<p><a href="https://watermark.silverchair.com/rdr043.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAuEwggLdBgkqhkiG9w0BBwagggLOMIICygIBADCCAsMGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMBFtO6-oaqCLF-DoGAgEQgIIClJs2ePrVgc6LFXQKuuocbEpqkksFD963CCu8iXuO1mY1cpulVbZ2bZLUS7fx8O4Z8piNb_MdE66fNJrCV6rBCyyIXUT8mjcfhzAEIbz1cRaoUox0bkNenKVS0Q5gAA1ZnTNGS7JM7pJpwxuDwO_VWW148ZTvsyFy0zwh4Nz7P8UTHdadBxBHz93Gz4l9y0OWD8GmABU3ashnUBIcMtlZlsCNm6g6R57DGZ8a8vHWWo5GyGwfp9fWcM7bKtQt9fhSRCG6hFMR6s11W9Y0iMsRbR2tKLkAulxdIgtzxTHfs7qpwO8jyoBqib8kxOQdOw69j9OvhEuax28aeePWidtfWo91UvJU7wpOzIZKjuVigMEBJDzon43YXll1ZYpBu7ubi30E1qWzGwqIh1N1rdP_gIi490DTz1xMOfHieZ6euiDfzn0d_Xb0JlIrF7jeC-Levf0vyCsa1iHd873Om3OX20ZeGCoY1Vdd1_CvSki34_GNT4_EDbU47mVkztGBjL3grdT8HsKH3Ml6q3ZbUjM3kRJEqW295DN5SlUsKUtI20j0rLYh40isZD_3VYxYA25F3Erh6hCUBrNtSaLTatsl9aUYIIrKFHfMLBYkSQz3nGmPJuZUVdW2ncVVNcNT2eey20cRwSRxLzbfbzIO0hYtKq0ySpHWTfTfy2hGh0EstR6eiXNRMKNqaY82h0FuHuQDBy-D94DMgsCRrDoRzJyzGaz_Yw4cL0ZTnkJ2gVNPU-sku5oYrw51zby8wwPR-SjbbjjPI7Ou7sqcNt0o46ykvOjBraKOPDbOtImLVgPz5N-bSLjnFVOptxRXNWLZ7T5ASsXu9BvfTFssXn9bJQcH2IwMFSMfmylg5kMg_plI6yVTujIVCw" rel="nofollow noreferrer">Imben and Kalyanaraman (2012)</a> discuss this possibility in section 3.1. They say that there may be theoretical benefits, but in practice it would be impossible to implement well, and do not consider this.</p>
<p>However <a href="https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA11757" rel="nofollow noreferrer">Calonico, Cattaneo, and Titiunik (2014)</a> do allow for this (see Remark 9), ostensibly with no problems. It's rarely implemented. One paper that uses this method is, <a href="https://www.journals.uchicago.edu/doi/full/10.1086/717453" rel="nofollow noreferrer">Carlson, Correia, and Luck (2022)</a>.</p>

CC BY-SA 4.0
2022-10-09T13:05:37.307Z
2024-07-03T14:26:52.680Z
2024-07-03T14:26:52.680Z
Michael Gmeiner
<p>Consider a regression discontinuity setting in which <span class="math-container">$x_2=1$</span> if and only if <span class="math-container">$x_1 \ge D$</span> and <span class="math-container">$x_2 = 0$</span> otherwise. The baseline regression discontinuity regression for some outcome, <span class="math-container">$y$</span>, is:</p>
<p><span class="math-container">$$y_i =\beta_0 +\beta_1 (x_{1i} -D)+\beta_2 x_{2i} +\beta_3 (x_{1i}-D)x_{2i} +u_i $$</span></p>
<p>This could be estimated with OLS. Alternatively, more complicated kernel estimation could be utilized. The key is that data are restricted to observations for which <span class="math-container">$x_{1i}$</span> is in a bandwidth  around <span class="math-container">$D$</span></p>
<p>My understanding is that <a href="https://www.jstor.org/stable/43616914?seq=1" rel="nofollow noreferrer">Calonico, Cattaneo, and Titiunik's</a>
(CCT) bandwidth minimizes mean squared error of the estimated coefficient for <span class="math-container">$x_2$</span> (that is, <span class="math-container">$\beta_2$</span>) when using a bias-correction approach. My understanding is that their method is the most recent innovation in terms of regression discontinuity bandwidths (after the <a href="https://www.jstor.org/stable/23261375?seq=1" rel="nofollow noreferrer">Imbens and Kalyanaraman 2012</a> bandwidth). If there is a more recent development, I would be delighted to learn of it.</p>
<p>It appears to me that the CCT bandwidth is symmetic, i.e., we'd restrict to data for which <span class="math-container">$x_1 \in [D-h, D+h]$</span> rather than asymmetric, as in <span class="math-container">$x_i \in [D-h_1, D+h_2]$</span> for which <span class="math-container">$h_1\ne h_2$</span>.</p>
<p>Are there any papers that develop theory in which an asymmetric bandwidth is optimal in some sense? Or are there any major implementations of regression discontinuity with an asymmetric bandwidth?</p>

<econometrics><regression>
Non-symmetric RD bandwidth?
Michael Gmeiner
# Non-symmetric RD bandwidth?

(Asked by: username_0 on 2022-06-14)

Consider a regression discontinuity setting in which $x\_2=1$ if and only if $x\_1 \ge D$ and $x\_2 = 0$ otherwise. The baseline regression discontinuity regression for some outcome, $y$, is:

$$y\_i =\beta\_0 +\beta\_1 (x\_{1i} -D)+\beta\_2 x\_{2i} +\beta\_3 (x\_{1i}-D)x\_{2i} +u\_i $$

This could be estimated with OLS. Alternatively, more complicated kernel estimation could be utilized. The key is that data are restricted to observations for which $x\_{1i}$ is in a bandwidth around $D$

My understanding is that [Calonico, Cattaneo, and Titiunik's](https://www.jstor.org/stable/43616914?seq=1)
(CCT) bandwidth minimizes mean squared error of the estimated coefficient for $x\_2$ (that is, $\beta\_2$) when using a bias-correction approach. My understanding is that their method is the most recent innovation in terms of regression discontinuity bandwidths (after the [Imbens and Kalyanaraman 2012](https://www.jstor.org/stable/23261375?seq=1) bandwidth). If there is a more recent development, I would be delighted to learn of it.

It appears to me that the CCT bandwidth is symmetic, i.e., we'd restrict to data for which $x\_1 \in [D-h, D+h]$ rather than asymmetric, as in $x\_i \in [D-h\_1, D+h\_2]$ for which $h\_1\ne h\_2$.

Are there any papers that develop theory in which an asymmetric bandwidth is optimal in some sense? Or are there any major implementations of regression discontinuity with an asymmetric bandwidth?

**Tags:** econometrics, regression

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## 1 answers

### Answer by username_0 on 2022-10-09. Score: 3 | Accepted answer

[Imben and Kalyanaraman (2012)](https://watermark.silverchair.com/rdr043.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAuEwggLdBgkqhkiG9w0BBwagggLOMIICygIBADCCAsMGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMBFtO6-oaqCLF-DoGAgEQgIIClJs2ePrVgc6LFXQKuuocbEpqkksFD963CCu8iXuO1mY1cpulVbZ2bZLUS7fx8O4Z8piNb_MdE66fNJrCV6rBCyyIXUT8mjcfhzAEIbz1cRaoUox0bkNenKVS0Q5gAA1ZnTNGS7JM7pJpwxuDwO_VWW148ZTvsyFy0zwh4Nz7P8UTHdadBxBHz93Gz4l9y0OWD8GmABU3ashnUBIcMtlZlsCNm6g6R57DGZ8a8vHWWo5GyGwfp9fWcM7bKtQt9fhSRCG6hFMR6s11W9Y0iMsRbR2tKLkAulxdIgtzxTHfs7qpwO8jyoBqib8kxOQdOw69j9OvhEuax28aeePWidtfWo91UvJU7wpOzIZKjuVigMEBJDzon43YXll1ZYpBu7ubi30E1qWzGwqIh1N1rdP_gIi490DTz1xMOfHieZ6euiDfzn0d_Xb0JlIrF7jeC-Levf0vyCsa1iHd873Om3OX20ZeGCoY1Vdd1_CvSki34_GNT4_EDbU47mVkztGBjL3grdT8HsKH3Ml6q3ZbUjM3kRJEqW295DN5SlUsKUtI20j0rLYh40isZD_3VYxYA25F3Erh6hCUBrNtSaLTatsl9aUYIIrKFHfMLBYkSQz3nGmPJuZUVdW2ncVVNcNT2eey20cRwSRxLzbfbzIO0hYtKq0ySpHWTfTfy2hGh0EstR6eiXNRMKNqaY82h0FuHuQDBy-D94DMgsCRrDoRzJyzGaz_Yw4cL0ZTnkJ2gVNPU-sku5oYrw51zby8wwPR-SjbbjjPI7Ou7sqcNt0o46ykvOjBraKOPDbOtImLVgPz5N-bSLjnFVOptxRXNWLZ7T5ASsXu9BvfTFssXn9bJQcH2IwMFSMfmylg5kMg_plI6yVTujIVCw) discuss this possibility in section 3.1. They say that there may be theoretical benefits, but in practice it would be impossible to implement well, and do not consider this.

However [Calonico, Cattaneo, and Titiunik (2014)](https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA11757) do allow for this (see Remark 9), ostensibly with no problems. It's rarely implemented. One paper that uses this method is, [Carlson, Correia, and Luck (2022)](https://www.journals.uchicago.edu/doi/full/10.1086/717453).


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