Continuity of the mapping (correspondence) of stationary distributions in Deviatov and Wallace (2001) model: an alternative (and natural) parameterization of monetary policy.

• Grant number: 24/07022-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): July 01, 2024
• Effective date (End): December 31, 2024
• Field of knowledge: Applied Social Sciences - Economics - Economic Theory
• Principal Investigator: Jefferson Donizeti Pereira Bertolai
• Grantee: Nathan Tomaz Machado
• Host Institution: Faculdade de Economia, Administração e Contabilidade de Ribeirão Preto (FEARP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In their study of optimal monetary policy, Deviatov and Wallace (2001) define a mapping $\mathcal{E}$ between a vector describing monetary policy $(\alpha, \delta) \in [0,1]^2$ and the set of stationary money distributions consistent with such a policy, $\mathcal{E}(\alpha,\delta)$. It is argued that the mapping (correspondence) $\mathcal{E}$ is poorly behaved in the neighborhood of the point where there is no monetary policy (i.e., $\alpha = \delta = 0$). This bad behavior consists of the fact that the set $\mathcal{E}(0, 0)$ is not unitary at the same time that $\mathcal{E}(\alpha, \delta)$ is unitary for values of $ (\alpha, \delta)$ close to $(0,0)$.According to initial results of the research agenda proposed in this project (reported below), this misbehavior is characterized by the lack of lower semicontinuity of the $\mathcal{E}$ correspondence.This project proposes to advance the analysis of this bad behavior, exploring in detail mathematical aspects of the model.Specifically, we want to show that the parameterization of monetary policy in the quantity of initial money $\mu \geq 0$ and in the creation of money per period $\alpha \in [0,1]$ is capable of making the set of stationary distributions continuous in monetary policy.That is, the existence of a continuous mapping (correspondence) $\Gamma$ between the vector $(\mu, \alpha)$ and the set of stationary money distributions consistent with such a policy is conjectured.The currency destruction parameter $\delta$, in this alternative approach, only fulfills the role of normalizing measurement units to "keep constant" the quantity of currency in the economy $\mu$.The scientific initiation activities proposed here conclude a long and robust academic trajectory of scientific training experienced by the student during (i) his graduation in Mathematics Applied to Business and (ii) his participation in the Economics, Mathematics and Computing Laboratory (LEMC) of the University of São Paulo (USP).