##
**After
unit root testing, what next?**

In the Part 1 of
this structured tutorials, we discussed Scenario 1: when the series are
stationary in levels that is

*I*(0) series and Scenario 2: when they are stationary at first difference. In the first scenario, it implies that any shock to the system in the short run quickly adjusts to the long run. Hence, only the long run model should be estimated. While for the second scenario, the relevance of the variables in the model is required, therefore there is need to test for cointegration. If there is cointegration, specify the long-run model and estimate VECM but if otherwise, specify only the short-run model and apply the VAR estimation technique and not VECM. In today’s lecture we consider the third scenario of when the variables are integrated of different orders.**Scenario 3: The series are integrated of different orders?**

1.
Should in case the series are integrated
of different orders, like the second scenario, cointegration test is also
required but the use of Johansen cointegration test is no longer valid.

2.
The appropriate cointegration test is
the

**Bounds test for cointegration**proposed by Pesaran, Shin and Smith (2001)
4. Similar to scenario 2, if series are not
cointegrated based on Bounds test, we are expected to estimate only the short
run. That is, run only the ARDL model (where variables are neither lagged nor
differenced). It is the

**of the model.**__static form__
5.
However, both the long run and short run
models are valid if there is cointegration. That is, run both ARDL and ECM
models.

**Bounds Cointegration Test in EViews**

In this example,
we use the

*Dar.xlsx*data on Nigeria from 1981 to 2014 and the variables are the log of manufacturing value-added (*lnmva*), real exchange rate (*rexch*) and gross domestic growth rate (*gdpgr*). The model examines the effect of real exchange rate on manufacturing sector while controlling for economic growth.**Note:**Cointegration test should be performed on the level form of the variables and not on their first difference. It is okay to also use the log-transformation of the raw variables, as I have done in this example.

**Step 1:**Load data into EViews (see video on how to do this)

**Step 2:**Open variables as a Group data (see video on how to do this) and save under a new name

**Step 3:**Go to

**Quick >> Estimate**

**Equation**

**>>**and specify the static form of the model which is stated as:

*lnmva*+

_{t}= b_{0}*b*+

_{1}rexch_{t}*b*+

_{2}gdpgr_{t}*u*

_{t}_{ }in the

**Equation Estimation Window**

**Step 4: Choose the appropriate estimation technique**

Click on the drop-down button in
front of

**Method**under**Estimation settings**and select**ARDL – Auto regressive Distributed Lag Models****Step 5: Choose the appropriate maximum lags and trend specification**

The lag length must be selected
such that the degrees of freedom (defined as

*n - k*) must not be less than 30. The**Constant**option under the**Trend specification**is also selected.**Step 6: Choose the appropriate lag selection criterion for optimal lag**

Click on

**Options**tab, then click on the drop-down button under**Model Selection Criteria**and select the**Akaike info Criterion (AIC)**, then click**Ok.****Step 7: Estimate the model based on Steps 3 to 6**

**Step 8: Evaluate the preferred model and conduct Bounds test**

The hypothesis
is stated as:

H

_{0}: no cointegrating equation
H

_{1}: H_{0}is not true
Rejection of the null hypothesis is at the relevant
statistical level, 10%, 5% level, 1%.

a. Click on

**View**on the Menu Bar
b. Click on

**Coefficient Diagnostics**
c. Select the

**Bounds Test**option
The following
result is displayed below:

Here is the
EViews result on the

**ARDL Bounds Test**of*lnmva, rexch*and*gdpgr*:EViews: ARDL Bounds Test Result Source: CrunchEconometrix |

**Step 9: Interpret your result appropriately using the following decision criteria**

The three
options of the decision criteria are as follows:

1. If
the calculated

*F*-statistic is greater than the critical value for the upper bound*I(1)*, then we can conclude that there is cointegration that is there is long-run relationship.
2. If
the calculated

*F*-statistic falls below the critical value for the lower bound*I(0)*bound, then we conclude that there is no cointegration, hence, no long-run relationship
3. The
test is considered inconclusive if the

*F*-statistic falls between the lower bound*I(0)*and the upper bound*I(1)*.**Decision**: The obtained

*F*-statistic of

**0.6170**falls below the lower bound

*I(0),*hence, we will consider only short run models since the variables show no evidence of a long-run relationship as indicated by the results from the Bounds test.

**[Watch video on how to conduct Bounds test for cointegration in EViews]**

If there are
comments or areas requiring further clarification, kindly post them below….