SLIM: Stochastic Learning and Inference in Nonlinear GMM Models

Abstract

We propose SLIM (Stochastic Learning and Inference in overidentified Models), a new scalable stochastic approximation algorithm for nonlinear GMMs with many nonseparable moments and parameters. SLIM is shown to be consistent and asymptotically normal without a consistent initial estimator or a globally convex GMM criterion. Random-scaling and plug-in based confidence set constructions remain valid when computational uncertainty can be non-negligible relative to sampling uncertainty. An optional second-order refinement achieves full-sample GMM efficiency. We develop $J$-tests for SLIM. The theoretical results are extended to models with clustered data of unequal cluster sizes. Monte Carlo experiments for a nonlinear demand system with 576 moments and 380 parameters demonstrate computational gains and scalability to one million observations. A LinkedIn application with 4.8 million college graduates illustrates clustered estimation and inference for first employment destinations.