Heckman Selection-Contaminated Normal Model
针对Heckman选择模型中误差项的正态假设在厚尾或异常值下不稳健的问题，提出用二元污染正态分布替代，并给出高效EM算法和可识别性证明，模拟和实例验证了模型有效性。
The Heckman selection model is one of the most well-renowned econometric models in the analysis of data with sample selection. This model is designed to rectify sample selection biases based on the assumption of bivariate normal error terms. However, real data diverge from this assumption in the presence of heavy tails and/or atypical observations. Recently, this assumption has been relaxed via a more flexible Student’s t-distribution, which has appealing statistical properties. This paper introduces a novel Heckman selection model using a bivariate contaminated normal distribution for the error terms. We present an efficient Expectation Conditional Maximization algorithm for parameter estimation with closed-form expressions at the E-step based on truncated multinormal distribution formulas. The point identifiability of the proposed model is also discussed, and its properties have been examined. Through simulation studies, we compare our proposed model with the normal and Student’s t counterparts and investigate the finite-sample properties and the variation in missing rate. Results obtained from two real data analyses showcase the usefulness and effectiveness of our model. The proposed algorithms are implemented in the R package HeckmanEM.