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We study a Lucas asset-pricing model that is standard in all respects, except that the representative agent’s subjective beliefs about endowment growth are distorted. Using constant-relative-risk-aversion (CRRA) utility, with a CRRA coefficient below ten, and fluctuating beliefs that exhibit, on average, excessive pessimism over expansions , and excessive optimism over contractions (both ending more quickly than the data suggest), our model is able to match the first and second moments of the equity premium and risk–free rate, as well as the persistence and predictability of excess returns found in the data. (JEL E44, G12) The Ohio State University and N.B.E.R; The Ohio State University; and The Ohio State University, respectively. We have benefited from comments from seminar participants at the University of Canterbury, the Chinese University of Hong Kong, Erasmus University, the Federal Reserve Bank of New York, Georgetown University, Michigan State University, the University of Montreal, Ohio State University, Victoria University of Wellington, and the University of Wisconsin. We thank Peter Bossaerts, John Campbell, Martin D.D. Evans, Peter Howitt, J. Huston McCulloch, James Nason, and two anonymous referees for useful comments on earlier drafts. Some of this work was conducted while Cecchetti was visiting the Department of Economics at the University of Melbourne, and while Mark was visiting the Tinbergen Institute, Rotterdam. Ever since Rajnish Mehra and Edward Prescott (1985) first articulated the equity premium puzzle, achieving an understanding of aggregate asset-price dynamics has occupied a central role in macroeconomic research. In their original statement of the problem, Mehra and Prescott asked whether the rational, complete markets asset-pricing model where the representative investor has constant relative risk aversion (CRRA) utility with a coefficient below 10 and a discount factor between 0 and 1, could account for the approximately 8 percent per annum sample mean return on the Standard and Poor’s index and the approximately 2 percent per annum sample mean return on relatively risk-free short-term bonds. Their answer was a resounding no, and the inability of that model to explain the first moment of asset-returns data has come to be known as the equity premium puzzle. The list of challenges taken up by aggregate asset-pricing theory has grown substantially since Mehra and Prescott’s original investigation. In addition to the mean equity premium and risk-free rate, this paper seeks to understand the volatility, persistence and long-horizon predictability of asset returns as well as their relationship to the business cycle. Because the power of models with common knowledge and fully rational agents to explain these aspects of asset-return dynamics has been poor [see Narayana R. Kocherlakota (1996) for a survey of this research], we take an alternative approach that allows for small departures from rationality in an otherwise standard Robert E. Lucas, Jr. (1978) representativeagent asset-pricing model of an endowment economy. The agents in our model satisfy the Mehra–Prescott criteria of having CRRA utility with a relative risk aversion coefficient below 10 and a discount factor below 1. Agents observe that the actual endowment process shifts stochastically between high and low growth states, but their beliefs about the transition probabilities that govern this switching deviate from the true probabilities. These belief distortions enter along two empirically plausible dimensions. First, we introduce systematic deviations of the subjective probabilities of transitions between high and low growth states. We motivate these distortions by showing how agents who use simple rules of thumb to estimate the transition probabilities governing endowment growth will form subjective probabilities that deviate from maximum likelihood estimates (MLE) obtained from U.S. per-capita consumption growth data. Rule-of-thumb estimates that imply relatively pessimistic beliefs about the persistence of the expansion state (with the subjective probability of continuation being lower than that the MLE) and relatively optimistic beliefs about the persistence of the contraction state (with the subjective probability of continuation being lower than the MLE), allow us to match the mean equity premium and risk-free rate found in the data and solve the equity premium puzzle. Unfortunately, systematic distortions alone are not sufficient to explain the volatility of