  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.
