Fast Instrument Learning with Faster Rates
This work addresses a specific problem in econometrics and causal inference for researchers and practitioners, offering incremental improvements in computational efficiency and flexibility.
The paper tackles nonlinear instrumental variable regression with high-dimensional instruments by proposing a simple algorithm that combines kernelized IV methods with an adaptive regression black box, achieving faster-rate convergence and adapting to latent feature dimensionality while avoiding expensive minimax optimization.
We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.