Introduction

In order to achieve her goals, an agent must decide a line of action (a behavioral rule). Mental representations of the environment and of the behavior of other agents are key in taking this decision. The availability of an adequate and appropriate information set and of cognitive capabilities to process information, in turn, are key in forming these mental models. In a context characterized by uncertainty, one of the most important cognitive process is expectation formation. In this chapter we overview the way in which rationality, behavioral rules and expectation formation are connected in modern macroeconomics.

In Section 4.2 we set the stage by discussing (optimal) decision-making in an environment of full rationality and certainty. From Section 4.3 on, we discuss the consequences of uncertainty – in its wide range of specifications – and expectation on individual decision making and on macroeconomic performance.

Section 4.3 is devoted to the theory of choice in the presence of measurable uncertainty (risk). Uncertainty is measurable when agents are able to attach probabilities to uncertain events. In this setting the probability distribution of the variable of interest replaces the true value of the variable (which is available only in the case of certainty) in the information set of the agent. We will provide simple examples of choice in the case of risk neutrality (Subsection 4.3.1) and risk aversion (Subsection 4.3.2). Moreover, we will discuss choice in a multi-period setting (Subsection 4.3.3).

We will show that it is straightforward, and extremely useful, to extend the notion of measurable uncertainty discussed in Subsections 4.3.1 and 4.3.2 to the multi-period setting. Also in a multi-period context, in fact, the true values of the variables of interest are replaced by probability distributions.

The Rational approach to Expectation formation (RE) is the natural candidate to model expectations in such a setting. In fact we introduce a Linear Stochastic Difference Equation at this early stage of the analysis.

We illustrate its solution by means of a graphical tool which exploits the two-way relationship between current and expected value of a variable of interest. The true (or actual or current) value of variable x is a function of the expectation of the same variable xe, in symbols x = f (xe) (represented by the True Value, or TV, schedule).