Dear Statalist,
I am currently working on a project where we have run RDD regressions on a heaped running variable. Because of particularities with the project, I am unable to use the usual "rdrobust" command as it does not allow for adjusting the standard errors in the way we need. Instead, I am forced to use only the standard "regress" command.
Background: In order to adjust my treatment estimates for rounding errors, I want to follow Y. Dong (2015). "Regression discontinuity applications with rounding errors in the running variable". In his paper, he proposes that the rounding error can be adjusted for by calculating the ATE based on certain distributional features. The method is nice and clean and, in theory, easy to implement.
However, and here is where I am stumped:
In estimating the bias adjusted error, Dong (2014) proposes that one first estimates the following regression (in the case of using four polynomials):
Y = d0 +d1X +d2X2 +d3X3 +d4X4 + (c0 +c1X +c2X2 +c2X3 +c4X4)T + e
Where d refers to the running variable in the pre-treatment period and c refers to the post-treatment period. However, as far as I understand it, d0 and c0 refer to separate intercepts for the pre- versus post-period, yet they are implemented in the same regression. How is still possible? Moreover, by usual logic, one of these terms should get kicked out due to perfect multicollinearity, right?
Similarly, upon reviewing Kolesár & Rothe (2018). "Inference in Regression Discontinuity Designs with a Discrete Running Variable", they present a similar OLS model that incorporates two separate pre-post intercepts. However, they do not dwell on how this is is performed, and I do not find anything written on this in terms of actual coding.
What is it here that I am not understanding?
Any help is greatly appreciated. I have been racking my brain all day to try to understand this to no avail.
Sincerely
Johan
I am currently working on a project where we have run RDD regressions on a heaped running variable. Because of particularities with the project, I am unable to use the usual "rdrobust" command as it does not allow for adjusting the standard errors in the way we need. Instead, I am forced to use only the standard "regress" command.
Background: In order to adjust my treatment estimates for rounding errors, I want to follow Y. Dong (2015). "Regression discontinuity applications with rounding errors in the running variable". In his paper, he proposes that the rounding error can be adjusted for by calculating the ATE based on certain distributional features. The method is nice and clean and, in theory, easy to implement.
However, and here is where I am stumped:
In estimating the bias adjusted error, Dong (2014) proposes that one first estimates the following regression (in the case of using four polynomials):
Y = d0 +d1X +d2X2 +d3X3 +d4X4 + (c0 +c1X +c2X2 +c2X3 +c4X4)T + e
Where d refers to the running variable in the pre-treatment period and c refers to the post-treatment period. However, as far as I understand it, d0 and c0 refer to separate intercepts for the pre- versus post-period, yet they are implemented in the same regression. How is still possible? Moreover, by usual logic, one of these terms should get kicked out due to perfect multicollinearity, right?
Similarly, upon reviewing Kolesár & Rothe (2018). "Inference in Regression Discontinuity Designs with a Discrete Running Variable", they present a similar OLS model that incorporates two separate pre-post intercepts. However, they do not dwell on how this is is performed, and I do not find anything written on this in terms of actual coding.
What is it here that I am not understanding?
Any help is greatly appreciated. I have been racking my brain all day to try to understand this to no avail.
Sincerely
Johan
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