13.3 Basics
- Observations of units below cutoff: We observe outcome under control condition
- Observations of units above cutoff: We observe outcome under treatment condition
- Below plots the average potential outcomes given the score, E[Yi(1)|Xi=x] and E[Yi(0)|Xi=x], against the score
![Skovron & Titiunik 2015, Fig. 2, p.6](www/rdd-skovrov-titiunik-2015-rdd-treatmenteffect-p6.png)
Skovron & Titiunik 2015, Fig. 2, p.6
- Regression function E[Yi(1)|Xi] is observed for values of the score to the right of the cutoff-because when X≥x0, the observed outcome Yi is equal to the potential outcome under treatment, Yi(1), for every i
- Same is true for E[Yi(0)|Xi] for values left to the cutoff
- Sharp RD treatment effect: Difference between limits of the treated and control average observed outcomes as the score converges to x0 is equal to the average treatment effect at x0
- …there are two approaches to estimating the “causal effect” that rest on different assumptions.