2021/08/09 by Guido Imbens, Guido W. Imbens, Nathan Kallus +4 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Econometrics (econ.EM) #Economic Policies and Impacts #FOS: Computer and information sciences #FOS: Economics and business #Methodology (stat.ME) #Spatial and Panel Data Analysis #Statistical Methods and Inference #econ.EM #stat.ME
paper · pdf · doi:10.48550/arxiv.2108.03849
arxiv created 2021/08/09 · openalex publication_date 2021/08/09 · arxiv updated 2021/08/10 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28
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.