Regulatory stress tests have become one of the main tools for setting capital requirements at the largest U.S. banks. The Federal Reserve uses confidential models to evaluate bank-specific outcomes for bank-specific portfolios in shared stress scenarios. As a matter of policy, the same models are used for all banks, despite considerable heterogeneity across institutions; individual banks have contended that some models are not suited to their businesses. Motivated by this debate, we ask, what is a fair aggregation of individually tailored models into a common model? We argue that simply pooling data across banks treats banks equally but is subject to two deficiencies: it may distort the impact of legitimate portfolio features, and it is vulnerable to implicit misdirection of legitimate information to infer bank identity. We compare various notions of regression fairness to address these deficiencies, considering both forecast accuracy and equal treatment. In the setting of linear models, we argue for estimating and then discarding centered bank fixed effects as preferable to simply ignoring differences across banks. We present evidence that the overall impact can be material. We also discuss extensions to nonlinear models.

翻译：监管压力测试已成为美国大型银行设定资本要求的主要工具之一。美联储使用机密模型，在共有压力情景下评估银行特有组合的银行特定结果。作为政策惯例，尽管各机构之间存在显著异质性，同一模型被应用于所有银行；个别银行认为某些模型并不适用于其业务。受此争论启发，我们探讨如何将个性化模型公平聚合为通用模型。我们认为简单合并所有银行数据虽能平等对待各银行，但存在两个缺陷：可能扭曲合法组合特征的影响，且易受隐含信息误导，将合法信息用于推断银行身份。我们比较了多种回归公平性概念以应对这些缺陷，兼顾预测准确性与平等对待。在线性模型设定下，我们主张估计并舍弃中心化银行固定效应，这优于简单忽略银行间差异。我们提供的证据表明整体影响可能具有实质性。同时，我们探讨了向非线性模型的扩展。