Estimation of marginal or partial effects of covariates x on various conditional parameters or functionals is often a main target of applied microeconometric analysis. In the specific context of probit models, estimation of partial effects involving outcome probabilities will often be of interest. Such estimation is straightforward in univariate models, and results covering the case of quadrant probability marginal effects in bivariate probit models for jointly distributed outcomes y have previously been described in the literature. This paper's goals are to extend Greene's results to encompass the general M≥2 multivariate probit (MVP) context for arbitrary orthant probabilities and to extended these results to models that condition on subvectors of y and to multivariate ordered probit data structures. It is suggested that such partial effects are broadly useful in situations wherein multivariate outcomes are of concern.

中文翻译：

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多元概率模型中的边际效应。

估计协变量 x 对各种条件参数或泛函的边际或部分影响通常是应用微观计量经济学分析的主要目标。在概率模型的特定背景下，涉及结果概率的部分效应的估计通常会引起人们的兴趣。这种估计在单变量模型中是简单的，并且覆盖联合分布结果 y 的双变量概率模型中象限概率边际效应情况的结果先前已在文献中描述过。本文的目标是将 Greene 的结果扩展为涵盖任意 orthant 概率的一般 M≥2 多元概率 (MVP) 上下文，并将这些结果扩展到以 y 子向量为条件的模型和多元有序概率数据结构。有人建议，这种部分效应在关注多变量结果的情况下广泛有用。