Econometric implications of non-exact present value models

Abstract

One of the most commonly used and, at the same time, rejected models in nance 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 extends the PVM by making it non-exact (NEPVM) in a simple way, allowing us to study situations where there are transitory deviations from the exact PVM. The proposed NEPVM is derived from similar non-arbitrage or equilibrium conditions the exact PVM comes from and it can explain some stylized economic facts that cannot be explained by exact PVMs. The rejection of the exact PVM produced by the standard volatility and cross-equation restriction tests is not enough to reject the NEPVM. We present the new variance bounds and crossequation restrictions implied by the NEPVM and we show how to test them. The paper nishes by analyzing empirically the cases of stock prices and dividends, and short- and longterm interest rates. For these cases we are unable to reject a simple NEPVM. This fact, together with the theoretical results contained in the paper, suggests that the proposed NEPVM could be compatible with some of the empirical finndings in the literature.