Engle and Granger in 1987, recommended that «If a set of variables are cointegrated,

then there exists a valid error correction representation of the data, and

viceversa». In other words, this mean that if two variables are cointegrated

there must be some force that will return the equilibrium error back to zero.

Engle and Granger in 1987, also suggested a two-step model for cointegration

analysis. For example, let’s say that we have an independent variable

and a dependent one

.

First of all,

it should be estimated the long-run equilibrium equation:

We run a OLS

regression and we have:

We solve the

above equation with respect to

and we have:

In practice a

cointegration test is a test which testes if the residuals are stationary. To examine

this, we run a ADF test on the residuals, with the MacKinnon (1991) critical

values adjusted for the specific number of variables of our model. If the hypothesis

of the existence of cointegration cannot be rejected, the OLS estimator, is

said to be super-consistent. This means that for a very big T there is no need

to include

variables in the model

The only thing that matters from the above test is the stationarity of

the residuals, if they are stationary we move to the second step. So, we save

the residuals and we prosed to the second step.

The second

step we use the unit root process for the stationarity of the residuals to the

next equation:

The above

equation does not include constant term because the residuals have been

calculated with the method of ordinary lest squares, so they have zero mean.

The test suggested from the Engle Granger is a little bit different from those of

the one of Dickey-Fuller. The hypothesis of this test is:

Ø

:

(no cointegration)

Ø

(cointegration)

The null hypothesis

can be rejected only when

(? is the critical value of Engle-Granger table).

The Engle-

Granger Test can be also used for more than two variables. The process is the

same with the one followed for two variables.

In conclusion

the cointegration process is a way to estimate the long run relation re else equilibrium

between two or even more variables. Engle and Granger in 1987 proved that if two

variables are cointegrated, then those variables have a long run relation

equilibrium, while in short run this may not be the case. The short run disequilibrium relation

can be proved with an Error Correction Mechanism (ECM). The equilibrium error

can be used to combine the long run with the short run with the help of ECM.

The equation of this model is:

Where:

Ø

: is the

equilibrium error

Ø

: is the short

run coefficient which has to be less than zero and more than -1.

Ø

and

: are the

first differences of

and

which are

and

is

We now can now

use the OLS because all the variables are

.

It is important

to point out that long run equilibrium is tested trough the significance of coincidence

. If

is significant then

causes

in the long run. In addition, the coefficient

measures the speed of adjustment toward the long

run equilibrium. The higher this coefficient the faster the return to the equilibrium.