Expected Shortfall (ES) is a coherent measure of tail risk that captures the average loss beyond a quantile threshold. Despite the growing literature on ES regression conditional on covariates, no existing work considers ES modeling in panel data settings where both cross-sectional and temporal dependencies are present. This paper introduces the panel ES regression model with a latent factor structure to capture cross-sectional dependence. We develop a two-stage estimation procedure robust to heavy-tailed errors, recovering the conditional quantile in the first stage and iteratively estimating the ES factor model in the second stage. Theoretically, we establish the consistency and asymptotic normality of the proposed two-step ES estimators and derive non-asymptotic error bounds for both the panel quantile and ES estimators. We also provide a non-asymptotic normal approximation for the standardized ES regression estimator, bridging asymptotic theory and finite-sample practice. Simulation evidence shows that the proposed method delivers substantial gains in both parameter estimation and factor recovery, particularly in the presence of latent tail dependence. An empirical application further indicates that the extracted ES factors carry distinct pricing information that is not captured by conventional mean or quantile-based approaches.

翻译：预期损失（ES）是一种度量尾部风险的一致风险测度，其捕捉的是超过分位数阈值的平均损失。尽管目前关于条件于协变量的ES回归文献日益增长，但尚无研究考虑面板数据环境下的ES建模，而面板数据同时存在截面依赖与时间依赖。本文提出一种具有潜在因子结构的面板ES回归模型，以捕捉截面依赖关系。我们开发了一种对重尾误差稳健的两阶段估计程序：第一阶段恢复条件分位数，第二阶段迭代估计ES因子模型。理论上，我们建立了所提出的两步ES估计量的一致性和渐近正态性，并推导了面板分位数和ES估计量的非渐近误差界。同时，我们为标准化ES回归估计量提供了非渐近正态逼近，从而弥合了渐近理论与有限样本实践之间的差距。模拟证据表明，所提方法在参数估计和因子恢复方面均具有显著优势，特别是在存在潜在尾部依赖的情况下。实证应用进一步表明，提取的ES因子携带有别于传统均值或分位数方法所捕获的独特定价信息。