We formalize the concept of “dark matter” in asset pricing models by quantifying the additional informativeness of cross-equation restrictions about fundamental dynamics. The dark-matter measure captures the degree of fragility for models that are potentially misspecified and unstable: a large dark-matter measure indicates that the model lacks internal refutability (weak power of optimal specification tests) and external validity (high overfitting tendency and poor out-of-sample fit). The measure can be computed at low cost even for complex dynamic structural models. To illustrate its applications, we provide quantitative examples applying the measure to (time-varying) rare-disaster risk and long-run risk models.

中文翻译：

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衡量资产定价模型中的“暗物质”

我们通过量化有关基本动态的交叉方程限制的额外信息，在资产定价模型中形式化了“暗物质”的概念。暗物质度量捕捉了可能被错误指定和不稳定的模型的脆弱程度：大的暗物质度量表明模型缺乏内部可反驳性（最佳规范测试的弱力量）和外部有效性（高过度拟合倾向和较差的输出）样本拟合）。即使对于复杂的动态结构模型，也可以以低成本计算该度量。为了说明其应用，我们提供了将该度量应用于（时变）罕见灾害风险和长期风险模型的定量示例。