and the equity premium would be zero. This works out because if the path of consumption and output are known with certainty at each date, then the investor's utility is also fixed. Consequently, the existence of a return premium can only be as a payment to the investor for accepting volatility in future consumption. Equation (5.2) gives us a road map for pinning down the size of the premium. Since the utility function depends on the mean and variance of the path of consumption, the level of risk aversion, and the rate of intertemporal substitution, it is reasonable that the asset pricing equation should depend on the same parameters. Thus, Mehra and Prescott propose the following: If we know the mean and variance of current and future consumption, the willingness to trade consumption across time, and the level of risk aversion, then we should be able to pin down the size of the equity premium. How would the parameters of the utility function and the economy (e.g., the average growth rate and variance of consumption) affect the equity premium? Intuitively, more uncertainty about future consumption (expressed, say, through the variance in consumption) should increase the equity premium. The reason for this is because more uncertainty about future consumption translates into more uncertainty about current utility. Similarly, since higher levels of risk aversion have a pronounced impact on utility they should be accompanied by increases in the equity premium, all else being equal. Finally, if an investor were not very willing to substitute future consumption for current consumption, then the equity risk premium should increase. To test their model, Mehra and Prescott directly estimate the variance of consumption, and find it to be quite low. They rely on the work of other researchers to pin down (or, in the parlance of real business cycle theorists, calibrate) the value of a. More specifically, Mehra and Prescott propose that values of a larger than 10 are not supported by the literature. They focus instead on values of a between one and two. They focus on values of |3 consistent with discount rates between 1 percent and 2 percent. The results of their analysis are quite provocative. What they find is that under reasonable assumptions about the mean and variance of consumption, and the willingness of investor/consumers to trade consumption across time, the value of the equity premium should be 40 basis points. This value is quite small relative to the historical average (at the time Mehra and Prescott wrote, the historical average was around 600 basis points). Consequently, Mehra and Prescott coined the term "the equity premium puzzle" to describe the difference between the historical average and the theoretical value of the equity risk premium. While the model that Mehra and Prescott used to analyze the equity premium is elegant, it is nonetheless an abstraction. In particular, this model assumes a particular utility function and that investors may trade in markets without frictions. As it turns out, in the absence of frictions, it is difficult to construct a function for investor preferences that reconciles observed equity returns with the standard axioms of utility theory used in economics. In response to this dilemma, Epstein and Zin (1991) propose a nonstandard utility function that can explain the equity premium puzzle without frictions. The more accepted resolution to the puzzle is to introduce frictions, an approach that Mehra and Prescott suggest in their original paper.