Testing for Granger causality in large mixed-frequency VARs

We analyze Granger causality testing in a mixed-frequency VAR, where the difference in sampling frequencies of the variables is large, implying parameter proliferation problems in case we attempt to estimate the model unrestrictedly. We propose several tests based on reduced rank restrictions, including bootstrap versions thereof to account for factor estimation uncertainty and improve the finite sample properties of the tests, and a Bayesian VAR extended to mixed frequencies. We compare these methods to a test based on an aggregated model, the max-test (Ghysels et al., 2016a) and an unrestricted VAR-based test (Ghysels et al., 2016b) using Monte Carlo simulations. An empirical application illustrates the techniques.