The Precision of Unconditional Estimators of the Equity Premium

Abstract

This paper has the purpose of providing unconditional estimators of the equity premium. In plain words the estimators are obtained by the constants in regressions of the equity premium on a constant. More than one specification is tried and more than one type of standard errors is implemented. The specifications include ordinary least squares, EGARCH, robust least squares, quantile regressions, and Markov switching regressions with two regimes. The analysis is repeated by adding in categorical variables that correspond to outliers. Theoretically these estimators of the equity premium are unbiased and consistent. All models are subjected to serial correlation tests on the residuals. These tests support the absence of serial correlation. This is conducive to the conclusion that the models are well specified and that the estimators are not only unbiased and consistent but also efficient. The paper gives point estimates and 95% confidence intervals of the equity premium, develops hypothesis tests, and reports point estimates of the standard errors. The results may help in assessing the magnitude of the equity premium and the precision with which this premium is measured. Keywords: Equity premium, Unconditional estimators, Robust standard errors, EGARCH, Ordinary least squares, Robust least squares, Quantile regressions, Markov switching regressions, Categorical outlier variables 1. Introduction The size of the equity risk premium has been the subject of intense investigation. Based on this research it is inferred that the equity premium is surely much larger than the short term T-bill rate. What is lacking in the literature is the extent of precision in estimating the equity premium. Rare are the studies that provide a standard error for the estimated equity premium. Dimson et al. (2008) are an exception. Other academicians, like Fama and French (2002) and Goetzmann and Ibbotson (2006), report point estimates and standard deviations from which it is difficult to derive standard errors. This paper finds that these standard errors are relatively large. Thus the major purpose of this paper is to offer as many precision estimates as possible by varying the model that is specified, while keeping these models simple. Two unbiased estimators of the equity premium are the unconditional mean and the unconditional median. The latter estimator is a natural input in quantile regressions. The first unconditional estimator can be obtained easily from a regression of the premium on a constant, and the precision of estimation is the precision with which this constant is estimated. More than one variant of this basic model is attempted. There is more disparity than commonness in the results. Especially crucial is whether or not the standard errors need to be adjusted for serial correlation and heteroscedasticity. Robust standard errors tend to produce larger standard errors, and consequently less precision. In addition each variant specification provides for a point estimate of the equity premium that is generally different ...