Liquidity, the Mundell–Tobin Effect, and the Friedman Rule

• Published date: 01 August 2024
• Author: LUKAS ALTERMATT,CHRISTIAN WIPF
• Date: 01 August 2024
• DOI: http://doi.org/10.1111/jmcb.12994

DOI: 10.1111/jmcb.12994

LUKAS ALTERMATT

CHRISTIAN WIPF

Liquidity, the Mundell–Tobin Effect, and the

Friedman Rule

We investigatehow a positive relation between ination and capital invest-

ment (the Mundell–Tobineffect, MT-E) affects optimal monetary policy in a

frameworkthat combines overlapping generations and new Monetarist mod-

els. We nd that ination rates above the Friedman rule are optimal if and

only if there is an MT-E. In the absence of the MT-E, the Friedman rule is

optimal. With an MT-E, increasing ination above the Friedman rule leads

to a rst-order welfare gain from increasing capital investment, and only to

a second-order welfare loss from reducing consumption in markets where

liquidity matters.

JEL codes: E4, E5

Keywords: new monetarism, overlappinggenerations, optimal monetary

policy

T F    optimal conduct of monetary

policy is the most signicant doctrine in monetary theory. Friedman (1969) argues

that optimal monetary policy should equate the private opportunity costs of holding

money (the nominal interest rate) to its social costs (which are zero). By this logic,

the optimal monetary policy should be deationary. This result is remarkably robust.

It has been found by Friedman himself in a model with money in the utility (Fried-

man 1969), but also in a variety of other monetary models such as cash-in-advance

The views expressed in this paper do not necessarily reect those of the Oesterreichische National-

bank. We thank Aleksander Berentsen and Cyril Monnet for their useful comments that greatly improved

the paper and our colleagues Mohammed Ait Lahcen, Lukas Voellmy, and Romina Ruprecht for many

insightful discussions. We thank Randall Wright, Pedro Gomis-Porqueras, Piero Gottardi, Garth Baugh-

man, Lucas Herrenbrueck, Dirk Niepelt, Harris Dellas, Mark Rempel, and seminar participants at the 2019

Mini Conference on Search and Money in Madison, the 2019 Workshopin Monetary Economics in Mar-

rakech, the 2020 Summer Workshopon Money, Payments, Banking and Finance, the University of Essex,

the University of Basel, and the University of Bern for valuablecomments and suggestions.

L Ais with the University of Essex (E-mail: lu.altermatt@gmail.com). CW

is with the Oesterreichische Nationalbank (E-mail: christian.wipf@protonmail.com).

Received May 11, 2022; and accepted in revised form August 17, 2022.

Journal of Money, Credit and Banking, Vol. 56, No. 5 (August 2024)

© 2022 The Authors. Journal of Money, Credit and Banking published by Wiley Periodicals

LLC on behalf of Ohio State University.

This is an open access article under the terms of the Creative Commons Attribution-NonCom-

mercial License, which permits use, distribution and reproduction in any medium, provided

the original work is properly cited and is not used for commercial purposes.

1236 :MONEY,CREDIT AND BANKING

(Grandmont and Younes1973, Lucas and Stokey 1987), spatial separation (Townsend

1980), and New Monetarism (Lagos and Wright 2005). However, most central banks

in developed economies follow an annual ination target of around 2% and try to

avoid deation. Thus, the debate about the optimality of the Friedman rule has con-

tinued ever since Friedman proposed it, with severalexplanations for optimal ination

rates above the Friedman rule being brought forward.1

In this paper, we study optimal monetary policy in the presence of a Mundell–

Tobin effect (MT-E; Mundell (1963) and Tobin (1965)). The MT-E postulates that

ination increases investment, the idea being that since ination reduces the return on

nominal assets, investment in capital becomes relatively more attractive and agents

substitute away from nominal assets into capital. Thus if agents underinvest in capital

at the Friedman rule, higher ination might increase welfare through an increase in

investment. We study this argument in an overlapping generations (OLG) framework

that also incorporates a market where money is useful to trade in the spirit of La-

gos and Wright (2005) (LW). The model features a basic liquidity-return trade-off:

Agents can hold nominal (money) or real (capital) assets, with money being more

liquid than capital, but capital being productive and thus more efcient to provide

for old-age consumption. The model combines two usually separated roles of money.

It is both used in intergenerational trade between young and old agents but also in

intragenerational trade between agents of the same generation. In this environment,

there may or may not be an MT-E, depending on the preferences of agents, the im-

plementation of monetary policy, and the liquidity of capital. This allows us to study

more carefully how the presence of an MT-E affects the optimality of the Friedman

rule.2

We nd that ination rates abovethe Friedman rule are optimal if and only if there

is an MT-E at the Friedman rule. In this case, increasing ination above the Friedman

rule leads to a rst-order welfare gain from increasing capital investment, and only

to a second-order welfare loss from reducing consumption resulting from intragener-

ational trade, and the optimal ination rate lies between the Friedman rule and zero.

Without an MT-E, this mechanism is not at play and the Friedman rule is optimal.

We also show that an MT-E is more likely to occur at the Friedman rule if agents’

demand for money is elastic and if capital is liquid.

From the policymaker’s point of view, the fundamental trade-off in our model is

that the Friedman rule delivers efciency in intragenerational trade, but a constant

price level is optimal regarding intergenerational trade. The reason for the latter point

1. Explanations for optimal ination rates above the Friedman rule include: incomplete taxation

(Aruoba and Chugh 2010, Finocchiaro et al. 2018); theft or socially undesirable activities nanced by

cash (Sanches and Williamson 2010, Williamson2012); labor market frictions (Carlsson and Westermark

2016); or pecuniary exernalities(Brunnermeier and Sannikov 2016). In New Keynesian models with sticky

prices, a constant price level is typically optimal as this eliminates inefciencies from price adjustment

costs. See Schmitt-Grohé and Uribe (2010) or Fuerst (2010) for an overview on the literature about opti-

mal ination rates.

2. We explain the relation of our approach to the existing literature in more detail in the literature

review below.