Firms’ money demand and monetary policy

• Published date: 01 August 2017
• DOI: http://doi.org/10.1111/1468-0106.12234
• Date: 01 August 2017

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ORIGINAL MANUSCRIPT

Firms’money demand and monetary policy

Romina Bafile

1

| Alessandro Piergallini

2

1

University of L'Aquila, L'Aquila, Rome,

Italy

2

University of Rome ‘Tor Vergata’, Rome,

Italy

Correspondence

Alessandro Piergallini, Department of

Economics and Finance, University of

Rome ‘Tor Vergata’, Via Columbia 2,

00133 Roma, Italy.

Email: alessandro.piergallini@uniroma2.it

JEL Classification: E41; E52.

Abstract

Standard New Keynesian models for monetary policy

analysis are ‘cashless’. When the nominal interest rate

is the central bank's operating instrument, the LM equa-

tion is endogenous and, it is argued, can be ignored. The

modern theoretical and quantitative debate on the

importance of money for monetary policy conduct, how-

ever, overlooks firms’money demand. Working in an

otherwise canonical New Keynesian setup, we show

that macroeconomic dynamics are critically affected by

the firms’money demand choice. Under the conven-

tional Taylor‐rule framework, we prove that equilibrium

determinacy may require either an active interest rate

policy, overreacting to inflation, or a passive interest rate

policy, underreacting to inflation, depending on the

elasticity of production with respect to cash balances.

We then develop a numerical analysis to evaluate our

theoretical results. We find that macroeconomic stabil-

ity is more likely to occur under an active, but not overly

aggressive, monetary policy stance. We also examine the

dynamic effects of forward‐looking feedback rules. We

show that, in this policy regime, indeterminacy is likely

to be induced by both active and passive rules, even for

relatively low productivity effects of money.

There is hardly any issue of a more fundamental nature, with regard to monetary

policy analysis, than whether such analysis can coherently be conducted in

models that make no explicit reference whatsoever to any monetary aggregate.

Bennett McCallum (2008, p. 1783).

Received: 26 January 2017 Accepted: 20 April 2017

DOI: 10.1111/1468-0106.12234

350 © 2017 John Wiley & Sons Australia, Ltd Pac Econ Rev. 2017;22:350–382.wileyonlinelibrary.com/journal/paer

1|INTRODUCTION

The purpose of this paper is to analyse the issue of equilibrium determinacy in a New Keynesian

model extended to incorporate money in the production function. We show that equilibrium

uniqueness and stability under Taylor (1993, 1999)‐type feedback policies critically depends

upon the elasticity of production with respect to real money balances. Our central result is that,

when liquidity affects the production process, a ‘passive’monetary policy stance, whereby the

nominal interest rate underreacts to the observed inflation rate, may well lead to determinacy,

in contrast with the theoretical predictions of the canonical New Keynesian framework, which

rule out accommodating interest rate policies for they always trigger undesirable sunspot fluctu-

ations. Conversely, an ‘active’monetary policy stance, and in particular an overly aggressive

interest rate policy, may no longer be compatible with macroeconomic stability. We also demon-

strate that equilibrium dynamics under ‘forward‐looking’monetary rules are altered. In this pol-

icy regime, we show that indeterminacy is likely to prevail irrespectively of the interest rate

feedback to expected inflation, even when productivity effects of money are relatively small, in

contrast with the typical result that moderately active forward‐looking policies ensure

determinacy.

Standard macroeconomic theory of the New Keynesian type uses ‘cashless’models for

monetary policy analysis (e.g. Clarida, Galí, & Gertler, 1999; Galí, 2003, 2008; Rotemberg

& Woodford, 1997, 1999; Taylor, 1999; Woodford, 2003). Under interest rate policy rules,

it is argued, it is not necessary to specify a money market equilibrium condition. The

Lagrange multiplier (LM) equation, typically derived employing the money‐in‐the‐utility‐

function approach àlaSidrauski (1967), is endogenous when the interest rate is the policy

instrument. Under a separable utility function, in particular, the LM equation is completely

recursive to the equilibrium system. That is, the model solution would be unchanged by

adding a money demand equation to the system. Under a non‐separable utility function,

the role of money in the IS equation resulting from the dependence of the marginal

utility of consumption on real money balances has been proved to be quantitatively negli-

gible (e.g. Andrés, López‐Salido, & Vallés, 2006; Ireland, 2004; McCallum, 2001; Woodford,

2003). Monetary aggregates can, thus, be ignored without altering policy implications

(Woodford, 2008).

This approach to the theoretical analysis of monetary policy, with no explicit reference to

money, arguably overlooks investigations into the role of money demand by firms. Empiri-

cally, in industrialized countries firms hold a considerable share of money supply. For

instance, Mulligan (1997) documents that US non‐financial firms held at least 50% more

demand deposit than households in the 1970–1990 period. In addition, firms’demand for

money as a share of the aggregate appears to be increasing over time. For instance, Bover

and Watson (2005) document that the US firms’share of M1 was 35% of the non‐financial pri-

vate sector in the mid‐1980s and 62% in 2000. In view of these remarkable stylized facts, the

present paper attempts to evaluate the role of firms’money demand in the monetary policy

transmission mechanism within an optimizing general equilibrium framework of the New

Keynesian type.

To elucidate the issue, we extend the baseline dynamic New Keynesian by employing the

money‐in‐the‐production‐function approach. As the discussion of the related literature in the

following section shall emphasize, the treatment of real balances as a factor of production

has a long history, which dates back at least to the seminal work by Friedman (1959), who

aptly argues that ‘businesses hold cash as a productive resource’(p. 334). Following this

BAFILE AND PIERGALLINI 351

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approach, we prove that monetary policy design turns out to be affected by the firms’money

demand choice.

In the canonical New Keynesian model, changes in the nominal interest rate affect aggregate

demand via the Euler equation, which describes the agents’intertemporal decision about the

optimal allocation between consumption and saving. However, when liquidity is relevant for

the production process, changes in the nominal interest rate also directly influence the firms’

demand for real balances, thereby affecting aggregate supply in the economy.

Specifically, when monetary policy is active, inflationary pressures are offset by increases

in the real interest rate, which dampen aggregate demand. This negative demand‐side effect

tends to be deflationary over time. In the cashless‐economy setup, in particular, this effect

brought about by an active monetary policy stance is necessary and sufficient to preserve

macroeconomic stability. Once firms’demand for real money balances is taken into account,

however, the rise in the nominal interest rate implied by a conventional monetary policy

feedback rule of the Taylor (1993, 1999)‐type also dampens output supply. This negative sup-

ply‐side effect tends, by contrast, to be inflationary over time. This implies that an active

monetary policy stance induces aggregate instability if it causes the supply‐side, inflationary

effect to prevail on the demand‐side, deflationary effect. The foregoing rationale explains

why, under the conventional Taylor‐rule framework, the existence of a unique and stable

rational expectations equilibrium may require either an active interest rate policy or a passive

interest rate policy, depending on the elasticity of production with respect to real

money balances.

The dispute over whether reacting to inflation aggressively is stabilizing or destabilizing has

important implications for monetary theory and policy. Hence, quantitative investigations of the

analytical findings derived in this paper are valuable. To this end we proceed by evaluating

numerically the model. To obtain a direct comparison with the relevant literature, we first

employ a relatively standard parameter configuration. Then, to address the robustness of the

numerical results, we perform a sensitivity analysis with respect to three critical parameters

interacting with the elasticity of production to cash balances; that is, the degree of nominal rigid-

ities, the households’relative risk aversion coefficient, and the inverse of the Frisch elasticity of

households’labour supply. Overall, the numerical results indicate that macroeconomic stability

is more likely to be guaranteed under an active, but not overly aggressive, interest rate feedback

policy responding to current inflation.

The plan of the paper is as follows. In Section 2, we lay out the paper's connections with

the literature. In Section 3, we set up the baseline model. In Section 4, we log‐linearize the

equilibrium conditions and analyse the resulting dynamics under the standard Taylor‐rule

framework. In Section 5, we investigate the model numerically and derive policy implications.

In Section 6, we extend the analysis to the case of a forward‐looking Taylor rule, reacting to

expected inflation. In Section 7, we examine the interactions between households’money

demand and firms’money demand, and check the robustness of our main findings. Section 8

concludes.

2|RELATED LITERATURE AND MODEL CHOICE

In the history of monetary theory and policy, a number of influential economists have advocated

that real money balances are a factor input and should, therefore, be included in the production

function. Prominent examples include Friedman (1959, 1969), Levhari and Patinkin (1968),

352 BAFILE AND PIERGALLINI

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