SLIM: Stochastic Learning and Inference in Overidentified Models

Xiaohong Chen, Min Seong Kim, Sokbae Lee, Myung Hwan Seo and Myunghyun Song
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Xiaohong Chen: Yale University
Min Seong Kim: University of Connecticut
Sokbae Lee: Columbia University
Myung Hwan Seo: Seoul National University
Myunghyun Song: Columbia University

No 2472, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 and inference procedures based on random scaling and plug-in methods, including plug-in, debiased plug-in, and online versions of the SarganÐHansen 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.

Pages: 98 pages
Date: 2025-10-23
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