# Double and Single Descent in Causal Inference with an Application to High-Dimensional Synthetic Control

arXiv: https://arxiv.org/abs/2305.00700 · HTML: https://mlsanity.com/paper/2305.00700/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 1 May 2023.

## Builds on (most cited first, 13 of 13)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [The Augmented Synthetic Control Method](https://mlsanity.com/paper/1811.04170/) (2018)
- [Interpolating Classifiers Make Few Mistakes](https://mlsanity.com/paper/2101.11815/) (2021)
- [Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data](https://mlsanity.com/paper/2207.14481/) (2022)
- [Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression](https://mlsanity.com/paper/2202.05245/) (2022)

## Built on by (most cited first, 4 of 4)

- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Prediction Risk and Estimation Risk of the Ridgeless Least Squares Estimator under General Assumptions on Regression Errors](https://mlsanity.com/paper/2305.12883/) (2023)
- [Benign overfitting beyond prediction: The ordinary least squares interpolator](https://mlsanity.com/paper/2309.15769/) (2023)
- [Targeted Synthetic Control Method](https://mlsanity.com/paper/2602.04611/) (2026)

## Abstract (arXiv)

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.