Capacity Investment under Demand Uncertainty: The Role of Imports in the U.S. Cement Industry

• DOI: http://doi.org/10.1111/jems.12135
• Date: 01 April 2016
• Published date: 01 April 2016
• Author: Jean‐Pierre Ponssard,Catherine Thomas,Guy Meunier

Capacity Investment under Demand Uncertainty:

The Role of Imports in the U.S. Cement Industry

GUY MEUNIER

INRA & Ecole Polytechnique

Guy.Meunier@polytechnique.edu

JEAN-PIERRE PONSSARD

CNRS & Ecole Polytechnique

Jean-Pierre.Ponssard@polytechnique.edu

CATHERINE THOMAS

London School of Economics, Centre for Economic Performance, and CEPR.

c.m.thomas@lse.ac.uk

Demand uncertainty is thought to influence irreversible capacity decisions. Suppose that local

demand can be sourced from domestic (rigid) production or from (flexible) imports. This paper

shows that the optimal domestic capacity is either increasing or decreasing with demand uncer-

tainty, depending on the relative level of the costs of domestic production and imports. We test

this relationship with data from the U.S. cement industry, in which the difference in marginal

cost between domestic production and imports varies across local U.S. markets because cement is

costly to transport over land. Industry data for 1999 to 2010 are consistent with the predictions

of the model. The introduction of two technologies to the production set—one rigid and one

flexible—is crucial to understanding the relationship between capacity choice and uncertainty

in this industry because there is no relationship between these two variables in aggregated U.S.

data. Our analysis reveals that the relationship is negative in coastal districts, and significantly

more positive in landlocked districts.

1. Introduction

The relationship between uncertainty and investment decisions has been the subject

of academic debate since the early work of Jorgenson (1971). As summarized in Abel

et al. (1996), theoretical arguments can be made to ensure either a positive or a negative

relationship between demand uncertainty and investment. A mean-preserving increase

in the variance of demand may induce a positive effect on the value of a marginal unit

of capital, and, hence, on investment, due to the increased probability of high demand

states. There may also be a counteracting negative effect when there is an option to delay

investment until uncertainty is partly resolved (Dixit and Pindyck, 1992). The findings

in the empirical literature reflect the ambiguity of these theoretical results (Carruthet al.,

2000).

Wethank Christian Belzil, Wenjie Chen, Amit Khandelwal, Bruce Kogut, Benjamin Lockwood, Dmitri Nizovt-

sev,Hendrik G. van Oss, Peter Schott, and seminar attendees at the 2010 International Industrial Organization

Conference, the 2010 Academy of Management, and George Washington University, the New Economic

School, and Columbia University for helpful comments. Benjamin Lockwood also provided excellent research

assistance. All errors are our own.

C2015 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume25, Number 2, Summer 2016, 455–486

456 Journal of Economics & Management Strategy

Webuild on the framework developed by Rothschild and Stiglitz (1971) in a model

adapted to characteristics of the cement industry, and we then explore the theoretical

predictions in U.S. data from the early 2000s. In this industry, local demand for cement

can be met by the output from two technologies: capital-intensive local production or

imports from abroad. Imports are a more flexible and less capital-intensive alternative

source of production to the output from local capacity, and the ability to import to a

market affects firms’ local investment decisions. The main contribution of the paper is

to explicate the role of the production set in the relationship between uncertainty and

investment.

There are three main reasons why the U.S. cement industry is an attractive in-

dustry in which to study this relationship: First, capacity decisions are major firm-level

decisions in this industry because cement production is very capital-intensive. Second,

the industry is regionally segmented in terms of supply and demand, and the market

structure is quite concentrated within each region. At the start of the 2000s, there were

114 active cement plants operating across the United States. Regions vary in the extent

of local demand uncertainty because it is affected by both the general business cycle and

the local cycles typical of the construction industry. Third, long-haul maritime imports

are responsive to fluctuations in U.S. domestic demand, and regional demand is often

met by a mix of local production capacity and imports from overseas controlled by

domestic cement producers.1

We develop a theoreticalmodel that captures these three characteristics. Each firm

in a local market has to make two decisions in sequence under imperfect Cournot

competition. First, it decides its local capacity. Second, after the level of demand in

the following period is revealed, the firm decides its production mix from its domestic

capacity and imports. In the context of the model, domestic capacity and imports can

be considered substitutable inputs, and they play roles similar to those of capital and

labor in Rothschild and Stiglitz’s model (Rothschild and Stiglitz, 1971). We extend their

results and show that the domestic capacity choice is either increasing or decreasing in

the level of uncertainty, depending on the relative marginal cost of the domestic versus

the import technology. Specifically, capacity is increasing with uncertainty if the cost of

imports is relatively large, and decreasing if the cost of imports is relatively small.

Our empirical analysis of the U.S. cement industry between 1999 and 2010 confirms

this contingent property: The nature of the relationship between demand uncertainty

and investment is related to local access to the flexible production technology—imports

from abroad. An increase in local demand uncertainty is associated with a significant

decrease in production capacity and average plant size only in coastal districts, and the

relationship is significantly more positive in landlocked districts. We also show that, at

the country level, the data reveal no clear aggregaterelationship between uncertainty and

investment. These results suggest that firms respond to an increase in uncertainty about

future returns from an investment by choosing to make smaller irreversible investments

only when imports are relatively cheap.

The significance of our empirical contribution stems from the fact that there is a

monotonic relationship between uncertainty and investment only when accounting for

variation in production-set flexibility across geographic markets. The model provides a

1. The USGS notes that, in the U.S. “ . . . since the early 1990s, the majority of cement imports have

been controlled by domestic cement producers, and they import only as needed to make up for production

shortfalls” (USGS, 2006, p. 166).

Capacity Investment under Demand Uncertainty 457

theoretical rationale for this fact, and the empirical evidence reveals that, without con-

trolling for production-set flexibility, the role of demand uncertainty would be obscured.

The rest of the paper is organized as follows: Section 2 develops the analytical

model. Section 3 reviews the literature related to both the model and the empirical work

in this industrial setting. It also includes a calibration of the model to some key industry

facts. Section 4 describes the data used in the paper. Section 5 develops the methodology

employed and gives the empirical results. Section 6 discusses some of the implications

of these results and concludes.

2. An Analytical Model

2.1. Setup

The inverse demand function for a given market is p(q,θ), in which pis the price

and qthe quantity sold in the market. Uncertainty is introduced through the random

variable θ, which is assumed to be distributed on the interval [θ;¯

θ], where the cumulative

distribution of θis given by F, assumed to be differentiable.The inverse demand function

p(q,θ) is assumed to be twice differentiable and strictly decreasing with respect to the

quantity qwhen qis positive. We also make the standard assumption that

∂p

∂q+q∂2p

∂q2<0, (A1)

which, when the market is served by a monopoly producer, ensures that the firm’s

revenue is concave with respect to its production. When the market is served by an

oligopoly, this assumption implies that the firm’s revenue is concave whatever the

production of its competitor, and that this marginal revenue is decreasing with respect

to its competitors’ production.2

To ensure that both the revenue and the marginal revenue are increasing with

respect to the draw θfrom the distribution F, where θcan be interpreted as a demand

shock, it is assumed that:

∂p

∂θ (q,θ)>0and∂p

∂θ +∂2p

∂θ∂qq>0. (A2)

This assumption will hold whenever uncertainty is additive or if uncertainty pertains

to, for example, incomplete information about market size.3

Turningto the supply side, a firm’s cost function for the home technology consists of

two terms: a linear per unit investment cost ckfor a capacity choice denoted kand a linear

per unit production cost ch.4The firm is unable to produce more than its capacity with

the home technology. For the foreign technology, there is no unit investment cost. This

technology is assumed to have a linear per unit production cost cfthat varies across local

markets. In the case of no uncertainty, the home technology is preferred to the foreign;

that is, it is assumed that: ch+ck<cf. Finally, it is assumed that local demand is high

enough to make some domestic investment worthwhile, so ¯

θ

θp(0, θ)dF >ch+ck,and

2. This ensures the uniqueness of the Cournot equilibrium in the oligopoly case.

3. This assumption rules out the possibility that a monopolist would reduce its output under a higher

draw of θ.Notethatifp(q,θ)=p(q/θ), the second part of A2 is equivalent to A1.

4. For simplicity, we assume thereis no fixed component to investment or production costs. Introducing

fixed costs does not affect the predictions of the model as long as investing remains profitable, which we

assume all through the model.