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

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 Xx0, 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.