Do Consumption-Based Asset Pricing Models Explain Own-History Predictability in Stock Market Returns?

We show that three prominent consumption-based asset pricing models - the Bansal-Yaron, Campbell-Cochrane and Cecchetti-Lam-Mark models - cannot explain the own-history predictability properties of stock market returns. We show this by estimating these models with GMM, deriving ex-ante expected returns from them and then testing whether the difference between realised and expected returns is a martingale difference sequence, which it is not. Furthermore, a semi-parametric test suggests that lagged returns have too much predictive power over current returns to be consistent with the state variables which explain market returns being the same as the state variables which explain market returns in any of the three models