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.

我们介绍了一种新的算法类别，即随机广义矩方法（SGMM），用于估计和推断（过识别的）矩约束模型。该SGMM是对流行的Hansen (1982)（离线）广义矩估计法的一种新型随机逼近替代方法，并具有快速、可扩展的实时数据流处理能力。我们建立了对于低效的在线两阶段最小二乘法（2SLS）和高效的SGMM，几乎确定的收敛性和（函数）中心极限定理。此外，我们提出了Durbin-Wu-Hausman和Sargan-Hansen的在线测试版本，可以无缝集成到SGMM框架中。大量的蒙特卡洛模拟表明，随着样本量的增加，SGMM在估计准确性和计算效率方面与标准（离线）GMM相匹配，从而显示了它在大规模和在线数据集上的实用价值。我们通过两个知名的具有大样本量的实证示例来证明我们方法的有效性。

SGMM: 广义矩量的随机逼近