Equity Premium and Dividend Yield regressions: A lot of noise, little information, confusing results

Suppose that the equity premium is forecasted by dividend yields. Even if such a relationship does exist, there is so much noise in the equity premium that estimation, inference and forecasting cannot be carried out using the faint signal coming from the dividend yields. For analyzing equity/dividend data, it is useful to quantify the signal in a given sample. We define an index of signal strength or information accumulation, by renormalizing the signal to noise ratio. The novelty in our parameterization is that the index of information accumulation explicitly influences rates of convergence and can even lead to inconsistent estimation, inconsistent testing, unreliable R^20s and no out of sample forecasting power. Indeed, we prove that if the signal to noise ratio is close to zero, forecasts from the existing model will not do better than the simple unconditional mean. Thus, it is not surprising that dividend yield forecasts of the equity premium cannot outperform its mean. The analytic framework is general enough to capture most previous econometric findings related to the equity/dividend relationship.