Interpreting log discontinuity in the density from McCrary test In the article by Justin McCrary "Manipulation of the running variable in the regression discontinuity design: A density test" (2008) he estimates log discontinuity in the density of democratic vote share.
He finds a 52% discontinuity but does not elaborate on how to interpret this 52%. Intuition might imply a 52% drop in the density but it seems unlikely graphically and very possible that this value could exceed 100%
Is it an arbitrary output best used for comparisons?
What would a value over 100% mean?
Thanks in advance
 A: I think 52% comes from two local linear regressions corresponding to simple arithmetic on Figure 5. This figure partition the assignment variable (percent voting in favor) into bins and calculates frequencies (the number of observations in each bin). These are the circles. Then you use these frequencies as the dependent variable in two local linear regressions, one for each side of the cut-off. These are shown by the solid black lines. 

Given how $\theta$ is defined in eq (3) here, and eyeballing the frequencies from the endpoints at the discontinuity, the percentage gap is 
$$100 \cdot \left( \frac{205-135}{135} \right) \approx 52\%$$
If there was no sorting around the discontinuity at 0.5 (the null hypothesis), you would expect the two lines to connect without a dip on the left (like they do in Figure 4), which would give you a gap of 0%. Under the alternative hypothesis, the density should increase discontinuously at 0.5 (since it is desirable for bills to pass).
So 52% is quite different from 0%. In fact, the t-statistic is 6.6, so it is very unlikely to see this gap happens by chance.
