Readings

  1. Mastering ‘Metrics: The Path from Cause to Effect
    Princeton University Press, 2014.
    Joshua D. Angrist and Jörn-Steffen Pischke
    (Chapter 4)

  2. What Happens When Extremists Win Primaries?
    American Political Science Review, 2015, 18-42.
    Andrew Hall

A guide to practice (as an additional resource)

  1. A Practical Introduction to Regression Discontinuity Designs
    Cambridge University Press, Cambridge, UK, 2019.
    Matias D. Cattaneo, Nicolás Idrobo, and Rocío Titiunik

In-class exercise

R code for exercise: Here

Data for exercise from Hall (2015): Here

Robustness checks and extensions

Note that there are more possibilities for robustness checks and extensions in regression discontinuity designs than those listed below. Others that aren’t listed will llikely be specific to the type of case being examined.

Sorting at the cut-off

  1. McCrary density test for sorting at the discontinuity.
    • e.g. Using DCdensity() in the rdd library in R
  2. If there is a possibility of sorting at the cut-off, run a “donut hole” RDD by simply removing all observations close to the cutoff and using the remaining data to fit the RDD model (Barreca et al. 2011, search for “donut”)

Placebo checks

  1. Fit RDD models to outcomes where we shouldn’t expect a discontinuity (e.g. any covariate that shouldn’t be affected by the discontinuity). We expect all null results here.
  2. Fit RDD models at cut-offs where we shouldn’t expect a discontinuity.
    • Test for a discontinuity at every possible cut-point. We expect all null results here.
    • Make sure to do this separately for the subset of data above and below the cut-off to avoid contamination from the actual treatment.

Outliers and functional form

  1. Estimate the regression discontinuity for a large set of bandwidths.
    • Graph estimates across the range of bandwidth
  2. Estimate the regression discontinuity for different polynomials
    • x, x2, x3
    • Graph estimates for a range of bandwidths and polynomials
  3. Calculate RDD esimtate using the “optimal” bandwidth (Imbens and Kalyanaraman 2012)
    • e.g. Using rdrobust() library from the rdrobust library in R
    • You basically have to do this in any RDD paper these days, and will likely serve as your main result
  4. If there are relatively few units in your data (e.g. districts nested within a few regions), remove each unit one at a time and re-run the RDD to see if one unit is driving the results

Sub-group analysis

  1. Test for treatment effect heterogeneity for theoeretically important sub-groups

Is your RDD a “politician characteristic regression discontinuity”?

Are you testing the effect of a characteristic of a politician or other actor? (e.g. the effect of electing a woman/person of color/someone with a criminal history etc.) There are issues to consider when doing so. See:

Can Close Election Regression Discontinuity Designs Identify Effects of Winning Politician Characteristics?
American Journal of Political Science, 2022, 494-510.
John Marshall