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Abstract:
Endogenous Uncertainty is that component of economic risk and market volatility which is propagated within the economy by the beliefs and actions of agents. The theory of Rational Belief (see Kurz [1994]) permits rational agents to hold diverse beliefs and consequently, a Rational Belief Equilibrium (in short, RBE) may exhibit diverse patterns of Endogenous Uncertainty. This paper shows that most of the observed volatility in financial markets is generated by the beliefs of the agents and the diverse market puzzles which are examined in this paper, such as the equity premium puzzle, are all driven by the structure of market expectations. To make the case for this theory we present a single RBE model, which builds on developments in Kurz and Beltratti [1997] and Kurz and Schneider [1996], with which we study a list of phenomena that have been viewed as "anomalies" in financial markets. The model is able to predict the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio;(ii) the long term mean and standard deviation of the risky rate of return on equities;(iii) the long term mean and standard deviation of the riskless rate;(iv) the long term mean equity premium.In addition, the model predicts (v) the GARCH property of risky asset returns;(vi) the Forward Discount Bias in foreign exchange markets.We also conjecture that an adaptation of the same model to markets with derivative assets will predict the appearance of "smile curves" in derivative prices.The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs. Given such diversity, some agents are optimistic and some pessimistic. We develop a simple model which allows agents to be in these two states of belief but the identity of the optimists and the pessimists fluctuates over time since at any date any agent may be in these two states of belief. In this model there is a unique parameterization under which the model makes all the above predictions simultaneously. That is, although the parameter space of the RBE is large, all parameterizations outside a small neighborhood of the parameter space fail significantly to reproduce some subset of variables under consideration. Any parameter choice in this small neighborhood requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. This higher intensity has a decisive effect on the market: it increases the demand for riskless assets, decreases the equilibrium riskless rate and increases the equity premium. In simple terms, the large equity premium and the lower equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The relative impact of these two groups of agents who are, at any moment of time, in the two states of belief is a direct consequence of the rationality of belief conditions and in that sense it is unique to an RBE. As for the correlation among the beliefs of agents, the paper shows that the dynamics of asset prices are strongly affected by such correlation. The pattern of correlation which was used in the model can be explained intuitively in terms of its effect on the dynamics of prices. The model correlation causes periods of price rises (i.e. bull markets) to develop slower than periods of decline (i.e. bear markets) hence the model dynamics do not permit prices to shoot directly from the bottom to the top but the opposite is possible and takes the form of market crashes.

Abstract:
Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental state variables. Market belief is observable, it is central to the empirical evaluation and we show how to extract it from the data. The asset pricing model we use is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive the equilibrium asset pricing and the implied risk premium. Our approach permits a closed form solution of prices hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions.

Our main result is that, above and beyond the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3-month and 6-month Treasury Bills. The annualized mean risk premium on holding such assets for 1-12 months is about 40-60 basis points and, on average, we find that the component of market belief in the risk premium at a random date exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2 months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. "bull" markets) are shown to be periods when the market risk premium declines while in periods of pessimism (i.e. "bear" markets) the market's risk premium rises. Hence, fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant.

Risk premium, heterogenous beliefs, market state of belief, asset pricing, Bayesian learning, updating beliefs, Rational Beliefs

Abstract:
This paper studies the dynamic volatility properties of a monetary economy in which agents hold Rational Beliefs (see Kurz (1994), (1997)) rather than Rational Expectations. Except for this feature the examined Rational Belief Equilibrium (in short, RBE) is entirely standard: markets are competitive, prices are flexible and all information is symmetric. The paper demonstrates

a) The RBE paradigm offers an integrated theory of real and financial volatility with a high volume of trade. Most volatility in an RBE is induced endogenously through the beliefs of agents.

b) Although our RBE assumes fully competitive markets in which prices are fully flexible,the diverse expectations of agents can explain most of the familiar features of monetary equilibria. This includes, money non-neutrality, Phillips curve and impulse response functions with respect to monetary shocks.

c) Agents with diverse but inconsistent beliefs may induce socially undesirable excess fluctuations even when the allocation is ex-ante Pareto optimal. Central bank policy should aim to reduce the endogenous component of this volatility.

Abstract:
We show diverse beliefs is an important propagation mechanism of fluctuations, money non neutrality and efficacy of monetary policy. Since expectations affect demand, our theory shows economic fluctuations are mostly driven by varying demand not supply shocks. Using a competitive model with flexible prices in which agents hold Rational Belief (see Kurz (1994)) we show that (i) our economy replicates well the empirical record of fluctuations in the U.S. (ii) Under monetary rules without discretion, monetary policy has a strong stabilization effect and an aggressive anti-inflationary policy can reduce inflation volatility to zero. (iii) The statistical Phillips Curve changes substantially with policy instruments and activist policy rules render it vertical. (iv) Although prices are flexible, money shocks result in less than proportional changes in inflation hence the aggregate price level appears "sticky" with respect to money shocks. (v) Discretion in monetary policy adds a random element to policy and increases volatility. The impact of discretion on the efficacy of policy depends upon the structure of market beliefs about future discretionary decisions. We study two rationalizable beliefs. In one case, market beliefs weaken the effect of policy and in the second, beliefs bolster policy outcomes and discretion could be a desirable attribute of the policy rule. Since the central bank does not know any more than the private sector, real social gain from discretion arise only in extraordinary cases. Hence, the weight of the argument leads us to conclude that bank's policy should be transparent and abandon discretion except for rare and unusual circumstances. (vi) An implication of our model suggests the current effective policy is only mildly activist and aims mostly to target inflation.

Monetary policy rules, Money non neutrality, Business cycles, Market volatility, Propagation mechanism, Capacity utilization, Heterogenous beliefs, Over confidence, Rational Belief, Optimism; Pessimism, Non stationarity, Empirical distribution