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.
翻译:人工神经网络(ANNS)可被视为非线性插座,可以比线性缩略图更有效地近近近高维变量的复杂功能。我们调查了非参数性工具变量(NPIV)模型中与实证经济学相关的中度高度共变体(NPIV)模型中各个非参数性非参数性能。我们为加权平均衍生物(WAD)的估算和推算提供了两种有效的估计和推算程序:一个或线性插座,具有最优加权的筛选最小距离(OP-OSMD)程序,以及一个筛选高效的评分(ES)程序。WAADA的估测员使用ANNE(NE)来近似未知的 NPIV功能性能(NP)模型性能(NP)和一级(NONA 平均变距值(OP)之间的测算和正值(ONPA)之间,比OO的测算更难的正值(O),比ODO(NO)更难的估测算,比OA(NO)更难的估测算。