We propose a parametric estimation procedure for linear panel data models with sample selection and heterogeneous coefficients that are present in both outcome model and selection model. Our two-step estimation procedure accounts for endogeneity from the selection process and endogeneity from correlation between the individual unobserved heterogeneity and the observed covariates using control function like methods. Conditional linear projections are used to establish a tractable approach that builds upon the original Heckman correction to sample selection. Monte Carlo simulations illustrate the finite sample properties of our estimator and demonstrate that our proposed estimator outperforms standard estimators. We apply the proposed approach to estimate gender differences in high-stakes time-constrained decisions using Elo ratings data from the World Chess Federation. When addressing both sources of endogeneity, we find a much larger gender skill gap and substantial differences across the genders in strategically selecting into time-constrained matches.

中文翻译：

---

具有异质系数的线性面板数据模型中的样本选择

我们提出了一种线性面板数据模型的参数估计程序，其中样本选择和异质系数都存在于结果模型和选择模型中。我们的两步估计程序解释了选择过程的内生性和使用控制函数等方法的个体未观察到的异质性和观察到的协变量之间的相关性的内生性。条件线性投影用于建立一种易于处理的方法，该方法建立在对样本选择的原始赫克曼校正的基础上。蒙特卡罗模拟说明了我们的估计器的有限样本属性，并证明我们提出的估计器优于标准估计器。我们应用所提出的方法，使用世界国际象棋联合会的 Elo 评级数据来估计高风险、时间有限的决策中的性别差异。在解决这两个内生性来源时，我们发现性别技能差距要大得多，而且不同性别在策略性选择时间有限的比赛方面存在巨大差异。