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.

This paper studies the time-series behavior of asset returns and aggregate consumption. Using a representative consumer model and imposing restrictions on preferences and the joint distribution of consumption and returns, we deduce a restricted log-linear time-series representation. Preference parameters for the representative agent are estimated and the implied restrictions are tested using postwar data.