Induced sparsity in the factor loading matrix identifies the factor basis, while rotational identification is obtained ex post by clustering methods closely related to machine learning. We extract meaningful economic concepts from a high-dimensional data set, which together with observed variables follow an unrestricted, reduced-form VAR process. Including a comprehensive set of economic concepts allows reliable, fundamental structural analysis, even of the factor augmented VAR itself. We illustrate this by combining two structural identification methods to further analyze the model. To account for the shift in monetary policy instruments triggered by the Great Recession, we follow separate strategies to identify monetary policy shocks. Comparing ours to other parametric and non-parametric factor estimates uncovers advantages of parametric sparse factor estimation in a high dimensional data environment. Besides meaningful factor extraction, we gain precision in the estimation of factor loadings.

中文翻译：

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简化形式因子增强 VAR——利用稀疏性来包含有意义的因子

因子加载矩阵中的诱导稀疏性识别因子基础，而旋转识别是通过与机器学习密切相关的聚类方法事后获得的。我们从高维数据集中提取有意义的经济概念，这些数据与观察到的变量一起遵循不受限制的简化形式的 VAR 过程。包括一套全面的经济概念允许进行可靠的基本结构分析，甚至是因子增强 VAR 本身。我们通过结合两种结构识别方法来进一步分析模型来说明这一点。为了解释大衰退引发的货币政策工具的转变，我们采用不同的策略来识别货币政策冲击。将我们的估计与其他参数和非参数因子估计进行比较，揭示了参数稀疏因子估计在高维数据环境中的优势。除了有意义的因子提取外，我们还可以精确地估计因子载荷。