SGMM: Stochastic Approximation to Generalized Method of Moments

TL;DR

This paper introduces SGMM, a stochastic approximation algorithm for generalized method of moments estimation, enabling fast, scalable, and real-time analysis of large and streaming datasets with theoretical guarantees.

Contribution

The paper presents SGMM as a novel stochastic approximation alternative to traditional GMM, with proven convergence, inference methods, and demonstrated efficiency in large-scale applications.

Findings

SGMM achieves estimation accuracy comparable to standard GMM.

SGMM offers significant computational efficiency improvements.

Online tests are effectively integrated within the SGMM framework.

Abstract

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.