The forcing variable cutpoint can either be exact or not exact:
- If the cutpoint is exact, the probability of treatment changes from zero to one at the cutpoint. In other words, all observations on one side of the cutpoint are in the treatment group (and actually received the treatment) and all observations on the other side of the cutpoint are in the control group (and didn’t receive the treatment). This is known as a sharp design.
- If the cutpoint is NOT exact, the probability of treatment doesn’t jump from zero to one at the cutpoint. In other words, there are individuals in each treatment group on BOTH sides of the cutpoint. This is known as a fuzzy design.
While this distinction may seem minor, it is actually incredibly important to recognize when to use sharp RDD as opposed to fuzzy RDD. Not only do the two approaches make different assumptions about the data, but they also require slightly different statistical methods.
We will focus on sharp RDD in this lesson, even though perfect compliance with the treatment assignment is not always realistic.
Play around with the interactive plot in the learning environment to see what different levels of “fuzziness” look like in a regression discontinuity design.
What does this mean with respect to our companies? As you change the degree of fuzziness, which small companies offer contribution matching? Which large companies are in violation of the law?