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Scalable likelihood-based inference for limited dependent variable models

David T. Frazier, Ruben Loaiza-Maya, Didier Nibbering

arXiv 14 Aug 2026 · Econometrics

arXiv:2608.13851 · PDF · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Botev, Z. I (2017) The normal law under linear restrictions: simulation and estimation via minimax tilting0.8435360%
2Hajivassiliou, V. A. and McFadden, D. L (1998) The method of simulated scores for the estimation of LDV models0.84333100%
3Chen, X., Lee, J. D., Tong, X. T., and Zhang, Y (2020) Statistical inference for model parameters in stochastic gradient descent0.7375440%
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6Bolduc, D (1999) A practical technique to estimate multinomial probit models in transportation0.64422100%
7Börsch-Supan, A. and Hajivassiliou, V. A (1993) Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models0.64422100%
8Danaher, P. J., Danaher, T. S., Smith, M. S., and Loaiza-Maya, R (2020) Advertising effectiveness for multiple retailer-brands in a multimedia and multichannel environment self0.64422100%
9Louis, T. A (1982) Finding the observed information matrix when using the EM algorithm0.64422100%
10Moulines, E. and Bach, F (2011) Non-asymptotic analysis of stochastic approximation algorithms for machine learning0.64422100%

Showing the top 10 of 43 scored citations.