Non-exact present value relations

One of the most cornmonly used and, at the same time. rejected models in finance and macroeconomics is the exact present value model (PVM), where a variable Yt is expressed as the expected value at time t of the sum of discounted future values of another variable Xt. This paper generalizes the PVM by making it non-exact (NEPVM) in a simple way, allowing us to study situations with time varying discount factors, transitory deviations from the exact PVM, as well as situations with correlated market returns. The proposed NEPVM satisfies all the equilibrium conditions the exact PVM does, but at the same time it is more robust in the sense that rejections produced by the standard volatility and cross-equation restriction tests are not enough to reject the NEPVM. The paper presents the new variance bounds and cross-equation restrictions implied by the NEPVM and it shows how to test them. This paper also shows how to discriminate between the exact PVM and the NEPVM by testing for a deeper level of cointegration: multicointegration. The paper finished by analyzing empirically the cases of stock prices and dividens. short-and long-term interest rates and farmland prices. Although the exact PVM is rejected in the first two examples, as the literature has largely reported, we are unable to reject the NEPVM. This fact, together with the theoretical results contained in the paper, suggests that the pro po sed NEPVM could be compatible with sorne of the empírical findings in the literature.