SGMM: Stochastic Approximation to Generalized Method of Moments
This provides a scalable solution for econometricians and data scientists handling streaming or large datasets, though it is incremental as it builds on existing GMM methods.
The paper tackles the problem of estimation and inference for overidentified moment restriction models by introducing Stochastic Generalized Method of Moments (SGMM), a stochastic approximation alternative to offline GMM, which matches offline GMM in estimation accuracy and gains computational efficiency for large-scale and online datasets.
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.