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Other tests for co-integration in Eqs.
An added bonus of this approach is that unlike other conventional tests for co-integration, it can be applied to studies that have a small sample size [27].
The basic testing procedure requires four steps: ADF and PP unit root tests, Bound tests for Co-integration, ARDL approach and VECM method.
The presence of a combination of order one and zero implies that we can confidently apply the Pesaran et al.'s ARDL methodology in our tests for co-integration.
In Eq. 3, the tests for co-integration are carried out by examining the joint significance of the lagged levels of the variables using the F-test where the null of no co-integration is defined by the following: H0: η 1 Y = η 2 Y = η 3 Y = η 4 Y = η 5 Y = 0 against the alternative that H1: η 1 Y ≠ 0, η 2 Y ≠ 0, η 3 Y ≠ 0, η 4 Y ≠ η 5 Y = 0.
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ARDL bound test for co-integration and VECM framework applied.
The variables should also be tested for co-integration, and adjusted and estimated accordingly (Munnell 1992).
To further consolidate on the co-integration nature of the variables, a residual unit root test for co-integration is carried out.
The process of testing for co-integration among variables should permit as much heterogeneity among the individual countries of the panel as possible.
According to [27], in testing for co-integration, if the computed F-statistic falls above the upper critical bounds, a conclusive inference can be made regarding co-integration without the need to know whether the series were I 0) or I(1).
The calculated F-statistics for co-integration are reported together with the diagnostic tests in Table 3.
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