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## Über dieses Buch

1. 1 Motivation and Definition of Topic To provide motivation and to help define the topic of this study, important links between specific areas of economic theory are first highlighted. (i) Learning and Rational Expectations Theory In a standard rational expectations setting, agents in equilibrium have all the information about the model that enables them to correctly forecast future payoff-relevant variables. What rational expectations theory in its standard form does not tell us is what happens outside a rational expectations equilibrium. Less than complete knowledge of the model is a possible way to represent a situation outside the rational expectations equilibrium. It is natural to assume that agents recognize error and optimally utilize all available external information to improve on their information level, i. e. learn. Based on the information acquired by learning they modify their behavior. Under certain conditions learning steers the economy to the rational expectations equilibrium (Spear (1989), Blume, Bray and Easley (1982), Townsend (1983». This literature shows that learning is a possible mechanism to acquire the necessary level of information that agents are assumed to possess in a rational expectations equilibrium and hence there is a clear link between rational expectations theory and the 2 theory of learning. This fact is also emphasized among others by Friedman (1975), Pesaran (1987) and DeCanio (1979). (ii) Rational Expectations and Econometrics The equilibrium consequences of the rational expectations hypothesis are discussed in a considerable body of literature - cf.

## Inhaltsverzeichnis

### I. Introduction

Abstract
To provide motivation and to help define the topic of this study, important links between specific areas of economic theory are first highlighted.
Balazs Horvath

Abstract
The theoretical foundations for this class of models have been summarized in Easley and Kiefer (1988). A discrete time decision problem is considered where the decisionmaker chooses an action r in each period to maximize total expected discounted reward depending on the action chosen and the outcome, a random variable. The conditional distribution f(.|r, ß) of the outcome given the action depends on an initially unknown parameter ß. The decisionmaker begins with a prior belief about the unknown parameter and at the end of each period updates it via Bayes’ rule utilizing the latest observations on the action taken and the outcome. Easley and Kiefer take the additional simplifying step of integrating out the outcome and redefining the maximand to be the total expected discounted mean reward where the mean is calculated with respect to the conditional distribution f(.|r,ß) and the belief distribution.
Balazs Horvath

### III. Econometric Implications

Abstract
Having formalized the concept of learning and the evolution of beliefs in a specific example we now proceed to show what the implications of learning for econometric practice are. Most of the concepts needed for this have now been defined, but some further technical econometric definitions will prove helpful by facilitating precise description of the effects.
Balazs Horvath

### IV. Simulation

Abstract
This chapter describes a simulation exercise based on variants of the first specification of the theoretical model presented in chapter II. Following the description of the design and the goals of the simulation, the algorithms for obtaining the passive learning and active learning sequence of controls are described. The insights yielded by the exercise are then presented separately for the case of passive and active learning. The software used was Gauss 1.49B.
Balazs Horvath

### V. Tests for Exogeneity

Abstract
Engle, Hendry and Richard (1983) and Hendry and Richard (1983) argue in a convincing manner that their notion of exogeneity is the natural one to use instead of classical (strict) exogeneity if the goal of the econometric ian is to use the simplest possible model without loss of relevant statistical information. Geweke (1984) on the other hand reveals the opposite side of the coin: while it is weak exogeneity that we are really after, that concept by itself cannot generate refutable hypotheses (see also Basmann (1965)). In other words, a model can always be constructed and parameters of interest can be chosen for which a designated set of variables is weakly exogenous — a simple way to do this is to specify the conditional model and the marginal model independently. Therefore weak exogeneity by itself does not supply enough restrictions that it can be subjected to statistical tests. So, in order to make weak exogeneity operational, concepts that generate empirically refutable hypotheses and which under reasonable assumptions are compatible with weak exogeneity are needed. And here is where we come a full circle: strict exogeneity is such a concept — though not the only one. Testing for strict exogeneity is possible (Sims (1972), Williams, Goodhart and Gowland (1976), Ciccolo (1978)), and such tests can be interpreted as joint tests of strict exogeneity and the assumptions that link weak exogeneity to strict exogeneity.
Balazs Horvath

### VI. Summary, Directions for Future Research

Abstract
The study has explored the econometric implications of the presence of an agent in the data generating mechanism who performs learning. It related the issues addressed to major areas in the literature. An illustrative model was presented in which even in the absence of any explicit dynamics the problem became nontrivial and dynamic by virtue of the presence of learning about the unknown parameter. The agent had to strike an optimal balance between current payoff maximization and generation of information in the future. The distinction between active and passive learning was made. On the basis of an argument on the curvature of the value function arising in the problem, active learning was shown to be generically optimal.
Balazs Horvath

### Backmatter

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