2021/04/18 by David A. Hirshberg, Hirshberg, David A.
Economics, Econometrics and Finance · Mathematics · #62J07 MSC-class: 62J07 (Primary) #Advanced Causal Inference Techniques #Economic Policies and Impacts #FOS: Mathematics #Monetary Policy and Economic Impact #Statistics Theory (math.ST) #math.ST #msc:62J07 #stat.TH
paper · pdf · doi:10.48550/arxiv.2104.08931
40 pages, 0 figures
arxiv created 2021/04/18 · openalex publication_date 2021/04/18 · arxiv updated 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional least squares with correlated error-in-variables with a focus on these uses. We use our results to derive conditions under which the synthetic control estimator is asymptotically unbiased and normal with estimable variance, permitting inference without assuming time-stationarity, unit-exchangeability, or the absence of weak factors. These results hold in an asymptotic regime in which the number of pre-treatment periods goes to infinity and the number of control units can be much larger (p ≫ n).