Byron Gangnes

Econ 427 lecture 23 slidesEcon 427 lecture 23 slides

Intro to Cointegration and Error Correction Models

Byron Gangnes

CointegrationCointegration• 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

CointegrationCointegration• 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.

Byron Gangnes

Bivariate CointegrationBivariate Cointegration

• We use Augmented Dicky-Fuller tests to find out whether this is the case.– Have to consult special tables for this.

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

(0)t ty x I

0t ty x Then cointegrating relationship is given by:

Byron Gangnes

Error-Correction ModelsError-Correction Models• If two variables are cointegrated, then we can also

represent the relationship as an error-correction model:

1 1t t t t ty y x x

• 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

ApplicationApplication• 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 approachesMultivariate 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.