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

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  • Jann Spiess
  • Guido Imbens
  • Amar Venugopal

Abstract

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.

Suggested Citation

  • Jann Spiess & Guido Imbens & Amar Venugopal, 2023. "Double and Single Descent in Causal Inference with an Application to High-Dimensional Synthetic Control," Papers 2305.00700, arXiv.org, revised Oct 2023.
  • Handle: RePEc:arx:papers:2305.00700
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    1. Nikolay Doudchenko & Guido W. Imbens, 2016. "Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis," NBER Working Papers 22791, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Masahiro Kato & Akari Ohda & Masaaki Imaizumi, 2023. "Asymptotically Unbiased Synthetic Control Methods by Distribution Matching," Papers 2307.11127, arXiv.org, revised May 2024.
    2. Yuan Liao & Xinjie Ma & Andreas Neuhierl & Zhentao Shi, 2023. "Economic Forecasts Using Many Noises," Papers 2312.05593, arXiv.org, revised Dec 2023.
    3. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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