Poisson Regression under Multivariate Sample Selection
多重样本选择下的泊松回归AI 解读 ↓
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多重样本选择下的泊松回归
- 研究问题
- 当计数结果只有在多个可能相关的选择条件同时满足时才可观测，如何识别与估计结果模型，并校正选择导致的偏差？
- 方法与思路
- 作者基于结果误差与选择误差的联合正态设定推导选择修正项，提出非线性最小二乘和 PPML 两步估计及稳健协方差估计。
- 材料陈述的贡献
- 摘要称，在适当支持与秩条件下无需排除限制也可识别结果参数，并建立两步估计的一致性；模拟中 PPML 的偏差与稳定性较好。
- 阅读关注点
- 应核对联合正态误差如何嵌入泊松模型、无排除限制识别的支持与秩条件，以及第一步误差如何进入协方差估计。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出完整识别条件，首次提出及模拟优势均属作者陈述，尚未独立核实。
原文摘要
This paper develops a Poisson regression model with multivariate sample selection, in which the outcome is observed only when several potentially correlated selection conditions are satisfied. To the best of our knowledge, this is the first Poisson sample selection model that allows for an arbitrary number of selection equations. We derive the conditional mean of the observed outcome under joint normality of the outcome and selection errors and obtain a multivariate selection-correction term. We prove identification of the model parameters and show that, under suitable support and rank conditions, the outcome parameters can be identified without an exclusion restriction. We also propose two-step estimation procedures based on nonlinear least squares and Poisson pseudo-maximum likelihood. To the best of our knowledge, this paper is the first to apply PPML to a Poisson regression model with sample selection. The consistency of both estimators is established, and a robust two-step sandwich covariance matrix is proposed to account for the estimation error from the first-step selection model. In addition, factorial moments are used to recover the variance of the latent outcome error and the correlations between the outcome and selection errors. Monte Carlo simulations show that ignoring sample selection leads to persistent bias when the outcome and selection errors are correlated, while the proposed PPML estimator substantially reduces this bias and is more stable than nonlinear least squares, especially under moderate and strong selection dependence.