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This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function,…

Statistics Theory · Mathematics 2021-09-14 Denis Nekipelov , Vira Semenova , Vasilis Syrgkanis

The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…

Machine Learning · Computer Science 2023-03-24 Andrew Bennett , Nathan Kallus

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to…

Weak identification arises in many statistical problems when key variables exhibit weak correlations-for example, when instrumental variables correlate weakly with treatment, or when proxy variables correlate weakly with unmeasured…

Statistics Theory · Mathematics 2025-11-12 Rui Wang , Kwun Chuen Gary Chan , Ting Ye

Models with Conditional Moment Restrictions (CMRs) are popular in economics. These models involve finite and infinite dimensional parameters. The infinite dimensional components include conditional expectations, conditional choice…

Econometrics · Economics 2024-11-01 Facundo Argañaraz , Juan Carlos Escanciano

Instrumental variable methods are widely used for causal inference, but identification becomes especially challenging when instruments are weak and potentially invalid. These challenges are particularly pronounced in Mendelian…

Methodology · Statistics 2026-04-01 Di Zhang , Minhao Yao , Zhonghua Liu , Baoluo Sun

We construct moment functions that are Neyman-orthogonal to a chosen order in parametric moment condition models. These moment functions reduce sensitivity to nuisance estimation error and, as such, offer a unified and tractable route to…

Econometrics · Economics 2026-05-12 Stéphane Bonhomme , Koen Jochmans , Whitney K. Newey , Martin Weidner

Instrumental variable (IV) regression can be approached through its formulation in terms of conditional moment restrictions (CMR). Building on variants of the generalized method of moments, most CMR estimators are implicitly based on…

Machine Learning · Computer Science 2024-05-21 Heiner Kremer , Bernhard Schölkopf

This paper develops an asymptotic theory for two-step debiased machine learning (DML) estimators in generalised method of moments (GMM) models with general multiway clustered dependence, without relying on cross-fitting. While cross-fitting…

Econometrics · Economics 2026-04-07 Kaicheng Chen , Harold D. Chiang

Developing robust inference for models with nonparametric Unobserved Heterogeneity (UH) is both important and challenging. We propose novel Debiased Machine Learning (DML) procedures for valid inference on functionals of UH, allowing for…

Econometrics · Economics 2025-07-21 Facundo Argañaraz , Juan Carlos Escanciano

We develop a unified framework for automatic debiased machine learning (autoDML) for inference on a broad class of statistical parameters. The framework applies to any smooth functional of a nonparametric M-estimand, defined as the…

Methodology · Statistics 2026-03-23 Lars van der Laan , Aurelien Bibaut , Nathan Kallus , Alex Luedtke

A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is…

Econometrics · Economics 2026-02-25 Stéphane Bonhomme , Koen Jochmans , Martin Weidner

I propose a locally robust semiparametric framework for estimating causal effects using the popular examiner IV design, in the presence of many examiners and possibly many covariates relative to the sample size. The key ingredient of this…

Econometrics · Economics 2024-05-01 Lonjezo Sithole

This paper proposes a flexible new framework for constructing Neyman-orthogonal scores in semiparametric models involving infinite-dimensional nuisance parameters. While locally estimation is vital for integrating machine learning into…

Methodology · Statistics 2026-04-30 Kun Ren , Wen Su , Li Liu , Ian W. McKeague , Xingqiu Zhao

Double machine learning provides $\sqrt{n}$-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an $n^{-1/4}$ rate. The key is to employ Neyman-orthogonal moment…

Machine Learning · Computer Science 2018-08-03 Lester Mackey , Vasilis Syrgkanis , Ilias Zadik

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first-…

Econometrics · Economics 2026-03-23 Denis Chetverikov , Jesper R. -V. Sørensen , Aleh Tsyvinski

Solving conditional moment restrictions (CMRs) is a key problem considered in statistics, causal inference, and econometrics, where the aim is to solve for a function of interest that satisfies some conditional moment equalities.…

Machine Learning · Statistics 2025-06-25 Daqian Shao , Ashkan Soleymani , Francesco Quinzan , Marta Kwiatkowska

Many economic models feature moment conditions that involve latent variables. When the latent variables are individual fixed effects in an auxiliary panel data regression, we construct orthogonal moments that eliminate first-order bias…

Econometrics · Economics 2026-02-10 Jiaqi Huang

We develop an estimator for treatment effects in high-dimensional settings with additive measurement error, a prevalent challenge in modern econometrics. We introduce the Double/Debiased Convex Conditioned LASSO (Double/Debiased CoCoLASSO),…

Econometrics · Economics 2024-08-28 Geonwoo Kim , Suyong Song

We propose employing a high-dimensional generalized method of moments (GMM) estimator, regularized for dimension reduction and subsequently debiased to correct for shrinkage bias (referred to as a debiased-regularized estimator), for…

Econometrics · Economics 2025-07-03 Victor Chernozhukov , Chen Huang , Weining Wang
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