## Fuzzy RD is IV

Fuzzy RD exploits discontinuities in the probability or expected value of treatment conditional on a covariate. The result is a research design where the discontinuity becomes an instrumental variable for treatment status instead of deterministically switching treatment on or off. To see how this works, let D; denote the treatment as before, though here D; is no longer deterministically related to the threshold-crossing rule, x; > xo■ Rather, there is a jump in the probability of treatment at xo, so that

r, I go(xi) if x; > xo

P[D; = 1|x;J = > , where gi (xo ) = go (xo)■

I gi(x;) if x; < xo

The functions go(x;) and g1(x;) can be anything as long as they differ (and the more the better) at xo. We’ll assume g1(xo) > go(xo), so x; > xo makes treatment more likely...

Read More