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

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, primitive, state variable. Market belief is observable, it is central to the empirical evaluation and we show how to measure it. 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 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 annual mean risk premium on holding such assets for 1-12 months is about 40-60 basis points and we find that, on average, the component of market belief in the risk premium 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

Abstract: We present a theoretical and empirical evaluation of the role of market belief in the structure of risk premia. To that end we employ a familiar asset pricing model for which we develop in detail the belief structure. The novelty in this development is the treatment of individual and market beliefs as Markov state variables. Moreover, the market belief is observable and the paper explains how we extract it from the data. The advantage of our formulation is that it permits a closed form solution of equilibrium prices hence we can trace the exact effect of market belief on the time variability of equilibrium risk premia. We present a model of asset pricing with diverse beliefs. We then explore the conditions under which diverse beliefs arise. We then derive the equilibrium asset pricing and the risk premium which the model implies. Since asset prices are affected by the dynamics of market belief, the component of market risk which is determined by the belief of agents is thus termed "Endogenous Uncertainty." The theoretical conclusions are tested empirically for investments in the futures markets, the bond markets. Our main theoretical and empirical result is that fluctuations in the market belief about state variables are a dominant factor determining the time variability of risk premia. More specifically, we show that when the market holds abnormally favorable belief about future payoffs of an asset the market views the long position as less risky and hence the risk premium on that asset declines. This means that fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is very strong and empirically very dominant. The strong effect of market belief on market risk premia offers two additional perspectives. First, it offers an additional way of showing (for those who have any doubt) that fundamental factors affect market dynamics but perceptions have equally important effect on volatility. Second, that market belief is actually an observable data which can be used for a deeper understanding of the basic causes of stochastic volatility and time variability of risk premia. JEL classification: D82, D83, D84, G12, G14, E27.

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Abstract: The paper contrasts theories that explain diverse belief by asymmetric private information (in short PI) with theories which postulate agents use subjective heterogenous beliefs (in short HB). We focus on problems where agents forecast aggregates such as profit rate of the S&P500 and our model is similar to the one used in the literature on asset pricing (e.g. Brown and Jennings (1989), Grundy and McNichols (1989), Allen, Morris and Shin (2006)). We first argue there is no a-priori conceptual basis to assuming PI about economic aggregates. Since PI is not observed, models with PI offer no testable hypotheses, making it possible to prove anything with PI. In contrast, agents with HB reveal their forecasts hence data on market belief is used to test hypotheses of HB. We show the common knowledge assumptions of the PI theory are implausible. The theories differ on four main analytical issues. (1) The pricing theory under PI implies prices have infinite memory and at each t depend upon unobservable variables. In contrast, under HB prices have finite memory and depend only upon observable variables. (2) The “Beauty Contest” implications of the two are different. Under PI today’s price depends upon today’s market belief about tomorrow’s mean belief which is correct and depends upon supply shock and inference from prices. Under HB it depends upon today’s market belief about tomorrow’s market beliefs. Tomorrow’s beliefs are, in part, beliefs about future beliefs and

Beauty contests under private information and diverse beliefs: how different?

www.elsevier.com/locate/jedc The role of expectations in economic fluctuations and the efficacy of monetary policy

Abstract: The paper contrasts implications of theories which explain diverse belief by asymmetric private information (in short PI) with theories which postulate agents use heterogenous probability models (in short HB). We focus on the use of such theories in solving problems where agents forecast economic aggregates such as the S&P500, growth rate of GDP, inflation rates, etc. We study implications of the two asset pricing theories with a model where each agents trades for two periods. Such a model has been used extensively in the literature on asset pricing (e.g. Brown and Jennings (1989), Grundy and McNichols (1989), Allen, Morris and Shin (2005)). On conceptual grounds we find that there is no basis to assuming PI about economic aggregates. In contrast, HB theories are naturally suited. Since PI is not observed, models with PI offer little in the way of testable hypotheses, making it possible to prove anything with PI. In contrast, agents who hold HB are happy to reveal their forecasts hence there is vast data on market belief which can be used to test hypotheses about the effect of diversity. The two asset pricing models differ on several central issues. (i) Models with PI introduce artificial “noise” such as unobserved shocks to the supply of securities to explain diversity of forecasts but diversity does not persist. It vanishes as the number of trading rounds increases. In contrast, HB theories have a natural renewal mechanism to explain the perpetual persistence of diversity; (ii) under both theories the market belief fails iterated expectations but, in economic substance, the Beauty Contest implications of the two are different. Under PI today’s price depends upon

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Diverse beliefs is an important mechanism for propagation 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 change in inflation hence aggregate price level is “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, 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, discretion is beneficial only in extraordinary cases. Hence, the weight of the argument suggests that policy should be transparent and abandon discretion except for rare