We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

翻译：摘要：本文提出一类新算法——随机广义矩方法（SGMM），用于（过度识别）矩约束模型的估计与推断。SGMM是对Hansen（1982）经典（离线）GMM的创新性随机逼近替代方案，可实现快速可扩展的计算，并具备实时处理流式数据集的能力。我们建立了低效在线两阶段最小二乘法与高效SGMM的几乎必然收敛性及（泛函）中心极限定理。此外，本文提出了可在SGMM框架内无缝集成的在线版Durbin-Wu-Hausman检验和Sargan-Hansen检验。大规模蒙特卡洛模拟表明，随着样本量增加，SGMM在估计精度上可与标准（离线）GMM媲美，且计算效率更优，充分体现其在大规模数据集与在线数据集中的实用价值。我们通过两个具有大样本量的经典实证案例进行概念验证，证实了该方法的有效性。