Expectations Models of the Term Structure and Implied Variance Bounds

Variance bounds are derived for general present-value relations involving the expected future values of any finite number of variables. The estimators of these bounds and the variance being bounded are then shown to have a joint distribution converging to that of the multivariate normal, with moments which can be consistently estimated from the data. As a special case of these results, it is shown that expectations models of the term structure imply upper and lower bounds on the variance of the long-term rate. These bounds are used to test a rational expectations model of long-term U.S. Treasury bond yields.