Transcript Intro to Cointegration

Econ 427 lecture 23 slides
Intro to Cointegration and Error
Correction Models
Byron Gangnes
Cointegration
• To integrated series are said to be cointegrated
when there is a linear combination of the two
series that is stationary
• This will happen, when y and x share a
common stochastic trend.
• The classic examples is consumption and
income. Look at a graph.
• This also generalizes to more than two
variables
Byron Gangnes
Cointegration
• Cointegration has some nice properties, in
particular parameter estimates are superconsistent.
– This means that the estimates converge to the true value
at a faster-than-normal rate.
– We are not “throwing away” potentially important
information about the levels by differencing the data.
• The problem is that cointegration tests have nonstandard distributions, like we saw for unit root
tests.
Byron Gangnes
Bivariate Cointegration
• yt and xt are cointegrated if there is some
parameter, beta, such that this linear combination
is stationary.
yt   xt  
I (0)
• We use Augmented Dicky-Fuller tests to
find out whether this is the case.
– Have to consult special tables for this.
Then cointegrating relationship is given by:
yt   xt  0
Byron Gangnes
Error-Correction Models
• If two variables are cointegrated, then we can also
represent the relationship as an error-correction
model:
yt    yt 1   xt 1   xt   t
• This has a nice economic interpretation:
– y can wander away from its long-run (equilibrium)
path in the short run, but will be pulled back to it by
the ECM over the longer term.
• If there are other stationary variables that affect
the short-run behavior of y, we can also include
them on the RHS.
Byron Gangnes
Application
•
Consumption-income example in EViews.
–
–
–
Check for unit roots
Test for cointegration : ls log(cons) c log(gdp) (5%
CV for this case is t=4.24)
Estimate the ECM (dynamic model) ls dlog(cons) c
ecm(-1) dlog(cons(-1)) dlog(gdp(-1))
•
–
–
(Should we impose a unit coefficient in the coint rel?)
Make model including necessary ECM identity
Forecast
Byron Gangnes
Multivariate approaches
• This bivariate cointegration approach is
know as he Engle-Granger model. It
assumes that one variable is endogenous
and the other exogenous
• Multivariate VAR-based approaches that
allow for all variables to be endogenous are
increasingly common.
– These Johanson approaches are implemented in
EViews.
Byron Gangnes