Gaussian affine term structure models attribute time-varying bond risk premia to changing risk prices driven by the conditional means of the risk factors, while structural models with recursive preferences credit it to stochastic volatility. We reconcile these competing channels by introducing a novel form of stochastic rate of time preference into an otherwise standard model with recursive preferences. Our structural model is affine and has analytical bond prices making it empirically tractable. We use particle Markov chain Monte Carlo to estimate the model, and find that time variation in bond term premia is predominantly driven by the risk price channel.