Estimating the Equity Premium

Existing empirical research investigating the size of the equity premium has largely consisted of a series of innovations around a common theme: producing a better estimate of the equity premium by using better data or a better estimation technique. The equity premium estimate that emerges from most of this work matches one moment of the data alone: the mean difference between an estimate of the return to holding equity and a risk-free rate. We instead match multiple moments of U.S. market data, exploiting the joint distribution of the dividend yield, return volatility, and realized excess returns, and find that the equity premium lies within 50 basis points of 3.5%, a range much narrower than was achieved in previous studies. Additionally, statistical tests based on the joint distribution of these moments reveal that only those models of the conditional equity premium that embed time variation, breaks, and/or trends are supported by the data. In order to develop the joint distribution of the dividend yield, return volatility, and excess returns, we need a model of price and return fundamentals. We document that even recently developed analytically tractable models that permit autocorrelated dividend growth rates and discount rates impose restrictions that are rejected by the data. We therefore turn to a wider range of models, requiring numerical solution methods and parameter estimation by the simulated method of moments.