
2
+
β
3
W
+
αD
+
u
(4)
where
D
is instrumented by
Z
, and
α
is the effect. Here
W
represents a vector of few
controls empirically defined as determinants of children stunting in Ecuador (World Bank,
2007) that where not already part on the index itself. Specifically, age of the kids in days,
sex, indigenous ethnicity, and mother´s height and education level. Tables with the results
and plots are presented next, including also the first stage (treatment discontinuity) and the
intention-to-treat estimates (outcome discontinuity). For this approach the bandwidth was
chosen based in means test of selected covariates for treated and control just around the
threshold, similar to Oosterbeek et al. (2008).
In fact, bandwidth choice is one of the challenges that the RDD faces, given the embedded
bias-variance trade-off (i.e. smaller bandwidth leads to less bias but higher variance, and vice
versa). This has motivated the development of non-parametric estimators, which root from
5
Usual IV assumptions hold, namely ignorability, first stage and monotonicity.
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