Regression discontinuity - Issue with optimal bandwidth estimation after a linear transformation of the forcing variable

[Giuditta Rusconi]

Dear all,

I am having issues with the estimation of an optimal bandwidth using the –rd- command (I am using Stata 14.1).

For a current research project I am using the –rd- command to estimate the optimal bandwidth (bw_m_opt) for a given spatial regression discontinuity design (see Imbens and Kalyanaraman, 2012). The forcing variable is defined as the distance to a border and is measured in meters. For representational reasons I decided to change the units of measurement from meters to kilometers (= m/1000). Doing this, I was expecting the optimal bandwidth in kilometers to be bw_km_opt = (bw_m_opt/1000).

Using the –rd- command yielded however very different results, which held true when I replicated the exercise with other datasets.

I will illustrate the issue using the example data set provided in the help file of the –rd- command:

Code:

* RD command - linear transformations

* Install -rd- and -rdbwselect-
net install rdrobust, from(http://www-personal.umich.edu/~catta...rdrobust/stata) replace
ssc inst rd, replace

* Use the example data set in help file
net get rd // command by Austin Nichols
use votex, clear


* linear transformation of the forcing variable - change scale
gen d_100 = d*100

sum d d_100

* RD using d / d_100 as forcing variable
rd lne d
rd lne d_100

* If I replicate this by using another user-written command –rdbwselect- specifying the Imbens and Kalyanaraman option (IK), I don’t encounter this issue.

rdbwselect lne d, bwselect(IK)
rdbwselect lne d_100, bwselect(IK)


Can someone help me figure out what causes this variation in the optimal bandwidth estimation? I would expect the optimal bandwidth not to be affected by a linear transformation.

Thank you in advance for your help.

Best,

Giudy

References:
Imbens, G. W., and K. Kalyanaraman. 2012. Optimal Bandwidth Choice for the Regression Discontinuity Estimator. Review of Economic Studies 79(3): 933-959.

[Sandra Akins]

Can you provide the rd and the rdbwselect results so we can compare?

[paulvonhippel]

Was this issue resolved? Giudy didn't provide results, but I can replicate her problem by running the code she provided.

[Giuditta Rusconi]

Hi Paul,

Thanks to Dr. Nichols (the author of the –rd- command) I was able to understand what is causing the “strange” behavior in the optimal bandwidth. The –rd- command implements the 2009 working paper algorithm to estimate the optimal bandwidth, where among other things the scale of the forcing variable is subject to an absolute condition, which causes problems when the its scale is changed (see equation (4.11) of the working paper). –rdbwselect- however is based on the algorithm presented in the 2012 version, which does not contain this condition.

For many applications both commands are very similar, but in my case I am using -rdbwselect-, since I need it to be stable when I vary the scale of the forcing variable.


Imbens, G., and Kalyanaraman, K.. 2009. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator." NBER WP 14726.
Imbens, G. W., and Kalyanaraman, K.. 2012. Optimal Bandwidth Choice for the Regression Discontinuity Estimator. Review of Economic Studies 79(3): 933-959.

[Joppe de Ree]

Thanks for posting this. I had the same problem but it happened when I rescaled my outcome variable. I can see though that this is really the same thing..