Optimal Monetary Policy in OLG Models with Long‐Lived Agents: A Note

• Date: 01 February 2014
• DOI: http://doi.org/10.1111/jpet.12050
• Published date: 01 February 2014
• Author: RYOJI HIRAGUCHI

OPTIMAL MONETARY POLICY IN OLG MODELS WITH

LONG-LIVED AGENTS:ANOTE

RYOJI HIRAGUCHI

Ritsumeikan University

Abstract

This note reexamines Crettez, Michel, and Wigniolle

(2002), who studied a two-period overlapping generations

model with cash-in-advance constraints and showed that a

combination of saving tax and monetary policy involving

positive nominal interest rates could achieve the first-best

allocation. The note shows that their result does not hold

if agents live for three periods. The implementation of the

first best requires the Friedman rule. If agents are long-

lived, saving tax cannot offset a distortion caused by the pos-

itive nominal interest rate.

1. Introduction

Crettez, Michel, and Wigniolle (2002, henceforth CMW) provide a two-

period overlapping generations (OLG) economy in which the Friedman rule

(henceforth FR) does not apply. They investigate a Diamond-type model with

partial cash-in-advance (CIA) constraints and show that the optimal mone-

tary policy is indeterminate if saving tax is available. This feature reflects a

redundancy of policy instruments.

We show that one way to reintroduce the FR is to add one period in such

a way that it kills the redundancy of the instrument. In the three-period OLG

model, the saving tax cannot offset the distortions by the positive nominal

interest rate. To achieve the first best, the government must follow the FR,

and the first best can actually be implemented as a competitive equilibrium

under the FR.

Ryoji Hiraguchi, Faculty of Economics, Ritsumeikan University, 1-1-1, Noji-Higashi,

Kusatsu, Shiga, Japan (rhira@fc.ritsumei.ac.jp).

I thank two anonymous referees for their comments.

Received February 14, 2009; Accepted October 29, 2011.

C2013 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 16 (1), 2014, pp. 164–172.

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