4.1 TEST
The section affirms that the model chosen above is appropriate by testing it for multicollinearity, heteroskedasticity, and omitted variable bias. After satisfying the conditions above, further tests of panel data are channelized.
4.1.1 Testing for multicollinearity
Multicollinearity is analyzed through VIF shown below. A vif of more than 10 means there is high multicollinearity in the model, explanatory variables are highly correlated. A vif of less than 10 implies there is no multicollinearity or moderate multicollinearity.
Table 3
Calculation of multicollinearity
VARIABLE | VIF | 1/VIF |
TELFBS | 4.85 | 0.206122 |
FBS | 3.27 | 0.305353 |
TELDFL | 2.77 | 0.361263 |
TELDM | 2.49 | 0.402203 |
UPOP | 2.48 | 0.402817 |
LOGFD | 2.32 | 0.430769 |
MEAN VIF | 3.03 | |
Source: Authors’ analysis |
The vif of all the variables ranges between 2 to 5, hence we can conclude that there is moderate multicollinearity. Our model satisfies the basic assumption of econometric evaluation. Hence we can proceed with the model. It is free of multicollinearity.
4.1.2 Testing for heteroskedasticity
There are two ways through which heteroskedasticity could be analyzed in the model:
Graphical method- In this method residuals are plotted against fitted values. If they don’t form any particular pattern and are scattered, they are free from the problem of heterogeneity otherwise the model has a problem of heterogeneity. In the graph below, the residuals plot cannot determine a specific pattern and, are scattered. Hence our model does not experience the consequences of heteroskedasticity.
Breusch-Pagan test for heteroskedasticity – This is a test for detecting whether the model suffers from the problem of heteroskedasticity or not. If our model fails to reject the null hypothesis then it will be determined that our variance is homogenous. The null hypothesis is set as homoskedastic and the alternative is set as heteroskedastic.
Table 4
Calculation of heteroscedasticity
\({\mathbf{c}\mathbf{h}\mathbf{i}}^{2}\left(1\right)\) | 3.76 |
Prob >\({\mathbf{c}\mathbf{h}\mathbf{i}}^{2}\) | 0.0525 |
Source: Authors’ analysis |
The calculated probability value is 0.0525 which exceeds 0.0500 benchmark (0.0525 > 0.0500) which is, 5% level of significance, hence it is insignificant and we failed to reject our null hypothesis of homoskedastic variance. Therefore, accept that our variance is homoskedastic. Hence our model does not experience the consequences of heteroskedasticity as well.
4.1.3 Testing for omitted variable bias
This test proves that we have included all the relevant variables in the model. Our model is free from the specification error of the omission of the relevant variable. If we reject the null hypothesis of, no relevant variable omitted then our model will have the consequences of omitted variable bias otherwise, our model will not have any relevant variable that is being omitted.
Table 5
Calculation for omitted variable bias
F(3,76) | 3.76 |
Prob > F | 0.6559 |
Source: Authors’ analysis
When the estimated probability-value is less than the significance level of 5%, then we fail to accept the (H0) null hypothesis and the (H1) alternative hypothesis is true and vice-versa. Here, the calculated p-value is 0.6559 which exceeds a 5% level of significance.(0.06559 > 0.0500). Hence our statistics are insignificant. We fail to reject H0 and hence accept that our model has no omitted variable.
The above three tests conclude that our model is fit to proceed ahead.
The Table 6 summaries, descriptive statistics of the variables used in the model.
Table 6
Summary statistic of the model
VARIABLE | OBS | MEAN | STANDARD DEVIATION | MIN | MAX |
GDP | 100 | 4.879424 | 3.829442 | -7.799994 | 14.23139 |
UPOP | 100 | 58.79107 | 19.5669 | 27.24 | 86.309 |
FBS | 87 | 3.24e + 07 | 7.07e + 07 | 1000 | 3.94e + 08 |
TELDFL | 100 | 15.60676 | 9.056403 | 1.735646 | 31.79035 |
TELDM | 100 | 67.37098 | 52.46879 | .1172554 | 165.661 |
TELFBS | 87 | 5.240434 | 6.555859 | .000589 | 27.7399 |
FDI | 99 | 352819.8 | 362836.2 | 12911.9 | 1488676 |
Source: Authors’ analysis |
The study is of five countries for which data is collected for 20 years, hence there are 100 observations. Observation of some variables is less than 100 as the data before 2000 was not available for these variables. The minimum broadband subscription was 1000 in 1998 for Brazil and the maximum was found to be for China in the year 2017, 394190000. The GDP was negative for the year 2009 in Russia and the maximum GDP in the data was seen for China for the year 2007,14.23139.
A panel data deals with pooled OLS, the FE, and the RE model. The panel data is strongly balanced implies that all the data contain all the observations of the same time points. The F- Statistic elucidate whether pooled OLS is a better approach than the FE model or vice-versa. Under, F- Statistic the null hypothesis is that the pooled OLS model is applicable and the alternative is set as using the FE model will give reliable results. Hence, on calculating F statistic it was 8.65 and its p-value was 0.000. Therefore it was less than a 5% significance level and we failed to accept the null hypothesis. Hence, using a FE model will result in more reliable results.
The Table 7 presents the estimates of the FE model and the RE model.
Table 7
FE Model and RE model statistic
VARIABLES | FIXED EFFECTS | RANDOM EFFECTS |
GDP | | |
UPOP | 0.2186471 (0.2143586) | -0.1261503* (0.0193751) |
FBS | 3.18000000000 (1.5100000000) | 2.0200000000* (6.11000000000) |
TELDFL | 0.2362072** (0.0865262) | 0.1869626* (0.0432241) |
TELFBS | -0.1923961*** (0.1097589) | -0.311836* (0.0804083) |
TELDM | 0.0467667** (0.0174285) | -0.0102819 (0.0075854) |
LOGFD | 2.167737* (0.6377007) | 1.068024** (0.361576) |
CONSTANT | -34.34762 (14.79669) | -2.069656 (4.376233) |
R-Square | 0.0123 | 0.6919 |
*1% level of significance,**5% level of significance,***10% level of significance |
Standard error values are in bracket.
Source: Authors’ analysis
The following analysis is done on 3 different levels of significance, 1% 5% and 10%. On analyzing the above table it was found that FBS is statistically significant at 1% significance level in the case of the RE model and is also positively related to GDP whereas it is insignificant at all levels of significance in the FE model and the result is that it does not influence GDP. Therefore, our foremost objective is to decide which model should be appropriate for our study and analysis.
The Hausman test is used to shed light on this question. The null hypothesis in the Hausman test is that the FE model and the RE model estimates do not contrast considerably. If we reject the null hypothesis then the RE model will be inappropriate because the individual effects in the RE model will probably correlate with one or more regressors. In such circumstances, the FE model is preferred over the RE model. Otherwise, the RE model will be chosen.
4.1.4 Hausman test
The test statistic in the Hausman test has an asymptotic \({\text{c}\text{h}\text{i}}^{2}\)distribution. The table below states chi2 value and p-value. Based on the p-value we will determine either to choose the RE model or the FE model.
Table 8
Calculation of Hausman test
Chi2(5) | 6.49 |
Prob > Chi2 | 0.2637 |
Source: Authors’ analysis
On analyzing the above test, the calculated probability-value is 0.2637. The calculated probability-value exceeds a 5% level of significance (0.2637 > 0.0500). This means that our statistic is insignificant and we fail to reject our null hypothesis of the RE model. Therefore, the RE model is applied for further analysis.
4.1.5 RE model
Table 9: The random effect model analysis,
Source: Authors’ analysis
The RE model is approximated through Feasible generalized least squares or generalized least squares. In the case of the RE model, OLS gives inappropriate results. Moving back to our research question, whether the fixed broadband subscription has significance on economic growth or not? On examing the p-value of FBS it was found to be 0.001. If the estimated probability-value exceeds a 5% significance level then we fail to reject our null hypothesis and we are supposed to accept our alternative hypothesis. Here, the calculated probability-value is found to be less than a 1% level of significance, 0.001 < 0.010. It also examined that the estimated value is less than a 5% significance level. It implies that our FBS is significant at both 5% and 1% significance level. When it is substantial then we fail to accept our Null hypothesis, that FBS does not affect GDP. Hence, accepting the alternative hypothesis it is proved that FBS has a considerable impact on the financial growth of nations.
Moving forward to analyze its correlation with GDP. It was ascertained that the sign is positive. Hence, a fixed broadband subscription is positively related to economic growth. With a 1 unit increment in FBS, there is a hike of 2.02e + 08 units of GDP, keeping other variables constant. The goodness of fit of a model is calculated from R square. In the above RE model, the calculated value of R square is 0.6919. Hence our model is approximately 69% appropriate.
4.1.6 Checking for heteroskedasticity
For detecting heteroskedasticity in the RE model there is no specific test. Hence we should find the robust standard error. If the robust standard error significantly differs from the standard error of the econometric model that is run without robust command then it implies that the model had a problem of heteroskedasticity and it has been taken into account.
Table 10
Standard errors and robust standard errors
VARIABLE | STANDARD ERRORS | ROBUST STANDARD ERRORS |
UPOP | 0.0193751 | 0.0117391 |
FBS | 6.11e + 09 | 2.91e + 09 |
TELDFL | 0.0432241 | 0.0234493 |
TELDM | 0.0075854 | 0.008378 |
TELFBS | 0.0804083 | 0.046121 |
LOGFD | 0.361576 | 0.2870942 |
CONSTANT | 4.376233 | 3.165682 |
Source: Authors’ analysis |
As it is visible from the Table 10 the standard errors are significantly different from the robust standard errors. Therefore, it is inferred that our model suffered from the consequences of heteroskedasticity. On using robust command we have corrected our model for heteroskedasticity. Hence, our model justifies the problem of heteroskedasticity as well.
Table 11
Random effect analysis with standard robust errors,
Source: Authors’ analysis
Concerning the significance of FBS, it was still found to have a considerable affect on the economic growth and is positively related with GDP. The calculated probability-value is 0.000 having significance at both 5% and 1% significance level. Hence, we fail to accept the Null hypothesis. With a unit increment in FBS, there is a hike of 2.02e + 08 units of GDP, keeping other variables constant.