Regression discontinuity design - discrete running variable

[Abbie Chapman]

I am conducting a sharp RD, with my running variable being the age of the woman in months. I am trying to calculate whether a particular legislation affected the age a woman gets married.
My dependent variable is age of marriage (agemar) and my running variable is age of the woman in months (agePCMAfunctionYrs), which is discrete since it is in months
Currently I am running the following command:
rdrobust agemar agePCMAfunctionYrs, c(15) covs(region religion) p(2)

However, because it is discrete I know I need to cluster the standard errors at the running variable level. I cannot see anywhere online how to do this - I would be very grateful if somebody would be able to say how I do this on STATA.

[Marcos Almeida]

Welcome to the Stata Forum / Statalist,

Well, to start, rdrobust is a user-written program and we shall state this beforehand.

Second, I have no experience with this ado file.

Finally, according to the help file, the option - vce(cluster clustervar) - will do the trick.

Hopefully that helps.

[Charles Calmeyn]

Hello Abbie, I have the same problem as you and I was wondering if you were able to solve your problem. If yes, how did you do it?

Kind regards,
Charles

[Johan Karlsson]

Dear all,

I am currently working on a similar problem and recent literature strongly advises against clustering on the running variable, despite its popularity. Rather, they show that a standard Eicker-Huber-White SE is generally more reliable, especially for local linear regressions.

For review, see Kolesár, Michal, and Christoph Rothe. 2018. "Inference in Regression Discontinuity Designs with a Discrete Running Variable." American Economic Review, 108 (8): 2277-2304.

In other words, it would appear that rdrobust is perhaps not suitable for a discrete running variable at all.

Best regards
Johan

[Johan Karlsson]

Update on the progress after some intense reading and coding:

For anyone going down this route in the future, RDrobust is likely insuitable for inference with discrete running variables as they are not nonparametrically identified, i.e., you cannot shrink the bandwidth around the treatment so that it approaches zero. See, for example; Yingying Dong (2015). "Regression discontinuity applications with rounding errors in the running variable". Journal of Applied Econometrics 30, 422-446.

What you need to do is instead to run a regular OLS regression with a local linear or local polynomial function of the running variable. Next, if possible, you need to approximate the measurement error from rounding off the variable, such as through aggregated statistics. Second best is to assume a uniform distribution. Lastly, you estimate the bias-adjusted ATE using the nth moments of the measurement error distribution based on the formulations in Dong (2015). Based on Kolesár et al. (2018), you are likely better off using Eicker-Huber-White SEs. If the running variable is time, you need to also adjust for autocorrelation.

[Anis Oger]

Maybe this is really stupid, but some of the authors behind rdrobust published a really understandable practitioners guide*. They argue when the number of distict values is large enough, rdrobust maybe fine as is. (then I would assume this would render clustering unneccessary because they already offer robust bias corrected confidence intervals). If not, they advise against identification based on the continuity assumption all together and refer to a local randomization based approach.
*Practical Introduction to Regression Discontinuity Designs: Extensions, In preparation for Cambridge Elements: Quantitative and Computational Methods for Social Science, Cambridge University Press.

[Marianna Portincasa]

Update on the progress after some intense reading and coding:

For anyone going down this route in the future, RDrobust is likely insuitable for inference with discrete running variables as they are not nonparametrically identified, i.e., you cannot shrink the bandwidth around the treatment so that it approaches zero. See, for example; Yingying Dong (2015). "Regression discontinuity applications with rounding errors in the running variable". Journal of Applied Econometrics 30, 422-446.

What you need to do is instead to run a regular OLS regression with a local linear or local polynomial function of the running variable. Next, if possible, you need to approximate the measurement error from rounding off the variable, such as through aggregated statistics. Second best is to assume a uniform distribution. Lastly, you estimate the bias-adjusted ATE using the nth moments of the measurement error distribution based on the formulations in Dong (2015). Based on Kolesár et al. (2018), you are likely better off using Eicker-Huber-White SEs. If the running variable is time, you need to also adjust for autocorrelation.

Did you read Anis's answer? what do you think? I read the same guide as Calonico and in fact he claims that rdobust can be used.

[Johan Karlsson]

Did you read Anis's answer? what do you think? I read the same guide as Calonico and in fact he claims that rdobust can be used.

I am unfortunately not familiar enough with RDrobust, but it could definitely be a contender. The RDiT approach is somewhat controversial though and does not really yield robust results. I have been advised against using it in a research setting. You will get somewhat more accurate results, but the question is if it can really be considered causal.