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Lorena Moreno
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Analiti a, Revista de análisis estadístico, Vol. 13 (1), 2017
bandwidth for the CI was allowed to be data driven and particular to the especification
8
.
The method for bandwidth selection procedure implemented was one common below and
above the threshold Coverage Error Rate (CER), instead of the MSE since the former is
optimal for statistical inference (Calonico et al., 2016a). Also, a tringular kernel regression
was used for all cases.
Given the particularity allowed for each specification, the main bandwidths are three
±
5,252,
±
6,338 and
±
6,248. Consequently, each model has a different sample specifically
1.142, 1.350 and 1.331 all reported in the tables. Correspondingly, for the CI bandwidths
and their sample.
As detailed in Table 8, the probability of treatment due to an eligible index increases sig-
nificantly ranging from 0,18 to 0,24 for the robust procedure. Compared to the conventional
non-parametric estimates, as well as to parametric, the values are larger. Signalling, that
even after correcting for possible bias, the instrument still influences the probability of pro-
gramme participation. In order visualize these first stage effects plots for each specification
are depicted in Figure 7
9
.
For the ITT effects I find statistical inference differences between procedures, and a very
similar path when comparing to the parametric results. The only significant robust estimate
belongs to specification (3), which could be interpreted as the isolated effect of the instrument
on the outcome. The 0,48 standard deviation decrease in HAZ refers to a main bandwidth
of 6,3, with 627 observations below the threshold and 704 to the right (Table 9). Figure 8
accounts for this estimates.
Finally, the local polynomial LATE estimates are detailed in Table 10. None of the
robust estimates are statistically distinguishable from 0, contrary to what happens with the
conventional and bias-corrected for the last model, where the conventional p-values can lead
to incorrect interpretation of the possible effect of the BDH. All estimates are lower than the
parametric (for each specification), though all in average are close to a -2-standard deviation
estimate.
8
After comparing the CI reduction for each more complex specification between a particular one and
a fixed one (corresponding to specification (1)), the largest percentages were associated to the non-fixed;
therefore, each model has its own CI bandwidth.
9
Software output estimates refer to what happens at the discontinuity. So, for instance, in (1) the original
was negative since there is a negative jump due to the decrease in the probability of treatment to the right
of the cutoff. Though, for comparability matters (with the parametric), the signs were inverted. The same
case for the ITT estimates. The Effect estimates are left unaffected.
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