Masa
March 03, 2022
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# Pythonで学ぶSynthetic Difference in Differences

Original Paper:
Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019.
https://www.nber.org/system/files/working_papers/w25532/w25532.pdf

March 03, 2022

## Transcript

1. ### with Python  Synthetic Difference in Differences  twitter @asas_mimi 1

Method 3. Synthetic Difference in Differences 4. Python pkg : pysynthdid 2
3. ### Original Paper: Arkhangelsky, Dmitry, et al. Synthetic difference in differences.

No. w25532. National Bureau of Economic Research, 2019. https://www.nber.org/system/files/working_papers/w25532/w25532.pdf 3
4. ### Difference in Differences (DID)  4 pre post outcome If there

had been no intervention, the outcome of the treatment group would probably have been here counterfactual treatment group control group pros Excellent interpretability cons Parallel trend assumption • DID requires the selection of a control group that has parallel trends in the treatment group and the pre-intervention period. • This selection may be arbitrary in some cases. e.t.c.

tr  N co  5
6. ### DID as a two-way fixed effect regression  Arkhangelsky, Dmitry, et

al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. unit ﬁxed effect time ﬁxed effect 6
7. ### Synthetic Control Method (SC)  ωSC vertical regression Estimating the ω

that regresses the treatment group from the control group in the pre-term ωSC Synthetic Control counterfactual observable outcome ADH restrictions (Abadie, Diamond and Hainmueller (2010)) SUM(ω) = 1 , non-negativity, no intercept Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. 7
8. ### Synthetic Control Method (SC)  SC regression formula : regression with

time ﬁxed effects and sc weights omit New!! Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. 8
9. ### Synthetic Difference in Differences (SDID)  ωSDID vertical regression + horizontal

regression - Estimating the ω that regresses the treatment group from the control group in the pre-term - The basic idea is the same as ADH SC. However, an intercept term and an L2 penalty term are introduced. λSDID non-negativity sum(λ)=1 with intercept L2 penalty Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. 9
10. ### Synthetic Difference in Differences (SDID)  The method of estimating ω

is slightly different from the classical one(ADH). non-negativity sum(λ)=1 with intercept L2 penalty Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. intercept “unexposed pre-trends perfectly match the exposed ones; rather, it is sufﬁcient that the weights make the trends paralle” L2 penalty “to increase the dispersion, and ensure the uniqueness, of the weight” Even if we don't get a perfect match, we can correct it later with unit ﬁxed effect (DID). 10
11. ### Synthetic Difference in Differences (SDID)  ωSDID vertical regression + horizontal

regression - Estimating the λ that regresses the post-term from the pre-term λSDID Objective variable: average outcome of post term non-negativity sum(λ)=1 with intercept Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. 11
12. ### Synthetic Difference in Differences (SDID)  Arkhangelsky, Dmitry, et al. Synthetic

difference in differences. No. w25532. National Bureau of Economic Research, 2019. 12
13. ### Synthetic Difference in Differences (SDID)  pre post outcome treatment group

synthetic control Synthetic Control Method ATTSC pre post outcome treatment group synthetic control Synthetic Difference in Differences 　 λ intercept ATTSDID Adjusting the reference point by λ 13
14. ### Reproduction experiment in Python  My notebooks are here:  https://github.com/MasaAsami/pysynthdid

These implementations were based on the following R package:  https://github.com/synth-inference/synthdid   14
15. ### Data  The following section examines the Tobacco Tax and Health

Protection Act of 1989 (California), famous dataset for Synthetic Control Method. see: 1988 California Proposition 99 ( https://en.wikipedia.org/wiki/1988_California_Proposition_99 ) 15

17. ### Setup & fitting  1989 2000 1970 1988 California = treated

Control (donor pool) 17

20. ### Comparison of results  pysynthdid result Arkhangelsky, Dmitry, et al. (2019)

table 1: Arkhangelsky, Dmitry, et al. Synthetic difference in differences. No. w25532. National Bureau of Economic Research, 2019. 20
21. ### Comparison of ω  Arkhangelsky, Dmitry, et al. Synthetic difference in

differences. No. w25532. National Bureau of Economic Research, 2019. ω is able to conﬁrm that the results were mostly consistent with the original paper. Also, it matches the results of the R package perfectly. typo?? 21
22. ### Comparison of λ  Arkhangelsky, Dmitry, et al. Synthetic difference in

differences. No. w25532. National Bureau of Economic Research, 2019. λ is almost identical to the original paper 22
23. ### Robust check for scale differences in donor pools  In following

note, we checked how the estimation results change with changes in the scale of the donor pool features. see: https://github.com/MasaAsami/pysynthdid/blob/main/notebook/ScaleTesting_of _DonorPools.ipynb Due to the L2 penalty term, mixing donor pools with extremely different orders may inﬂuence the results. In such a case, it may be better to consider logarithmic transformation, etc., as in a normal regression model.  23