Rational Belief Equilibrium Research Articles

Endogenous Fluctuations and the Role of Monetary Policy

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.

Money non-neutrality in a Rational Belief Equilibrium with financial assets

In Rational Beliefs Equilibria money is generically non-neutral. Given the expectational perspective proposed by the Theory of Rational Belief Equilibrium, we show that one of the most important factors in the emergence of money non-neutrality is played by Endogenous Uncertainty. This, in contrast to the Rational Expectations results of money neutrality and policy ineffectiveness, leads to a scenario in which monetary policy has an impact on the real economy and price volatility. The heterogeneity of beliefs together with the distribution and intensity of agents' states of optimism/pessimism can amplify the real effect of monetary policy and/or generate endogenous fluctuations in the economy which are not explained by any exogenous shock. We claim that money non-neutrality is mostly an expectations driven phenomenon. Indeed, additional assumptions of asymmetry of information and/or unanticipated monetary policy are not needed to explain the real effect of monetary policy as it is customary in the New Classical Theory.

Endogenous Uncertainty and Market Volatility

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.

Endogenous Uncertainty: A Unified View of Market Volatility

Endogenous Uncertainty: A Unified View of Market Volatility

Social States of Belief and the Determinants of the Equity Risk Premium in A Rational Belief Equilibrium

September 4, 1997 We review the issues related to the formulation of endogenous uncertainty in rational belief equilibria(RBE). In all previous models of RBE, individual states of belief were the foundation for the construction of the endogenous state space where individual states of belief were described with the method of assessment variables. This approach leads to a lack of anonymity where the belief of each individual agent has an impact on equilibrium prices but as a competitor he ignores it. The solution is to study a replica economy with a finite number of types but with a large number of agents of each type. This gives rise to type-states which are distributions of beliefs within each type. The state space for this economy is then constructed as the set of products of the exogenous states and the social states of belief which are vectors of distributions of all the types. Such an economy leads to RBE which do indeed solve the problem of anonymity. We then study via simulations the implications of the model of RBE with social states for market volatility and for the determinants of the equity risk premium in an RBE. Under i.i.d. assessments one uses the law of large numbers to induce a single social state of belief and we show that the RBE of such economies have the same number of prices as in rational expectations equilibrium (REE). However, the RBE may exhibit large fluctuations if agents are allowed to hold extreme beliefs. Establishing 5% boundary restrictions on beliefs we show that the model with a single social state of belief cannot explain all the moments of the observed distribution of returns. We then introduce correlation among beliefs and this leads to the creation of new social states. We next show that under correlation among beliefs the model simulations reproduce the values of four key moments of the empirical distribution of returns. The observed equity premium is then explained by two factors. First, investors demand a higher risk premium to compensate them for the endogenous increase in the volatility of returns. Second, at any moment of time there are both rational optimists as well as rational pessimists in our financial markets and such a distribution leads automatically to a decrease in the riskless rate and to an increase of the risk premium. We show that correlation among beliefs of agents leads to fluctuations over time in the social distribution of beliefs and such fluctuations add to endogenous volatility and to a higher equilibrium equity risk premium. JEL Classification Numbers: D58, D84, G12.

Endogenous Uncertainty in a General Equilibrium Model with Price Contingent Contracts

This paper views uncertainty and economic fluctuations as being primarily endogenous and internally propagated phenomena. The most important Endogenous Uncertainty examined in this paper is uncertainty which arises when agents do not have structural knowledge and are compelled to make decisions on the basis of their We assume that agents adopt Rational Beliefs as in Kurz [1994a]. The trading of endogenous uncertainty is accomplished by using Price Contingent Contracts (PCC) rather than the Arrow-Debreu contingent contracts. The paper provides a full construction of the price which requires the expansion of the exogenous space to include the state of beliefs. This construction is central to the analysis of equilibrium with endogenous uncertainty and the paper provides an existence theorem for a Rational Belief Equilibrium with PCC. It shows how the PCC completes the markets for trading endogenous uncertainty and lead to an allocation which is Pareto optimal. The paper also demonstrates that endogenous uncertainty is generically present in this new equilibrium.

Coordination and correlation in Markov rational belief equilibria

This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.

Rational belief structures and rational belief equilibria

Rational belief structures and rational belief equilibria

Rational belief structures and rational belief equilibria

The paper introduces some simplifying tools and methods for studying Rational Beliefs and for proving existence of Rational Belief Equilibria. We identify a set of stable non-stationary stochastic processes, named SIDS processes. Furthermore we introduce the concept of a Rational Belief Structure, which formulates the Rational Beliefs of the agents as beliefs about the distribution of exogenous variables and the beliefs of other agents. The use of the developed apparatus is demonstrated by showing existence of a set of Rational Belief Equilibria in an Overlapping Generations Model with money and one commodity.

Coordination and correlation in Markov rational belief equilibria

Coordination and correlation in Markov rational belief equilibria

Endogenous uncertainty in a general equilibrium model with price contingent contracts

This paper views uncertainty and economic fluctuations as being primarily endogenous and internally propagated phenomena. The most important Endogenous Uncertainty examined in this paper is price uncertainty which arises when agents do not have structural knowledge and are complelled to make decisions on the basis of their beliefs. We assume that agents adopt Rational Beliefs as in Kurz [1994a]. The trading of endogenous uncertainty is accomplished by using Price Contingent Contracts (PCC) rather than the Arrow-Debreu state contingent contracts. The paper provides a full construction of the “price state space” which requires the expansion of the exogenous state space to include the “state of beliefs.” This construction is central to the analysis of equilibrium with endogenous uncertainty and the paper provides an existence theorem for a Rational Belief Equilibrium with PCC. It shows how the PCC completes the markets for trading endogenous uncertainty and lead to an allocation which is Pareto optimal. This paper also demonstrates that endogenous uncertainty is generically present in this new equilibrium.

On rational belief equilibria

We study equilibria in which agent's belief are rational in the sense of Kurz [1994]. The market is formulated by specifying a stochastic demand function and a continuum of producers, each with a quadratic cost function who must select their output before knowing prices. Holding Rational Beliefs about future prices, producers maximize expected profits. In a Rational Belief Equilibrium (RBE) agents select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data. It is shown that there exists a continuum of RBE's and they could entail very different patterns of time series for the economy and consequently different aggregate levels of longterm volatility. Since the model contains exogenously specified random variables, the difference in the level of long-term volatility of prices among the different RBE's arises endogenously as an “amplification” of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such “amplification.”