Jackknife Instrumental Variable Inference

2026-04-16

AI Summary

This study addresses linear regression models plagued by numerous potentially weak instrumental variables, endogeneity, and heteroskedasticity. It proposes a novel class of jackknife-based test statistics for hypotheses concerning the full parameter vector or general linear restrictions. Constructed within the generalized method of moments framework, the proposed tests exhibit a chi-square mixture as their asymptotic null distribution; by appropriately adjusting the objective function, they attain a standard chi-square limit, substantially enhancing inferential practicality and interpretability. Both theoretical analysis and Monte Carlo simulations demonstrate superior finite-sample performance, notably outperforming Anderson–Rubin–type procedures. The methodology is successfully applied to UK Biobank data, uncovering a causal effect of alcohol consumption on body mass index (BMI).

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Graphical ModelsIntelligent Robots: State Estimation

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsUser Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

This paper introduces a class of jackknife-based test statistics for linear regression models with endogeneity and heteroskedasticity in the presence of many potentially weak instrumental variables. The tests may be used when considering hypotheses on the full parameter vector or hypotheses defined as linear restrictions. We show that in the limit and under the null the proposed statistics are distributed as a combination of chi squares but by modifying the objective function we derive more familiar chi square limits. An extensive simulation study shows the competitive finite sample properties of the proposed tests in particular against Anderson-Rubin-type of statistics. Finally, we provide an empirical illustration that applies the proposed tests to study the effect of alcohol consumption on body mass index using genetic variants as instrumental variables using the UK Biobank.

Problem

• instrumental variables
• endogeneity
• heteroskedasticity
• weak instruments
• hypothesis testing

Innovation

• Jackknife
• Instrumental Variables
• Weak Instruments
• Heteroskedasticity
• Chi-square Approximation