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

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