Public spending, monetary policy and macroeconomic instability

• Published date: 01 June 2022
• Author: Zhiming Fu,Antoine Le Riche
• Date: 01 June 2022
• DOI: http://doi.org/10.1111/jpet.12562

Received: 18 January 2021

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Accepted: 5 December 2021

DOI: 10.1111/jpet.12562

ORIGINAL ARTICLE

Public spending, monetary policy and

macroeconomic instability

Zhiming Fu

1

|Antoine Le Riche

1,2

1

School of Economics, Sichuan

University, Chengdu, China

2

CAC–IXXI, Complex Systems Institute,

Lyon, France

Correspondence

Antoine Le Riche, School of Economics,

Sichuan University, Chengdu 610065,

China.

Email: antoineleriche@scu.edu.cn

Abstract

We analyze sunspot‐driven fluctuations in a standard

neoclassical growth model with money holdings and

public spending. In our economy, money is needed for

transaction purpose, while public spending is financed

through a flat income tax. Public spending includes an

incompressible component and a variable part, and the

latter exerts positive externalities on private utility or

production. Our theoretical results show that the com-

position of public spending and externalities have im-

portant effects on local stability properties. First, in the

absence of externalities, there is a unique steady state,

and local indeterminacy depends on the interplay be-

tween the share of the cash ‐in‐advance constraint and

the intertemporal elasticity of substitution of consump-

tion. Second, in the presence of externalities, multiple

equilibria might emerge under weak enough production

externality, while uniqueness of the steady state prevails

under strong production or under consumption ex-

ternality. We further show that weak production/con-

sumption externality or strong consumption externality

could generate local (in)determinacy of the steady state

depending on the share of the cash‐in‐advance con-

straint while strong production externality generates

local determinacy of the steady state. Finally, based on

numerical examples, we show that an increase in the

variable public spending and the income tax rate exert a

local stabilizing effect while externalities promote lo-

cally the likelihood of local indeterminacy.

J Public Econ Theory. 2022;24:580–608.wileyonlinelibrary.com/journal/jpet580

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© 2021 Wiley Periodicals LLC

1|INTRODUCTION

Existing literature, such as Leeper (1991), Schmitt‐GrohéandUribe(2000) and Benhabib and

Eusepi (2005), has examined the implications of the interaction between monetary and fiscal

policies on macroeconomic stability. In these studies, money holding is introduced either for

transaction motivation or to generate utility, while fiscal authority is assumed to collect taxes to

finance useless public spending. This is in contrast to empirical findings which show that public

spending is useful, that is, it exerts positive externalities on private production (Aschauer, 1989;

Cook & Munnell, 1990; Garcia‐Mila & McGuire, 1992;Hulten&Schwab,1991) and private utility

(Aschauer, 1985;Fiorito&Kollintzas,2004;Karras,1994;Ni,1995).

This paper examines how the usefulness as well as the composition of public spending

affect macroeconomic stability of an one‐sector monetary economy. In our framework, the

demand for money is motivated on the ground of a fractional cash‐in‐advance (CIA) constraint

on consumption expenditures (See Hahn & Solow, 1997), while public spending consists of an

incompressible component and a variable part. The latter component is useful as it enters the

production function of individual firms or the utility function of households.

1

To the best of our

knowledge, we are the first to apply this framework to analyze the impact of useful public

spending and the composition of public spending on local stability properties of a monetary

economy.

It is well known that when fiat money is required for transaction motivation, the stationary

solutions of monetary economies may have richer stability features than those of nonmonetary

environments (Carlstrom & Fuerst, 2003; Woodford, 1994).

2

It is due to the fact that the

demand for money represents a friction in the capital market whose real value is determined by

the price level and thus by the inflation path which in turns affects the whole structure of the

relative prices. On top of that, productive or utility‐enhancing public spending facilitates

the occurrence of local indeterminacy in an one‐sector real business cycle model with flat taxes,

see Cazzavillan (1996), Fernandez et al. (2004) and Guo and Harrison (2008).

3

In fact, the

relationship between public purchases of goods and services, and households' private con-

sumption is an important aspect to understand the demand‐side effects of a fiscal policy rule.

Our paper moves current studies one‐step further by considering the impact of the composition

of public spending.

4

In our framework, both production and consumption externalities, the composition of

public spending and flat income tax rate may have important implications on local stability. To

disentangle the impact of externalities and that of the composition of public spending, we

compare three different configurations which are featured, respectively, by: (1) the composition

of public spending and absence of externalities; (2) the composition of public spending and

consumption externality; (3) the composition of public spending and production externality.

In the economy free of externality, we show that a unique steady state occurs. Such a steady

state is locally indeterminate when the share of the CIA constraint is low enough or when the share

of the share of CIA constraint is high enough and the intertemporal elasticity of substitution (IES)

of consumption is low, we refer to these conditions as Bosi and Magris (2003) conditions.

1

Thus, variable and useful public spending are used interchangeably below.

2

See a detailed discussion of the impact of transaction motivation of money on aggregate stability below.

3

Lloyd‐Braga et al. (2008) extend this analysis with distortionary taxes.

4

This has important influences on the existence of multiple equilibria and stability properties of the model economy as

in Abad et al. (2020).

FU AND LE RICHE

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