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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.

Nusrat

Nusrat A Jimi
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  • Does [this](https://stats.stackexchange.com/questions/121750/fuzzy-rdd-issue/121806#121806) help? – dimitriy May 18 '18 at 01:35
  • Hello Dimitriy, Thank you very much for the link. As per the link, the first code is correct. But I am confused (not being able to understand the theoretical and intuitive reasoning) why z_d will end up in the second stage equation. Will not that violate the exclusion restriction given given that d is used as the instrument? I mean, if I consider Fuzzy RD as an local IV model, how can the instrument appear in the second stage! – Nusrat A Jimi May 18 '18 at 02:13
  • There was question about this a couple of days ago. Click on the RD tag. – dimitriy May 18 '18 at 02:30

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