I show that the Parameterized Expectations Algorithm (PEA) can be naturally generalized via the bias-corrected Monte Carlo (bc-MC) operator, initially proposed to solve economic models using neural networks. When combined with a parameterized …
Introduction This blog post is about my work on a generalization of the Parameterized Expectations Algorithm, available here.
The Parameterized Expectations Algorithm (PEA) is a classic computational approach to numerically “solve” economic models with rational expectations, i.e. finding an approximate solution. Usually, to solve economic models of this type, one has to find a policy function (e.g. how much to consume today, given a current level of capital) that satisfies a functional equation that holds in expectation (e.g. the Euler equation). The PEA flips this idea on its head: if we know the expectation term, we can recover the unknown policy function. For several reasons, this works better this way.
Introduction In this blog post, I am going to present my recent work on the bias-corrected Monte Carlo operator, or more compactly “bc-MC operator”, which was recently published here in the JEDC. In this paper, I propose a new methodology to combine Monte Carlo and neural networks to solve large scale economic models. In this blog post, my goal is to give an intuitive description of this method.
Theory Structure of economic models In many cases, solving an economic model involves finding a policy function \(g(.)\), which is a mapping from a state vector \(s\) to a decision vector \(a\). Usually, it is assumed that the economy is hit by random disturbances, which is usually modelled as zero-mean innovation vector \(\varepsilon\), often considered to be normally distributed. The policy function \(g(.)\) is such that the following stochastic equation holds: