Cross-sectional
dependency test
The choice of additional econometric tests
employed in empirical research, such as co-integration and unit root tests, in
panel analysis is heavily influenced by cross-sectional dependence across
variables. As a result, it is predicted that cross-sectional dependency will
significantly affect the statistical characteristics of panel unit root tests.
However, when applied to data series with cross-sectional dependence,
first-generation panel unit-root tests exhibit size distortions and
insufficient power (O'Connell, 1998). Therefore, this feature must be
considered in our panel analysis because of the influence of cross-sectional
dependency on test results. In addition, a cross- sectional dependence test may
be used to assess or validate the use of conventional ADF and PP unit root, or
employs second-generation panel unit root testing should be used. In addition,
Pesaran (2004) proposes an alternative CSD test that does not need a prior
model and may be applied to several model parameters. Under the null hypothesis
of no cross-sectional dependency, the Pesaran CD test statistic has the
following qualities:
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The LM test for CD by Pesaran (2015) can
handle slope heterogeneity and cross-sectional issues in a small sample.
However, it usually assumes that the observed test statistics for the studied
residuals (u) are asymptomatically distributed, thus CD N. (0, 1). The result
discussion shows Pesaran's (2015) and Pesaran's (2007) CD testing results.
Thus, a unit root test must account for CD limitations to confirm a long-term
relationship between variables. This study uses Pesaran's CADF and CIPS panel
unit root test. In addition, the Im IPS unit root test was enhanced (2003).
Panel unit root
We cannot continue with the traditional panel unit
root tests since our panel has a cross-sectional reliance on the examined
variables (also known as first-generation panel unit root tests). As a result,
we depend on unit root tests that might potentially take into consideration the
use of cross-sectional data, which are of the second generation. The next
generation of diagnostic tools will be created using heterogeneity as its primary
support structure. We also designed a new version of the original IPS test
using its statistical framework, which is referred to as the Cross-sectionally
Augmented Dickey-Fuller, or CADF, for short. Even though oil prices have
structural fractures, the researcher nonetheless used the unit root test, which
was validated using cross-sectional dependence by Karavias and Tzavalis [18].
Because the tests are invariant under the null to the initial condition, there
is no need to make any assumptions about the nature of the data prior to
carrying out the test, which is not the case with other fixed-T tests. This is
in contrast to the situation where assumptions must be made to carry out other
fixed-T tests. In addition to being resistant to linear trends, the tests do
not depend on the coefficients of the deterministic components. Within the
scope of this thesis, we provide xtbunitroot, a brand-new software that
executes the panel-data unit-root tests developed by Karavias and Tzavalis. In
this study, we presented xtbunitroot, a recently built community-contributed
software that employs structural breakdowns in panel data to apply the
unit-root tests devised by Karavias and Tzavalis. This program was made
possible by the community's contributions (2014). With the use of this first
command, panel unit-root testing that includes structural fractures is a
possibility. Furthermore, it is possible to test for either one or two
structural fractures, depending on the environment. It also allows for errors
that are not normal, dependency, and nonlinear trends, as well as
heteroscedasticity in cross-sectional analyses. The xtbunitroot command was
used for four variables taken from a bank's balance sheet. The results showed
that the bank's noninterest income, assets, and equity returns are stable over
time. Total assets, on the other hand, do not stay the same over time. In the
meanwhile, the idea that Karavias and Tzavalis are discussing may be
characterized as follows:
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In the above equation, the drift under null
hypothesis is ?i, while the trend coefficient are ?i and
?2,i.
Panel
co-integration test
The
validity of this research is examined via the use of three standard panel
co-integration tests. These tests are designed to ascertain whether or not a
panel analysis constitutes a connection that is sustained throughout time.
First, the Pedroni, Kao, and Johansen Fisher co-integration test was used to
investigate the degree to which the correlation was stable over time. Second,
Pedroni was the first to construct a battery of tests in 1997, 1999, 2000, and
2004 that consider heterogeneity in co-integration analysis. Pedroni created
these tests [19]. In Pedroni's test, it is permissible for cointegrated vectors
to experience both short-term and long-term variations. The co-integration test
developed by Kao considers the variable nature of the co-integration vectors
[20]. Nevertheless, hyperbolic equality causes a violation of the criterion
that independent variables must be endogenous. This requirement must be met for
the model to be valid. In addition, the co-integration test developed by Kao
and based on the Engle-Granger framework was used in this research. The Kao
test for the existence of a constant may be calculated by determining the
long-term variance using the Schwarz criteria and then using the Newey-West
estimators to analyze the data. Table 4 displays the findings that may be
obtained by applying the test to the panel data set. The relevance of the
probability value was highlighted in the findings of the Kao co-integration
test, which suggested that the null hypothesis of no co-integration was incorrect
and should be rejected. On the other hand, the hypothesis of no co-integration,
known as the null hypothesis, was shown to be true. In order to accomplish
this, we used the Johansen co-integration test to investigate the
co-integrating link between GDP growth and inflation in the leading
oil-exporting countries all around Africa. The Sren Johansen co-integration
test has the potential to confirm the co-integration time series. The Johansen
method of multivariate co-integration is based on using an error correction
formulation of a p-order Vector Autoregressive model with Gaussian error. This
formulation is the foundation of the Johansen technique.
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Where ? is most first difference operator, ri
= -(1-A1…….Ai) is the coefficient matrix indicating
short-run changes, and II denotes by II = -(1-A1………-Ai)
is an n&n matrix, where I is an identity of the matrix whose rank
determines amount of co-integrating vectors. However, two likelihood ratio
tests were developed by Johansen for testing the number of co-integration
vectors ®. Mathematically, the trace test can be expressed as follows:
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And maximum eigenvalue test statistics given
by:
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Trace statistics check the null hypothesis of
no co-integration H0: r = 0 against the alternative of more than 0
co-integration vector H1: r > 0, whereas maximal Eigenvalue statistics test
the null hypothesis of r against the alternative of r + 1 co-integrating
vectors.