Asymmetric Monotone Comparative Statics for the Industry Compositions

• Published date: 01 May 2017
• Author: Anders Rosenstand Laugesen
• Date: 01 May 2017
• DOI: http://doi.org/10.1111/roie.12269

Asymmetric Monotone Comparative Statics for the

Industry Compositions

Anders Rosenstand Laugesen*

Abstract

Within a standard model of international trade with heterogenous firms and two asymmetric countries, we

derive sufficient conditions for monotone comparative statics (MCS) for the industry composition. This

model outcome is defined as first-order stochastic dominance shifts in the equilibrium distributions of all

activities across active firms. MCS for the industry composition occurs in a country that experiences a

decline in its costs of serving the foreign market and meanwhile experiences an increasein its level of com-

petition. In the other country, the industry-level implications are exactly opposite. These clear industry-level

results hold whilefirms respond asymmetrically to the trade shock.

1. Introduction

In this paper, we analyze the responses of firms and industries to exogenous industry-

wide trade shocks within a heterogenous-firms model of international trade with monopo-

listic competition 

alaMelitz (2003) and Melitz and Redding (2014). Only the most pro-

ductive firms serve the foreign market and are exposed to the demand levels in each of

the two asymmetric countries. A demand level comprises an inverse measure of the level

of competition in the industry.

1

Within this standard and general model of international

trade, we derive sufficient conditions for a model outcome dubbed monotone compara-

tive statics (MCS) for the industry composition. This model outcome is defined as first-

order stochastic dominance (FSD) shifts in the equilibrium distributions of all activities

across active firms. An activity refers to any choice variable at the discretion of the firm

subject to the constraint that activities are complementary at the firm level.

The possibility of MCS for the industry composition relies on a class of productivity

distributions that contains the commonly used Pareto distribution, namely the class of

productivity distributions where log-productivity is distributed with nonincreasing haz-

ard rate. When log-productivity is distributed with nonincreasing hazard rate, it is

shown that MCS for the industry composition occurs in a model country that experien-

ces both a decline in its costs of serving the foreign market and an induced decline in

its own demand level. An induced increase in the level of competition is likely to occur

after the unilateral trade shock. We also present two useful examples where it is cer-

tain to occur. In the nonliberalizing country, the industry-level implications are shown

to be exactly opposite. Hence, asymmetrical and unilateral trade liberalizations are

likely to imply a model outcome that we name asymmetric MCS for the industry com-

positions when productivities are distributed for instance Pareto. Importantly, these

* Rosenstand Laugesen: Aarhus University, Fuglesangs All

e 4, 8210 Aarhus V, Denmark. E-mail:

arl@econ.au.dk. Tel: 145-30253599. The author thanks Peter Bache, Kristian Behrens, Leif Danziger,

Peter Egger, Peter Neary, Allan Sørensen, two anonymous referees and seminar participants in Paris,

Saint Petersburg and Venice for helpful comments.

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C2016 John Wiley & Sons Ltd

Review of International Economics, 25(2), 362–382, 2017

DOI:10.1111/roie.12269

monotone and strong industry-level implications hold while firms in a given country

respond asymmetrically and nonmonotonely to the trade shocks.

One can get a flavor of the meaning of these results by looking at the benchmark model

by Melitz and Redding (2014) with two asymmetrical countries. This example is nested in

the model below under the common and convenient assumption of an outside industry

large enough to determine the wage rate. The heterogenous firms in this example face

two complementary activities: labor demand for variable production and export behavior.

Within this example, the present paper shows that a unilateral trade liberalization

(through a decrease in the fixed or variable trade costs of serving the foreign market)

implies MCS for the industry composition in the liberalizing country if and only if log-

productivity is distributed with a nonincreasing hazard rate.

2

MCS for the industry com-

position means that the firm-size distribution makes an FSD shift to the right and that the

fraction of exporters increases in the liberalizing country. In the nonliberalizing country,

the firm-size distribution makes a shift to the left while the fraction of exporters

decreases. Note that the industry-level implications are exactly opposite for the nonliber-

alizing country implying that we obtain asymmetric MCS for the industry compositions.

Let us emphasize three important points related to the specific example above. First,

the added structure obtained by analyzing the specific trade model in Melitz and Redding

(2014) implies that asymmetric MCS for the industry compositions now certainly occurs

when log-productivity is distributed with nonincreasing hazard rate. This is because the

level of competition certainly increases in the liberalizing country as we argue by using

parts of the analysis in Demidova and Rodriguez-Clare (2013). Second, the added struc-

ture in the example also implies that log-productivity being distributed with nonincreas-

ing hazard rate is not only sufficient but now also necessary for obtaining asymmetric

MCS for the industry compositions. This implies that the industry-level results mentioned

in the example certainly do not hold when productivity is Frechet or log-normally distrib-

uted. The intuition is as follows. When log-productivity is distributed with nonincreasing

hazard rate, we are assured a sufficient mass of exiting and entering low-productivity firms

(with low activity levels) in the liberalizing and nonliberalizing countries, respectively.

This assures asymmetric MCS for the industry compositions. Third, the models pre-

sented by Melitz (2003) and Melitz and Redding (2014) effectively work as a back-

bone in many related trade models. This implies that the results of the example

above also hold for other specific trade models with complementary activities such

as the model of Bustos (2011) when the liberalizing country is a small open econ-

omy and wages are determined through an outside industry.

3

This is because the

activities labor demand for variable production, exporting behavior and technology

upgrading are complementary in the Bustos (2011) model. Furthermore, the level of

competition certainly increases in the small open liberalizing country, as argued

below, and productivities are Pareto distributed in Bustos (2011).

The approach of the present paper reveals how one can often obtain clear-cut indus-

try-level results during comparative statics in specific and nested trade models without

having to fully solve these general-equilibrium models. The presented technique works

even when (the potentially discrete) shocks and countries are asymmetric, as is

most often the case, and when the model setup is flexible enough to encompass

several recent and prominent trade models. The apparent complexity is handled by apply-

ing the monotonicity theorem of Topkis (1978). This monotonicity theorem, known from

operations research and the work of Milgrom and Roberts (1990), for example, does a lot

of the hard work for us when it is combined with some admittedly quite simple decompo-

sitions of the comparative static effects. Interestingly, the monotonicity theorem allows

for a discontinuous (and hence nondifferentiable) profit function. This is convenient

ASYMMETRIC MCS FOR THE INDUSTRY COMPOSITIONS 363

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C2016 John Wiley & Sons Ltd