Random Subspace Local Projections

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
function in a Monte Carlo exercise where we simulate data from a real business cycle model with fiscal
foresight. (ii) Our results suggest that random subspace methods are more accurate than factor models
if the underlying large data set has a factor structure similar to typical macroeconomic data sets such as
FRED-MD. (iii) Our approach leads to differences in the estimated impulse response functions relative to
standard methods when applied to two widely-studied empirical applications.