We present a new set of algorithms called Stochastic Generalized Method of Moments (SGMM) for estimating and inferring on moment restriction models that are overidentified. Our SGMM algorithm is a novel alternative to the widely used offline GMM algorithm proposed by Hansen (1982), offering fast and scalable implementation that can handle real-time streaming datasets. We prove the almost sure convergence and the (functional) central limit theorem for both the inefficient online 2SLS and the efficient SGMM algorithms. Additionally, we introduce online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be easily integrated into the SGMM framework. Through extensive Monte Carlo simulations, we demonstrate that as the sample size increases, the SGMM algorithm achieves estimation accuracy comparable to the standard offline GMM algorithm while providing significant computational efficiency advantages. This indicates the practical value of SGMM for both large-scale and online datasets. To further illustrate the effectiveness of our approach, we showcase its performance on two well-known empirical examples with large sample sizes.
Stochastic Approximation to Generalized Method of Moments: An Overview (arXiv:2308.13564v1 [econ.EM])
