Instrumental Variable Estimation of Nonparametric Models

2003/09/01 by Whitney K. Newey, James L. Powell · 905 citations
Engineering · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Conditional expectation #Conditional independence #Control Systems and Identification #Econometrics #Estimator #Identification (biology) #Instrumental variable #Least-squares function approximation #Mathematics #Nonparametric statistics #Statistical Methods and Inference #Statistics

paper · doi:10.1111/1468-0262.00459

published in Econometrica 71(5), 1565-1578 (Wiley)

openalex publication_date 2003/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In econometrics there are many occasions where knowledge of the structural relationship among dependent variables is required to answer questions of interest. This paper gives identification and estimation results for nonparametric conditional moment restrictions. We characterize identification of structural functions as completeness of certain conditional distributions, and give sufficient identification conditions for exponential families and discrete variables. We also give a consistent, nonparametric estimator of the structural function. The estimator is nonparametric two-stage least squares based on series approximation, which overcomes an ill-posed inverse problem by placing bounds on integrals of higher-order derivatives.

Cited by

• Identification and Estimation of Hedonic Models
• Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects
• Learning Theory for Kernel Bilevel Optimization
• Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments
• Identification, Doubly Robust Estimation, and Semiparametric Efficiency Theory of Nonignorable Missing Data With a Shadow Variable
• Estimating Causal Effects With Observational Data: Guidelines for Agricultural and Applied Economists
• Causal Inference in Possibly Nonlinear Factor Models
• Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression
• Comparing Two Proxy Methods for Causal Identification
• Spatio-Temporal Hierarchical Causal Models
• Causal aggregation: estimation and inference of causal effects by constraint-based data fusion
• The Sample Complexity of Online Strategic Decision Making with Information Asymmetry and Knowledge Transportability
• Using spatial modeling to address covariate measurement error
• Nonparametric Identification and Estimation of Causal Effects on Latent Outcomes
• Tests of exogeneity in duration models with censored data
• Treatment Effect Estimation with Noisy Conditioning Variables
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach
• Projective Graph Residualization: Variation-Allocation Frontiers for Control-Function IV
• Semiparametric Proximal Causal Inference
• Adversarial Visual Robustness by Causal Intervention
• Machine learning in agricultural and applied economics
• Towards Identifiability of Hierarchical Temporal Causal Representation Learning
• Extending the scope of instrumental variable methods
• A Selective Review of Negative Control Methods in Epidemiology
• Congestion in cities: Can road capacity expansions provide a solution?
• Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning
• Learning Deep Features in Instrumental Variable Regression
• Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data
• Coupling Generative Modeling and an Autoencoder with the Causal Bridge
• The influence function of semiparametric estimators
• A Class of Algorithms for General Instrumental Variable Models
• Kernel Instrumental Variable Regression
• Asymptotic Theory for IV-Based Reinforcement Learning with Potential Endogeneity
• Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder
• Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regression
• Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach
• Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models
• Functional linear instrumental regression under second order stationarity
• Proximal Causal Inference for Complex Longitudinal Studies
• On Deep Instrumental Variables Estimate
• On the asymptotic validity of confidence sets for linear functionals of solutions to integral equations
• On rate optimal local estimation in nonparametric instrumental regression
• Uniform Inference for Characteristic Effects of Large Continuous-Time Linear Models
• Generalized Random Forests
• A review of instrumental variable estimators for Mendelian randomization
• A confounding bridge approach for double negative control inference on causal effects
• Stratification-based Instrumental Variable Analysis Framework for Nonlinear Effect Analysis
• Causal inference via implied interventions
• Kernel Methods for Unobserved Confounding: Negative Controls, Proxies,\n and Instruments
• Leveraging specificity for causal inference in observational studies
• Causal inference with confounders missing not at random
• Foundation Models for Causal Inference via Prior-Data Fitted Networks
• Demystifying Spectral Feature Learning for Instrumental Variable Regression
• Estimation of heterogeneous individual treatment effects with endogenous treatments
• Quasi-Bayesian Dual Instrumental Variable Regression
• Density Ratio-Free Doubly Robust Proxy Causal Learning
• Causality and Generalizability: Identifiability and Learning Methods
• Theory for identification and Inference with Synthetic Controls: A Proximal Causal Inference Framework
• Consistent Estimation of Models Defined by Conditional Moment Restrictions
• Sequential Treatment Effect Estimation with Unmeasured Confounders
• The Identification Zoo: Meanings of Identification in Econometrics
• Nonparametric Identification in Structural Economic Models
• Nonparametric methods for inference in the presence of instrumental variables
• Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models
• On deconvolution with repeated measurements
• Reinforcement Learning with Continuous Actions Under Unmeasured Confounding
• Instrumental Variable Regression via Kernel Maximum Moment Loss
• Methodology and convergence rates for functional linear regression
• Assignment at the Frontier: Identifying the Frontier Structural Function and Bounding Mean Deviations
• Nonparametric identification of dynamic models with unobserved state variables
• Instrumental Variable Treatment of Nonclassical Measurement Error Models
• Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution
• Instrumental Variables: An Econometrician's Perspective
• Quantile Models with Endogeneity
• Estimating Demand with Recentered Instruments
• Semiparametric Causal Discovery and Inference with Invalid Instruments
• Relaxing parametric assumptions for non-linear Mendelian randomization using a doubly-ranked stratification method. [europepmc]
• Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution. [europepmc]
• Estimating Time-Varying Exposure Effects Through Continuous-Time Modelling in Mendelian Randomization. [europepmc]
• Instrumental variable estimation for compositional treatments. [europepmc]
• Stratification-based instrumental variable analysis framework for nonlinear effect analysis. [europepmc]
• Relaxing parametric assumptions for non-linear Mendelian randomization using a doubly-ranked stratification method [europepmc]

Related

• Nonparametric Instrumental Regression
• Nonparametric Identification and Estimation with Independent, Discrete Instruments
• Nonparametric Identification in Structural Economic Models
• Nonparametric Instrumental Variables Estimation Under Misspecification
• Nonparametric Instrumental Variable Inference with Many Weak Instruments