NONNEUTRALITY OF MONEY IN DISPERSION: HUME REVISITED

• Author: Tao Zhu,Gu Jin
• DOI: http://doi.org/10.1111/iere.12387
• Published date: 01 August 2019
• Date: 01 August 2019

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 3, August 2019 DOI: 10.1111/iere.12387

NONNEUTRALITY OF MONEY IN DISPERSION: HUME REVISITED∗

BYGUJIN AND TAO ZHU1

Central University of Finance and Economics, China; Hong Kong University of Science

and Technology, Hong Kong

For a class of standard and widely used preferences, a one-shot money injection in a standard matching model

can induce a significant and persistent output response by dispersing the distribution of wealth. Decentralized

trade matters for both persistence and significance. Following the injection, the price response may be sluggish,

the markup may move up with output, and both the interest rate and the inflation rate may drop below their

trend levels.

1. INTRODUCTION

First published in 1752, Of Money articulates Hume’s view of nonneutrality of money that

has been influential for centuries:

When any quantity of money is imported into a nation, it is not at first dispersed into many hands; but

is confined to the coffers of a few persons, who immediately seek to employ it to advantage. . .. It is

easy to trace the money in its progress through the whole commonwealth; where we shall find, that it

must first quicken the diligence of every individual, before it encrease the price of labour. (Hume, 1987,

p. 172)

Often present in modern writings (see, e.g., Friedman 1987; Lucas 1996; Wallace 1997), this

passage seems to relate a stimulating effect of a money injection to (a) a limited participation

in the market from which money is injected and (b) a dispersion (i.e., diffusion) process in

the market from which injected money gradually reaches all people in the economy. But is

there any mechanism by which a limited participation and a dispersion process can make

an injection stimulating? Here we explore such a mechanism against the familiar matching

model of Trejos and Wright (1995) and Shi (1995) with general individual money holdings, a

model that accommodates a limited participation by nondegenerate wealth distributions and

a gradual dispersion process by decentralized trade.2We apply a class of standard and widely

used preferences for quantitative exercises and concentrate on one-shot money injections.

Our parameterized model has two salient features. First, aggregate output would increase in a

steady state if people’s incentives to trade were not changed, but the distribution of wealth were

more dispersed. The main force behind is simple and intuitive: a reduction in a poor seller’s

wealth results in a much larger increment in production than a reduction in a rich seller’s.

Second, people’s incentives along a transition path to the steady state are very close to their

incentives in the steady state. These two features imply that if a redistributional shock disperses

∗Manuscript received November 2017; revised August 2018.

1We are thankful to two anonymous referees for their valuable comments that have improved the article. Zhu

acknowledges the support by RGC, Hong Kong under the grant GRF647911. Please address correspondence to: Tao

Zhu, Department of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong

Kong. Phone: 852-2358-7601. E-mail: taozhu@ust.hk

2The canonical form of the model, one with divisible money and with no upper bound on the individual holdings,

has a central role in the New Monetarism literature (see Williamson and Wright, 2010) in that much of the literature is

built on its tractable versions, for example, Lagos and Wright (2005) and Shi (1997).

1329

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(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1330 JIN AND ZHU

(stretches) the steady-state distribution of money but maintains the quantity of money, there is

an immediate significant output response.

Decentralized trade obviously adds persistence to the output response by slowing down the

dispersion (diffusion) of redistributed money, and it has a more critical role. Suppose that a

competitive market substitutes for decentralized trade as in a Bewley model. If there is no

change in the price level, then the wealth redistribution may still have the same output effect as

above; but for the market to clear, nominal prices must fall below the steady-state level in the

transition path, which, in turn, dilutes sellers’ incentives to produce and dampens the output

response. That is, a wealth redistribution is able to exploit the steady-state incentives to trade—

in particular, poorer sellers’ much stronger incentives to produce—because these incentives are

preserved by decentralized trade in the transition path.

A money injection can disperse the wealth distribution when it is regressive. As output,

the price in each meeting along the transition path is very close to the meeting price in the

postinjection steady state. The injection may redistribute the mass of meetings so that aggregate

output moves above the postinjection steady-state level (which is equal to the preinjection

steady-state level) and the average price across meetings moves below the postinjection steady

state level (which increases from the preinjection steady-state level proportionally to the change

in the quantity of money). Thus, a positive output response may co-occur with nominal rigidity,

but the co-occurrence does not mean causality in either way.

To discipline our exercises, we endogenize regressiveness of each money injection by endog-

enizing a limited participation (in receiving injected money). With a unitary CRRA coefficient

and a unitary Frisch elasticity of labor supply, a 1% accumulative increase in the money stock

can induce a more than 4% accumulative increase in output over 20 quarters. There is a Phillips

curve in that the output and price responses are proportional to the increase in the money stock.

For plausible parameter values, nominal rigidity emerges, and the markup moves up with out-

put. When the model includes nominal government bonds (issued before pairwise meetings and

financed by inflation), the injection keeps to induce a significant and persistent output response;

following the injection, there is a liquidity effect, and the inflation rate may first drop below the

trend level, a phenomenon analogous to the price puzzle found by VAR studies.

It is not new that a money injection is nonneutral when it redistributes wealth (see Friedman,

1969).3But, as is well known, redistributing wealth or not, monetary shocks do not generate

significant and persistent output responses in a large class of models absent of imposed nominal

rigidity (see, e.g., Chari et al., 2000). Although one may therefore choose to impose nominal

rigidity on a model, there is always criticism of the assumption that people cannot change prices

when they want.4In this context, our contribution is to show that flexible price can be consistent

with the output-response pattern in concern and that nominal rigidity may not be the cause but

may be a part of nonneutrality of money.

We spell out the basic model, parameterization, and the procedure for quantitative exercises

in Section 2. Section 3 demonstrates the two salient features of the model and the critical role

of decentralized trade. The one-shot regressive injection is introduced in Section 4. The model

with bonds is analyzed in Section 5. In Section 6, we offer some discussion of our model and

future works.

2. THE BASIC MODEL

The model is the one formulated by Trejos and Wright (1995) and Shi (1995) with general

individual money holdings. Time is discrete, dated as t≥0. There is a unit mass of infinitely

lived agents. At each period, each agent has the equal chance to be a buyer or a seller. Each

3Notably, redistribution effects are explored by the early and some late contributions in the limited-participation

literature; see, for example, Grossman and Weiss (1983), Rotemberg (1984), Alvarez et al. (2002), and Williamson

(2008, 2009).

4See Head et al. (2012) for a comprehensive review of the literature.