13.5 Estimation: Randomization-Based Approach

  • Explicitly assumes that RDD induces randomized experiment in window near the cutoff (local randomization assumption)49
    • Assumption: Local randomization = Location just above/below cutoff is random
    • Stricter: Assumes flat functions in small window around cutoff (see Skovron and Titiunik 2015, Fig. 9)
    • Possibly better with few observations and discrete (non-continuous) running variables
      • Q: Why? (Hint: Think of fitting curve to few data points; Continuity vs. mass points) (Skovron and Titiunik 2015, 21)50
  • Large samples: Use difference in averages of observed outcomes in treatment and control group
  • Small samples: Fisherian approach

References

Skovron, Christopher, and Rocıo Titiunik. 2015. “A Practical Guide to Regression Discontinuity Designs in Political Science.”

  1. “we understand the randomization-based approach as implying not only that the treatment assignment is probabilistic and unrelated to the potential outcomes in a window around the cutoff, but also that in this window the potential out-comes depend only on whether the score exceeds the cutoff and not on the score’s particular value” (Skovron and Titiunik 2015, 20)↩

  2. With few observations any curve that we fit to the data will be strongly affected by single observations. Hence, it’s probably better just to take the mean across all (flat function). The same is true for discrete running variables. A curve that we fit will be strongly affect by mass points (e.g. points on the discrete variable where we have a lot of observations). Hence, again it’s better to depart from the local randomization assumption.↩