SLIM: Stochastic Learning and Inference in Overidentified Models
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909879452565504 |
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| author | Chen, Xiaohong Kim, Min Seong Lee, Sokbae Seo, Myung Hwan Song, Myunghyun |
| author_facet | Chen, Xiaohong Kim, Min Seong Lee, Sokbae Seo, Myung Hwan Song, Myunghyun |
| contents | 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 $n = 10^6$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_20996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SLIM: Stochastic Learning and Inference in Overidentified Models Chen, Xiaohong Kim, Min Seong Lee, Sokbae Seo, Myung Hwan Song, Myunghyun Econometrics Computation Machine Learning 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 $n = 10^6$. |
| title | SLIM: Stochastic Learning and Inference in Overidentified Models |
| topic | Econometrics Computation Machine Learning |
| url | https://arxiv.org/abs/2510.20996 |