13.2 Basics

  • \(X_{i}\): Score/Running variable with \(x_{0}\) as a known cutoff
  • \(Z_{i}\) = Assignment variable; \(1(X_{i} \geq x_{0})\), \(0\) otherwise
  • \(D_{i}\): Treatment actually recieved
  • Sharp RDD: Units comply perfectly with their assignment; \(Z_{i} = D_{i}\) for all i
  • Fuzzy RDD: \(Z_{i} \neq D_{i}\)
  • Q: Can you give an example of \(X_{i}\), \(Z_{i}\) and \(D_{i}\) for a concrete person, e.g., thinking of access to a Master program?
Skovron & Titiunik 2015, Fig. 1, p.5

Skovron & Titiunik 2015, Fig. 1, p.5

  • Fuzzy RDD can be redefined as a sharp RDD where treatment of interest is the treatment assignment