# Fuzzy RDD in Stata with two cutoff points

I am running a Fuzzy Regression Discontinuity Design using 2SLS.

If I specified the model (and most importantly the IVs) correctly as i have never worked on a RDD before. The difference to the usual case is that i'm considering not just one but two cutoff points/discontinuities.

The running variable is age and the two cutoff points are at 60 and 65. Also, I limited the bandwidth manually to a specific range.

My data has the following form:

Y: Outcome of interest Z: Running variable (age of the individual) T: Treatment D1: equals one if Z is above 60 (cutoff 1), =0 if to the left of 60 D2: equals one if Z is above 65 (cutoff 2), =0 if to the left of 65

• i.e., when an individual is above 65 both binary variables D1 and D2 would equal 1.

This is what I have been doing:

xtivreg Y (T= D1 D2) Z c.Z#D1 c.Z#D2 i.year, fe vce(cluster ID) first

The interactions between Z (age) and the two cutoff points D1 and D2 should allow for different age-trends above each of the two discontinuities. Momentarily, I'm not (yet) considering a quadratic or even cubic age-trend.

Also, I'm very interested in the point estimates from the first-stage regression - I would like to know how the possibility of receiving the treatment changes when an individual crosses these two thresholds.

These are the results from the first-stage regression:

Treatment

• Z -0.033
• c.Z#D1 0.062
• c.Z#D2 -0.079
• D1 -3.56
• D2 5.29

With respect to the first cutoff point at 60, my interpretation would be that an individual which is 60.5 years old has on average a 19.1 percentage points higher probability of receiving the treatment than someone who is just below the first threshold. With respect to the second cutoff point at 65, an individual which is 65.5 years old has on average a 11.55 percentage points higher probability of receiving the treatment than someone who is just below the second threshold.

These results (also some calculated mean probabilities) are in line with the findings from a graph which shows the relation between treatment T and the forcing variable Z.

1. Would this be a correct way of estimating the model? Or have i overlooked something?

2. Does my specification of both IVs D1 and D2 make sense?