On the solution of the variational optimisation in the rational inattention framework

TL;DR

This paper critically examines the solution existence in the variational optimisation problem within the rational inattention framework, revealing non-existence in common cases and limited solutions under specific restrictions.

Contribution

It demonstrates that solutions generally do not exist for key objective functions in the rational inattention model, highlighting limitations of the existing solution method.

Findings

Solution generally does not exist for quadratic and logarithmic objectives.

A solution can be constructed for linear-quadratic objectives under parameter restrictions.

The approach is unlikely to be broadly applicable to diverse economic models.

Abstract

I analyse the solution method for the variational optimisation problem in the rational inattention framework proposed by Christopher A. Sims. The solution, in general, does not exist, although it may exist in exceptional cases. I show that the solution does not exist for the quadratic and the logarithmic objective functions analysed by Sims (2003, 2006). For a linear-quadratic objective function a solution can be constructed under restrictions on all but one of its parameters. This approach is, therefore, unlikely to be applicable to a wider set of economic models.