SIZE, OPENNESS, AND MACROECONOMIC INTERDEPENDENCE

• DOI: http://doi.org/10.1111/iere.12208
• Date: 01 February 2017
• Author: Roland Straub,Alexander Chudik
• Published date: 01 February 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 1, February 2017

SIZE, OPENNESS, AND MACROECONOMIC INTERDEPENDENCE∗

BYALEXANDER CHUDIK AND ROLAND STRAUB1

Federal Reserve Bank of Dallas,U.S.A; European Central Bank, Germany

One common, simplifying assumption in open economy macroliterature is that the rest of the world can be thought of

as a representative economy. This article formally investigates conditions under which this assumption can be justified

using a multicountry general equilibrium model as a laboratory. We derive the conditions that ensure the existence

of the equilibrium and study the properties of the equilibrium using large Nasymptotics. Thereby, we show that the

two-country framework is a valid approximation only for economies that have diversified trade linkages and only when

there is no globally dominant economy among the foreign economies.

1. INTRODUCTION

What determines the impact of foreign shocks on the domestic business cycle? What are the

features that drive macroeconomic interdependence? These questions remain of high impor-

tance in an increasingly open and globalized world. The analysis of macroeconomic interdepen-

dence, however, has been so far constrained in several dimensions in both the empirical and the

theoretical literature.

In the empirical literature, the difficulty of analyzing macroeconomic interdependence starts

by recognizing the “curse of dimensionality” that is associated with estimating an unrestricted

system featuring a relatively large number of endogenous macroeconomic variables.2There

are two main approaches to mitigate the so-called curse of dimensionality in the literature:

(i) shrinkage of the parameter space and (ii) shrinkage of data. Bayesian estimation, which

circumvents the dimensionality problem via imposition of priors on the parameters of the

model, is an example of shrinkage of the parameter space.3A much more common practice is to

deal with the high dimensionality problem in the open economy macroeconomic literature using

the second approach, shrinkage of data. Under this approach, the rest of the world is typically

approximated with one representative economy, which is constructed as the cross-sectional

(trade-) weighted average of foreign economies.4In the theoretical literature, variables of the

representative foreign economy can be treated either as endogenous or as exogenous with

respect to the variables of the home economy. The latter case is usually labeled as the so-called

∗Manuscript received December 2012; revised July 2015.

1Earlier version of the article was circulated under the title: “Equilibrium of a Large Multicountry DSGE Model.”

We are greatly indebted to Hashem Pesaran for his support and many useful discussions. We are grateful to the editor

and the anonymous referees for valuable comments. We would also like to thank Seppo Honkapohja and Rupert Gatti

for their guidance during the earlier stages of this research and Kevin Sheedy and Dennis Novy for comments and

helpful discussions. All errors are our responsibility. The views expressed in this article are those of the authors and

do not necessarily reflect those of the Federal Reserve Bank of Dallas or the European Central Bank. Please address

correspondence to: Alexander Chudik, Federal Reserve Bank of Dallas, 2200 N. Pearl Street, Dallas, TX 75201. E-mail:

alexander.chudik@dal.frb.org.

2Even with as few as four macroeconomic variables per country, it is not possible to reliably estimate an unrestricted

VAR featuring more than two economies due to the size of typical macroeconomic data sets.

3See, for example, Canova and Ciccarelli (2004) or Canova and Ciccarelli (2009) for Bayesian multicountry VAR

models with an application to G7 economies. Priors could be derived from a theoretical model, as discussed in Del

Negro and Schorfheide (2004).

4This approach is prevalent in both theoretical and applied work, including the recent Global VAR (GVAR)

literature started by Pesaran et al. (2004).

33

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

34 CHUDIK AND STRAUB

small-open economy framework.5In such a framework, a rise in trade openness is generally

associated with an increase in macroeconomic interdependence.

But under what conditions is the assumption of a representative foreign economy justified?

And what is the relationship between openness, the size of the economy, and the degree

of macroeconomic interdependence in an alternative framework that addresses some of the

deficiencies of the two-country models?

In this article, we answer these questions by examining the properties of the equilibrium of an

N-country open economy model. Our theoretical setup draws on recent contributions of open

economy general equilibrium models as discussed in Benigno and Benigno (2003), Chari et al.

(2002), Corsetti and Pesenti (2001), Gali and Monacelli (2005), Kollmann (2001), and Schmitt-

Grohe and Uribe (2003) to mention just a few. First, we show the existence of a well-defined

equilibrium in our N-country model and derive the conditions that characterize the equilibrium.

Second, we apply large Nasymptotics to simplify the equilibrium solution of the model.

Indeed, large Nasymptotics, which are commonly used in the panel data literature but

rarely in theoretical macroliterature, turn out to be very useful and necessary in simplifying the

complex equilibrium solution, even under a general pattern of weak cross-sectional dependence

of all idiosyncratic shocks to individual economies.6In particular, large Nasymptotics allow us to

formally define various concepts such as that of “negligible impact,” the notion of neighborhood

effects and global dominance, and to establish order of magnitude restrictions on the coefficients

of the model, which, in turn, significantly simplify the equilibrium solution (as N→∞).7As

a result, large Nasymptotics allow us to study how restrictions on the parameters of the

model (namely, those defining steady-state bilateral foreign trade share matrix) affect the

equilibrium solution and to assess, thereby, the properties of the dynamic equilibrium under

various scenarios about the size and openness of individual economies.

Interestingly, the analysis of the representative foreign economy assumption provides new

insights into the relationship between macroeconomic interdependence and openness. The

results presented in this article indicate that the degree of macroeconomic interdependence

is not necessarily connected to the notion of trade openness as usually contemplated. In fact,

an increase in openness could well lead to a decreased dependence of the home economy

on foreign shocks. Furthermore, the assumption that an economy is small and open does not

justify approximating the rest of the world with one representative economy, constructed by

a cross-sectional (trade-)weighted average of the rest of the world, or justify the asymptotic

exogeneity of foreign variables. Our findings suggest that the degree of trade diversification is

a key parameter in the chosen setup.

We identify an intuitive analogy with the asset market literature (Chamberlain, 1983; Cham-

berlain and Rothschild, 1983) and the literature on large cross-sectional aggregation (Granger,

1987; Forni and Lippi, 1997). It is well known that only systemic risk has a bearing on effectively

diversified portfolios. In a similar spirit, only those components with strong cross-sectional

dependence (common factors) survive aggregation. Similar reasoning applies here. If a coun-

try diversifies its foreign trade and there is no globally dominant economy among the foreign

economies, then (asymptotically as N→∞) the representative foreign economy assumption

is justified. In this setup, the equilibrium solution for domestic endogenous variables does

5Note that the small-open economy framework is subject to two crucial assumptions; (i) the economy is small and

has no impact on the rest of the world and (ii) the rest of the world can be aggregated into a representative economy.

In our article, we focus on the implication of the second assumption (regardless of the size of economy) and identify

under which conditions the aggregation of foreign economies is justified.

6The concept of weak and strong cross-sectional dependence, formally defined in Chudik et al. (2011), will be

applied to the multicountry open economy model. See also Bailey et al. (2016) for further discussion of cross-section

dependence.

7Restrictions that bind only in the limit as the number of variables approaches infinity are also used in Chudik and

Pesaran (2011), who consider econometric analysis of infinite-dimensional VAR models. This article utilizes limiting

restrictions on the bilateral foreign trade flows and studies the equilibrium properties as the number of countries

becomes large.