and T all belong in the structural model. Individuals that live on the fringes of the village
boundary might be relatively more cut-off from the centre of economic activity so that their
spatial location covaries with their outcomes. Likewise, if the program is means-tested and a
baseline survey is not available, then P might also belong in the structural model. However,
there is no obvious reason to expect that the interaction between D and P belongs in the
structural equation. Thus, a more plausible data sampling process might be:
yij = α + βDi + γPij + δTij + {η(Di × Pij) + vi + ij }
'-------------------------{z-------------------------}
composite error
where i = 1, . . . , N indexes villages, j = 1, . . . , Mi indexes the Mi sampled households in
village i, and vi and ij are project and household-specific error terms respectively. As before,
yij is a measure of consumption. Under this type of data sampling process, if (Di × Pij)
is to be considered a valid IV, we must assume η = 0, otherwise it could be the case that
cov((Di × Pij ), uij ) 6= 0, where uij = vij + ij . On the other hand, if we assume η = 0, we can
then construct a Wald type of estimator using Di × Pij as an IV for Tij . We show in appendix
A.2 that this IV turns out to resemble a Wald type of estimator that consistently estimates the
average treatment effect. Formally,
~
διv
.y|D,P
∆T |D,P
δ ■ .
∆T |D,P
where .y|D,P and .T |D,P are defined explicitly in appendix A.2.
5.2 Regression Discontinuity Design
With this approach, researchers take advantage of extant discontinuities that occur as the
result of the policy itself to try and identify the impact of the programme. Discontinuities may
be generated by programme eligibility criteria, thereby making it possible to identify impact
by comparing differences in the mean outcomes for individuals on either side of the critical
cutoff point determining eligibility. For example, in Israel, if a class size exceeds forty students,
a second class is introduced to cater for this increase in student numbers. Hence there is a
discontinuity between the levels of 40 students and 41 students in a grade respectively, or 80
and 81, and so forth. This allows researchers to observe differences immediately ab ove and
immediately below the threshold level (Angrist and Lavy, 1999). Similar work has been done
in South Africa with respect to welfare responses resulting from access to the state Old Age
Pension which has an age eligibility criteria. Health outcomes for children, girls in particular,
are shown to be significantly better in households that have pension-eligible members (aged 60
and above) as opposed to households that do not (with household members aged 55-59) (Duflo,
2001). As with PSM, regression discontinuity only gives the mean impact for a selected sample
of participants, namely those in the neighbourhood of the cutoff point.
A key identifying assumption is that there is no discontinuity in counterfactual outcomes at
the point of discontinuity. This is made difficult if the discontinuity is generated by an eligibility
requirement that is geographically specific or one that coincides with political jurisdiction, since
this in itself might suggest pre-existing differences in the outcomes of interest. Moreover, it is
assumed that the evaluator knows the eligibility requirements for participation and that these
can be verified and measured. Where eligibility is based on some criteria such as age, this is
relatively easy to do. However, if eligibility for a programme relies on a means-test, verification
of pre-intervention status becomes more difficult since incomes are only observed ex-post in a
cross-sectional survey. In these instances, a baseline survey helps to control for pre-intervention
differences.
Buddelmeyer and Skoufias (2004) use cutoffs in PROGRESSAs eligibility rules to measure
impacts of the program and find that discontinuity design gives a good approximation for almost
all outcome indicators when compared to estimates obtained through randomization.
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