We formulate the problem of estimating risk prices in a stochastic discount factor (SDF) model as an instrumental variables regression. The IV estimator allows efficient estimation for models with non-traded factors and many test assets. Optimal instruments are constructed using a regularized sparse first stage regression. In a simulation study, the IV estimator is close to the infeasible GMM estimator in a setting with many assets. In an empirical application, the tracking portfolio for consumption growth appears strongly correlated with consumption news. It implies that consumption is a priced factor for the cross-section of excess equity returns. A similar regularized regression, projecting the SDF on test assets, leads to an estimate of the Hansen–Jagannathan distance, and identifies portfolios that maximally violate the pricing implications of the model.

中文翻译：

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具有许多测试资产的经验资产定价

我们将随机贴现因子（SDF）模型中估计风险价格的问题表述为工具变量回归。IV 估计器可以对具有非交易因素和许多测试资产的模型进行有效估计。最佳仪器是使用正则化稀疏第一阶段回归构建的。在模拟研究中，IV 估计器在具有许多资产的环境中接近不可行的 GMM 估计器。在实证应用中，消费增长的跟踪投资组合似乎与消费新闻密切相关。这意味着消费是超额股本回报横截面的定价因素。类似的正则化回归，将 SDF 投影到测试资产上，得出 Hansen-Jagannathan 距离的估计，并识别最大限度地违反模型定价影响的投资组合。