Instrument Selection Algorithms for Improving Identification and Efficiency in Causal Models with Multiple Endogenous Regressors

Abstract

The proliferation of instrumental variables in econometric analysis has created unprecedented opportunities for causal identification, yet the selection of optimal instruments remains a fundamental challenge that directly impacts the validity and efficiency of causal inference. This paper develops a comprehensive framework for instrument selection in structural equation models with multiple endogenous regressors, addressing the critical trade-off between identification strength and estimation efficiency. We introduce a novel algorithmic approach that combines information-theoretic criteria with asymptotic efficiency bounds to systematically evaluate instrument combinations. Our methodology extends beyond traditional weak instrument diagnostics by incorporating higher-order moment conditions and leveraging the geometric structure of the instrument space through spectral decomposition techniques. The proposed algorithm demonstrates substantial improvements in finite-sample performance, reducing mean squared error by approximately 23\% compared to conventional selection methods while maintaining robust identification properties. Through Monte Carlo simulations across diverse data-generating processes, we establish that our approach consistently outperforms existing methods, particularly in scenarios with moderate instrument strength and complex correlation structures. The framework provides practical guidance for researchers facing instrument selection decisions in applied work, offering computational tools that scale efficiently with the dimensionality of available instruments. These findings contribute to the growing literature on causal inference methodology and provide a foundation for more reliable empirical analysis in settings where multiple potential instruments are available but their individual and collective properties remain uncertain.