We present a novel single-stage procedure for instrumental variable (IV) regression called DualIV which simplifies traditional two-stage regression via a dual formulation. We show that the common two-stage procedure can alternatively be solved via generalized least squares . Our formulation circumvents the first-stage regression which can be a bottleneck in modern two-stage procedures for IV regression. We also show that our framework is closely related to the generalized method of moments (GMM) with specific assumptions. This highlights the fundamental connection between GMM and two-stage procedures in IV literature. Using the proposed framework , we develop a simple kernel-based algorithm with consistency guarantees. Lastly, we give empirical results illustrating the advantages of our method over the existingtwo-stage algorithms .
We present a novel algorithm for instrumental variable (IV) regression , DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that the two-stage procedure for nonlinear IV regression can be reformulated as a convex-concave saddle-point problem . Our formulation circumvents the first-stage regression which is a potential bottleneck in real-world applications. Based on this new approach , we develop a simple kernel-based algorithm with a closed-form solution. Empirical results show that we are competitive to existing, more complicated algorithms for instrumental variable regression .
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single-stage procedure
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called DualIV
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regression
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Inspired by problems in stochastic programming, we
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common
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can alternatively be solved via generalized least squares
for nonlinear IV regression can be reformulated as a convex-concave saddle-point problem
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can be a bottleneck in modern two-stage procedures for IV regression. We also show that our framework is closely related to the generalized method of moments (GMM) with specific assumptions. This highlights the fundamental connection between GMM and two-stage procedures in IV literature. Using the proposed framework
is a potential bottleneck in real-world applications. Based on this new approach
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consistency guarantees. Lastly, we give empirical results illustrating the advantages of our method over the existingtwo-stage algorithms
a closed-form solution. Empirical results show that we are competitive to existing, more complicated algorithms for instrumental variable regression