{"ID":2851388,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20996","arxiv_id":"2510.20996","title":"SLIM: Stochastic Learning and Inference in Overidentified Models","abstract":"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 achieving full-sample GMM efficiency 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 demand system with 576 moment conditions, 380 parameters, and $n = 10^5$, 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 $n = 10^6$.","short_abstract":"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 neith...","url_abs":"https://arxiv.org/abs/2510.20996","url_pdf":"https://arxiv.org/pdf/2510.20996v2","authors":"[\"Xiaohong Chen\",\"Min Seong Kim\",\"Sokbae Lee\",\"Myung Hwan Seo\",\"Myunghyun Song\"]","published":"2025-10-23T20:50:35Z","proceeding":"econ.EM","tasks":"[\"econ.EM\",\"stat.CO\",\"stat.ML\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}