# Fuzzy Regression Discontinuity Design (fuzzy RDD)

I am doing fuzzy RDD recently and I am facing some challenging moment dealing with Stata. I am using the command -rdplot- and -rdrobust-. I have some questions regarding the fuzzy RDD and the commands;

1. When the cut-offs is not known, is it still possible to seek for a discontinuity using fuzzy RDD (or the sharp one)?

2. the -rdrobust- command has an option fuzzy(treatment) to implement the fuzzy RDD, it has results on the coefficient. Let say my outcome variable is LN number of passengers, running variable is a distance between two cities. When I run the fuzzy RDD using a specific cut-off, I obtained significant result with the value of coefficient is 7.833. What does it mean? I read a paper by Imbens and Lemieux (2007) as "the ratio of the jump in the regression of the outcome on the covariate to the jump in the regression of the treatment indicator on the covariate". So, how do I interpret the 7.833?

Thank you.

• On (2), see this question about fuzzy RD as IV, a kind of Wald estimator. As far as interpretation, you need to say more about what the treatment is. Jul 27, 2016 at 1:48
• Thank you. So, the number can not be interpreted directly? It is more useful if I claim only the sign of the coefficient? Jul 28, 2016 at 2:48
• @putut_purwandono If LN is natural log, then the effect of treatment is a semi-elasticity which corresponds to an astounding $100 \cdot (\exp{7.833} - 1) = 252,148.55\%$ increase in passengers. Jul 28, 2016 at 6:10

They essentially run a series of regressions of treatment on a dummy that equals 1 after each possible cutoff point and choose the one cut-off that gives the highest $R^2$ of the regression.