Empirical asset pricing models with possibly unnecessary risk factors are increasingly common. Unfortunately, they can yield misleading statistical inferences. Unlike previous studies, we estimate the identified set of SDFs and risk prices compatible with a given model’s asset pricing restrictions. We also propose tests that detect problematic situations with economically meaningless SDFs unrelated to the test assets. Empirically, we estimate linear subspaces of SDFs compatible with popular extensions of the traditional and consumption versions of the CAPM, which are typically two-dimensional. Moreover, we often find that all the SDFs in those linear spaces are uncorrelated with the test assets’ returns.

带有可能不必要的风险因素的实证资产定价模型越来越普遍。不幸的是，它们可能会产生误导性的统计推断。与以前的研究不同，我们估计了与给定模型的资产定价限制兼容的已识别的 SDF 和风险价格集。我们还建议使用与测试资产无关的经济上无意义的 SDF 来检测问题情况的测试。根据经验，我们估计 SDF 的线性子空间与 CAPM 的传统和消费版本的流行扩展兼容，通常是二维的。此外，我们经常发现那些线性空间中的所有 SDF 都与测试资产的收益不相关。