On the Misspecification of Linear Assumptions in Synthetic Controls

Achille O. R. Nazaret, Claudia Shi, David Blei
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3790-3798, 2024.

Abstract

The synthetic control (SC) method is popular for estimating causal effects from observational panel data. It rests on a crucial assumption that we can write the treated unit as a linear combination of the untreated units. In practice, this assumption may not hold, and when violated, the resulting SC estimates are incorrect. This paper examines two questions: (1) How large can the misspecification error be? (2) How can we minimize it? First, we provide theoretical bounds to quantify the misspecification error. The bounds are comforting: small misspecifications induce small errors. With these bounds in hand, we develop new SC estimators specially designed to minimize misspecification error. The estimators are based on additional data about each unit. (E.g., if the units are countries, it might be demographic information about each.) We study our estimators on synthetic data; we find they produce more accurate causal estimates than standard SC. We then re-analyze the California tobacco program data of the original SC paper, now including additional data from the US census about per-state demographics. Our estimators show that the observations in the pre-treatment period lie within the bounds of misspecification error and that observations post-treatment lie outside of those bounds. This is evidence that our SC methods have uncovered a true effect.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-nazaret24a, title = { On the Misspecification of Linear Assumptions in Synthetic Controls }, author = {Nazaret, Achille O. R. and Shi, Claudia and Blei, David}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3790--3798}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/nazaret24a/nazaret24a.pdf}, url = {https://proceedings.mlr.press/v238/nazaret24a.html}, abstract = { The synthetic control (SC) method is popular for estimating causal effects from observational panel data. It rests on a crucial assumption that we can write the treated unit as a linear combination of the untreated units. In practice, this assumption may not hold, and when violated, the resulting SC estimates are incorrect. This paper examines two questions: (1) How large can the misspecification error be? (2) How can we minimize it? First, we provide theoretical bounds to quantify the misspecification error. The bounds are comforting: small misspecifications induce small errors. With these bounds in hand, we develop new SC estimators specially designed to minimize misspecification error. The estimators are based on additional data about each unit. (E.g., if the units are countries, it might be demographic information about each.) We study our estimators on synthetic data; we find they produce more accurate causal estimates than standard SC. We then re-analyze the California tobacco program data of the original SC paper, now including additional data from the US census about per-state demographics. Our estimators show that the observations in the pre-treatment period lie within the bounds of misspecification error and that observations post-treatment lie outside of those bounds. This is evidence that our SC methods have uncovered a true effect. } }
Endnote
%0 Conference Paper %T On the Misspecification of Linear Assumptions in Synthetic Controls %A Achille O. R. Nazaret %A Claudia Shi %A David Blei %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-nazaret24a %I PMLR %P 3790--3798 %U https://proceedings.mlr.press/v238/nazaret24a.html %V 238 %X The synthetic control (SC) method is popular for estimating causal effects from observational panel data. It rests on a crucial assumption that we can write the treated unit as a linear combination of the untreated units. In practice, this assumption may not hold, and when violated, the resulting SC estimates are incorrect. This paper examines two questions: (1) How large can the misspecification error be? (2) How can we minimize it? First, we provide theoretical bounds to quantify the misspecification error. The bounds are comforting: small misspecifications induce small errors. With these bounds in hand, we develop new SC estimators specially designed to minimize misspecification error. The estimators are based on additional data about each unit. (E.g., if the units are countries, it might be demographic information about each.) We study our estimators on synthetic data; we find they produce more accurate causal estimates than standard SC. We then re-analyze the California tobacco program data of the original SC paper, now including additional data from the US census about per-state demographics. Our estimators show that the observations in the pre-treatment period lie within the bounds of misspecification error and that observations post-treatment lie outside of those bounds. This is evidence that our SC methods have uncovered a true effect.
APA
Nazaret, A.O.R., Shi, C. & Blei, D.. (2024). On the Misspecification of Linear Assumptions in Synthetic Controls . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3790-3798 Available from https://proceedings.mlr.press/v238/nazaret24a.html.

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