Price Levels in Heterogeneous-Agent Models

TL;DR

This paper analyzes a continuous-time heterogeneous-agent model of the Fiscal Theory of the Price Level, demonstrating the existence of multiple equilibria with different price levels due to constant primary deficits.

Contribution

It establishes the existence of multiple stationary equilibria in a continuous-time heterogeneous-agent model with fiscal policy, linking mean-field game theory to price level analysis.

Findings

Existence of two stationary equilibria with constant primary deficits

Multiple price levels can coexist in the model

Mathematical proof of equilibrium multiplicity

Abstract

We study a model of the Fiscal Theory of the Price Level (FTPL) in a Bewley-Huggett-Aiyagari framework with heterogeneous agents. The model is set in continuous time, and ex post heterogeneity arises due to idiosyncratic, uninsurable income shocks. Such models have a natural interpretation as mean-field games, introduced by Huang, Caines, and Malham\'e and by Lasry and Lions. We highlight this connection and discuss the existence and multiplicity of stationary equilibria in models with and without capital. Our focus is on the mathematical analysis, and we prove the existence of two equilibria in which the government runs constant primary deficits, which in turn implies the existence of multiple price levels.