Analysing I(2) Systems by Transformed Vector Autoregressions*
| Author | Heino Bohn Nielsen,Hans Christian Kongsted |
| Published date | 01 July 2004 |
| Date | 01 July 2004 |
| DOI | http://doi.org/10.1111/j.1468-0084.2004.00084.x |
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Analysing I(2) Systems by Transformed Vector
Autoregressions*
Hans Christian Kongstedand Heino Bohn Nielsenà
Centre for Applied Microeconometrics, Institute of Economics, University of
Copenhagen, Copenhagen, Denmark (e-mail: hans.christian.kongsted@econ.ku.dk)
àInstitute of Economics, University of Copenhagen, Copenhagen, Denmark
Abstract
We characterize the restrictions imposed by the minimal I(2)-to-I(1) transfor-
mation that underlies much applied work, e.g. on money demand relationships
or open-economy pricing relationships. The relationship between the param-
eters of the original I(2) vector autoregression, including the coefficients of
polynomially cointegrating relationships, and the transformed I(1) model is
characterized. We discuss estimation of the transformed model subject to
restrictions as well as the more commonly used approach of unrestricted
reduced rank regression. Only a minor loss of efficiency is incurred by
ignoring the restrictions in the empirical example and a simulation study. A
properly transformed vector autoregression thus provides a practical and
effective means for inference on the parameters of the I(2) model.
I. Introduction
This paper is motivated by a rich empirical literature applying cointegration
analysis in examining the levels and the growth rates of macroeconomic
variables and their relationships. Some important examples are relationships
that involve the growth rates of nominal variables, e.g. the rate of inflation,
*We thank Allan Wu¨rtz and the participants of the ESEM 2002 meeting in Venice and the
European Central Bank for their comments. Kongsted gratefully acknowledges financial support
from the Danish Social Sciences Research Council under the project ‘Macroeconomic Transmission
Mechanisms in Europe: Empirical Applications and Econometric Methods’. The activities of the
Centre for Applied Microeconometrics (CAM) are financed by a grant from the Danish National
Research Foundation.
JEL Classification numbers: C32, C51, C52, F41.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 66, 3 (2004) 0305-9049
379
Blackwell Publishing Ltd, 2004. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK
and 350 Main Street, Malden, MA 02148, USA.
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