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  3. Causal Inference with R - Instrumental Variables & RDD

Exercise

Examining Manipulation in Regression Discontinuity Design

As we have mentioned, the main idea with Regression Discontinuity is that there should not be any difference in the people on either side of the cutoff. So a big part of RD analysis is to check whether this is actually true in our data. For example, the distributions of our variables should be the same on both sides of the cutoff. If people choose which side of the cutoff in order to influence the outcome, then we might worry that people on either side of the cutoff are not comparable.

Let's look at this by revisiting the NBA data we used before in previous exercises. In that data, we saw that teams that are losing by 1 or 2 points at halftime end up winning the games a lot more than you would expect. If the coaches and players know this is true, they might try to manipulate the score so that they are the ones losing by 1 or 2 at halftime (perhaps because they read that research paper published in Management Science!). If we look at a density plot of our data, we would see this as a kind of lump in the distribution on one side next to the cutoff, instead of a smooth curve in our data density.

So we will check the data to check our distributions near the cutoff with the statistical McCrary test, which tests whether there is a discontinuity in the data frequency distribution around the cutoff. We will look at plots and at the p-values of the McCrary tests, and if the p-values are at or below .05, then we can be 95% confident that manipulation has occurred. So let's find out if that is true in this NBA data.

Instructions

100 XP
  • 1) Examine the structure of the dataframe NBA
  • 2) Using the function DCdensity to run a McCrary test and examine the plot the distribution of data near the cutoff
  • 3) Check the statistical significance of the McCrary test through its p-value
  • 4) Decide if the data is suitable for a regression discontinuity analysis
  • 5) Using a new dataset, check updated data for manipulation via a McCrary test
  • 6) Check this new McCrary test for statistical significance
  • 7) Decide if this new data is suitable for a regression discontinuity analysis