This study investigates the time-varying effects of international uncertainty shocks. I use a global vector autoregressive model with drifting coefficients and factor stochastic volatility in the errors to model the G7 economies jointly. The measure of uncertainty is constructed by estimating a time-varying scalar driving the innovation variances of the latent factors, which is also included in the conditional mean of the process. To achieve regularization, I use Bayesian techniques for estimation, and rely on hierarchical global–local priors to shrink the high-dimensional multivariate system towards sparsity. I compare the obtained econometric measure of uncertainty to alternative indices and discuss commonalities and differences. Moreover, I find that international uncertainty may differ substantially compared to identically constructed domestic measures. Structural inference points towards pronounced real and financial effects of uncertainty shocks in all considered economies. These effects are subject to heterogeneities over time and the cross-section, providing empirical evidence in favor of using the flexible econometric framework introduced in this study.