Transcript Chapter 14 - Facultypages.morris.umn.edu

CHAPTER 14
COINTEGRATION AND ERROR
CORRECTION MODELS
Damodar Gujarati
Econometrics by Example
COINTEGRATION
 There is a unique case where a regression of a nonstationary series
on another nonstationary series does not result in spurious
regression.
 This is the situation of cointegration.
 If two time series have stochastic trends (i.e., they are
nonstationary), a regression of one on the other may cancel out the
stochastic trends, which may suggest that there is a long-run, or
equilibrium, relationship between them even though individually the
two series are nonstationary.
 Keep in mind that unit root and nonstationarity are not
synonymous. A stochastic process with a deterministic trend is
nonstationary but not unit root.
Damodar Gujarati
Econometrics by Example
TESTS OF COINTEGRATION
 Engle-Granger (EG) and augmented Engle-Granger
(AEG) tests
 In the context of testing for cointegration, the Dickey-Fuller
(DF) and augmented Dickey-Fuller (ADF) tests are known as
Engle-Granger (EG) and augmented Engle-Granger (AEG) tests,
which are now incorporated in several software packages.
 Shortcomings of the EG methodology
 If you have more than three variables, there might be more than
one cointegrating relationship.
 Once we go beyond two time series, we will have to use
Johansen methodology to test for cointegrating relationships
among multiple variables.
Damodar Gujarati
Econometrics by Example
UNIT ROOT TESTS AND COINTEGRATION TESTS
 Tests for unit roots are performed on single time series, whereas
cointegration deals with the relationship among a group of
variables, each having a unit root.
 It is better to test each series for unit roots, as some of the series
in a group may have more than one unit root, in which case they
will have to be differenced more than once to make them
stationary.
 If two time series Y and X are integrated of different orders then the error
term in the regression of Y and X is not stationary and this regression
equation is said to be unbalanced.
 On the other hand, if the two variables are integrated of the same order,
then the regression equation is said to be balanced.
Damodar Gujarati
Econometrics by Example
COINTEGRATION AND ERROR CORRECTION
MECHANISM (ECM)
 Granger Representation Theorem: If two variables Y and X are
cointegrated, the relationship between the two can be expressed
as an error correction mechanism (ECM).
 The ECM postulates that changes in the dependent variable
depend on changes in the independent variable and the lagged
equilibrium error term, ut-1.
 If this error term is zero, there will not be any disequilibrium between the
two variables and in that case the long-run relationship will be given by
the cointegrating relationship.
 But if the equilibrium error term is nonzero, the relationship between the
two variables will be out of equilibrium.
 For multiple time series, we need to use the vector error correction
model (VECM).
Damodar Gujarati
Econometrics by Example