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Maximum simulated likelihood estimation of the panel sample selection model

机译：面板样本选择模型的最大模拟似然估计

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Heckman's (1976, 1979) sample selection model has been employed in many studies of linear and nonlinear regression applications. It is well known that ignoring the sample selectivity may result in inconsistency of the estimator due to the correlation between the statistical errors in the selection and main equations. In this article, we reconsider the maximum likelihood estimator for the panel sample selection model in Keane et al. (1988). Since the panel data model contains individual effects, such as fixed or random effects, the likelihood function is more complicated than that of the classical Heckman model. As an alternative to the existing derivation of the likelihood function in the literature, we show that the conditional distribution of the main equation follows a closed skew-normal (CSN) distribution, of which the linear transformation is still a CSN. Although the evaluation of the likelihood function involves high-dimensional integration, we show that the integration can be further simplified into a one-dimensional problem and can be evaluated by the simulated likelihood method. Moreover, we also conduct a Monte Carlo experiment to investigate the finite sample performance of the proposed estimator and find that our estimator provides reliable and quite satisfactory results.
机译：Heckman（1976，1979）的样本选择模型已用于许多线性和非线性回归应用研究中。众所周知，由于选择和主要方程中的统计误差之间的相关性，忽略样本的选择性可能导致估计器的不一致。在本文中，我们重新考虑了Keane等人的面板样本选择模型的最大似然估计。 （1988）。由于面板数据模型包含单个效应，例如固定效应或随机效应，因此似然函数比经典Heckman模型复杂。作为文献中似然函数的现有推导的替代方法，我们证明了主方程的条件分布遵循闭合偏正态（CSN）分布，其中线性变换仍为CSN。尽管似然函数的评估涉及高维积分，但我们表明该积分可以进一步简化为一维问题，并且可以通过模拟似然法进行评估。此外，我们还进行了蒙特卡洛（Monte Carlo）实验，以研究拟议估计量的有限样本性能，并发现我们的估计量提供了可靠且令人满意的结果。

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