# Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimators

arXiv: https://arxiv.org/abs/2110.06763 · HTML: https://mlsanity.com/paper/2110.06763/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 44 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Deep ReLU network approximation of functions on a manifold](https://mlsanity.com/paper/1908.00695/) (2019)
- [Neural Network Approximation: Three Hidden Layers Are Enough](https://mlsanity.com/paper/2010.14075/) (2020)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)

## Built on by (most cited first, 5 of 5)

- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [A Unified Framework of Policy Learning for Contextual Bandit with Confounding Bias and Missing Observations](https://mlsanity.com/paper/2303.11187/) (2023)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves](https://mlsanity.com/paper/2301.00092/) (2022)
- [DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimation](https://mlsanity.com/paper/2408.02045/) (2024)

## Abstract (arXiv)

Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional variables more effectively than linear sieves. We investigate the performance of various ANNs in nonparametric instrumental variables (NPIV) models of moderately high dimensional covariates that are relevant to empirical economics. We present two efficient procedures for estimation and inference on a weighted average derivative (WAD): an orthogonalized plug-in with optimally-weighted sieve minimum distance (OP-OSMD) procedure and a sieve efficient score (ES) procedure. Both estimators for WAD use ANN sieves to approximate the unknown NPIV function and are root-n asymptotically normal and first-order equivalent. We provide a detailed practitioner's recipe for implementing both efficient procedures. We compare their finite-sample performances in various simulation designs that involve smooth NPIV function of up to 13 continuous covariates, different nonlinearities and covariate correlations. Some Monte Carlo findings include: 1) tuning and optimization are more delicate in ANN estimation; 2) given proper tuning, both ANN estimators with various architectures can perform well; 3) easier to tune ANN OP-OSMD estimators than ANN ES estimators; 4) stable inferences are more difficult to achieve with ANN (than spline) estimators; 5) there are gaps between current implementations and approximation theories. Finally, we apply ANN NPIV to estimate average partial derivatives in two empirical demand examples with multivariate covariates.