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Lorena Moreno
98
Analiti a, Revista de análisis estadístico, Vol. 13 (1), 2017
Figure 3:
Pseudo-RSII index (full sample)
Note:
The frequency histogram is overlaid with a normal density plot.
Since they are both very similar and there are no significant deviations from
the mean values of the sample, there is no skewness.
given the treatment status (
D
i
) and the assignment covariate (
X
), are continuous around
the threshold (c) (Imbens and Lemieux, 2008). When the cutoff only partly influences the
treatment exposure, the fuzzy design is appropriate (Hahn et al., 2001). In this context, and
given the characteristics of the programme it was sensible to use this method. The following
pairs up the empirical reasoning of the method to specificities of the case.
Following Angrist and Pischke (2008), in the fuzzy RDD the discontinuity can be seen as
an instrumental variable for the treatment status in order to account for the potential bias
derived from the probabilistic function, in the following way:
P
(
D
i
= 1
|
x
i
) =
g
1
(
x
i
)
if x
i
≤
c
g
0
(
x
i
)
if x
i
> c
, g
1
(
c
) =
g
0
(
c
)
(1)
assume
g
1
(
x
0
)
> g
0
(
x
0
)
The interpretation of (1) is that there is a jump in the probability, with functional form
g
(
.
), of receiving the transfer at the threshold
c
= 28
,
2. Beneficiaries (
D
i
= 1) should have
at most an RSII value
x
i
of 28,2, while non-eligible households should have higher values.
This association can also be written as:
E
[
D
i
|
x
i
] =
P
(
D
i
= 1
|
x
i
) =
g
0
(
x
i
) + [
g
1
(
x
i
)
−
g
0
(
x
i
)]
Z
(2)
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