Jackknife Instrumental Variable Inference

TL;DR

This paper develops jackknife-based test statistics for linear regression models with endogeneity and weak instruments, demonstrating their theoretical properties and practical effectiveness through simulations and an empirical UK Biobank study.

Contribution

It introduces a new class of jackknife-based tests for endogeneity with many weak instruments, with theoretical distribution results and improved finite sample performance.

Findings

Proposed tests are asymptotically chi-square distributed under the null hypothesis.

Simulation results show competitive performance against existing Anderson-Rubin tests.

Empirical application demonstrates the tests' usefulness in genetic instrumental variable analysis.

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.