We use variational inference (VI), a technique from the machine learning literature, to estimate a mortality-based Bayesian model of nursing home quality accounting for selection. We demonstrate how one can use VI to quickly and flexibly estimate a high-dimensional economic model with large datasets. Using our facility quality estimates, we examine the correlates of quality and find that public report cards have near-zero correlation. We then show that in contrast to prior literature, higher quality nursing homes fared better during the pandemic: a one standard deviation increase in quality corresponds to 2.5% fewer Covid-19 cases

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