Abstract: The 'unusually uncertain' phase in the global financial markets has inspired many researchers to study the effects of ambiguity (or 'Knightian uncertainty') on the decisions made by investors and its implications in the capital markets. We contribute to this literature by using the time-varying GARCH model of Amado and Terasvirta (2011) to analyse whether the increasing uncertainty has caused excess volatility in the US and European government bond markets. In our model, volatility is multiplicatively decomposed into a stable conditional variance and time-varying unconditional volatility components. We suggest that the time-varying risk is captured by the conditional volatility parameters, whereas the time-variation in the unconditional volatility is driven by the level of uncertainty in the markets.