Many weak instrumental variables (IVs) are routinely used in the health and social sciences to improve identification and inference of the treatment effect of interest, along with a broad collection of data on potential confounding factors in the hope that the IV assumptions hold within each data stratum. We propose a new debiased continuous-updating generalized method of moments estimator with multi-task learning of the IV propensity scores to simultaneously address the biases from a diverging number of weak IVs as well as first-step regularized estimation of nuisance regression functions in high-dimensional potential confounding factors. We develop a new multi-task learning theory for generalized linear models under a general sub-Gaussian design to establish valid inference in the many weak IVs asymptotic regime under appropriate sparsity conditions. We evaluate the proposed method via extensive Monte Carlo studies and an empirical application to investigate the returns to education.

翻译：许多弱工具变量（IV）在健康和社会科学中被常规使用，以改善感兴趣的治疗效应的识别与推断，同时结合大量潜在混杂因素数据，希望工具变量假设在每个数据层内成立。我们提出了一种新的去偏连续更新广义矩估计方法，结合多任务学习工具变量倾向得分，以同时处理发散数量弱工具变量带来的偏差以及高维潜在混杂因素中第一步正则化估计干扰回归函数的问题。我们为广义线性模型在一般次高斯设计下发展了一种新的多任务学习理论，以在适当稀疏条件下建立许多弱工具变量渐近框架下的有效推断。我们通过广泛的蒙特卡洛研究以及一个关于教育回报的实证应用来评估所提出方法。