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 computational 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. This involves the choice of tuning parameters for the unknown NPIV, the conditional expectations and the optimal weighting function that are present in both procedures but also the choice of tuning parameters for the unknown Riesz representer in the ES procedure. 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)可被视为非线性直径内存,它比线性内存更能有效地接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的计算性表现。我们为加权平均衍生物(WAD)提供了两个用于估算和推断的高效程序:一个或分化插座插座,其最优加权最小距离(OP-OSMD)程序,以及一个筛选高效评分(ES)程序。WAD的估算员使用非参数来接近未知的 NNEIV 功能,是根性正常正常和一级等等。我们为执行两种高效程序提供了详细的执业者食谱。这涉及为未知的 NPIV、 有条件的预期和最佳加权功能,两种程序同时为给定的Riz(OP) 有效评分(OS) 程序(ODO) 的调量参数选择了某些未知当前代表的调值。我们比较了SNNIS Sideal Supal Supal Supal Supal Supal 。