In the short-run, bond risk premia exhibit pronounced spikes around major economic and financial crises. In contrast, long-term bond risk premia feature cyclical swings. We empirically examine the predictability of the market variance risk premium—a proxy of economic uncertainty—for bond risk premia and we show the strong predictive power for the one month horizon that almost entirely disappears for horizons above one year. The variance risk premium is largely orthogonal to well-established bond return predictors—forward rates, jumps, yield curve factors, and macro variables. We rationalize our empirical findings in an equilibrium model of uncertainty about consumption and inflation which is coupled with recursive preferences. We show that the model can quantitatively explain the levels of bond and variance risk premia as well as the predictive power of the variance risk premium while jointly matching salient features of other asset prices.