A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models
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多项 Probit 模型离散概率模拟矩的平滑方法
- 研究问题
- 在多项 Probit 模型的模拟矩估计中，如何平滑离散模拟变量，以便模拟导数和数据变化，并减少对大量模拟抽样的需求？
- 方法与思路
- 作者提出适用于 Probit 问题的因子分析平滑法，提供相应算法，并通过蒙特卡洛比较该方法与重要性抽样的表现。
- 材料陈述的贡献
- 摘要称模拟概率无偏且取值在零到一之间，方差总小于未平滑估计，并在一大类概率下小于重要性抽样估计。
- 阅读关注点
- 应核对因子分析表示的适用条件、平滑算法与导数模拟方式，并检查无偏性和方差比较的证明及蒙特卡洛设计。
- 阅读边界
- 作者说明该方法适用范围较一般误差结构的平滑方法窄；摘要未给出全部条件，方差优势不能直接解释为参数估计总体更优。
原文摘要
THERE HAS BEEN MUCH INTEREST over the years in estimating discrete choice models. However, with the exception of multinomial logit models, agents have been restricted to few choices so that multivariate integrals could be feasibly integrated numerically.2 Pakes and Pollard (1989) and McFadden (1989) have independently developed the method of simulated moments (MSM) to deal with estimating a wide class of models of which high order discrete choice models are a subset. One of the problems a researcher must handle when using MSM for a discrete choice model is how to smooth the discrete simulated random variables. This is necessary to keep small the number of draws required to simulate derivatives and to simulate variation in the data. Geweke (1989) and McFadden (1989) have suggested importance sampling methods (and other methods) to smooth the simulated variables for general error structures. In this paper, I present a factor analytic smoothing method that can be applied to probit problems. Although it is not as general as the methods Geweke and McFadden suggest, it is easy to use and has clear intuition. Furthermore, simulated probabilities will be unbiased, will be bounded between zero and unity, and will have smaller variances than unsmoothed probabilities always and smaller variances than importance sampling estimates for a large class of probabilities. The second section of this paper develops notation, defines the problem, and presents the smoothing method and an algorithm to employ it. The last section presents Monte Carlo comparisons of the smoothing method to the importance sampling method.