Reduced‐form factor augmented VAR—Exploiting sparsity to include meaningful factors

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Abstract
Summary: 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.

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