Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradients
This work addresses causal effect estimation in the presence of unobservable confounders for researchers in econometrics and statistics, offering a novel algorithmic approach with incremental improvements in flexibility and stability.
The paper tackled nonparametric instrumental variable regression by developing a functional stochastic gradient descent algorithm that directly minimizes populational risk, achieving superior stability and competitive performance compared to state-of-the-art methods, with theoretical bounds on excess risk and demonstrated flexibility for binary outcomes.
Instrumental variables (IVs) provide a powerful strategy for identifying causal effects in the presence of unobservable confounders. Within the nonparametric setting (NPIV), recent methods have been based on nonlinear generalizations of Two-Stage Least Squares and on minimax formulations derived from moment conditions or duality. In a novel direction, we show how to formulate a functional stochastic gradient descent algorithm to tackle NPIV regression by directly minimizing the populational risk. We provide theoretical support in the form of bounds on the excess risk, and conduct numerical experiments showcasing our method's superior stability and competitive performance relative to current state-of-the-art alternatives. This algorithm enables flexible estimator choices, such as neural networks or kernel based methods, as well as non-quadratic loss functions, which may be suitable for structural equations beyond the setting of continuous outcomes and additive noise. Finally, we demonstrate this flexibility of our framework by presenting how it naturally addresses the important case of binary outcomes, which has received far less attention by recent developments in the NPIV literature.