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Methods in Labor Economics

# Selection process is known assignment to treatment

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Unformatted text preview: fixed threshold. Selection process is known: Assignment to treatment and control is not random Fortin – Econ 560 Lecture 0 But, we know the assignment rule influencing how people are assigned or selected in to treatment There is a known cut-off in treatment assignment (SRD) (or in probability of treatment receipt as a function of one or more continuous variables (FRD) that generates a discontinuity in the treatment recipiency rate at that point It is like an experiment around the cutoff: Assignment to treatment by covariate value, assign all units with 1{ ≥ } to treatment in the SRD design = The assignment variable may itself be associated with the potential outcomes, but this association is assumed to be smooth (continuous), So any discontinuity in the conditional distribution of the outcome, indexed by the value of this covariate at the cutoff value, is interpreted as evidence of a causal effect of the treatment: = [ (1) − (0)| = ] Fortin – Econ 560 Lecture 0 Forcing variable Fortin – Econ 560 Lecture 0 More formally, under Assumption 1 (Continuity of Conditional Regression Functions) [ (0)| = ] and [ (1)| = ] are continuous in = lim ↓ [ | = ] − lim ↑ [ | = ] = lim → [ (1)| = + ] − lim → [ (0)| provided that these limits exist. This suggests that “in principle” you can estimate on each side arbitrarily close to the cutoff. = −] as the difference in means In practice, this depends on having lots of data within ε of the cutoff and raises the question of how close to the cutoff do you have to be. RDD is often described as a “close cousin” of a randomized experiment or as a “local randomized experiment.” To see the difference, consider an experiment in which each participant is assigned a randomly generated number, c, from a uniform distribution over the range [0,1]. Fortin – Econ 560 Lecture 0 Units with c ≥ 0.5 assigned to treatment; units with c < 0.5 assigned to control This randomized experiment can be thought of as an RD where th...
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