Parameterized Expectations

Overview

We know from Chapter 1 that there are two ways to characterize the solution of a Ramsey problem or, more generally, of a recursive dynamic general equilibrium (DGE) model: (1) in terms of a policy function that relates the model's decision or control variables to the model's state variables or (2) in terms of a system of stochastic difference equations that determines the time paths of the model's endogenous variables. The method presented in this chapter rests on yet a third solution concept. In the Rational expectations equilibrium of a recursive DGE model agents' conditional expectations are time invariant functions of the model's state variables. The parameterized expectations approach (PEA) applies methods from function approximation (see Section 11.2) to these unknown functions. In particular, it uses simple functions instead of the true but unknown expectations and employs Monte Carlo techniques to determine their parameters.

The PEA has several advantages vis-a-vis both the value function iteration approach and the extended path algorithm. In contrast to the former, it does not suffer as easily from the curse of dimensionality and, therefore, can be applied to models with many endogenous state variables. Unlike the latter, it deals easily with binding constraints. Our applications in Section 5.3 illustrate these issues.