Cointegration analysis in practice

1
Cointegration analysis in practice

• Engle-Granger 2 step, and 1 step, estimation
  procedures

2
Applications Of Engle-Granger Two-Step Procedure

• Cointegration in Practice

3
Testing For Cointegration

• Pretest the variables for their order of
  integration
• Estimate the Long Run Equilibrium Relationship
• Estimate the Error Correction Model
• Assess Model Adequacy

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Pretest the variables for their order of
integration

• By definition cointegration necessitates that
  the variables be
• integrated of the same order

• Use DF or ADF tests to determine the order of
  integration

• If variables are I(0) - Standard Time Series
  Methods
• If the variables are integrated of different
  order
• (one I(0), one I(1) or I(2) etc) than it is
  possible to conclude
• that the two variables are not cointegrated
• If the variables are I(1), or are integrated of
  the same order,
• go on

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Estimate the Long Run Equilibrium Relationship
Estimate the long run relationship
If the variables are cointegrated, an OLS
regression yields a super-consistent estimator
of the cointegrated parameter ?0 and ? 1. There
is a strong linear relationship.
Use the residual (e) of the estimated long run
relationship. If (e) is STATIONARY (according to
DF criteria) than we can conclude that the series
are COINTEGRATED
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Estimate the Error Correction Model
If the variables are cointegrated, the residual
from the equilibrium regression can be used to
estimate the Error Correction Model
Using the saved residual from the estimation of
the long-run relationship, we can estimate the
ECM as
Grangers representation theorem if a set of
variables are cointegrated then there always
exists an error correcting formulation of the
dynamic model and vice versa
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Assess Model Adequacy
Asses if the ECM model you have estimate is
appropriate using a General - Specific modelling
approach
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Problems With Engle-Granger Two Step Procedure
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Some authors are uncomfortable with the two stage
approach. Any mistake introduced in the first
step, is carried forward in the second step.
As long as the equation is balanced, an
unrestricted ECM model can be at least as
efficient as a two step EG method in defining
long run relationships and short run dynamics
This means estimating the following ECM model
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Consider for example the Consumption-Income model
analysed in a previous lecture.
Modelling LC by OLS Variable Coefficient
Std.Error t-value t-prob PartR2 Constant
0.013285 0.080615 0.165 0.8696
0.0004 LYd 0.98530 0.011002
89.557 0.0000 0.9925 DW 0.322
First step
Second Step
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Same Estimation with Free Parameters
Does it make a difference?
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In this case not very much
From the long term relation estimation
Inserting this term in the dynamic equation we
have estimated
Substituting the first in the second we have
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Therefore with EG two step we obtain
With the standard ECM procedure we have
Sometimes the second way is more efficient
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Second Problem
We have assumed that Economic Theory can guide in
determining the dependent and the independent
variable, like in the Consumption Function.
What if this is not possible?
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Given three variables (y,w,z) you have three
possible long run relationship,
and three possible ECM models
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These weaknesses limit the applicability of
the EG two step procedure. We need to introduce a
technique that considers cointegration not
only between pairs of variables, but also in a
system
This technique is the ML approach of Johansen