Feasible IV Regression without Excluded Instruments

TL;DR

This paper introduces a new linear ICM estimator that enables feasible instrumental variable regression without the need for excluded instruments, maintaining identification strength and improving size control.

Contribution

It proposes a computationally efficient linear ICM estimator that allows consistent estimation without excluded instruments and provides a relevance test, addressing limitations of existing methods.

Findings

Better size control with multiple instruments

Maintains plausible estimates without excluded instruments

Favorable performance in simulations and empirical example

Abstract

The relevance condition of Integrated Conditional Moment (ICM) estimators is significantly weaker than the conventional IV's in at least two respects: (1) consistent estimation without excluded instruments is possible, provided endogenous covariates are non-linearly mean-dependent on exogenous covariates, and (2) endogenous covariates may be uncorrelated with but mean-dependent on instruments. These remarkable properties notwithstanding, multiplicative-kernel ICM estimators suffer diminished identification strength, large bias, and severe size distortions even for a moderately sized instrument vector. This paper proposes a computationally fast linear ICM estimator that better preserves identification strength in the presence of multiple instruments and a test of the ICM relevance condition. Monte Carlo simulations demonstrate a considerably better size control in the presence of multiple instruments and a favourably competitive performance in general. An empirical example illustrates the practical usefulness of the estimator, where estimates remain plausible when no excluded instrument is used.