I am using a Fuzzy Regression Discontinuity Design for the first time and this maybe a very basic question to some. I am estimating the Fuzzy RD with 2SLS.
Suppose, my data is of the following form:
z: is the running variable. If z > 0, then the individual is assigned to treatment;
d: equals one if z > 0 (assignment to treatment);
t: equals one if individual is treated;
y: is the outcome of interest and is a binary variable.
I am running a 2SLS in stata doing something like this (at this moment, I am not using powers of z in my model).
Code: ivregress 2sls y (t = d) z z_d, robust
where: z_d is an interaction term between the running variable and the indicator of assignment to treatment.
My question is, should I instrument this interactions as well? For example, something like the following:
Code: ivregress 2sls y ( t z_t = d z_d) z , robust
or include only the interaction between the assignment variable and the running variable (as I was doing before)?
I would really appreciate your suggestions and advice. Many thanks in advance.