Strategic inventories under limited commitment

• DOI: http://doi.org/10.1111/1756-2171.12292
• Author: Raffaele Fiocco,Fabio Antoniou
• Published date: 01 September 2019
• Date: 01 September 2019

RAND Journal of Economics

Vol.50, No. 3, Fall 2019

pp. 695–729

Strategic inventories under limited

commitment

Fabio Antoniou∗

and

Raffaele Fiocco∗∗

In a dynamic storablegood market where demand changesover time, we investigate the producer’s

strategic incentives to hold inventories in response to the possibility of buyer stockpiling. The

literature on storable goods has demonstrated that buyer stockpiling in anticipation of higher

future prices harms the producer’s profitability, particularly when the producer cannot commit

to future prices. We show that the producer’s inventories act as a strategic device to mitigate the

loss from the lack of commitment. Our results provide a rationale for the producer’s inventory

behavior that sheds new light on the well-documented empirical evidence about inventories.

1. Introduction

Inventory management is essential for a firm’s viability in many industries. Although the

share of inventory investment in gross domestic product (GDP) is relatively small, changes

in inventories constitute a significant component of economic fluctuations. During the recent

financial crisis, the reduction in inventories accounted for 29% of the decline in GDP (Wang,

Wen, and Xu, 2014).

Traditional reasons for inventories are driven by technological features, such as production

smoothing over time in the presence of convex production costs and stockout avoidance when

production takes time and cannot be immediately adjusted to demand shocks (e.g., Aguirre-

gabiria, 1999; Anupindi, Chopra, Deshmukh, Van Mieghem, and Zemel, 2012; Arrow, Harris,

∗University of Ioannina and Humboldt University of Berlin; fabio.antoniou@wiwi.hu-berlin.de.

∗∗University of Bergamo; raffaele.fiocco@unibg.it.

Weare grateful to the Editor David P.Myatt and two anonymous referees for their insightful comments and suggestions. We

are also indebted to Helmut Bester, Gorkem Celik, EvangeliaChalioti, Luca Colombo, Alessandro De Chiara, Evangelos

Dioikitopoulos, Ricardo Flores-Fillol, Sotiris Georganas, Jochen G¨

onsch, Dongyu Guo, Matthias Hunold, Elisabetta

Iossa, Eugen Kovac, Matthias Lang, Ester Manna, Carolina Manzano Tovar, Joao Montez, Andras Niedermayer,Patrick

Rey, Joel Sandon´

ıs, Emanuele Tarantino, and Bernd Theilen for their helpful advice. We also thank the participants at

the seminars at the University of Ioannina (January 2017), University of Duisburg-Essen (July2017), Free University of

Berlin (July 2017), Catholic University of Milan (November2017), University of Barcelona (February 2018), University

of Cergy-Pontoise(February 2018), as well as the participants at the following meetings: CESC in Barcelona (May 2017),

Trobada URV-UA in Alicante (June 2017), CRETE in Milos (July 2017), JEI in Pamplona (September 2017), BECCLE

in Bergen (June 2018), and EARIE in Athens (September 2018).

C2019, The RAND Corporation. 695

696 / THE RAND JOURNAL OF ECONOMICS

and Marschak, 1951; Arvan and Moses, 1982; Holt, Modigliani, Muth, and Simon, 1960; Kahn,

1987; Krishnan and Winter, 2007; Krishnan and Winter, 2010; Nahmias, 2008; Zipkin, 2000).

The empirical evidence indicates that inventories are procyclical and production is more variable

than sales (e.g., Blanchard, 1983; Blinder, 1986; Ramey and West, 1999; Wen, 2005). Informa-

tion about production and inventory activities is generally available in industry reports, financial

statements, and balance sheets. Such information is also collected in accurate databases.1

The presence of intermediaries and arbitrageurs in the commodity markets suggests that

buyers also exhibit incentivesto store. A recent strand of the empirical literature has systematically

documented buyer stockpiling in anticipation of higher future prices in markets for various

intermediate and final goods (e.g., Erdem, Imai, and Keane, 2003; Hall and Rust, 2000; Hendel

and Nevo, 2004; Hendel and Nevo, 2006a; Hendel and Nevo, 2006b; Pesendorfer, 2002).

The storage activities of firms and their customers have been examined separately in the

literature so far. In this article, weprovide a unified framework in order to investigate the inventory

behavior of a producer vis-`

a-vis forward-looking buyers that are willing to store in anticipation

of higher future prices. Abstracting from the aforementioned classical technological reasons for

inventories, we show that a producer unable to commit to future prices has strategic incentives

to hold inventories when dealing with the prospect of buyer stockpiling. Our results provide

theoretical support for the main stylized facts about the firms’ inventory activities.

We focus our attention on storable goods, which are perishable in consumption but can

be stored for future consumption. Typical examples include a number of intermediate goods

(e.g., oil, coffee, and wheat) and groceries that can be purchased in advance and stored. In

order to characterize the strategic role of the producer’s inventories, we build on the seminal

article of Dudine, Hendel, and Lizzeri (2006), which considers a dynamic storable good market

with deterministic time-varying demand where a monopolistic producer cannot commit to future

prices and faces a continuum of competitive buyers availableto stockpile the good in anticipation

of higher future prices. Dudine, Hendel, and Lizzeri (2006) show that the excessively high

future prices driven by the producer’s lack of commitment trigger buyer stockpiling, which is

ex ante profit detrimental in that it reduces future sales occurring at higher prices. As a result of

wasteful buyer stockpiling, the producer’s profits and consumer surplus are lower than under full

commitment, which unambiguously reduces aggregate welfare. In this setting, we introduce the

opportunity for the firm to accumulate production in the form of inventories available for future

sales. A practical example is the oil market in the United States, where a large oil producer (or

refiner) generally supplies competitive distributors (or directly the petrol stations) and gathers

some quantity in its depositories to cover the future demand. The distributors (and petrol stations)

are also endowed with storage capacities. In many other markets for storable goods—such as

bananas, bauxite, coffee, copper, diamonds, iron ore, mercury, phosphates, and tin—supply

is relatively concentrated, with some producers possessing large market power. Competitive

speculators trade these goods and engage in stockpiling activities.2

In our baseline framework, the firm’s production costs are linear and do not vary over time.

Moreover, demand evolves deterministically. Hence, there is no scope for the well-documented

technological motives for inventories, and the producer shall engage in inventory activities only

for strategic purposes. Under full commitment, the producer does not benefit from holding

inventories, because it can credibly announce a price sequence that removes buyer stockpiling,

and inventories would only result in a mere loss due to their holding costs. However, when the

producer is unable to commit to future prices, this conclusion is no longer valid, and inventories

can emerge in equilibrium. To understand the rationale for this result, it is important to realize

that the costs of inventories are sunk once they have been incurred. A producer that cannot

1For instance, since 1962, Standard & Poor’s Compustat has provided financial, statistical, and market data about

companies throughout the world. Information about the 100 largest companies traded on the US stock exchanges can be

regularly found at www.stock-analysis-on.net.

2Governments can also implement stockpiling policies, especially in order to protect against future supplydisr up-

tions (e.g., Nichols and Zeckhauser, 1977).

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commit to future prices accumulates inventories as a strategic device to reduce future costs,

which alleviates the producer’s temptation to charge higher future prices and weakens the buyer

stockpiling incentives.

We find that under certain circumstances, despite the lack of commitment, the producer

holds the amount of inventories that maximizes the ex ante profits, and the constraint of se-

quential optimality is slack in equilibrium. As under full commitment, buyer stockpiling is fully

removed, which occurs at the additional cost of holding inventories. Remarkably, this solution is

implementable only if the unit cost of production is large enough. Prima facie, this might seem

counterintuitive, because one could expect a more efficient producer to find inventories more

attractive. The rationale for this result arises from the strategic nature of inventories.To illustrate

ideas, consider a two-period setting. The inventory level accumulated in the first period to serve

the demand in the second period is associated with a second period price at which the quantity

sold coincides with inventories. When the unit cost of production is large enough, the ex ante

optimal level of inventories is sufficiently small so that in the second period the producer does

not succumb to the temptation to discard some inventories and to set a price above the level at

which inventories are fully sold. Moreover, as long as the unit inventory holding cost is relatively

small, the firm does not have any incentive to produce some additional quantity in the second

period, either. Given that the producer shall charge the second period price at which the quantity

sold coincides with inventories, the ex ante optimal inventory level is also sequentially optimal.

Anticipating that the sunkness of inventory costs alleviates the producer’s temptation to charge

higher future prices, buyers abstain from any stockpiling activity. Therefore, inventories consti-

tute a strategic device to mitigate the producer’s loss from the lack of commitment. Notably, the

producer accumulates in the first period the amount of inventories that covers the entire second

period demand in order to removeb uyerstockpiling, which represents only a portion of the second

period demand. This suggests that inventories and buyer stockpiling are imperfect substitutes in

equilibrium. When holding inventories is costless, inventoriesbecome a fully effective instrument

to prevent buyer stockpiling, and the full commitment outcome is restored.

If the unit cost of production is small enough, the ex ante optimal level of inventories is

relatively large and in the second period the producer cannot refrain from discarding a portion of

the inventories accumulated in the first period and from setting a second period price above the

level at which inventoriesare fully sold. In other words, the ex ante optimal level of inventories is

not sequentially optimal and cannot be sustained in equilibrium. Wes how that, even in this case,

inventories can playa strategic role in mitigating the buyer stockpiling incentives. It follows from

our previous discussion that inventories must be distorted away from the ex ante optimal level,

and the constraint of sequential optimality is binding in equilibrium. Inventories are not a fully

effectiveinstr ument to alleviatethe buyer stockpiling incentives, even when their holding costs are

nil. As a result, the producer’s inventories and buyer stockpiling can now coexist in equilibrium.

When the unit cost of production is relatively large, and therefore the ex ante optimal

inventory level is also sequentially optimal, inventories generally lead to lower prices, even

though they involveholding costs. The rationale for this apparently surprising result stems from the

strategic nature of inventories,which mitigate the producer’s temptation to set higher future prices

and soften the buyer stockpiling incentives. Hence, despite being used in the producer’s private

interest, inventories increase consumer surplus and aggregate welfare. As shown in Section 6,

this conclusion deserves some qualifications when the unit cost of production is relatively small,

and therefore the equilibrium inventory level departs from the ex ante optimal level. Equilibrium

prices exhibit peculiar features that merit some attention. For instance, we find that a lower unit

inventory holding cost may lead to higher prices.

Our article provides a novel strategicrationale for the fir ms’ inventory activities, which does

not lie in the specific production technologies assumed by the traditional inventory theories. As

discussed in Section 9, our results shed new light on the empirical evidence about inventories

described above. The predictions of our model lend themselves to empirical or experimental

validation and can stimulate further investigationinto the firms’ inventory management. A relevant

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