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128<br />

4.7 Common support for <strong>the</strong> treated<br />

The first step is to discard from <strong>the</strong> treatment group those members whose propensity<br />

score is beyond <strong>the</strong> limits <strong>of</strong> that <strong>of</strong> <strong>the</strong> distribution <strong>of</strong> propensities <strong>of</strong> <strong>the</strong> comparison<br />

group. This form <strong>of</strong> <strong>the</strong> common support was used in <strong>the</strong> multiple treatments matching<br />

protocol <strong>of</strong> Gerfin and Lechner (2000) p22, where <strong>the</strong> minima and maxima <strong>of</strong> <strong>the</strong> treated<br />

propensities defined <strong>the</strong> common support region, in this case simplified by only one<br />

treatment and comparison group. Thus <strong>the</strong> propensity for <strong>the</strong> treated and comparisons<br />

only covers <strong>the</strong> same interval. This is <strong>the</strong> application <strong>of</strong> <strong>the</strong> rule <strong>of</strong> common support<br />

expressed in equation 4 <strong>of</strong> <strong>the</strong> <strong>the</strong>ory in section 4.3. There is support in <strong>the</strong> comparator<br />

group for <strong>the</strong> treatment group member if a propensity value between 0 and 1 exists<br />

amongst <strong>the</strong> comparisons for each propensity <strong>of</strong> <strong>the</strong> treatment group. Those individuals<br />

discarded for non-support have least similarity. The members <strong>of</strong> <strong>the</strong> treatment group are<br />

discarded for non-support if <strong>the</strong>ir propensity to participate in SYETP is lower than <strong>the</strong><br />

minimum score or higher than <strong>the</strong> maximum score <strong>of</strong> those in <strong>the</strong> comparison group.<br />

Those cases discarded for non-common support are not comparable, because for <strong>the</strong><br />

treated <strong>the</strong>re is no comparable non-participant.<br />

The distributional summaries in Table 4.5 give <strong>the</strong> four largest and smallest propensity<br />

scores observed in <strong>the</strong> treatment and comparison group. In this case, application <strong>of</strong> <strong>the</strong><br />

rule <strong>of</strong> common support has no effect on <strong>the</strong> treatment group, as <strong>the</strong> distribution for <strong>the</strong><br />

SYETP treatment propensities always lies within <strong>the</strong> bounds <strong>of</strong> <strong>the</strong> comparison group.<br />

The maximum comparison group propensity to take part in SYETP is 0.5458441, and <strong>the</strong><br />

minimum is 0.0000598. However, <strong>the</strong>re are just 2 cases in <strong>the</strong> comparison group with<br />

propensities greater than <strong>the</strong> maximum <strong>of</strong> <strong>the</strong> SYETP treatment group (<strong>the</strong>se are not<br />

clearly visible in <strong>the</strong> histogram as <strong>the</strong> bar is so thin due to low number <strong>of</strong> cases). For <strong>the</strong><br />

SYETP treatment group, <strong>the</strong> maximum comparison group propensity to take part in<br />

SYETP is 0.5258619 and <strong>the</strong> minimum is 0.0147686. In this case, <strong>the</strong>re are no SYETP<br />

participants for whom <strong>the</strong>re are not comparable non-participants.

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