Engle and Granger Test with EViews

There are several tests of cointegration. The Engle and Granger (1987) is the most fundamental test.

The Engle and Granger (1987) require 2 step method;

1)Estimate the original model;

\({{Y}_{t}}={{\beta }_{0}}+{{\beta }_{1}}{{X}_{t}}+{{u}_{t}}\)                       (1)

2)Obtain the residual from Eq(1) ;

\({{\hat{u}}_{t}}={{Y}_{t}}-{{\hat{\beta }}_{o}}-{{\hat{\beta }}_{1}}{{X}_{t}}\)                     (2)

and then test the unit root by DF method ;

\(\Delta {{\hat{u}}_{t}}={{a}_{1}}{{\hat{u}}_{t-1}}+{{e}_{t}}\)                     (3)

Estimating with EViews

To run an example for Engle and Granger cointegration test, we use the data Macro.

Lets now we want to test the cointegration between the gdp (gross domestic product) and pdi (personnel disposable income) series.

Before we going through the test, let we first look the plot between these two series.

Click the icon for gdp and pdi simultaneously, and then right click mouse and then select Open > as Group.

Save the group by click Object\Name…

 

And lets we named it by group01, and then click OK.

From the group window group01, at the window bar, click View \Graph…

 

From the Graph Options window, select

Graph Type – Basic Type

General: Basic graph

Spesific: Line & Symbol

And then, click OK.

 

The graph for gdp and pdi series show the strong trend and these two series is seem moving together.

Perform the unit root test for variables gdp and pdi to make sure that all the variables is in I(1) condition.

To perform the ADF test for gdp series, click the gdp icon. At Series : GDP window bar, select View\Unit root test…

 

 

In Unit Root test window, select

Test type : Augmented Dickey-Fuller

Test for unit root in : Level

Include in test equation : Tend and intercept

Lag length : Automatic selection – Akaike information Criterion

and then click OK.

 

 

The results show that, the unit root is exists at level form for gdp series.

To test the gdp in first difference form, we follows the step before but in Unit Root test window, we now select; 

Test for unit root in : 1st difference

 

and then click OK

 

The results show that gdp series is stationary at 5% significant level.

Now, we do the same step for the pdi series. 

The results for pdi series at level form;

 

and for pdi series at first difference;

 

which it show clearly that the pdi series is non-stationary at level form, but stationary at the first difference form at 1% significance level.

After we satisfies that each series, namely gdp and pdi is I(1) condition based on the ADF test,  now we can perform the Engle-Granger cointegration test.

First, we need to estimate the model as in Eq(1). Select Quick\Estimate Equation…

 

In  Spesification tab window, type  pdi c gdp.

and for Estimation settings, select Method: LS – Least Squares (NLS and ARMA)

and then, click OK.

 

Save the equation results by click Object\Name… and then lets we named it by eq01, and then click OK.

Second, we need to obtain the residual as in Eq(2). To do this, in Equation : eq01 window, click Proc\Make Residual Series…

       

and click OK .

The new icon data series for residual with name resid01 from estimation in step 1 will exists.

And then, we perform the unit root test for resid01 series as in Eq(3). Click the resid01 icon and at window bar, select View\Unit Root Test…

 

 

In Unit Root Test window, select

Test type : Augmented Dickey-Fuller

Test for unit root in : Level

Include in test equation : None

Lag length : User specified : 0

and then click OK.

 

The Dickey Fuller test for residual show that the statistic value is -2.968. 

Noted that since we are basing this test upon estimated values of the residuals, the critical values will be different from the critical table of Dickey and Fuller (1979). That means, we cannot use the critical value supplied by EViews in the estimation output table.

The proper critical values for a test of cointegration are given table below. There are three sets of critical values. Which set we use depends on whether the residuals \({{\hat{u}}_{t}}\) are derived for regression equation; (1) without a constant term, (2) with a constant term, and (3) with a constant term and time trend.

Based on critical values for the cointegration test for model (2), our results show that we fail to reject the null hypothesis for no cointegration.

Beside we use the long way to test the cointegration test based on the residual what we have done before, EViews also provide the Engle-Granger cointegration test by the simple click.

To do this, click the group icon group01 again. At window bar, click View\Cointegration Test > Single-Equation Cointegration Test…

 

In Cointegration Test Spesification window, select

Test method : Engle-Granger

Lag specification : Fixed(User-specified)

Lags : 0

and then click OK.

 

 

The probability values are derived from the MacKinnon response surface simulation results.  The output results provide the Engle-Granger tau-statistic (\(t\)-statistic) and normalized autocorrelation  coefficient (which we term the \(z\)-statistic).

The results show that, as PDI is dependent variables, the values of tau-statistic is -2.968 (same as we get from the residual step method before)  and the \(z\)-statistic is -15.306. Both statistics fail to reject the null hypothesis of no cointegration. 

The evidence clearly suggest that the PDI and GDP are not cointegrated.