Myunghyun Song Publications

We propose SLIM (Stochastic Learning and Inference in overidentified Models), a scalable stochastic approximation framework for nonlinear GMM. SLIM forms iterative updates from independent mini-batches of moments and their derivatives, producing unbiased directions that ensure almost-sure convergence. It requires neither a consistent initial estimator nor global convexity and accommodates both fixed-sample and random-sampling asymptotics. We further develop an optional second-order refinement and inference procedures based on random scaling and plug-in methods, including plug-in, debiased plug-in, and online versions of the Sargan–Hansen J-test tailored to stochastic learning. In Monte Carlo experiments based on a nonlinear EASI demand system with 576 moment conditions, 380 parameters, and n = 105 , SLIM solves the model in under 1.4 hours, whereas full-sample GMM in Stata on a powerful laptop converges only after 18 hours. The debiased plug-in J-test delivers satisfactory finite-sample inference, and SLIM scales smoothly to n = 106.

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.