<p>There is some work on the asymptotic consistency like the <a href="https://www.jmlr.org/papers/volume19/17-777.pdf" rel="nofollow noreferrer">Robust Synthetic Control by Amjad et al (2018)</a>, also the study of <a href="https://www.degruyter.com/document/doi/10.1515/jci-2016-0026/html" rel="nofollow noreferrer">Firpo and Possebom 2016</a> discusses asymptotic inference.</p>

CC BY-SA 4.0
2021-08-16T20:47:38.490Z
Yeah. Thanks for this. It looks like there isn't anything of the "Consistent and Asymptotically Normal" result as GMM or MLE do. I guess also asymptotics aren't really relevant because there are often few controls and time periods.

Thanks anyway!
Michael Gmeiner
CC BY-SA 4.0
2021-08-16T20:56:12.210Z
@MichaelGmeiner oh I thought you will be happy with just some asymptotic inference, as you say it is very unlikely it would be possible to have  asymptotic normality with this sort of model
1muflon1
CC BY-SA 4.0
2021-08-16T22:17:27.287Z
Oh, I'm happy you sent these! It's good to be aware that there is some work on the subject.
Michael Gmeiner
CC BY-SA 4.0
2021-08-17T13:32:35.723Z
Also @1muflon1 I don't know if you care, but I found another. https://www.tandfonline.com/doi/full/10.1080/01621459.2021.1965613?casa_token=clj1BGUMYb0AAAAA%3AjOHH1q3RRe8VF7HT0uiDYc7Z3XvIlXlW9REFFdNiw7yqW_GGpeZTSNa8hLjIA6Qxojk1P-R9Dz4
Michael Gmeiner
CC BY-SA 4.0
2021-08-16T19:30:22.953Z
2021-08-16T19:30:22.953Z
1muflon1
<p>I'm aware of the basics of the synthetic control method, and that permutation tests are commonly used for inference.</p>
<p>Are there papers that develop asymptotic theory? i.e. if the regression approach to create weights is used (as in the <em>synth</em> command), and the number of control groups and pre-treatment time periods goes to infinity, are there papers proving consistency or asymptotic normality?</p>

<econometrics><synthetic-control>
Synthetic Control Asymptotics
Michael Gmeiner
# Synthetic Control Asymptotics

(Asked by: username_0 on 2021-08-16)

I'm aware of the basics of the synthetic control method, and that permutation tests are commonly used for inference.

Are there papers that develop asymptotic theory? i.e. if the regression approach to create weights is used (as in the *synth* command), and the number of control groups and pre-treatment time periods goes to infinity, are there papers proving consistency or asymptotic normality?

**Tags:** econometrics, synthetic-control

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## 1 answers

### Answer by username_1 on 2021-08-16. Score: 1 | Accepted answer

There is some work on the asymptotic consistency like the [Robust Synthetic Control by Amjad et al (2018)](https://www.jmlr.org/papers/volume19/17-777.pdf), also the study of [Firpo and Possebom 2016](https://www.degruyter.com/document/doi/10.1515/jci-2016-0026/html) discusses asymptotic inference.

> **Comments:**
> **username_0**: Yeah. Thanks for this. It looks like there isn't anything of the "Consistent and Asymptotically Normal" result as GMM or MLE do. I guess also asymptotics aren't really relevant because there are often few controls and time periods.  Thanks anyway!  
> **username_1**: @MichaelGmeiner oh I thought you will be happy with just some asymptotic inference, as you say it is very unlikely it would be possible to have  asymptotic normality with this sort of model  
> **username_0**: Oh, I'm happy you sent these! It's good to be aware that there is some work on the subject.  
> **username_0**: Also @1muflon1 I don't know if you care, but I found another. https://www.tandfonline.com/doi/full/10.1080/01621459.2021.1965613?casa_token=clj1BGUMYb0AAAAA%3AjOHH1q3RRe8VF7HT0uiDYc7Z3XvIlXlW9REFFdNiw7yqW_GGpeZTSNa8hLjIA6Qxojk1P-R9Dz4  

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