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SLIM: Stochastic Learning and Inference in Overidentified Models

Author

Listed:
  • Xiaohong Chen

    (Yale University)

  • Min Seong Kim

    (University of Connecticut)

  • Sokbae Lee

    (Columbia University)

  • Myung Hwan Seo

    (Seoul National University)

  • Myunghyun Song

    (Columbia 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.

Suggested Citation

  • Xiaohong Chen & Min Seong Kim & Sokbae Lee & Myung Hwan Seo & Myunghyun Song, 2025. "SLIM: Stochastic Learning and Inference in Overidentified Models," Cowles Foundation Discussion Papers 2472, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2472
    as

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    File URL: https://cowles.yale.edu/sites/default/files/2025-10/d2472.pdf
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    References listed on IDEAS

    as
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