Reduced Inequalities as Factor of Sustainable Development : The Analysis Under Econometric Models

The paper proposes a different approach for the analysis of the sustainable development in the context of 2030 Agenda. The authors defined and used a cumulative model. For the beginning, the authors compare the dependent variable with the regressors of the four reporting entities: EU28, Romania, Turkey and Switzerland. These entities cover EU, the country of the authors, a candidate country and non-EU country, as well. The analysis is focused on the Goal 10 from the 2030 Agenda Sustainable Development, covers 2000–2017 and is based on the latest official data from Eurostat. The model used by the authors generated high statistical representativeness. The statistical tests demonstrate the model’s homogeneity. A distinct part of the paper is focused on the risk analysis. The authors basically propose a distinct approach which is usefully for the central and regional decision makers. The statistical period took into consideration is good enough to support pertinent conclusions. The analysis leads to the conclusion that Romania can decrease the disparities regarding the sustainable development. On the other hand, the Romania’s progress in achieving sustainable development’s targets is lowest than the EU average. The model proposed in the paper supports the decision makers in achieving a more performant management regarding sustainable development goals. The paper represents a theoretical approach with great applicability to economic development.


Introduction
The implementation of a new sustainable development agenda was finally accepted on September 2015 [1].The United Nations established 17 goals for the next 15 years, in order to ensure poverty's end, planet's protection and prosperity for all.
The European Union, as regional organisation, adopted the sustainable development agenda and pointed out its approach on this [2].
According to the above two documents, the 2030 Agenda Sustainable Development goals are the following:

•
end poverty in all its forms everywhere; • end hunger, achieve food security and improved nutrition and promote sustainable agriculture; • ensure healthy lives and promote well-being for all at all ages; • ensure inclusive and equitable quality education and promote lifelong learning opportunities for all; • achieve gender equality and empower all women and girls; • ensure availability and sustainable management of water and sanitation for all; • ensure access to affordable, reliable, sustainable and modern energy for all; • promote sustained, inclusive and sustainable economic growth, full and productive employment and decent work for all; • build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation; • reduce inequality within and among countries; • make cities and human settlements inclusive, safe, resilient and sustainable; • ensure sustainable consumption and production patterns; • take urgent action to combat climate change and its impacts; • conserve and sustainably use the oceans, seas and marine resources for sustainable development; • protect, restore and promote sustainable use of terrestrial ecosystems, sustainably manage forests, combat desertification, and halt and reverse land degradation and halt biodiversity loss; • promote peaceful and inclusive societies for sustainable development, provide access to justice for all and build effective, accountable and inclusive institutions at all levels; • strengthen the means of implementation and revitalize the Global Partnership for Sustainable Development.
The present paper points out the idea of using a different approach in analysing the Agenda's goals starting to the 10th goal (reduce inequality within and among countries).The same analysis can be extended to the other 16 goals, as well.
This approach is different from that of Ming-Chuan Y., Qiang M., Sang-Bing T. and Yi D., who analysed the 8th goal connected to innovation [3].Other specialists pointed out the impact of the unsustainable development on socio-economic and environment trends [4].
A distinct approach puts into analysis the urban sustainability under the new challenges related to urban population increasing and climate change [5].Some researchers are focused on sustainability for different industries.One of them proposes a sustainability index for the automotive industry [6].
In the same way, other research analyses the sustainability of the water consumption and pollution across the Latin America and Caribbean [7].The importance of the sustainable development led to the need of defining and building business models for sustainability [8][9][10][11][12].
An interesting review of the literature on sustainability transitions covers 386 journal articles during 1995-2014 and concludes that the role of actors and agency in this literature is very complex [13].The need of a sustainable urban development was connected to the cities' key role for general development across the world [14].
A distinct research realises the connection between sustainability and circular economy.The paper succeeds in finding eight different relationship types able to point out the similarities and differences between sustainability and circular economy [15].
The best facing to the sustainability's challenges is the collaboration between government, business environment and stakeholders.More, the government would be incorporated again into the models of effective corporate governance [16].
An interesting approach takes into consideration the mechanisms which perceived job insecurity influences both mental and physical health and on the effect of unemployment on depression [17].
The sustainability depends on investment.This is why the national budget has an important impact in the sustainable development.The connection between budget and sustainability in candidate countries becomes very important [18].
On the other hand, the sustainability can be analysed in connection with Europe 2020 Strategy, which is focused on economic performance and competitiveness [19].
The same competitiveness is pointed out at industrial level in a very interesting paper [20].
The above literature leads to the conclusion of defining and implementing of new performant models for sustainable development.The present paper proposes such models.

Materials, Model, and Methods
The model proposed in this paper is applied to the following economic entities: EU28, Romania, Turkey, and Switzerland.We choose Romania as first analysed entity because is one European state with high economic growth and big gap on sustainable development.Moreover, the latest two economic entities were chosen as candidate EU country and as non-EU country in the same Europe, because we wanted to cover whole diversity of the economic sustainability across Europe.
The model takes into consideration the average trend for 43 economic entities, including the Member States and other non-EU economies (The all 43 economic entities cover: EU-28, EU-27, EU-19, EU-18, Belgium, Bulgaria, Czech Republic, Denmark, Germany, Estonia, Ireland, Greece, Spain, France, Croatia, Italy, Cyprus, Latvia, Lithuania, Luxembourg, Hungary, Malta, Netherlands, Austria, Poland, Portugal, Romania, Slovenia, Slovakia, Finland, Sweden, United Kingdom, Iceland, Norway, Switzerland, Montenegro, Former Yugoslav Republic of Macedonia, Albania, Serbia, Turkey, Bosnia and Herzegovina, United States and Japan).The analysis covers 2000-2017 and is based on the latest official data from Eurostat.The same analysis is focused on the Goal 10 from the 2030 Agenda Sustainable Development, which points out specific sustainable development indicators.The model is representing our original approach.
Figure 1 presents the research analysis scheme which covers three steps.The first step points out the identification procedure in data collecting, the building of the data basis and the indicators used in analysis, including literature review for identifying similarly models or experts' opinion in the area.This step is the same as conceptualisation and its finalisation and validation allow the access to the second step: model defining and statistical testing of the 8 points from 10th goal of the Strategy.
The resulted data are tested under statistical procedures and the model validation allows the pass to the final step: the risk  In order to realise the sustainability analysis, the paper used the Eurostat's data for all 43 economic entities.Moreover, the analysis quantified 43 trend statistical averages and realised tend analyses using mobile average computing to Romania, EU28, Turkey and Switzerland [17].
The statistical data on 2000-2017 have been disseminated statistically, using the impact weights, in order to calculate Romania's sustainable development gaps in relation to the four reporting entities.
As a result, the general evolution table for the eight indicators from the 1 st hypothesis was built.The data were translated by the dedicated software Gretl to models of sustainability analysis for each indicator.It is used as a platform for econometric analysis.The latest version of the software is Gretl-2018b.The models are cumulative and compare the dependent variable with the regressors of the four reporting entities.The general model can be defined as: where V-dependent variable for Romania relative to each indicator presented under 1s hypothesis; V1-V4-regressors obtained by reporting Romania's trends to each of the 4 reporting entities; , , , -regression coefficients; -residual variable.
The data has been modelled in order to validate the model by calculating statistical In order to realise the sustainability analysis, the paper used the Eurostat's data for all 43 economic entities.Moreover, the analysis quantified 43 trend statistical averages and realised tend analyses using mobile average computing to Romania, EU28, Turkey and Switzerland [17].
The statistical data on 2000-2017 have been disseminated statistically, using the impact weights, in order to calculate Romania's sustainable development gaps in relation to the four reporting entities.
As a result, the general evolution table for the eight indicators from the 1st hypothesis was built.The data were translated by the dedicated software Gretl to models of sustainability analysis for each indicator.It is used as a platform for econometric analysis.The latest version of the software is Gretl-2018b.The models are cumulative and compare the dependent variable with the regressors of the four reporting entities.The general model can be defined as: where V-dependent variable for Romania relative to each indicator presented under 1s hypothesis; V 1 -V 4 -regressors obtained by reporting Romania's trends to each of the 4 reporting entities; α, β, γ, δ-regression coefficients; ε-residual variable.
The data has been modelled in order to validate the model by calculating statistical representativeness, homogeneity and data consistency and obtaining information on the relevance of the model for the analysed phenomenon.

Results
The applying of the general model to the Goal 10 indicators in 2030 Agenda leads to the following conclusions.
The model generated a statistical representativeness of 0.988 for "Purchasing power adjusted GDP per capita (G10RI1)" (Table 1).Moreover, the value for test F is close to 0 and the error is normally distributed for the Chi-square statistical test.The equation for the smallest squares regression model is: The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a homogenic distribution for the dependent variable in relation to the regression variable (see Figure 2).The model quantifies the indicator Purchasing power adjusted GDP per capita (G10RI1) and points out that Romania is broadly in line with its sustainability objectives promoted by 2030 Agenda for this indicator.
The second indicator, "Adjusted gross disposable income of households per capita (G10RI2)" (Table 2), has a statistical representativity of 0.993 and value for test F close to 0, but lower than that of the 1st indicator.The error is normally distributed for the Chi-square statistical test (p-value 0.003), according to the regression model: The statistical tests support the model homogeneity: Model 2: OLS, using observations 1-17; Dependent variable: G10RI2R.The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a homogenic distribution for the dependent variable in relation to the regression variable (see Figure 3).The statistical tests support the model homogeneity (Table 3), as: The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a less homogenic distribution for the dependent variable in relation to the regression variable.An inflexion point can be found in the peak of the Gauss' curve.As a result, a difference between normal and predicted evolutions appears in the inflexion point (see Figure 4).The same model points out that Romania faces to a deficit regarding poverty eradication (vulnerable point of 2030 Agenda).The analysis is connected to the indicator "Relative median at-risk-of-poverty gap" and concludes that Romania has the lowest trend between the eight analysed indicators.
"Gini coefficient of equivalised disposable income (G10RI4)" (Table 4) supports the model in generating the greatest statistical representativity (1.0).The value for test F is close to 0, but lower than those of the above three indicators.The error is normally distributed for the Chi-square statistical test (p-value 0.83) and the model equation becomes: The same statistical tests demonstrate the model homogeneity, as:  The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a relative homogenic distribution for the dependent variable in relation to the regression variable.An inflexion point can be found on the downward slope of the Gauss' curve (see Figure 5)."Gini coefficient of equivalised disposable income (G10RI4)" (Table 4) supports the model in generating the greatest statistical representativity (1.0).The value for test F is close to 0, but lower than those of the above three indicators.The error is normally distributed for the Chi-square statistical test (p-value 0.83) and the model equation becomes: The same statistical tests demonstrate the model homogeneity, as: The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a relative homogenic distribution for the dependent variable in relation to the regression variable.An inflexion point can be found on the downward slope of the Gauss' curve (see Figure 5).The model demonstrates that, under "Gini coefficient of equivalised disposable income (G10RI4)", Romania is broadly in line with its sustainability objectives promoted by 2030 Agenda for this indicator.
The indicator "Income share of the bottom 40% of the population (G10RI5)" (Table 5) leaded the model to generate a statistical representativity of 1.0 and a value for test F is close to 0 (close to the above last indicator).The error is normally distributed for the Chi-square statistical test (p-value → 0),) and the model equation becomes: The statistical tests demonstrate once again the model's homogeneity:  The model demonstrates that, under "Gini coefficient of equivalised disposable income (G10RI4)", Romania is broadly in line with its sustainability objectives promoted by 2030 Agenda for this indicator.
The indicator "Income share of the bottom 40% of the population (G10RI5)" (Table 5) leaded the model to generate a statistical representativity of 1.0 and a value for test F is close to 0 (close to the above last indicator).The error is normally distributed for the Chi-square statistical test (p-value → 0),) and the model equation becomes: The statistical tests demonstrate once again the model's homogeneity:  The histogram distribution and prediction diagrams on confidence interval of 95% estimate a non-homogenic distribution for the dependent variable in relation to the regression variable.The maximum point can be found in the peak slope of the Gauss' curve (see Figure 6).The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a non-homogenic distribution for the dependent variable in relation to the regression variable.The maximum point can be found in the peak slope of the Gauss' curve (see Figure 6).The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a non-homogenic distribution for the dependent variable in relation to the regression variable.The accumulation is achieved at the maximum point of the Gaussian curve but with collinearity on the trend evolution (see Figure 8).The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a non-homogenic distribution for the dependent variable in relation to the regression variable.The accumulation is achieved at the maximum point of the Gaussian curve but with collinearity on the trend evolution (see Figure 8).The histogram distribution and prediction diagrams on the confidence interval of 95% estimate a non-homogenic distribution for the dependent variable in relation to the regression variable (see Figure 9).The model demonstrates the impact of the indicator "EU imports from developing countries by country income groups (G10RI9)" and explains that Romania is broadly in line with its sustainability objectives promoted by 2030 Agenda for this indicator.

Discussion
The analysis of the modelling statistical data allows to represent the gaps as matrixes and to realise the risk panel regarding Romania's sustainability on Goal 10 compared to the 4 reporting entities, according to a matrix model, as the following: where: rij ∈ [0, 2], 0 = sustainability, 1 = vulnerability and 2 = risk, with rij = 2* The calculation of the risk coefficients is presented in Table 9.
According to Table 9, there is an oscillating evolution of the annual risk mitigation regarding the  The model demonstrates the impact of the indicator "EU imports from developing countries by country income groups (G10RI9)" and explains that Romania is broadly in line with its sustainability objectives promoted by 2030 Agenda for this indicator.

Discussion
The analysis of the modelling statistical data allows to represent the gaps as matrixes and to realise the risk panel regarding Romania's sustainability on Goal 10 compared to the 4 reporting entities, according to a matrix model, as the following: where: r ij ∈ [0, 2], 0 = sustainability, 1 = vulnerability and 2 = risk, with r ij = 2* G10RIR_AVG * G10RIR_UE28 G10RIR_S * G10RIR_T . The calculation of the risk coefficients is presented in Table 9.According to Table 9, there is an oscillating evolution of the annual risk mitigation regarding the sustainable development.This evolution is quantified by a trend equation as: y = −0.008x+ 0.8676 (see Figure 10).From the significance of the risks, the most significant weights belong to the indicators "Purchasing power-adjusted GDP per capita" and "Adjusted gross disposable income of households per capita", according to Figure 11.
The above figure describes the main impact risk areas across the first quadrant.These areas are represented (above 52%) by the following: "Gross disposable income of households per capita" (24%) and "Purchasing power-adjusted GDP per capita" (28%).The other indicators in the analysis have the lowest signification risk weights, which cover 48% (see Figure 10, second quadrant).From the significance of the risks, the most significant weights belong to the indicators "Purchasing power-adjusted GDP per capita" and "Adjusted gross disposable income of households per capita", according to Figure 11.
The above figure describes the main impact risk areas across the first quadrant.These areas are represented (above 52%) by the following: "Gross disposable income of households per capita" (24%) and "Purchasing power-adjusted GDP per capita" (28%).The other indicators in the analysis have the lowest signification risk weights, which cover 48% (see Figure 10, second quadrant).Table 9's transposition to the risk in Table 10 is realized according to the value allocation:  The evolution in the risk table (Table 10) points out information regarding the risk trend in Romania.All nine indicators in the table belong to 10th objective from the 2030 Agenda and represent the risk presence under "Purchasing power-adjusted GDP per capita", the risk decreases under "Adjusted gross disposable income of households per capita", and the average risk for other indicators are as follows: "Income share of the bottom 40% of the population", "Asylum applications by state of procedure", and "EU imports from developing countries by country income groups".According to the sustainability approach, Romania succeeded in having positive results for: "Relative median at-risk-of-poverty gap", "Gini coefficient of equivalized disposable income", and "People at risk of income poverty after social transfers".This analysis supports further research that is able to quantify the risk sustainability impact on: GDP, Private consumption, Public consumption, Gross fixed capital formation, Exports of goods and services, and the Imports of goods and services.

Conclusions
The above analysis leads to the conclusion that Romania is able to decrease the disparities regarding the sustainable development, except for two indicators: "Relative median at-risk-ofpoverty gap" and "People at risk of income poverty after social transfers".On the other hand, Romania's progress in achieving the sustainable development targets is lower than the EU average.
The general econometric model for the quantification of sustainable development that is proposed in this paper can be used for the other 16   The evolution in the risk table (Table 10) points out information regarding the risk trend in Romania.All nine indicators in the table belong to 10th objective from the 2030 Agenda and represent the risk presence under "Purchasing power-adjusted GDP per capita", the risk decreases under "Adjusted gross disposable income of households per capita", and the average risk for other indicators are as follows: "Income share of the bottom 40% of the population", "Asylum applications by state of procedure", and "EU imports from developing countries by country income groups".According to the sustainability approach, Romania succeeded in having positive results for: "Relative median at-risk-of-poverty gap", "Gini coefficient of equivalized disposable income", and "People at risk of income poverty after social transfers".This analysis supports further research that is able to quantify the risk sustainability impact on: GDP, Private consumption, Public consumption, Gross fixed capital formation, Exports of goods and services, and the Imports of goods and services.

Conclusions
The above analysis leads to the conclusion that Romania is able to decrease the disparities regarding the sustainable development, except for two indicators: "Relative median at-risk-of-poverty gap" and "People at risk of income poverty after social transfers".On the other hand, Romania's progress in achieving the sustainable development targets is lower than the EU average.
The general econometric model for the quantification of sustainable development that is proposed in this paper can be used for the other 16 goals from the 2030 Agenda.The model supports the decision makers in achieving a more performance management regarding sustainable development goals.

Figure 2 .
Figure 2. The dependent variable in relation to the regression variable for G10RI1.Source: authors' contribution using Gretl software.

Figure 2 .
Figure 2. The dependent variable in relation to the regression variable for G10RI1.Source: authors' contribution using Gretl software.

Figure 3 .
Figure 3.The dependent variable in relation to the regression variable for G10RI2.Source: authors' contribution using Gretl software.

Figure 3 .
Figure 3.The dependent variable in relation to the regression variable for G10RI2.Source: authors' contribution using Gretl software.

Figure 4 .
Figure 4.The dependent variable in relation to the regression variable for G10RI3.Source: authors' contribution using Gretl software.

Figure 4 .
Figure 4.The dependent variable in relation to the regression variable for G10RI3.Source: authors' contribution using Gretl software.

*
*, ***: The regression coefficients are proving that the probability density function is disturbed at 0.07, and the figures have medium statistical significance, better than model 1, model 2 and model 3. Test for normality of residual; Null hypothesis: error is normally distributed; Test statistic: Chi-square (2) = 0.371175; with p-value = 0.830616.

Sustainability 2018 ,
10, x FOR PEER REVIEW 11 of 23 risk-of-poverty gap" and concludes that Romania has the lowest trend between the eight analysed indicators.

Figure 5 .
Figure 5.The dependent variable in relation to the regression variable for G10RI4.Source: authors' contribution using Gretl software.

*
*, ***: The regression coefficients are proving that the probability density function is disturbed at 0.04, and the figures have high statistical significance, better than model 1, model 2, model 3 and model 4. Test for normality of residual; Null hypothesis: error is normally distribute; Test statistic: Chi-square (2) = 16.724; with p-value = 0.000233572.
figures have high statistical significance, better than model 1, model 2, model 3 and model 4. Test for normality of residual; Null hypothesis: error is normally distribute; Test statistic: Chi-square (2) = 16.724; with p-value = 0.000233572.

Figure 6 .
Figure 6.The dependent variable in relation to the regression variable for G10RI5.Source: authors' contribution using Gretl software.
: The regression coefficients are proving that the probability density function is disturbed at 0.01, and the figures have high statistical significance.Test for normality of residual; Null hypothesis: error is normally distributed; Test statistic: Chi-square (2) = 4.50435; with p-value = 0.10517.

Figure 8 .Figure 8 .
Figure 8.The dependent variable in relation to the regression variable for G10RI7.Source: authors' contribution using Gretl software.Forecast evaluation statistics Mean Error: 0.00026005 Mean Squared Error: 0.00069148 Root Mean Squared Error: 0.026296 Mean Absolute Error: 0.018066 Mean Percentage Error: −0.016463 Mean Absolute Percentage Error: 1.786

23 Figure 9 .
Figure 9.The dependent variable in relation to the regression variable for G10RI9.Source: authors' contribution using Gretl software.

Figure 9 .
Figure 9.The dependent variable in relation to the regression variable for G10RI9.Source: authors' contribution using Gretl software.
table's building, research's conclusions and dissemination.modelregarding Romania's performances improving in relation to Goal 10 from 2030 Agenda can be developed by mathematical quantification of the gaps; 7.The analysis covers n = 17 years (2000-2017), in order to have enough time period.This period defines the time between Romania's adhering starting negotiations (15 February 2000, Romania's adhering to the EU (1 January 2007) and the economic post-adhering progresses.
*: The regression coefficients are proving that the probability density function is disturbed at 0.14, and the figures have medium statistical significance.Test for normality of residual; Null hypothesis: error is normally distributed; Test statistic: Chi-square (2) = 4.31103; with p-value = 0.115843.
***: The regression coefficients are proving that the probability density function is disturbed at 0.1, and the figures have medium statistical significance, better than model1.Test for null hypothesis of normal distribution: Chi-square (2) = 6.708 with p-value 0.03494.
The model quantifies the indicator "Adjusted gross disposable income of households per capita (G10RI2)", and points out that Romania is broadly in line with its sustainability objectives promoted by 2030 Agenda for this indicator, as well."Relativemedian at-risk-of-poverty gap" represents the indicator with a statistical representativity of 0.998, a value for test F close to 0, but lower than those of the above two indicators.The error is normally distributed for the Chi-square statistical test (p-value 0.75), according to the regression model:
**, ***: The regression coefficients are proving that the probability density function is disturbed at 0.07, and the figures have medium statistical significance, better than model 1, model 2 and model 3. Test for normality of residual; Null hypothesis: error is normally distributed; Test statistic: Chi-square (2) = 0.371175; with p-value = 0.830616.

Table 7 .
OLS, using observations 1-17.Dependent variable: G10RI7R.The regression coefficients are proving that the probability density function is disturbed at 0.01, and the figures have high statistical significance.Test for normality of residual; Null hypothesis: error is normally distributed; Test statistic: Chi-square (2) = 4.50435; with p-value = 0.10517. ***:

Table 9 '
s transposition to the risk in Table10is realized according to the value allocation: Figure 10.The annual risk trend equation.Source: authors' contribution using Gretl software.