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Lorena Moreno
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Analiti a, Revista de análisis estadístico, Vol. 13 (1), 2017
Figure 6:
Probability of treatment
Note:
there is a decrease in the probability Treatment (D) at the discon-
tinuity cutoff 28,2, in around 14% given a local polynomial smoothed fit of
the RSII index score.
5.2 Parametric estimates
After testing various specifications used in empirical studies in the thematic area, and specif-
ically for the Ecuadorian case, three
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were chosen: (1) linear (2) quadratic (3) quadratic
with covariates, all with robust household clustered variance estimation. Estimates were
computed for up to a
±
10 window; though, the vicinity selected was
±
3, since it was the
one where most of the covariates shows not significant differences between eligibility groups
(Appendix 2). The cross-tabulation of the instrument and the treatment for this disconti-
nuity sample as well as the mean z-score by compliance status are included in Appendix 3.
The first stage estimates are presented in Table 5.
I find that having a RSII score at least as low as 28,2 is translated in a significant increase
in the probability of receiving the BDH transfer of around 18%-19%. The F-statistics for the
null hypothesis that the instrument does not induces significant variation, have associated p-
values
<
0,05, though the statistics range from 5,5 to 6,8 (Appendix 4), which are lower than
the required minimum of 10 for non-weak instruments (Stock et al., 2002). Additionally,
there is a concern about the statistical inference due to the reduced sample size which sums
up to 662. In fact, these arguments justify the application of the alternative approach.
Nonetheless, what is more important is that the instrument is uncorrelated with the error
term in the HAZ equation, to ensure the local “randomization”. It is arguable that given
the arbitrary cutoff and the flexible functional form of the index, the last should not be
correlated with unobserved confounders determining the anthropometric outcome.
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Additionally, one specification for different slopes was included (
X
∗
Z
), though the first stage estimates
were not significant. Therefore, not reported.
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