Making correct decisions concerning the variables’ stationary properties is crucial for selecting an appropriate regression approach. Furthermore, determining the long-run nexus between dependent, independent, and control variables is an important step before moving on to our main estimation technique.
4.2. Co-Integration on Panel Data
Pedroni (
2000) has proposed various tests to address the null hypothesis of no co-integration for both homogeneous and heterogeneous panels. This author proposes an extension to the case where cointegration relationships involve more than two variables. These tests take into account heterogeneity through parameters that differentiate individuals. The heterogeneity can be located at the level of the cointegration relationship or at the level of short-run dynamics. The results are presented in
Table 8 below.
Table 9 below presents the seven
Pedroni (
2000) tests of stationarity at the residual level or the target of each relationship that links the sustainable development index as a function of macroeconomic variables, digital economy indicators, and institutional variables for the two groups of developed and developing countries. All of the calculated statistics are lower than the critical value of the centered normal distribution that is reduced to the 5% risk threshold. So, we accept the existence of a long-term relationship and estimate it using the Fully Modified Least Squares (FM-OLS) technique, which was initially proposed by
Phillips and Hansen (
1990) and then extended by
Phillips (
1995). The estimation results are listed in
Table 9.
The estimation of the long-term relationships that link the sustainable development index to the explanatory variables by the modified-least-squares technique with respect to trade openness is significantly negligible. This implies that the contribution of trade openness to this index is very low and even marginal on the socio-economic prosperity of the developed countries. It is also true that the impact of population growth on this sustainable development is very low despite being negative and significant.
On the other hand, the elasticity of this index with respect to gross fixed capital formation is high. Nevertheless, the impact of public spending on this sustainable development is very modest, but remains significant. Mobile subscriptions are less involved in this development, but broadband subscriptions have a strong influence on this sustainable development.
Hence, the development of the digital economy is ensured by the massive use of the Internet and broadband subscriptions. Thus, it is clear that the institutional variables have a negative contribution to this sustainable development.
Estimates of the long-run relationship between social and human development in developing countries are also significant except for public spending. Unlike developed countries, we observe that external openness causes a slight decline in sustainable development of these countries. Similar to developed countries, the population growth rate causes a decline in the sustainable development index of developing countries although the size of this decrease is much greater in these countries than in developed countries.
It is also worth noting that the sustainable development index in developing countries is very flexible with regard to gross fixed capital formation, and the contribution of public expenditure is very marginal. The digital economy indicators have very marginal contributions to socio-economic development, as the elasticity of this index relative to these indicators tends toward zero and are significant. Furthermore, while our hypothesis assumes a clear negative link between corruption and sustainable development, the empirical results reveal only a marginal effect. Corruption control and corruption index have very marginal effects on the socio-economic development of these twenty-seven developing countries. This does not necessarily contradict the theory, but rather suggests that in many developing economies, corruption may be so embedded within institutional structures that its developmental impact is more subtle, normalized, or indirect. Furthermore, widely used corruption indices primarily capture perception-based data, which may not fully reflect the diverse ways corruption manifests or affects specific components of sustainability. These findings highlight the importance of considering contextual factors and measurement approaches when analyzing the role of corruption in development processes. Hence, the human development of developed countries is ensured by this digital economy, but the latter has no contribution to the sustainable development of developing countries.
We now turn to the analysis of the linear fit of each long-run relationship estimated by the fully modified technique within an Error Correction Model (ECM).
This ECM combines the deterministic equilibrium (where variables are stationary by first difference) and long-run equilibrium (where variables are stationary by linear combination), provided that the unit root tests reveal that the residuals or target are stationary at the level. The estimation results of the ECMs are presented in
Table 10 below.
Estimating the deterministic and long-run equilibrium using the modified-least-squares method for the sample of developed countries yields non-significant positive coefficients in the short run for the variables GRP, PUBC, INTU, CPI, and CoCr. However, we observe a very high repercussion of the two numerical indicators, FBS and MS, on the HDI which is reflected by significantly positive coefficients at a threshold of 5%. As for the effect of the TOP variable, it is significantly positive but remains weak. For developing countries, the coefficients of the digital variables are significantly zero. Therefore, the digital economy does not influence the HDI of these countries in the short term
The residuals of each lagged long-run relationship have a negative and significant coefficient. Hence, there is an adjustment mechanism that brings each sustainable development target back to a partially stable situation in the long-term.
This mechanism allows for rectifying the disequilibrium of these relationships over the long-term in developed and developing countries, which are around 2.45% and 0.59%, respectively.
4.3. System GMM Estimation
The estimation of dynamic models of panel data provides a set of techniques, most used of which are notably the methods of
Anderson and Hsiao (
1982) and
Arellano and Bond (
1991). Although with the first method we achieve convergent estimator, this technique does not exploit all of the conditions of the moments, and it does not take into account the structure in terms of the error. Therefore, in this study, we chose
Arellano and Bond’s (
1991) method, which is more efficient. See
Hendayanti and Nurhidayati (
2023) for a more detailed presentation of this model.
The Hausman Test for endogeneity checks whether certain explanatory variables in a regression model are endogenous. For the null hypothesis (H0), in each case, the variable is exogenous (i.e., not correlated with the error term). Since all p-values < 0.05, we reject H0 for all variables at the 5% significance level. This confirms that each variable is endogenous, and OLS is not appropriate. To address this endogeneity, you should use the GMM or 2SLS by utilizing valid instrumental variables for consistent estimation.
Furthermore, the results of the Arellano-Bond test are presented in
Table 11, illustrating that the AR (2) test resulted in a value for the prob = 0.446 > 0.05, failing to reject H
0 (no second-order serial correlation in the residuals of the differenced equation) and that autocorrelation does not happen. In addition, Breusch–Pagan test indicates that the null hypothesis of homoscedasticity is rejected because the
p-value (0.018) is less than 0.05, and this confirms that there is heteroscedasticity in the model. All of these results are good sign of the validity and consistency of the GMM model.
The results of the Human Development Index (HDI) estimation lagged by a single period, along with macroeconomic variables, digital economy indicators, and institutional variables in the developed and developing countries, according to the “one-step” and “two-step” procedures of
Arellano and Bond (
1991), as shown in
Table 12 below.
From
Table 12, we deduce that the estimation of the dynamic model using the two-step technique of
Arellano and Bond (
1991) leads to more consistent results than the one-step technique (
Roodman, 2009). The two-step Generalized Method of Moments (GMM) estimator, developed by
Arellano and Bond (
1991), is well-suited for dynamic panel data with a short time dimension and potential endogeneity. The inclusion of a lagged dependent variable introduces bias that conventional estimators, like fixed or random effects, cannot address. Additionally, variables such as internet use, capital formation, and corruption are likely endogenous. The Arellano–Bond approach overcomes these issues by using internal instruments and eliminating unobserved country-specific effects through first differencing. We apply the two-step estimator with robust standard errors, which enhances efficiency and accounts for heteroskedasticity. Diagnostic tests support the model’s validity; the AR(2) test confirms no second-order autocorrelation, and the non-significant Sargan test indicates that the instruments are valid. Thus, the two-step GMM results serve as the basis for our analysis.
The first observation concerns the coefficient of the lagged variable in this dynamic model, which takes a positive and significant sign for both developed and developing countries. Of course, the level of development achieved yesterday can only improve today’s situation.
In the context of developing countries, the obtained results show that broadband subscription, internet users, control of corruption, gross fixed capital formation, and population change have significant coefficients but with different signs.
The results for Fixed-Broadband Subscriptions (FBS), Anti-Corruption Rate (CoCr), and Population Growth Rate (GPR) show positive impacts on sustainable development, with coefficients of 0.4121, 0.0689 and 0.0498, respectively. In contrast, both the GFCF and INTU variables show a negative effect on sustainable development, with coefficients of −0.2965 and −0.3081, respectively. These variables are significant in our model at a 1% risk level. These results, while contrary to the predominant literature, highlight the unique developmental challenges faced by many developing economies. In such contexts, increased internet use may not contribute to sustainable development if digital infrastructure is poorly distributed or if usage patterns do not support productivity and environmental awareness. Similarly, fixed capital formation may fail to deliver developmental benefits if investments are misallocated, inefficiently managed, or undermined by weak institutions and governance structures. This suggests that technological inputs and capital accumulation alone are insufficient; they must be complemented by effective policy frameworks, institutional quality, and capacity-building measures to translate into meaningful and sustainable outcomes.
The coefficients of Mobile Subscriptions (MS) and Trade Openness of the economy (TOP) variables were positive, but not significant. It is noteworthy that the PCI variable had a negative coefficient (−0.2024) and was not significant. Although Public Consumption (PUBC) significantly affected the Human Development Index, its effect remained negative and very weak.
Concerning developed countries, our findings indicate that Mobile Subscriptions (MS) and Internet Users (INTU) present positive and significant coefficients at the 1% and 5% levels, respectively, while the coefficient of Broadband Subscription (FBS) is negative. Furthermore, the INTU variable has a positive and significant effect on the HDI at a 1% threshold. In fact, a 1% increase in the number of internet users contributes to a 1.4357% increase in sustainable development. Similarly, the contribution of trade openness to sustainable development is positive, with a coefficient of 0.1898.
We also observe a notable difference in the signs for gross fixed capital formation in our estimated model for the two groups of countries. Indeed, although the GFCF coefficient is significant at the 1% level, it is positive (0.3122) for developed countries and negative (−0.2965) for developing countries. Moreover, the coefficients of the institutional variables differ between the two groups of countries. The coefficient of Control of Corruption (CoCr) is positive and significant at the 1% level only for developing countries. However, the estimated coefficients of the Corruption Perspective Index have different signs, as follows: −0.2024 for developing countries and 0.1643 for developed countries. These signs remain non-significant in both cases.
As already mentioned, the impact of the Internet on sustainable development is significantly positive. Thus, the deployment of fixed Internet, beyond being a simple communication tool, as it appears to be in developing countries, plays an important role as basic digital infrastructure affecting almost all sectors of developed economies. This may illustrate the differences in how people use technologies. Regarding the population growth rate variable in developing countries, its estimated coefficient shows a positive contribution to sustainable development. For its part, the corruption control variable positively affects sustainable development in developing countries. However, the estimation result is surprising for developed countries, as its coefficient is negative and non-significant. This could be explained on the one hand, by the abuse of power through corruption practices, which can hinder economic and social development, and, on the other hand, by the non-application of sanctions which renders distinct measures to combat corruption ineffective. When it comes to trade openness, it seems to play a key role in developed countries. This shows that economies that are relatively open to the outside world are developing faster than those that are relatively less liberalized. Thus, thanks to this openness, countries can acquire the needed equipment for digital development.