We demonstrated the importance of including inequity in a more comprehensive way, permeating the social dimension and not exclusively limited to income. In the case of infant mortality, education revealed to be more relevant, along with health production, even though inequity was highly significant in the governance dimension alone. Avendano  demonstrated that infant mortality was not explained by income inequality, most likely because the majority of countries with health policies favorable to its reduction acted intersectorally, presenting more homogeneous income distributions.
Countries with a socialist past or that showed an earlier and long lasting model of the Welfare State in the capitalist system, seem to show greater resilience of their health levels in periods of adversity, providing additional protection in relation to the economic crises of capitalism, far beyond their wealth [41,42,43]. In this sense, we observed that the Slavic and Ottoman regions show differential levels of efficiency, even in poorer locations, such as Central Asian countries. The Germanic region, in addition to some countries in the Anglo-Saxon (Canada and United Kingdom) and Latin (France) regions have high levels of efficiency, consistent with more extended social protection. This residual effect, from the socio-historical point of view, manifests itself more as life expectancy than infant mortality, considering the cumulative effect observed in the first one, although prioritizing education also has an effect on the latter. The most affected countries, in this sense, are those that have undergone a more accelerated globalization process, without the prior consolidation of social protection mechanisms, such as the countries of Central America and Asia (south and southeast).
It is noteworthy that those countries belonging to the BRICS (Brazil, Russia, India, China and South Africa) or MIST (Mexico, Indonesia, South Korea and Turkey) have results far below what would be expected from previous predictions, largely due to inequities and the huge income and political power concentrations among the dominant elites, which even hinder economic growth. South Africa stands out negatively in this aspect, in our analysis (60 to 73%), whereas South Korea shows high efficiency results (97 to 98%). The extreme inequalities observed in Brazil, India and South Africa, as well as in Middle East countries, hinder social mobility, access to quality education and productivity. Their causes vary widely, but issues deeply rooted in societies, such as racism and racial segregation, the institutionalization of a caste system, excessive deregulation and the excessive exploitation of natural resources, are important determinants for these results .
There is a strong correlation between the statistical methods applied, in agreement with Joumard , demonstrating that the possibility of gain in life expectancy or infant mortality reduction should be undertaken by public authorities, from a perspective of expanding health resources, which should not be wasted, and where equity should be given its deserved importance, ideally not only income related but also socially concerned . In the case of infant mortality, it is important to prioritize education and the aspects related to health production, such as births performed by skilled professionals, care seeking due to diarrhea in children under 5 years and the reduction in HIV incidence. Income inequality remains in the background in this matter, with equitable access to education and health being more important. On the other hand, direct spending on health (out-of-pocket) has a deleterious association with infant mortality.
Most studies that employ DEA develop their analysis in two stages; thus, after the efficiency operationalization, regressions are performed to evaluate the factors that influence inefficiency. In these evaluations, the Gini coefficient is usually tested; therefore, only income inequality is more frequently analyzed, sometimes remaining as a significant variable, together with per capita income [45, 46]. These authors found an inverse association between the proportion of public funding and health systems efficiency, which leads to the discussion about the relationship between the public-private mix (differences in the public and private funding ratios) and health efficiency, which was not significant in several studies . Berger and Messer  found an association between the proportion of health spending, healthy lifestyles and a higher level of education with reduced mortality. Income inequalities were not significantly associated; additionally, the increase in the proportion of public spending was associated with higher mortality, as opposed to outpatient coverage by private insurance.
Or , on the other hand, showed an association between a high proportion of public funding and lower levels of infant mortality; however, it did not influence life expectancy at age 65. He demonstrated that a high number of per capita physicians is associated with lower rates of premature mortality, perinatal and infant mortality, as well as increased life expectancy at age 65 and a lower incidence of heart disease. Verhoeven et al. . also demonstrated the association between higher levels of efficiency with a higher proportion of immunization and medical consultations. Conversely, they demonstrated that most inefficiencies should be attributed to the lack of cost-effectiveness in the acquisition of medical resources, mainly medication, in addition to high expenditures on the salaries of health professionals, in line with the neoclassical economic theory, prioritizing the relationship between health production and health levels, concealing the financial capital movement .
In our analysis, the density of physicians was a significant variable only in the bivariate analysis. Overall, financial resources remained with greater strength in the analyzed models, with more rigorous results in comparison with physical resources and in agreement with most of the analyzed articles . In the analysis of mortality from preventable causes, using the fixed effects model, the density of physicians was a relevant variable regarding resources, although it did not remain in the final model where the care seeking due to diarrhea in children under 5 years and inequity prevailed.
Differently from many authors, Elola et al. , considered that per capita health expenditure explains a greater proportion of the variance in infant mortality than per capita GDP. Health expenditures are inversely correlated with premature mortality in women and positively correlated with life expectancy in women. Contrastingly, among the assessed European countries, income distribution was not an explanatory variable for the health level. Countries with universal health systems showed greater efficiency in reducing infant mortality, compared to countries with social security. However, no statistical association was found between the health system organization and the health level. More important than the health system organization, the direction towards health financing as a society’s priority, which is sensitive to an equitable distribution, seems to better determine health levels [52, 53].
It is known that a limitation of the DEA methodology is that the efficiency frontier is built based on the comparison between countries; therefore, in our analysis, we tried to include other variables in the model, considering distinct health-production process stages and selecting an output oriented slack model, in order to mediate the construction of this frontier. Dhaoui  carried out an efficiency analysis of the countries in North Africa and the Middle East and found that the per capita income did not influence the results, and that the health level did not prevent countries with intermediate results from remaining on the efficiency frontier. The authors found a positive association with private health financing and corruption control. In our analysis, corruption control was protective for the variable mortality from preventable causes, but it did not remain in the final model.
It is important to consider the reasons why the governance variables proposed by the World Bank, political regimes and financial globalization did not remain in the final models. These variables are relevant and often praised by governments; however, in our study, they did not determine health levels. Thus, we realize that governance is important to increase the transparency of decisions, social participation in democratic regimes and citizenship, when fighting for social rights. The great challenge is the search for the proper balance between globalization and the implementation of measures necessary to reduce infant mortality, aimed at reducing inequities in education and health. Corruption prevention can help to increase the effective proportion of health expenditure and reduce inequities caused by inappropriate privileges. However, the final determinant effect of health levels and efficiency is more strongly related to health equity, education, the proportion of health expenditure and health prevention. There is no trade-off between health equity and the increase of the average health level of the population Joumard et al. .
In our study, the variable Government Effectiveness remained as a significant variable and inversely related to the prevalence of chronic diseases in the governance dimension, when analyzing the proportion of DALYs per chronic diseases. However, it did not remain in the final model, unlike its correlate, the rule of law. In the analysis of the world happiness index, it remained in the final model with a positive sign. Lionel  analyzed data from 150 countries, according to income, concluding that the emission of carbon dioxide, per capita GDP, the control of corruption, population density, the age ranges of the population and government effectiveness were decisive for health expenditure efficiency. This efficiency was obtained by the DEA, based on per capita health expenditure, considering the results in life expectancy at birth and infant mortality.
It is important to note that the variable Rule of Law also remained as relevant in the model for determining life expectancy in the governance dimension. In other words, the capitalist system, based on the construction of the Rule of Law, relies on private property and the implementation of contracts and allows a longer survival, although this survival is linked to a higher proportion of years of life lost due to disability and chronic diseases. However, in the final model, what actually remained as relevant was health expenditure and its distribution, considering social inequities beyond the income.
The variable voice and accountability also showed significant results, but only in the partial models of the governance dimension. This variable captures the perception about the extent of citizens’ participation in the choice of government, as well as freedom of expression, association and media freedom. According to Lancee and Werfhorst , social participation is modified by inequities in health, with lower participation of vulnerable groups in societies with a high degree of inequity.
Ravangard et al.  studied the technical efficiency of the health systems in the organization for economic cooperation, between 2004 and 2010 and found significant associations between per capita GDP and current per capita health expenditure regarding life expectancy and infant and child mortality. No associations were found regarding variables related to physical or environmental resources, such as education and smoking. In our study, we found an association between environmental variables, such as malnutrition, hypertension, fatal occupational injuries and lack of basic sanitation, and both effects, with obesity, alcohol consumption and the prevalence of diabetes mellitus showing an inverse association with infant mortality, showing the contradictions between the scarcity and excess of consumption in capitalism . We understand that these results express a disturbing reduction in social status, because although financial resources are essential, as also demonstrated in our analysis, equally important is how they are distributed, under what perspectives and how they are configured in society. Therefore, Biggs et al.  demonstrated that in times of reduction or stabilization of poverty and inequity, the relationship between material living conditions (per capita GDP) positively influenced health levels, both mediated by life expectancy and infant mortality. On the contrary, when there was an increase in poverty and/or inequity, there was only a residual effect between the studied variables.
Pritchett and Filmer  demonstrated that the variation in infant mortality between countries was mainly attributed to a set of variables: per capita income and income distribution, education among women, ethnic fragmentation and the predominant religion. Public health expenditure was of little importance. However, these variables are not widely available for international comparisons. Therefore, it was not possible to test the variables ethnicity and religion.
The main limitations of this article are related to the different data sources used for international comparisons, which are not always complete and show some discrepancies in their construction. Many variables are not yet available, especially when considering the construction of historical series. Health policies are also not subject to evaluation in this format, despite generating inequities .
The ways social inequities are measured are also quite restricted, as it would be interesting to measure the social status perception, in addition to social position, in the perspective of evaluating social stratification.
The analyzed aggregated data can also hide important relationships within countries, which would be detected at the individual and local levels . However, only comparisons between different countries and sociocultural regions allow us to detect differences that would not be perceived in more homogeneous regions, even with more disaggregated data.
Moreover, any mathematical model tends to reduce the reality. However, aiming to operationalize the elements that we deem relevant to their restoration, we understand that the methods used in this study were the most appropriate ones. Furthermore, the operationalization of the totality of reality is an impossible task and makes it difficult to propose alternatives.