The long-run and short-run relationships between innovation and economic growth are explained in this section. The research is presented in this part. The Augmented Dickey-Fuller (ADF) test is used in the following sub-sections of the chapter unit root tests: Following the findings of these stationarity tests, long-run relationships between the variables under investigation were tested. The ARDL method is used to capture the changes in the relationship between innovation and growth. Econometric Views (E-Views) version 10 statistical software is used for these estimations and diagnostic testing.
4.1 Results of the Unit Root Tests
A unit root was found by using an analysis of each of the five-time time series variables. The Augmented Dickey-Fuller (ADF) t-tests for the individual time series are shown in Table 4.1, along with their first differences.
4.1.1 Augmented Dickey-Fuller (ADF) Test
Tables 4. 1 below summarize the results of the Augmented Dickey-Fuller (ADF) unit root test at their levels and first differences, respectively. At the 5% significance level, t-statistics indicate that a unit root can be rejected for the first difference but not for the levels for all variables. As a result, at some levels, all of the variables are non-stationary since their critical value exceeds their computed values. The I(1) process, on the other hand, considers all variables to be stationary at their first difference (table 4.1 ).
Table 4.1 ADF test Results at Levels and fist differences
Variables
|
at level
|
first differences
|
|
Intercept
|
Critical Values at 5% level
|
intercept and trend
|
Critical Values at 5% level
|
Intercept
|
Critical Values at 5% level
|
intercept and trend
|
Critical Values at 5% level
|
Log(gdp)
|
0.027932
|
-2.954021
|
-2.868351
|
-3.552973
|
-4.215503
|
-2.89358
|
-4.52051
|
-3.45995
|
Log(edexp)
|
-1.68600
|
-2.954021
|
-1.454621
|
-3.552973
|
-3.176478
|
-2.895109
|
-3.041859
|
-3.46229
|
Log(patent)
|
-1.45339
|
--3.653730
|
-4.602430
|
--4.26273
|
-9.730483
|
-2.617434
|
-9.72489
|
-4.27327
|
Log(RD)
|
-0.55841
|
-2.617434
|
-4.171007
|
-3.209642
|
-8.252050
|
-3.653730
|
-8.11381
|
-3.21236
|
Log(capital)
|
0.770046
|
-2.954021
|
-1.778045
|
-3.552973
|
-5.601471
|
-2.957110
|
-6.01780
|
-3.55775
|
Log(labour)
|
-0.70245
|
-2.954021
|
-2.744074
|
-3.552973
|
-5.592953
|
-2.957110
|
-5.51414
|
-3.55775
|
Log(EERT)
|
-0.25146
|
-2.954021
|
-1.762080
|
-3.552973
|
-3.562404
|
-2.957110
|
-3.49271
|
-3.55775
|
Break unit root test at level and first differences
Tables 4. 2 below summarize the results of the Break unit root test at their levels and first differences, respectively. At the 5% significance level, t-statistics indicate that a unit root can be rejected for the first difference but not for the levels for all variables. As a result, at some levels, all of the variables are non-stationary since their critical value exceeds their computed values. The I(1) process, on the other hand, considers all variables to be stationary at their first difference (table 4.2 ).
Table 4.2 Break unit root test Results at Levels and fist differences
Variables
|
at level
|
first differences
|
|
Intercept
|
Critical Values at 5% level
|
intercept and trend
|
Critical Values at 5% level
|
Intercept
|
Critical Values at 5% level
|
intercept and trend
|
Critical Values at 5% level
|
Log(gdp)
|
0.545794
|
4.193627
|
-2.964801
|
-4.643519
|
-13.69676
|
-4.193627
|
-14.75712
|
-4.643519
|
Log(EDEXP)
|
4.463406
|
-4.193627
|
-3.658887
|
-4.272251
|
-5.964958
|
-4.193627
|
-6.160944
|
-4.272251
|
Log(patent)
|
-0.732469
|
-4.193627
|
-4.523806
|
-4.272251
|
-9.010556
|
-4.193627
|
-8.826774
|
-4.272251
|
Log(RD)
|
0.648372
|
-4.193627
|
-2.401163
|
-4.272251
|
-5.049283
|
-4.193627
|
-8.143103
|
-4.272251
|
Log(capital)
|
3.717630
|
-4.193627
|
-4.635027
|
-4.854031
|
-5.394723
|
-4.193627
|
-6.300273
|
-4.643519
|
Log(labour)
|
-1.207215
|
-4.193627
|
-3.402399
|
-4.272251
|
-9.060485
|
-4.193627
|
-8.996177
|
-4.272251
|
Log(EERT)
|
3.010121
|
-4.193627
|
-2.302198
|
-4.272251
|
-4.076573
|
-3.863839
|
-3.954532
|
-3.387514
|
Sources: Eviews 10 result
Tables 4. 3 below summarize the results of the PP unit root test at their levels and first differences, respectively. At the 5% significance level, t-statistics indicate that a unit root can be rejected for the first difference but not for the levels for all variables. As a result, at some levels, all of the variables are non-stationary since their critical value exceeds their computed values. The I(1) process, on the other hand, considers all variables to be stationary at their first difference (table 4.1 ).
Table 4.3 PP unit root test at a level and first differences
Variables
|
at level
|
first differences
|
|
Intercept
|
Critical Values at 5% level
|
intercept and trend
|
Critical Values at 5% level
|
Intercept
|
Critical Values at 5% level
|
intercept and trend
|
Critical Values at 5% level
|
Log(gdp)
|
0.368230
|
-2.95402
|
-2.866716
|
-3.552973
|
-5.74383
|
-2.957110
|
-5.617694
|
-3.557759
|
Log(EDEXP)
|
0.876807
|
-2.954021
|
-2.817754
|
-3.552973
|
-6.653705
|
-2.957110
|
-7.924089
|
-3.557759
|
Log(patent)
|
-1.453393
|
-2.615817
|
-4.602430
|
-3.552973
|
-11.25886
|
-2.957110
|
-11.15290
|
-3.557759
|
Log(RD)
|
-0.324442
|
-2.954021
|
-2.712358
|
-3.552973
|
-5.749406
|
-2.957110
|
-5.652868
|
-3.557759
|
Log(capital)
|
0.770047
|
-2.954021
|
-1.778046
|
-3.552973
|
-5.601485
|
-2.957110
|
-6.017819
|
-3.557759
|
Log(labour)
|
-0.721049
|
-2.954021
|
-2.718632
|
-3.552973
|
-9.639239
|
-2.957110
|
-16.19734
|
-3.557759
|
Log(EERT)
|
-0.251464
|
-2.954021
|
-1.762080
|
-3.552973
|
-3.562404
|
-2.957110
|
-3.492710
|
-3.557759
|
Sources: Eviews 10 result
Determination of Optimal Lag Length
The number of lags included in the VAR model determines the result of the co-integration test, hence it's frequently preceded by a test of optimal lag length. The best lag length of the VAR model for the co-integration test is calculated using the information criteria.
A critical element in the specification of VAR models and co-integration analysis is the determination of the lag length that could optimally suit the model since all inferences in the model depend on the correct lag order specification. The estimates of a model whose lag length differs from the true lag length are inconsistent. In this study, the determination of the optimal lag order for the VAR model was performed using the Akaike information criterion (AIC), Schwarz information criterion (SC), and Hannan-Quinn information criterion (HQ). In each criterion, the lag with the minimum criterion value is selected as the optimum lag length for the model. Assuming that the data series of the five macroeconomic variables follow a VAR model, we applied the information criteria to specify the order.
Table 4.4 Lag Length
Lag
|
LogL
|
LR
|
FPE
|
AIC
|
SC
|
HQ
|
0
|
-64.63245
|
NA
|
2.08e-07
|
4.477028
|
4.797658
|
4.583308
|
1
|
131.6307
|
294.3947
|
2.25e-11
|
-4.726917
|
-2.161879
|
-3.876680
|
2
|
222.6202
|
96.67633*
|
2.64e-12*
|
-7.351260*
|
-2.541814*
|
-5.757065*
|
Sources:- EViews result
The findings of the unit root test revealed that the variables at mixed levels are stationary. Before using the ARDL bound test, the author double-checked the model's optimal lag duration. The sequence of the ARDL model is primarily determined by the selection criteria for the optimal lags. The author used the AIC method (Akaike Information Criterion) to determine the ideal lag length, which was found to be (1,0,0,1) as shown in the diagram below.
ARDL Bounds Test for Co-integration
The bound test result of the F statistics value is crucial in determining whether it is bigger or smaller than the upper bond's essential values. There is long-run co-integration if the null hypothesis of the bound test is rejected, which indicates that the F statistic is bigger than the upper limit's critical values. If the F statistic is less than the upper bound's critical values, there is no long-run co-integration, and the null hypothesis is accepted.
Table 4.5 ARDL Bounds Test for Co-integration
Test Statistic
|
value
|
K
|
F- statistic
|
23.84534
|
6
|
Critical Value Bounds
|
Significance
|
I(0) Bound
|
I(1) Bound
|
10%
|
1.99
|
2.94
|
5%
|
2.27
|
3.28
|
2.5%
|
2.55
|
3.61
|
1%
|
2.88
|
3.99
|
Sources:- EViews result
Using unrestricted intercept and no trend, the result shows that the value of the F-statistic is greater than the critical value of both lower and upper bounds at 10% and 5% levels of significance. This confirms the existence of a long-term link between economic growth and innovation. In the ARDL bound test, F statistics is 23.84534, which is higher than both the lower and upper bound critical values. At the 1% significance level, the null hypothesis H0 is rejected, indicating that co-integration occurs for this equation. As a result, the dependent variable (GDP) and independent factors have a long-run co-integrated relationship (innovation).
ARDL Long-run Coefficients Estimation
R-squared is less than the DW statistic (0.99<2.318), indicating that the regression model is not spurious. Table 4 shows the long-run ARDL and elasticities model chosen based on AIC.
Table 4.6 model good fit
R-squared
|
0.999499
|
Mean dependent var
|
13.11382
|
Adjusted R-squared
|
0.998892
|
S.D. dependent var
|
0.964042
|
S.E. of regression
|
0.032097
|
Akaike info criterion
|
-3.741813
|
Sum squared resid
|
0.014423
|
Schwarz criterion
|
-2.917337
|
Log likelihood
|
77.86901
|
Hannan-Quinn criter.
|
-3.468523
|
F-statistic
|
1644.258
|
Durbin-Watson stat
|
2.185521
|
Prob(F-statistic)
|
0.000000
|
|
|
|
Sources : Eviews result
From the long run part of the model, the study found that capital, labor, innovation, and human capital were statistically significant and had a positive effect on the growth of the Ethiopian economy (Table 4.6 )
Table 4.7 long -run estimate ARDL model
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
LOG(LABOUR)
|
1.554116
|
0.391150
|
3.973200
|
0.0014
|
LOG(CAPITAL)
|
0.130655
|
0.043205
|
3.024063
|
0.0091
|
LOG(PATENT)
|
0.070611
|
0.031390
|
2.249502
|
0.0411
|
LOG(RD)
|
0.262467
|
0.034153
|
7.684937
|
0.0000
|
LOG(EERT)
|
0.184926
|
0.100174
|
1.846052
|
0.0861
|
LOG(EDEXP)
|
0.112576
|
0.063008
|
1.786698
|
0.0957
|
Sources: Eviews Result
In this study, the ARDL model is chosen by AIC. The results indicated that capital, labor, innovation, and human capital were statistically significant and had a positive effect on the growth of the Ethiopian economy.
Research and development: - Research and development's impact on economic growth the long-term outcome revealed that R&D had a direct impact on economic growth. The results of the ARDL model in the above table indicate that there is a positive and statistically significant relationship between R&DS with economic growth. The result shows a coefficient of 0.262 and a p-value of 0.000, which is significant at a 1% significance level (Table 4.7). This result showed that both research and development and economic growth are moving in the same direction in Ethiopian economic growth. Research and development can help businesses increase productivity by uncovering new and better ways to design, fabricate, and assemble products, as well as new ways to provide services. R&D is a crucial engine of economic growth since it encourages innovation, inventiveness, and progress. R&D spending can be capital-intensive, but it can also lead to breakthroughs that drive both profitability and customer well-being. R&D leads to innovations and innovation, which enhances manufacturing quality and allows for the updating of old technologies. R&D investment will ensure economic progress. This result is supported by different Author's examples, Falk (2007) constructed a dynamic empirical model to determine the importance of R&D investment in OECD nations' long-run economic growth. The study reported that R&D spending was found to be positively connected to GDP growth. KUO & YANG( 2008) indicated that R & D investment and technology imports all contributed considerably to China's economic growth. According to the findings, R & D had the same elasticity to economic growth as technology.
.Enrolment ratio on tertiary education: - The impact of the enrolment ratio on tertiary education on economic growth the long-run result showed that the enrolment ratio in tertiary education directly influences economic growth. The above table shows that there is a positive and statistically significant association between enrolment ratio in tertiary education and economic growth based on the results of the ARDL model. The result has a coefficient of 0.18 and a p-value of 0.08, which is statistically significant at a 10% level (Table 4.7). This indicates that in this study, the enrolment ratio for tertiary education expansion and economic growth are moving in the same direction. Education gives people the skills and information they need to adapt their economies to new technologies that help them grow. In most countries around the world, enrollment rates and years of schooling have increased, owing to consecutive generations of parental involvement in their children's education within the confines of a stable household. Gumus & Kayhan ( 2012) indicated that the relationship between economic growth and school enrollment rates in turkey’s time-series evidence reveals that there is no direct association between changes in GDP per capita and school enrolment rates at the tertiary level. According to another study in Cambodia by Viracheat et al., (2011)the correlation coefficient between the gross enrollment ratio (GER) in higher education and the per capita gross domestic product is 0.992, indicating that the two are positively associated in the regression analysis, which reveals that per capita GDP has a significant positive impact on the country's total enrollment growth in higher education.
Patent: - The impact of patents on economic growth According to the long-term results, patents had a direct impact on economic growth. The above table shows that there is a positive and statistically significant association between patents and economic growth based on the results of the ARDL model. At a 1% significance level, the result indicates a coefficient of 0.7 and a p-value of 0.04, which is significant (table 4.7). This result demonstrates that in Ethiopia, both patents and economic growth are moving in the same direction. National patents help to boost the national industry by allowing local businesses to attract foreign investment and develop export-ready products. Profits from patent exploitation can be used to fund additional research and development, thus boosting commercial and industrial growth. Stronger IP protection makes it easier to transfer high-tech items to emerging countries, thereby expanding the stock of knowledge and enhancing productivity growth, which leads to total economic growth. A patent can be a valuable commercial tool for innovators, allowing them to establish exclusivity over a novel product or technique, build a strong market position, and earn additional cash through licensing. During the research and development (R & D) stage of the technological life cycle, patent protection is typically sought.
Education expenditure: - The influence of education spending on the economy Education spending had a direct impact on economic growth in the long run, according to the results. The above table shows that there is a positive and statistically significant association between education spending and economic growth, according to the results of the ARDL model. The result has a coefficient of 0.11 and a p-value of 0.09, which is significant at a 10% level (Table 4.7). This finding indicates that in Ethiopia, both education spending and economic growth are moving in the same direction. Education spending, which is a measure of education quantity, represents human capital formation, which can result in a trained workforce. This trained worker force can increase the productivity of both physical and human resources, resulting in increased economic growth. According to Otieno (2016), the Kenyan government spends 30% of its budget on education. Education has a considerable positive effect on economic growth. The findings of the study reveal a link between education spending and economic growth in Kenya. The level of education of Kenya's workforce has an impact on the country's economic growth or production level. The empirical results show that education expenditure per worker has a positive and significant impact on economic growth both in the long run and short run in Kenya. Almajdob & Marikan (2019) used balanced panel data from 2000 to 2014 to examine the dynamics of education and economic growth expenditure in five major Arab countries. Pedroni, Kao, and Johansen Fisher's co-integration results reveal that in all countries, there is a long-term balance between education and economic growth expenditure. According to the study, education is a key component of economic growth in all five Arab Spring countries.
The Short-Run ARDL Model
According to Zariah cited to Banerjee, J.J,&R, (1998) the error correction term (EC) that captures the speed of adjustment of a given dependent variable shows that a variable moves towards its long-run equilibrium position if there is a single shock. It also shows how quickly the variable converges to restore equilibrium in the dynamic model and it should have a statistically significant coefficient with a negative sign. The highly significant EC term further confirms the existence of a stable long-run relationship. It also implies that the deviation from the long-run equilibrium level of the current period is corrected by ECM percentages in the next period to bring back equilibrium.
It is well known that the ECM coefficient is theoretically expected to be between -1 and 0. If there is positive ECM, the process does not converge in the long run, leading to problems in the model’s specification, data issues including structural breaks, and the presence of autocorrelation. Therefore, the result shows that the ECM term is statistically significant with a negative sign of 0.90, implying that the speed of adjustment is 90 percent per year so that 90 percent of shock in the system of the equation can be corrected in a quarter.
Table 4.8 Short-Run ARDL Model
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
C
|
-19.81853
|
0.880129
|
-22.51775
|
0.0000
|
@TREND
|
-0.058064
|
0.002620
|
-22.16341
|
0.0000
|
DLOG(GDP(-1))
|
0.092615
|
0.041839
|
2.213617
|
0.0440
|
DLOG(LABOUR)
|
0.341601
|
0.145357
|
2.350093
|
0.0340
|
DLOG(PATENT)
|
-0.011453
|
0.010053
|
-1.139266
|
0.2737
|
DLOG(PATENT(-1))
|
-0.045427
|
0.009835
|
-4.618774
|
0.0004
|
DLOG(RD)
|
-0.015429
|
0.012755
|
-1.209643
|
0.2464
|
DLOG(RD(-1))
|
-0.241142
|
0.018808
|
-12.82102
|
0.0000
|
DLOG(EERT)
|
-0.205522
|
0.065363
|
-3.144296
|
0.0072
|
DLOG(EDEXP)
|
-0.011428
|
0.021591
|
-0.529296
|
0.6049
|
DLOG(EDEXP(-1))
|
-0.067525
|
0.021326
|
-3.166315
|
0.0069
|
CointEq(-1)*
|
-0.907809
|
0.039996
|
-22.69722
|
0.0000
|
On top of the speed of adjustment, the ECM term allows the long-run behavior of the endogenous variables to converge to their long-run equilibrium relationship while allowing a wide range of short-run dynamics. The highly significant error correction term further confirms the existence of a stable long-run relationship. Some coefficients of ECM in the model are statistically significant and negative as expected and support the validity of the equilibrium relationship between the variables in the long run. This also indicates a high rate of convergence to the equilibrium, which implies that a deviation from the long-term equilibrium is corrected by 90 percent over each year.
Granger Causality Test
Granger Causality test is applied to confirm whether there is a causal relationship between the variables encompassed in our empirical investigation. The discovery of stationary variables and co-integration between the innovation proxy and GDP immediately implies that there is long-run causality in at least one direction, either from the innovation proxy to GDP or vice versa. Therefore, it would be useful to test long-run non-causality if cointegration is found. The result of the long-run causality between innovation and economic growth is presented in Table 4.9.
Table 4.9 Pairwise Granger Causality Tests
Null Hypothesis:
|
Obs
|
F-Statistic
|
Prob.
|
LOG(LABOUR) does not Granger Cause LOG(GDP)
|
32
|
8.79419
|
0.0011
|
LOG(GDP) does not Granger Cause LOG(LABOUR)
|
0.93411
|
0.4053
|
LOG(CAPITAL) does not Granger Cause LOG(GDP)
|
32
|
0.93171
|
0.4062
|
LOG(GDP) does not Granger Cause LOG(CAPITAL)
|
4.78251
|
0.0167
|
|
|
|
|
|
|
|
|
LOG(PATENT) does not Granger Cause LOG(GDP)
|
32
|
5.38081
|
0.0108
|
LOG(GDP) does not Granger Cause LOG(PATENT)
|
2.18140
|
0.1324
|
LOG(RD) does not Granger Cause LOG(GDP)
|
32
|
18.9005
|
7.E-06
|
LOG(GDP) does not Granger Cause LOG(RD)
|
0.39688
|
0.6763
|
LOG(EERT) does not Granger Cause LOG(GDP)
|
32
|
0.39617
|
0.6767
|
LOG(GDP) does not Granger Cause LOG(EERT)
|
4.84689
|
0.0159
|
LOG(EDEXP) does not Granger Cause LOG(GDP)
|
32
|
0.82889
|
0.4473
|
LOG(GDP) does not Granger Cause LOG(EDEXP)
|
2.17649
|
0.1329
|
The causal relationship between innovation and the economic growth of the country was analyzed with the application of the causality test. Table (4.9) indicates that both the null hypothesis that capital does not Granger causes economic growth and economic growth does not Granger because capital is rejected. While the null hypothesis that economic growth does not Granger causes labour is not rejected and the null hypothesis that labour does not granger causes economic growth is not rejected. This result indicates that bidirectional causality between labour and economic growth running from labour to economic growth and running from economic growth to labour, this result also supported by In this simple analysis study author took the data on Labor force and GDP in the years of 2002-2009 of Bangladesh and found the correlation between Labor force and GDP (Hossain, 2012) , while the null hypothesis that economic growth does not Granger causes education expenses is rejected and the null hypothesis that education expenses does not granger cause economic growth is rejected. While the null hypothesis that economic growth does not Granger causes education enrolment is not rejected and the null hypothesis that education enrolment does not granger cause economic growth is rejected. This result indicates that unidirectional causality between education enrolment and economic growth running from education to economic growth. These results provide evidence in support of the innovation proxy-led growth hypothesis and as well as the existence of reverse causality. Innovation indicators is one of the fundamental reasons for economic growth in Ethiopia and economic growth also causes innovation indicators to grow. Therefore effort should be direct towards policies that will enhance economic growth (GDP), such as human capital technological development, which will prepare required facility technology the result also support (Gebrehiwot, 2014) bidirectional relationship between real GDP per capita and education implies that education (tertiary school enrolment) is not only a cause for real GDP per capita change but it is also an effect.). And also the null hypothesis that economic growth does not Granger causes patent is rejected and the null hypothesis that patent does not granger cause economic growth is rejected. This result indicates that unidirectional causality between patent and economic growth running from patent to economic growth. The null hypothesis that economic growth does not Granger causes RD is rejected and the null hypothesis that RD does not granger cause economic growth is rejected. This result indicates that unidirectional causality between RD and economic growth running from patent to economic growth.
Diagnostic Tests
Test for residual autocorrelation
A time series is said to be autocorrelated if each term is correlated with its predecessor so that the variance of each term is partially explained by regressing each term on its predecessor. The result of the T-test, F-test, or the confidence interval will become invalid due to the variances of estimators tend to be underestimated or overestimated. Due to the invalid hypothesis testing, it may lead to misleading results on the significance of parameters in the model. In this study to test for the existence of autocorrelation, the popular Breusch-Godfrey Serial Correlation LM Test was employed. The hypothesis for the Breusch-Godfrey Serial Correlation LM test was formulated as follows:
H0: There is no autocorrelation problem in the model.
H1: There is an autocorrelation problem in the model.
α = 0.05 Decision Rule: Reject H0 if p-value less than significance level. Otherwise, do not reject H0.
Table 10 Breusch-Godfrey Serial Correlation LM Test:
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F-statistic
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0.604586
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Prob. F(2,12)
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0.5621
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Obs*R-squared
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2.929289
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Prob. Chi-Square(2)
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0.2312
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As shown in Table 4.10, all versions of the Breusch-Godfrey serial correlation LM test statistic (F-statistic, Chi-Square) gave the same conclusion that there was no evidence for the presence of autocorrelation in this particular study. Since the p-values of 0.5621 and 0.2321 for F-statistic and Chi-Square respectively were in excess of 0.05, the null hypothesis should not be rejected.
Test for residual heteroscedasticity
Regardless of the level of the independent variable, the error term's variance remains constant. The error terms are considered to be homoscedastic if this assumption holds true. Park Test, Glesjer Test, Breusch-Pagan-Goldfrey Test, Whites Test, and Autoregressive Conditional Heteroscedasticity (ARCH) Test are some of the tests used to discover the Heteroscedasticity problem. The Breusch-Pagan-Goldfrey Test was employed to determine the presence of heteroscedasticity in this study. The following is the hypothesis for the Heteroscedasticity test:
H0: There is no Heteroscedasticity problem in the model.
H1: There is a Heteroscedasticity problem in the model. α = 0.05
The Decision Rule is Reject H0 if the p-value is less than significance level. Otherwise, do not reject H0.
Table 11 Heteroskedasticity Test: Breusch-Pagan-Godfrey
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F-statistic
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0.607999
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Prob. F(17,14)
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0.8361
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Obs*R-squared
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13.59104
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Prob. Chi-Square(17)
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0.6958
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In this investigation, all variants of the Breusch-Pagan-Goldfrey statistic (F-statistic and Chi-Square) reached the same conclusion: there was no evidence of heteroscedasticity. The null hypothesis should not be rejected because the p-values for F-statistic and Chi-Square, respectively, were 0.8361 and 0.6958.
Test for Normality
The null hypothesis in normality test is that the error terms are normally distributed. This study used Jarque-Bera test statistic to This study used JarqueBera Test (JB test) to find out whether the error term is normally distributed or not. The hypothesis for the normality test was formulated as follow:
H0: Error term is normally distributed
H1: Error term is not normally distributed
α = 0.05 The Decision Rule is Reject H0 if p-value of Bera-Jarque test is less than significance level. Otherwise, do not reject H0.
Indicate that distribution of the time series observation is symmetric about its mean. The Jarque-Bera statistic has a P-value of 0.845251 implies that the p-value for the Jarque-Bera test is greater than 0.05 which indicates that there was no evidence for the presence of abnormality in the data. Thus, the null hypothesis that the data is normally distributed should not be rejected since the p-value was considerably in excess of 0.05
Model Stability
The cumulative sum of recursive residuals test (CUSUM test) and the cumulative sum of squares of recursive residuals test (CUSUMQ test) are applied to the residuals of the models to check the stability of long-run coefficients that form the error-correction term in combination with short-run dynamics. In order to infer that the model's short run dynamics and long run parameters are stable, the CUMSUM and CUSUMSQ statistics must stay inside a 5% critical constraint.
Both the CUSUM and CUSUMSQ plots do not cross the 5% crucial lines, showing that the estimated coefficients are stable across the study period, making the regression coefficients dependable and suitable for policymaking.