  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.
