Guido Imbens, Nathan Kallus, Xiaojie Mao
arXiv 9 Aug 2021 · Statistics — Methodology · 6 citations (OpenAlex)
arXiv:2108.03849 · PDF · DOI · OpenAlex · Extracted main text
We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences transformation identifies the effect. We show that analogous, albeit more complex, transformations exist in the more general linear factor model, providing a new means to identify the effect in that model. In fact many such transformations exist, called bridge functions, all identifying the same causal effect estimand. This poses a unique challenge for estimation and inference, which we solve by targeting the minimal bridge function using a regularized estimation approach. We prove that our resulting average causal effect estimator is root-N consistent and asymptotically normal, and we provide asymptotically valid confidence intervals. Finally, we provide extensions for the case of a linear factor model with time-varying unmeasured confounders.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Yifan Cui, Hongming Pu, Xu Shi, Wang Miao, and Eric Tchetgen Tchetgen (2020) Semiparametric proximal causal inference | 0.811 | 4 | 2 | 100% |
| 2 | Ben Deaner (2021) Proxy controls and panel data | 0.811 | 4 | 2 | 100% |
| 3 | Wang Miao, Zhi Geng, and Eric J Tchetgen Tchetgen (2018) Identifying causal effects with proxy variables of an unmeasured confounder | 0.737 | 3 | 3 | 67% |
| 4 | Alberto Abadie, Alexis Diamond, and Jens Hainmueller (2009) Synthetic control methods for comparative case studies: Estimating the effect of california's tobacco control program | 0.737 | 3 | 2 | 100% |
| 5 | Eric J Tchetgen Tchetgen, Andrew Ying, Yifan Cui, Xu Shi, and Wang M… (2020) An introduction to proximal causal learning | 0.737 | 3 | 2 | 100% |
| 6 | Muhammad Jehangir Amjad, Devavrat Shah, and Dennis Shen (2018) Robust synthetic control | 0.644 | 2 | 2 | 100% |
| 7 | Jeffrey M Wooldridge (2010) Econometric analysis of cross section and panel data | 0.644 | 2 | 2 | 100% |
| 8 | Susan Athey, Mohsen Bayati, Nikolay Doudchenko, Guido Imbens, and Kh… (2021) Matrix completion methods for causal panel data models self | 0.585 | 3 | 1 | 100% |
| 9 | Nathan Kallus, Xiaojie Mao, and Masatoshi Uehara (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach self | 0.511 | 3 | 2 | 33% |
| 10 | Ruoxuan Xiong and Markus Pelger (2020) Large dimensional latent factor modeling with missing observations and applications to causal inference | 0.511 | 3 | 2 | 33% |
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