I am currently running computations through a "Fuzzy" Regression discontinuity Design. Suppose my data are in the following form:
- $Z$: assignment variable; if $Z > Z_0$ then the person is assigned to the treatment with a certain probability $p_D$ (since we are in the "fuzzy" RDD framework, $p_D<1$).
- $D$: treatment status; $D=1$ if the person is treated, 0 otherwise.
- $X$: set of exogenous variables.
- $Y$: Binary outcome variable.
To my knowledge - see e.g.  - running a fuzzy RDD is equivalent to apply Instrumental Variables using $Z$ as instrument (hence at the first stage we should have $D$ regressed on $Z$ and $X$).
In order to estimate the model through Stata I used the following code:
biprobit (Y = X D) (D = X Z)
According to some research I have done - see Nichols' pdf at  - the
-biprobit- package should be required because of the binary nature of the endogenous variable ($D$).
Do you find the above codes correct? Is it also possible to use a simple linear probability model like this?
ivregress 2sls Y X (D=Z)
Thanks fo any help,
 Angrist, J. D., Pischke, J. (2008). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.