Financial globalisation and spillovers have gained immense prominence over the last two decades. Yet, powerful cross-border financial spillover channels have not become a standard element of structural monetary models. Against this background, we hypothesise that New Keynesian DSGE models that do not feature powerful financial spillover channels confound the effects of domestic and foreign disturbances when confronted with the data. We derive predictions from this hypothesis and subject them to data on monetary policy shock estimates for 29 economies obtained from more than 280 monetary models in the literature. Consistent with the predictions from our hypothesis we find: Monetary policy shock estimates obtained from New Keynesian DSGE models that do not account for powerful financial spillover channels are contaminated by a common global component; the contamination is more severe for economies that are more susceptible to financial spillovers in the data; and the shock estimates imply implausibly similar estimates of the global output spillovers from monetary policy in the US and the euro area. None of these findings applies to monetary policy shock estimates obtained from VAR and other statistical models, financial market expectations and the narrative approach.