It is well-known that interest rates and inflation rates are extremely persistent, yet they are best modeled and understood as stationary processes. These properties are contradictory in the workhorse Gaussian affine term structure model in which the persistent data often result in unit roots that imply non-stationarity. We resolve this puzzle by proposing a macro-finance term structure model with volatility-induced stationarity. Our model employs a level-dependent conditional volatility that maintains stationarity despite presence of unit roots in the characteristic polynomial corresponding to the conditional mean. Compared to the Gaussian affine term structure model, we improve out-of-sample forecasting of the yield curve and estimate term premia that are economically plausible and consistent with survey data. Moreover, we show that volatility-induced stationarity affects the error-correcting mechanism in a system of interest rates, inflation, and real activity.