Constructing Multi‐Country Rational Expectations Models
| Date | 01 December 2014 |
| Published date | 01 December 2014 |
| DOI | http://doi.org/10.1111/obes.12046 |
812
©2013 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 76, 6 (2014) 0305–9049
doi: 10.1111/obes.12046
Constructing Multi-Country Rational Expectations
Models*
Stephane Dees†, M. Hashem Pesaran‡, L. Vanessa Smith§ and Ron
P. Smith¶
†European Central Bank, Frankfurt-am-Main, Germany
(e-mail: stephane.dees@ecb.europa.eu)
‡University of Southern California, Los Angeles, USA; Trinity College, Cambridge, UK
(e-mail: pesaran@usc.edu; mhp1@cam.ac.uk)
§University of Cambridge, Cambridge, UK (e-mail: lvs21@cam.ac.uk)
¶Birkbeck College, London, UK (e-mail: r.smith@bbk.ac.uk)
Abstract
This article considers some of the technical issues involved in using the global vector
autoregression (GVAR) approach to construct a multi-country rational expectations (RE)
model and illustrates them with a new Keynesian model for 33 countries estimated with
quarterly data over the period 1980–2011. The issues considered are: the measurement
of steady states; the determination of exchange rates and the specification of the short-
run country-specific models; the identification and estimation of the model subject to
the theoretical constraints required for a determinate rational expectations solution; the
solution of a large RE model; the structure and estimation of the covariance matrix and
the simulation of shocks. The model used as an illustration shows that global demand and
supply shocks are the most important drivers of output, inflation and interest rates in the
long run. By contrast, monetary or exchange rate shocks have only a short-run impact in
the evolution of the world economy. The article also shows the importance of international
connections, directly as wellas indirectly through spillover effects. Overall, ignoring global
inter-connections as country-specific models do, could give rise to misleading conclusions.
I. Introduction
The multi-country, cointegrating global vector autoregression (GVAR), has proved an
effective tool for a range of purposes, including forecasting, counterfactual analysis and
investigating the transmission of shocks across economies or markets. The GVAR Hand-
book edited by di Mauro and Pesaran (2013) provides a review of many applications of
the GVAR approach. Smith and Galesi (2013) provide a toolbox for constructing GVARs.
*ForStephane Dees, the views expressed in this article do not necessarily reflect the views of the European Central
Bank or the Eurosystem. The other authors are grateful to the European Central Bank for financial support.
JEL Classification numbers: C32, E17, F37, F42.
Constructing multi-country rational expectations models 813
The GVAR has the advantage that country-specific models can be easily estimated with
the current values of foreign variables being treated as weakly exogenous, an assump-
tion that is found to be generally acceptable after testing. The structure allows for both
between country and within country cointegration, dealing with the issue originally raised
by Banerjee, Marcellino and Osbat (2004). The country-specific models can be combined
to form a system which treats all variables as endogenous. Even though the presence of
the current foreign variables gives the GVAR a simultaneous equations type structure, it is
subject to the critique that its shocks cannot be given simple economic interpretations as
demand,supply or monetary policy shocks. Dynamic stochastic general equilibrium, DSGE,
models do generate shocks that can be given such a simple interpretation, but extending
DSGE models to a multi-country frameworkis not straightforward. Existing open-economy
DSGE models tend to consider either two countries of comparable size, such as the euro
area and the US, or small open economy models where the rest of the world is treated as
exogenous. But it is the interaction between many countries that is often crucial for ques-
tions about the global economy. Carabenciov et al. (2008, pp. 6) who consider developing
multi-country models, state that: ‘Large scale DSGE models show promise in this regard,
but we are years away from developing empirically based multi-country versions of these
models’.
This article considers some of the technical issues involved in using a GVAR approach
to construct a multi-country rational expectations (RE) model, similar to those used within
the DSGE literature. The approach involves estimating a set of country-specific rational
expectations models and then combining them to solve the system as a whole. Such a model
can be used to identify the contribution of domestic and international demand, supply, and
monetary policy shocks to business cycle fluctuations. We illustrate the various issues
involved in the analysis of multi-country RE models with a multi-country new Keynesian
(MCNK) model encompassing 33 countries. The country specific models are kept simple
intentionally and have the familiar standard three equation structure comprising a Phillips
curve, an aggregate demand or IS curve, and a Taylor rule. To capture the multi-country
nature of the analysis each country model also includes an exchange rate equation with the
exception of the model for the US whose currency serves as the numeraire. The country
specific models are also augmented with an AR(1) equation for oil prices. The countries
are indexed by i=0,1, 2,…, N, with the US denoted as country 0. The MCNK model thus
explains output, inflation, short interest rates and exchange rates, but not long interest rates
and equity prices which are included in the GVAR of Dees et al. (2007). This is because
there are no widely accepted standard structural models for the term structure or equity
premium. The MCNK model is estimated over 1980Q3-2011Q2 and has 131 variables.1
Developing a multi-country model faces a number of important challenges and we
discuss these in turn. The issues considered are: the measurement of steady states in section
II; the specification of the short-run individual country models and the determination of
exchange rates in section III; the identification and estimation of the model subject to the
1This article was previously circulated under the title: “Supply, Demand and Monetary Policy Shocks in
a Multi-Country New Keynesian Model”, where a shorter sample 1980Q1-2006Q4 and a slightly different
specification were used. All results in this article are obtained using the MCNK Matlab program available
at https://sites.google.com/site/gvarmodelling/mcnk-modelling. A short non-technical introduction to the MCNK
approach is available in Smith (2013).
©2013 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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