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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. [1] - 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 [2] - 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,

Stefano

[1] Angrist, J. D., Pischke, J. (2008). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.

[2]: http://www.google.it/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CDQQFjAA&url=http://www.stata.com/meeting/chicago11/materials/chi11_nichols.pdf&ei=GvVnUvKOFIPv4gT-moH4DQ&usg=AFQjCNGv9pmEIOIvhVsmmMq38q05pRbFbg&bvm=bv.55123115,d.bGE

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This is partial answer. I think you should probably use both the biprobit and the ivreg/ivreg2 commands to check how robust your effects are. I like the biprobit approach given your data, but it does make some strong assumptions (no heteroskedasticity, no hetrogenous effects, normality of errors).* However, there's also a dedicated RD command in Stata called rdrobust. It can handle the fuzzy design and may be installed with:

net install rdrobust, from(http://www-personal.umich.edu/~cattaneo/rdrobust) replace

You can find an intro to the command in Cattaneo, Calonico, and Titiunik's Stata Journal paper Robust Data-Driven Inference in the Regression-Discontinuity Design.


*Austin Nichols' simulation results indicate that the marginal effects may be less sensitive than the latent index function parameters to biprobit assumption violations. The LPM model is also not always the model of steel that A&P make it out.

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  • $\begingroup$ Thank you very much. Actually I am applying fuzzy RDD on some simulations where, for simplicity, errors are normally distributed and homoschedasticity holds. Still, my DGP is characterized by heterogeneity. I am wondering if it is possible to address it through the the -biprobit- approach. $\endgroup$ – Stefano Lombardi Oct 23 '13 at 18:02
  • $\begingroup$ In theory, it's problematic since you're dividing $\beta_i$ by $\sigma_i=\sigma$ to get to the standard normal. However, according to Austin, biprobit is remarkably robust to variability in the treatment effect (random coefficients) in simulation. $\endgroup$ – Dimitriy V. Masterov Oct 23 '13 at 18:16

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