适用于有限因变量模型的可扩展似然推断

中文摘要 AI 辅助

有限因变量模型是实证经济学的核心，但当似然包含对潜在变量的高维积分时，基于似然的推断无法实现。本文提出了随机估计梯度上升（Stochastically Estimated Gradient Ascent，SEGA），这是一种适用于有限因变量模型的可扩展估计方法。利用费希尔恒等式，SEGA将难以处理的似然得分替换为在潜在变量的单次条件抽样下评估的无偏增广数据得分，并将该得分嵌入随机梯度上升算法中。我们证明，通过足够多的迭代，SEGA在渐近意义上等价于不可行的最大似然估计量。本文还提出了一种基于费希尔恒等式和路易斯恒等式的方差估计量，使推断能够以常规方式进行。将其应用于品牌选择和家庭需求的实例，证明了SEGA在大规模离散选择和删失需求模型中进行推断的实用性。

英文摘要

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.

发表机构

• Department of Econometrics and Business Statistics, Monash University（蒙纳士大学计量经济学与商业统计系）

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