2023/05/01 by Jann Spiess, Guido W. Imbens, Spiess, Jann +3 · 1 voice
Mathematics · #Advanced Causal Inference Techniques #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2305.00700
openalex publication_date 2023/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units. In such models, there may be so many free parameters that the model fits the training data perfectly. We first investigate high-dimensional linear regression for imputing wage data and estimating average treatment effects, where we find that models with many more covariates than sample size can outperform simple ones. We then document the performance of high-dimensional synthetic control estimators with many control units. We find that adding control units can help improve imputation performance even beyond the point where the pre-treatment fit is perfect. We provide a unified theoretical perspective on the performance of these high-dimensional models. Specifically, we show that more complex models can be interpreted as model-averaging estimators over simpler ones, which we link to an improvement in average performance. This perspective yields concrete insights into the use of synthetic control when control units are many relative to the number of pre-treatment periods.