MONEY CYCLES

• Author: Andrew Clausen,Carlo Strub
• Date: 01 November 2016
• Published date: 01 November 2016
• DOI: http://doi.org/10.1111/iere.12198

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 4, November 2016

MONEY CYCLES∗

BYANDREW CLAUSEN AND CARLO STRUB1

University of Edinburgh, U.K.; University of St. Gallen, Switzerland

Operating overheads are widespread and lead to concentrated bursts of activity. To transfer resources between

active and idle spells, agents demand financial assets. Futures contracts and lotteries are unsuitable, as they have

substantial overheads of their own. We show that money—under efficient monetary policy—is a liquid asset that leads

to efficient allocations. Under all other policies, agents follow inefficient “money cycle” patterns of saving, activity, and

inactivity. Agents spend their money too quickly—a hot-potato effect of inflation. We show that inflation can stimulate

inefficiently high aggregate output.

1. INTRODUCTION

Operating overheads are widespread. Workers prepare for work by dressing profession-

ally, traveling to work—often in peak traffic—refamiliarizing themselves with their work plans

(leaving family plans on hold), and checking in with colleagues. In manufacturing, significant

engineering effort is applied to replace inventories with just-in-time production. But, when

overheads cannot be engineered away, activities are concentrated into bursts and batches. For

example, oil tankers have high operating costs leading to large volumes being transported at

a time, retailers restock with large deliveries, dry cleaners concentrate into batches due to the

fixed cost of heating the drums, and income tax is evaluated every year. These bursts lead to

demand for financial assets: Holding large inventories typically involves trade credit, consign-

ment, or futures contracts, and workers’ rosters might be chosen by lottery. However, these

assets all involve substantial overheads of their own. All of these assets involve the possibility of

default, which is minimized with costly credit checks, collateral, and intermediation. Lotteries

are particularly cumbersome: (i) To prevent default, money, or some collateral would have to

be posted before the winner is announced, and (ii) lotteries have a divisibility problem; for

example, five people are required if they would all like a 60% chance to work 100 hours (or

win $100). However, there is one asset with very little overhead, namely, money. Instead of

buying from suppliers using trade credit, buyers could use money saved from previous sales

to pay on delivery. Instead of random shift rosters, workers might decide to produce more on

work days and save money to fund days off. Money is divisible, recognizable, and storable,

giving it minimal transaction costs. Does this mean money is useful for overcoming overheads

in productive activities?

To answer this question, we study a simple economy with a single productive activity. Output

can be produced from labor, where an overhead of labor is required to begin production,

∗Manuscript received March 2013; revised September 2014.

1We are very grateful to Lu´

ıs Ara ´

ujo, Costas Azariadis, Aleksander Berentsen, Danielle Catambay, Boyan

Jovanovic, Leo Kaas, Timothy Kano, Philipp Kircher, Nobuhiro Kiyotaki, Andreas Kleiner, Ricardo Lagos, Junsang

Lee, George Mailath, Jochen Mankart, Iourii Manovskii, Steven Matthews, Guido Menzio, Cyril Monnet, Makoto

Nakajima, Borghan Narajabad, Peter Norman, Stanislav Rabinovich, Xavier Ragot, Andrei Shevchenko, Robert

Shimer, John Stachurski, Hongfei Sun, Christopher Waller, Liang Wang, Warren Weber, Randall Wright, partici-

pants of the Fed Chicago Money Workshop, and anonymous referees for helpful feedback. Carlo Strub thanks the

Swiss National Science Foundation for financial support. Please address correspondence to: Andrew Clausen, School of

Economics, University of Edinburgh, Room 3.06, 31 Buccleuch Place, Edinburgh, EH8 9JT, United Kingdom. E-mail:

Andrew.Clausen@ed.ac.uk.

1279

C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1280 CLAUSEN AND STRUB

and there is diminishing marginal productivity. Output is nonstorable and must be traded or

consumed immediately. We compare the social planner’s preferred allocations with equilibrium

allocations in which the agents can hold and trade money.

Focusing our attention on a utilitarian social planner, we find that he prefers to allocate equal

consumption to all agents. He prefers to make all work shifts the same length but is indifferent

between all feasible work shift allocations. This generalizes the results by Rogerson (1988) and

Prescott et al. (2009). The key step is to show that the social planner’s problem with overheads

is equivalent to a convexified social planner’s problem in which the production technology no

longer has any overheads.

Can money achieve utilitarian-optimal allocations? We first study monetary equilibria when

money is supplied with lump-sum taxation to support deflation at the rate of time preference,

that is, the Friedman rule. We find that all equilibria involve a working class and possibly a

leisure class of agents. Working-class agents consume the same amount every period, produce

more than they consume in the long run, and may sometimes take a vacation. Members of the

leisure class consume more than the working class and never work. Equilibria in which the

leisure class is absent are utilitarian-optimal.

However, money is not perfectly frictionless and is rarely supplied at the Friedman rule.

How does money perform away from socially optimal monetary policy? We develop a theory

that characterizes all stationary symmetric monetary equilibria. We find that only equilibria ap-

proximating the utilitarian-optimal working-class equilibria exist. In these equilibria, all agents

proceed through a “money cycle” pattern of finite length of saving, production, and consump-

tion. All aggregates are stationary—agents are at different phases of their cycle at any given

moment. There is a hot-potato effect of inflation that induces agents to spend their money too

quickly on consumption and hence render these money cycle equilibria inefficient.

We highlight some surprising features of our model by refuting four conjectures that we

argue are natural in the context of the monetary literature. First, we show that inflation need

not depress economic activity even in a model of complete information. Second, we show that

even when consumption and leisure are normal goods, wealthier agents do not consume more

and work less. Third, we show that Baumol–Tobin style Ss cycles are not the only possible money

cycle structure. Finally, we show that symmetric equilibria need not exist, and two money cycles

can coexist in asymmetric equilibria.

Our work is related to three strands of literature. One literature is about the optimal alloca-

tion of labor when there are large setup costs. In the Rogerson (1988) model, labor is indivisible.

He found that lotteries are efficient for convexifying the indivisibility. In Prescott et al. (2009),

households choose their work intensity in continuous time when facing a nonconcave pro-

duction function. In this setting, equilibria with complete markets are utilitarian-optimal. Our

work characterizes all utilitarian-optimal allocations, shows that efficient monetary policy is

equivalent to complete markets, and characterizes equilibria under realistic monetary frictions.

Another literature is about financial frictions in converting financial assets into money. The

only asset in our model is money, and this literature suggests a path forward for introducing

other assets. Baumol (1952) and Tobin (1956) study a partial equilibrium model of money,

when there is a fixed cost of liquidating an asset with high return. They show that an Ss pol-

icy is optimal (unlike in our setting). Alvarez et al. (2002) also think about a fixed cost of

liquidating financial assets but assume that agents cannot hold money across periods. Kaplan

and Violante (2014) numerically explore a model with a fixed cost of liquidating high-return

assets and calculate the equilibrium response to fiscal stimulus payments. Their equilibrium

calculations are complicated but have a nature similar to our money cycle equilibria. Their

agents proceed through Ss cycles involving a single liquidation, but we expect more com-

plicated patterns akin to our money cycles would arise with an increasing marginal cost of

liquidation.

Finally, our work is related to several monetary theories based on double-coincidence fric-

tions in the tradition of Kiyotaki and Wright (1989). Faig (2008) and Menzio et al. (2013)

explore the use of money and lotteries to smooth out an overhead, namely, sellers forgo the