Methods in Labor Economics

# Let 0 denote the outcome if the observation unit i is

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Unformatted text preview: n unit i is not treated. If unit i is treated, we cannot observed this counterfactual or potential outcome. Fortin – Econ 560 Lecture 0 Letting be a dummy variable equal to 1 when an observation unit is treated and to 0 when it is not, the observed outcome for unit i can be written as (0) =0 (1 − ) (0) + (1) = = (1) =1 It is assumed that an observed outcome depends only on treatment to which unit i is assigned and not on the allocation of other units. This assumption is called stableunit-treatment-value assumption (SUTVA). Thus we cannot hope to observe (1) − (0) for a particular unit i, which the true causal effect. For each unit, the comparison of the potential outcome under treatment and the potential outcome under control. We may observe the average difference in the potential outcomes as the average causal effect or average treatment effect: = [ (1) − (0) ] = [ (1)] − [ (0) ] Fortin – Econ 560 Lecture 0 A comparison of the observation units that are treated and non-treated gives [ | = 1] − [ | = 0 ] = [ (1)| = 1] − [ (0)| = 0 ] = [ (1)| = 1] − [ (0)| = 1] + [ (0)| = 1] − [ (0)| = 0 ] = [ (1) − (0)| = 1] + { [ (0)| = 1] − [ (0)| = 0 ]} where the last terms in braces capture the difference in the average outcomes between treated and non-treated units in the absence of treatment, it is called the selection bias. Other possible average causal effects can be defined, such as the effect of treatment on the treated: = [ (1) − (0)| = 1] = [ (1)| = 1] − [ (0)| = 1 ] If the treatment is randomly assigned, (1), (0) ⊥ the assignment to treatment is independent of potential outcomes, the assignment is also said to be ignorable. The selection bias will vanish and we can expect the treatment-control difference to provide an unbiased estimate of the average treatment effect. If the treatment is not randomly assigned, the comparison of treated and nontreated units will contain a term not due to treatment. Fortin – Econ 560 Lecture 0 In the absence of a true experimental design (randomized data), a quasiexperimental (QE) method may be the best alternative. The RD design i...
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