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This makes the method computationally efficient and capable of handling information sets as large as those typically handled by factor models and Factor Augmented VARs. When applied to the problem of forecasting key macroeconomic variables, the method outperforms constant parameter benchmarks and compares well with large (parametric) Bayesian VARs with time\u2010varying parameters. The tool can also be used for structural analysis. As an example, we study the time\u2010varying effects of oil price shocks on sectoral U.S. industrial output. 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