Scalable likelihood-based inference for limited dependent variable models

2026-08-13

AI Summary

This study addresses the computational intractability of high-dimensional integrals in likelihood inference for limited dependent variable models by proposing the SEGA algorithm. Integrating Fisher’s identity with stochastic gradient ascent, this method achieves scalable estimation via unbiased augmented-data scores. Furthermore, variance estimators constructed using Fisher and Louis identities are proven to be asymptotically equivalent to maximum likelihood estimates. Experiments on large-scale discrete choice and truncated demand models demonstrate that SEGA significantly enhances computational efficiency while preserving valid statistical inference. Consequently, this work provides a practical solution for high-dimensional limited dependent variable modeling, effectively bridging the gap between computational scalability and rigorous statistical theory in complex econometric applications.

Abstract

Limited dependent variable models are central to empirical economics, but likelihood-based inference is infeasible when likelihoods involve high-dimensional integration over latent variables. This paper proposes Stochastically Estimated Gradient Ascent (SEGA), a scalable estimation approach for limited dependent variable models. Using Fisher's identity, SEGA replaces the intractable likelihood score with an unbiased augmented-data score evaluated at a single conditional draw of the latent variables, and embeds this score in a stochastic gradient ascent algorithm. With sufficiently many iterations, we show that SEGA is asymptotically equivalent to the infeasible maximum likelihood estimator. A variance estimator based on Fisher's and Louis' identities is proposed that allows inference to proceed in the usual manner. Applications to brand choice and household demand demonstrate the usefulness of SEGA for conducting inference in large-scale discrete-choice and censored-demand models.

Problem

• Limited dependent variable models
• Likelihood-based inference
• High-dimensional integration
• Latent variables

Innovation

• Stochastically Estimated Gradient Ascent
• Limited Dependent Variable Models
• Fisher's Identity
• Scalable Likelihood Inference
• Augmented-Data Score