Synthetic Control: Math Explained
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- Опубликовано: 7 сен 2024
- This is a follow up video to my explanation of synthetic control. I focus on the math behind the method.
I use the following paper for the explanation:
Andersson, Julius J. "Carbon taxes and CO 2 emissions: Sweden as a case study." American Economic Journal: Economic Policy 11.4 (2019): 1-30.
If you are more curious about the method, check out:
Abadie, Alberto, Alexis Diamond, and Jens Hainmueller. "Synth: An R package for synthetic control methods in comparative case studies." Journal of Statistical Software 42.13 (2011).
Disclaimer: If you use R, always use the improveSynth function of the following package: cran.r-project...
The algorithm of Abadie's synth package seldom converges!!!
nice and clear explanation, hope you make some tutorial on how to use it in R
Have you already found a relevant source that explains how to use it in R?
@@Alex-ko1cihave you?
@@disintegrators6940 have you?
@@disintegrators6940have you found it by any chance?😊
If you have a simple example illustrating the exact steps in calculation, that would be really helpful. May be an idea for a video.
Great video. Overarching concept and math was very easy to follow! Thanks
Very clear! Thank you very much!
Hello, thank you for the great video. I'm curious about this; if the intervention group consists of a large number of people and it's difficult to regulate the control group, can we still apply the synthetic control method? Or is there a possibility of obtaining unhealthy results?
Yes you can, you would just make a separate synthetic control for every person in the intervention group,
Thank you very much. It's really clear. But I have a question. The initial value of matrix V is randomly set, right? Then we can get a vector W*(V). Taking it back to (y1- Wy0)^2, we can get the value of the difference. At second round, we set another V, and repeat the above procedure and get a new value of difference....After several iteration, we can choose the best V which corresponding to the smallest value of differenc. My question is that is there any algorithm in searching V ? I guess the value of V will not be randomly selected at very round.Thanks again.
The idea is to iterate on V as well. So Both V and W are tweaked in each iteration, eventually reaching equilibrium (which should exist and be unique since this afaics is a convex optimization problem)
Thanks, but I want to know in the process of reaching equilibrium, how to searching value of matrix V at very round is the best? Or which way is the fast in the process of reaching equilibrium.
@@kristianwichmann9996
@@kristianwichmann9996 This is a great idea but it lacks even moderate rigor. I can probably easily incorporate nonsense that shares the same trend dynamics and it would be included.... Maybe add false positive controls like knockoff generation; bilevel controls; residual analysis (residual non-stationarity; clustering in the extremes; residual features etc) etc etc. This is basically a simplistic sparse tracking with a different application.
But isn’t the counterfactual only as good as your construction of your model of synthetic control?
Absolutely.