We introduce a new regression method that relates the mean of an outcome variable to covariates, given the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse economic scenarios, which receive increasing interest in managing macroeconomic and financial risks, among many others. In the terminology of the systemic risk literature, our method can be interpreted as a regression for the Marginal Expected Shortfall. We propose a two-step procedure to estimate the new models, show consistency and asymptotic normality of the estimator, and propose feasible inference under weak conditions allowing for cross-sectional and time series applications. The accuracy of the asymptotic approximations of the two-step estimator is verified in simulations. Two empirical applications show that our regressions under adverse conditions are valuable in such diverse fields as the study of the relation between systemic risk and asset price bubbles, and dissecting macroeconomic growth vulnerabilities into individual components.

翻译：我们提出一种新的回归方法，在“不利条件”——即某困扰变量处于其尾部区间——下，建立结果变量均值与协变量之间的关系。该方法能够将经典均值回归定制到不利经济情景中，这在管理宏观经济和金融风险等诸多领域受到日益关注。根据系统性风险文献的术语，我们的方法可解释为边际预期损失回归。我们采用两步估计法来估计新模型，证明了估计量的一致性和渐近正态性，并在允许横截面和时间序列应用的弱条件下提出了可行的推断方法。通过模拟验证了两步估计量渐近近似的准确性。两项实证应用表明，我们的不利条件回归在系统性风险与资产价格泡沫关系研究以及将宏观经济增长脆弱性分解为各组成部分等不同领域均具有重要价值。