The Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, in some applications, the distribution of the error term departs significantly from normality, for instance, in the presence of heavy tails and/or atypical observation. In this paper, we explore the Heckman selection-t model where the random errors follow a bivariate Student’s-t distribution. We develop an analytically tractable and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student’s-t distributions. Simulation studies show the vulnerability of the Heckman selection-normal model, as well as the robustness aspects of the Heckman selection-t model. Two real examples are analyzed, illustrating the usefulness of the proposed methods. The proposed algorithms and methods are implemented in the new R package HeckmanEM.

在选择样本的数据分析中，Heckman选择模型可能是最受欢迎的计量经济学模型。该模型的分析基于误差项的正态性假设，但是，在某些应用中，误差项的分布与正态性大相径庭，例如在存在大量尾巴和/或非典型观察的情况下。在本文中，我们探索了Heckman选择-t模型，其中随机误差遵循双变量Student-t分布。我们开发了一种分析上易处理且高效的EM类型算法，用于迭代计算参数的最大似然估计，并将标准误差作为副产品。该算法在E步具有封闭形式的表达式，该表达式依赖于截断的Student-t分布均值和方差的公式。仿真研究显示了Heckman选择-正态模型的脆弱性，以及Heckman选择-t模型的鲁棒性方面。分析了两个真实的例子，说明了所提出方法的有用性。所提出的算法和方法在新版本中得以实现R包HeckmanEM。