Efficient estimation of causal parameters via neural networks

Résumé

Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves. In general, nonlinear sieves (including ANNs) can approximate unknown nonlinear functions of high dimensional variables more effectively than linear sieves, but are computationally more demanding. In this talk, I present three recent papers on semiparametric efficient estimation of causal parameters via ANN approximation of unknown functions of high dimensional covariates. The first paper is about efficient estimation of general treatment effects using ANN with a diverging number of confounders. ( a paper by Xiaohong Chen, Ying Liu, Shujie Ma and Zheng Zhang; arXiv: https://arxiv.org/abs/2009.07055 ). The second paper is about efficient estimation of averaged (cross-) price elasticity and other expectation functionals of nonparametric demand functions of endogenous and exogenous covariates. ( a paper by Jiafeng Chen, Xiaohong Chen, and Elie Tamer). The third paper is about optimal estimation of functionals (could be root-n or slower than root-n estimable) of general nonparametric conditional moment restriction models via ANN for time series data. (a paper by Jiafeng Chen, Xiaohong Chen and Yuan Liao). All papers demonstrate the advantage of ANN sieves over linear sieves in estimating nonparametric causal models with high dimensional covariates. In particular, Paper 2 considers ANN efficient estimation of expectation functionals, such as (weighted) averaged partial derivatives and averaged partial means of nonparametric instrumental variables (NPIV) regressions. We estimate the expectation functional and the ANN sieve approximated NPIV functions jointly by minimizing a modified optimally weighted minimum distance criterion. This joint ANN sieve optimization automatically leads to the efficient estimation of regular (i.e., root-$n$ estimable) functionals. Sufficient conditions are provided for the validity of the root-$n$ asymptotic normality and the bootstrap consistency. For models with high dimensional regressors and moderate sample sizes, simulation studies of partially linear NPIV models and real data applications indicate that single-hidden layer ANN sieves perform well, and is not sensitive to the choice of ANN activation functions (Relu vs Sigmoid) or the number of hidden layers of ANN. In particular, the single-hidden layer ANN sieve can recover underlying true additive structure in simulations, and can recover flexible covariates' effects on price elasticities in gasoline demand.