Model Averaging and Double Machine Learning - paper title - stacked DDML approach

Aug 3, 2026

This paper pairs double/debiased machine learning (DDML) with stacking, a model averaging method to estimate structural parameters. Two stacking variants are introduced for DDML: short-stacking, which uses DDML cross-fitting to lower computational cost, and pooled stacking, which enforces common stacking weights across folds. Calibrated simulation studies and two empirical applications on gender gaps in citations and wages show improved robustness to partially unknown functional forms versus approaches relying on a single pre-selected learner. Stata and R implementations are provided.

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Abstract

Introduction

arXiv :2401 .01645v2 [ econ .EM] 25 Sep 2024 Model Averaging and Double Machine Learning ∗ Achim Ahrens† Christian B. Hansen‡ Mark E. Schaffer§ Thomas Wiemann‡ September 27, 2024 Abstract This paper discusses pairing double/debiased machine learning (DDML) with stacking, a model averaging method for combining multiple candidate learners, to estimate structural parameters. In addition to conventional stacking, we consider two stacking variants available for DDML: short-stacking exploits the cross-fitting step of DDML to substantially reduce the computational burden and pooled stacking enforces common stacking weights over crossfitting folds. Using calibrated simulation studies and two applications estimating gender gaps in citations and wages, we show that DDML with stacking is more robust to partially unknown functional forms than common alternative approaches based on single pre-selected learners. We provide Stata and R software implementing our proposals. Keywords: causal inference, partially linear model, high-dimensional models, super learners, nonparametric estimation JEL: C21, C26, C52, C55, J01, J08 ∗ Acknowledgment: Many thanks to Elliott Ash, Daniel Björkegren, David Cai, Ben Jann, Michael Knaus, Rafael Lalive, Moritz Marbach, Martin Huber, Blaise Melly, Gabriel Okasa, and Martin Spindler for helpful discussions and comments. We are also thankful for the helpful feedback we have received atthe AI+Economics Workshop at the ETH Zürich in 2022, the Italian and Swiss Stata meetings in 2022, the 2022 Machine Learning in Economics Summer Institute in Chicago, the LISER workshop “Machine Learning in Program Evaluation, High-dimensionality and Visualization Techniques,” the 2022 Scotland and Northern England Workshop in Applied Microeconomics, the IAAE Annual Conference in 2023, the London 2023 Stata meeting, the 2023 Stata Economics Virtual Symposium and the European Summer Meetings of the Econometric Society in 2023 . We also thank anonymous reviewers for their feedback and suggestions. All remaining errors are our own. Note: An earlier version of the paper was presented under the title “A Practitioners’ Guide to Double Machine Learning.” Conflict of interest: The authors declare that they have no conflict of interest. Data: The authors provide replication code through the Journal of Applied Econometrics Data Archive and share data for all examples with the exception of the application in Section 5 .1. †Corresponding author. ETH Zürich, Leonhardshalde 21, 8092 Zürich, Switzerland. Email: achim . [ahrens@gess.ethz.ch](ahrens@gess.ethz.ch) ‡University of Chicago, United States. Email: [Christian.Hansen@chicagobooth.edu](Christian.Hansen@chicagobooth.edu) (Hansen), [wiemann@uchicago.edu](wiemann@uchicago.edu) (Wiemann). § Heriot-Watt University, Edinburgh, United Kingdom and IZA Institute of Labor Economics. Email: [M.E.Schaffer@hw.ac.uk](M.E.Schaffer@hw.ac.uk). 1 Introduction Motivated by their robustness to partially unknown functional forms, supervised machine learning estimators are increasingly leveraged for causal inference. For example, lasso-based approaches such as the post-double-selection lasso (PDS lasso) of Belloni, Chernozhukov, and Hansen (2014) have become popular estimators of causal effects under conditional unconfoundedness in applied economics (e.g. Gilchrist and Sands, 2016; Dhar, Jain, and Jayachandran, 2022) . Yet, a recent literature also raises practical concerns about the use of machine learning for causal inference. Wüthrich and Zhu (2023) find that lasso often fails to select relevant confounders in small samples while inference based on linear regression performs relatively well. Giannone, Lenza, and Primiceri (2021) and Kolesár, Müller, and Roelsgaard (2023) argue that the sparsity assumption, on which the lasso fundamentally relies, is frequently not plausible in economic data sets. Angristand Frandsen (2022) show that conditioning on confounders using random forests

FAQs

How does the paper combine DDML with stacking for estimating structural parameters?

The paper integrates DDML estimators with stacking, treating stacking as a way to average or select among multiple candidate learners when estimating common causal parameters.

What are the two stacking variants proposed for DDML?

The paper proposes short-stacking, which exploits DDML cross-fitting to reduce computational burden, and pooled stacking, which enforces common stacking weights across cross-fitting folds to improve stability.

What evidence supports the robustness claims of stacking-based DDML?

Calibrated simulation studies and empirical applications estimating gender gaps in citations and wages show greater robustness to partially unknown functional forms than alternatives built on single pre-selected learners.

Aug 3, 2026

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