Econ 427 lecture 27 slides

1
Econ 427 lecture 27 slides

• Intro to Cointegration and Error Correction Models

2
Class Forecasting Project

• Project management team is contacting you will
  requested changes or suggestions
  
• Please return final versions to them by midnight,
  this Thursday, November 29
  
• Your final report should include both your
  economic conditions survey and your forecast
  writeup
  
• Be sure to include in an appendix the regression
  models used, model selection information and any
  diagnostics
  
• We will have a forecast forum next Tuesday, Dec.
  4
  
• We will meet that day in Saunders 515 and we may
  get a few students or faculty dropping by
  
• Please prepare a brief (5-7 minute) Powerpoint
  summary for your sector
  
• Project managers need this by Sunday night.

3
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

4
Cointegration

• Cointegration has some nice properties, in
  particular parameter estimates are
  super-consistent.
  
• 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
  non-standard distributions, like we saw for unit
  root tests.

5
Bivariate Cointegration

• yt and xt are cointegrated if there is some
  parameter, beta, such that this linear
  combination is stationary.

• 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
6
Error-Correction Models

• If two variables are cointegrated, then we can
  also represent the relationship as an
  error-correction model

• 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.

7
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 t4.24)
  
• 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

8
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.