We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated over different combinations of subsets of these controls. We document three key results: (i) Our approach can successfully recover the impulse response functions across Monte Carlo experiments representative of different macroeconomic settings and identification schemes. (ii) Our results suggest that random subspace methods are more accurate than other dimension reduction methods if the underlying large dataset has a factor structure similar to typical macroeconomic datasets such as FRED-MD. (iii) Our approach leads to differences in the estimated impulse response functions relative to benchmark methods when applied to two widely studied empirical applications.

The Beveridge-Nelson decomposition based on autoregressive models produces estimates of the output gap that are strongly at odds with widely held beliefs about transitory movements in economic activity. This is due to parameter estimates implying a high signal-to-noise ratio in terms of the variance of trend shocks as a fraction of the overall forecast error variance. When we impose a lower signal-to-noise ratio, the resulting Beveridge-Nelson filter produces a more intuitive estimate of the output gap that is large in amplitude and highly persistent, and it typically increases in expansions and decreases in recessions. Notably, our approach is also reliable in the sense of being subject to smaller revisions and predicting future output growth and inflation better than other trend-cycle decompositions that impose a low signal-to-noise ratio.