Equity Prices Under Bayesian Doubt About Macroeconomic Fundamentals

I present a consumption-based explanation of a number of phenomena in the aggregate equity market. The model invokes the recursive utility function of Epstein and Zin (1989), configured with the plausible parameters of the average coefficient of the aversion to late resolution of uncertainty of about 22, and the elasticity of intertemporal substitution of 1.5. Statistically hard to discriminate in less than 80 years of data from the ubiquitous model of real consumption growth, the endowment process is specified as being subject to sporadic large shocks and incessant small shocks. The large infrequent shocks, modelled by means of a four-state hidden Markov chain, display interesting macroeconomic regularities, occuring at both the business-cycle, and a lower, frequencies. Despite the fact that the levels of endowments are observable, the source of their variation cannot be detected perfectly, facing investors with a complex signal-extraction problem. The associated posterior probabilities provide a natural link between the observed asset value fluctuations and the economic uncertainty within the rational Bayesian learning framework. Although computationally arduous, having to be solved on a high-performance computing machine in a low-level language, the model is able to account for (i) the observed magnitude of the equity premium, (ii) the low and stable risk-free rate, (iii) the magnitude and the countercyclicality of risk prices, (iv) the average levels and the procyclicality of price-dividend and wealth-consumption ratios, (v) the long-horizon predictability of risk premia, and (vi) the overreaction of price-dividend ratio to bad news in good times, all within the conceptually simple representative-agent framework.