Mordecai Kurz

On the structure and diversity of rational beliefs

SummaryThe paper proposes that the theory of expectations be reformulated under the assumption that agents do not know the structural relations (such as equilibrium prices) of the economy. Instead, we postulate that they can observe past data of the economy and form probability beliefs based on the data generated by the economy. Using past data agents can compute relative frequencies and the basic assumption of the theory is that the system which generates the data is stable in the sense that the empirically computed relative frequencies converge. It is then shown that the limit of these relative frequencies induce a probability on the space of infinite sequences of the observables in the economy. This probability is stationary. Abelief of an agent is a probability on the space of infinite sequences of the observable variables in the economy. Such a probability represents the “theory” or ∌ypothesis” of the agent about the mechanism which generates the data. A belief is said to becompatible with the data if under the proposed probability belief the economy would generate the same limit of the relative frequencies as computed from the real data. A theory which is “compatible with the data” is a theory which cannot be rejected by the data. A belief is said to be aRational Belief if it is (i) compatible with the data and (ii) satisfies a certain technical condition. The Main Theorem provides a characterization of all Rational Beliefs.

Endogenous Uncertainty and Market Volatility

Abstract. We advance the theory that the distribution of beliefs in the market is the most important propagation mechanism of economic volatility. Our model is based on the theory of Rational Beliefs (RB) and Rational Belief Equilibrium (RBE) developed by Kurz (1994, 1997). We argue that the diverse market puzzles which are examined, such as the equity premium puzzle, are all driven by the structure of market expectations. In support of our view, we present an RBE model with which we study financial markets. The model is able to simulate 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 observed pattern of the predictability of long returns on assets, and (vii) the Forward Discount Bias in foreign exchange markets. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs such that some agents are optimistic and some pessimistic about future capital gains. The model has a unique parameterization under which the model makes all the above predictions simultaneously. The parameterization 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. In simple terms, the large equity premium and the low 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 paper also studies the effect of correlation of beliefs among investors. It shows that the main effect of such correlation is on the dynamic patterns of asset prices and returns and is hence important for studying such phenomena as stochastic volatility.

On Rational Belief Equilibria

SummaryWe study equilibria in which agents 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 RBEs 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 RBEs arises endogenously as an “amplification” of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such “amplification.”

The General Instability of a Class of Competitive Growth Processes

In recent papers [1, 2] Frank Hahn has raised serious doubts regarding the stability properties of neoclassical growth theory.

TECHNOLOGY AND SCALE IN ELECTRICITY GENERATION

The question of returns to scale in public utilities is a much debated issue. In this study, the productive process of electricity generation is examined and a modified substitution model is employed, permitting differentiation between returns to scale to labor and to other factors. The method employed here allows us to isolate the impact of technological progress on (steam) electricity generation. We find that increasing returns to scale prevail throughout, and that the main impact of technology was registered during the 1950s. This study covers the period 1937-59.

Equilibrium in a Finite Sequence of Markets with Transaction Cost

Publisher Summary The work extends the results of an earlier paper by Hahn ; it presents a model of a barter economy with a sequence of markets in which each trader operates with his own transaction technology. An equilibrium is proved to exist and the efficiency of equilibrium is discussed.

Power and Taxes in a multi-commodity economy

Taxation and redistribution in a democratic majority-rule society are analyzed, using the Harsanyi-Shapley non-transferable utility value. The context is that of a multi-commodity pure exchange economy. Two approaches are treated: one in which taxes are in kind and exchange takes the form of barter; and one in which taxes are in money, exchange takes the form of sale and purchase, and prices are determined by a process of supply and demand. It is shown that in the presence of a non-atomic continuum of agents, the two approaches are equivalent, but that this is not so when there are only finitely many agents. It is also shown that the value exists under both approaches, and a characterization is found in the non-atomic case.

Coordination and Correlation in Markov Rational Belief Equilibria

SummaryThis 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 others effect on market demand and resulting in reduced price volatility.

Unemployment equilibrium in an economy with linked prices

Wage inflexibility has been widely regarded in modern writing as a cause of unemployment. Almost any Keynesian or non-Walrasian equilibrium which involves equilibrium excess supplies also contain some form of wage or price inflexibility. Yet the micro mechanism of wage inflexibility, its causes and form remains somewhat a mystery. In this paper we study the allocation of resources in an economy in which prices of some goods or services are linked to other goods or services. This is not wage “rigidity” in the traditional sense but it is a form of rigidity which is widely observed. Following the recent literature on non-Walrasian equilibrium (see, for example, Dreze (1975), Barro and Grossman (197 l), Grandmont and Laroque (1976), Malinvaud (1977) and many others) one would expect the allocation to be attained via a set of quantity constraints on net trades. We show in this paper, however, that the allocation mechanism in the economy will not require a general set of limitations on excess supplies and excess demands but rather will tend to have the following two properties:

Experimental approach to the determination of the demand for public goods

Abstract The paper proposes a new method of estimating the demand for public goods in view of the ‘free rider’ problem. The idea is to establish an experimental setting in which only a random sample of the population is investigated. Alternative experiments are then proposed with the intent of discovering the true individual demand. First a statistical method is proposed to estimate the bias in response. Then, a random environment is created and it is shown under what conditions a successful elicitation of the demand is possible.