On a numerical and graphical technique for evaluating some models involving rational expectations

Campbell and Shiller (1987) proposed a graphical technique for the present value model which consists of plotting the spread and theoretical spread as calculated from the cointegrated vector autoregressive model. We extend these techniques to a number of rational expectation models and give a general de¯nition of spread and theoretical spread. The main results are the asymptotic distributions of the variance ratio, noise ratio, and correlation between the estimated spread and theoretical spreads. We derive sup tests for the recursively calculated quantities. Finally we apply the methods to two previous studies by Campbell and Shiller (1987) and Engsted (2002).