This paper proposes a new family of specification tests and applies them to affine term structure models of the London Interbank Offered Rate (LIBOR)-swap curve. Contrary to Dai and Singleton (2000), the tests show that when standard estimation techniques are used, affine models do a poor job of forecasting volatility at the short end of the term structure. Improving the volatility forecast does not require different models; rather, it requires a different estimation technique. The paper distinguishes between two econometric procedures for identifying volatility. The “cross-sectional” approach backs out volatility from a cross section of bond yields, and the “time-series” approach imputes volatility from time-series variation in yields. For an affine model, the volatility implied by the time-series procedure passes the specification tests, while the cross-sectionally identified volatility does not. This is surprising, since under correct specification, the “cross-sectional” approach is maximum likelihood. One explanation is that affine models are slightly misspecified; another is that bond yields do not span volatility, as in Collin-Dufresne and Goldstein (2002).