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：我们提出了一类新算法——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。我们的SGMM是对经典Hansen（1982）（离线）GMM的一种新颖随机逼近替代方案，提供了快速且可扩展的实现，能够实时处理流式数据集。我们建立了几乎必然收敛性，以及低效在线两阶段最小二乘法和高效SGMM的（泛函）中心极限定理。此外，我们提出了Durbin-Wu-Hausman和Sargan-Hansen检验的在线版本，可无缝集成到SGMM框架中。大量蒙特卡洛模拟表明，随着样本量增加，SGMM在估计精度上与标准（离线）GMM相当，并在计算效率上更具优势，凸显其在大规模数据集和在线数据集中的实用价值。我们通过两个知名的大样本实证案例概念验证，展示了该方法的有效性。