Macroeconomic forecasting and structural analysis through regularized reduced-rank regression

This paper proposes a strategy to detect and impose reduced-rank restrictions in medium vector autoregressive models. In this framework, it is known that Canonical Correlation Analysis (CCA) does not perform well because inversions of large covariance matrices are required. We propose a method that combines the richness of reduced-rank regression with the simplicity of naive univariate forecasting methods. In particular, we suggest to use a proper shrinkage estimator of the autocovariance matrices that are involved in the computation of CCA, thus obtaining a method that is asymptotically equivalent to CCA, but it is numerically more stable in finite samples. Simulations and empirical applications document the merits of the proposed approach both in forecasting and in structural analysis.