Linking Human Development and the Financial Responsibility of Regions: Combined Index Proposals Using Methods From Data Envelopment Analysis

Several indicators on human development and capabilities have been introduced in recent decades that measure the level of absolute deprivations and freedoms of people. However, these indicators typically do not consider to what extent regions and countries efficiently spend their limited financial resources on improving human development. This is an important shortcoming because regions typically face different financial constraints in developing social policies and promoting human development. In this article, we advance methods from Data Envelopment Analysis (DEA) to measure absolute capability values and the social efficiency of 129 Brazilian mesoregions, considering their heterogeneous financial means. We present a new indicator called Capability Index Adjusted by Social Efficiency (CIASE) that evaluates the human development performance of regions based on their absolute levels of deprivations as well as their social efficiency in translating limited financial resources into human development. Moreover, we introduce a Deprivation and Financial Responsibility based Prioritization Index (DFRP) that helps to identify priority regions for higher public expenditures in human development. Our results for the case of Brazil show that several poor regions perform relatively better in terms of social efficiency than in terms of absolute human development. Conversely, several rich regions perform relatively worse in terms of social efficiency than in terms of absolute values. Thus, our analysis shows how DEA methods can help to bridge perspectives that are often presented by politics as antagonistic, but instead could be strong allies for development: attending to human deprivation and promoting social efficiency.


Introduction
The human development and capability approach argues that the expansion of human freedom, and thus the reduction of deprivations and multidimensional poverty, is the essential goal and driver of development (Sen 1982(Sen , 1988UNDP 2016). An extensive amount of research has shown that focusing on human capabilities and freedom, instead of mere focus on commodities or economic growth, allows for a better understanding of a wide range of social phenomena, such as poverty, inequality, or the quality of life (Sen 1982(Sen , 1988Nussbaum 2000;UNDP 1993UNDP , 2016. A number of indicators that are based on human capabilities rather than income have been proposed, such as the Human Development Index (HDI), the Human Development Index Adjusted for Inequality (HDIAD), or the Multidimensional Poverty Index (MPI) (UNDP 2016;Ul Haq 1973;Alkire and Foster 2011). These indicators help policy-and decision-makers to compare the absolute level of human development and deprivation in their regions and countries and identify potential bottlenecks.
Nevertheless, these absolute indicators of human development and deprivation do not measure to which extent policy-and decision-makers make good use of limited financial resources for the sake of human development improvements in their region or country (Despotis 2005a(Despotis , 2005bReig-Martínez 2013). Consequently, these absolute indicators do not incorporate some essential aspects of development policies: namely (i) the scarcity of financial resources, (ii) the efficiency of development expenditures, and (iii) the political willingness of other regions and countries to invest in certain regions based on the perception of efficient use of their financial support. The human development approach made an important point in emphasizing that not only income and growth should be considered as means and goals of development. Moreover, they showed human deprivation, such as hunger, is frequently rather a problem of distribution than of economic production and wealth (Dreze and Sen 1990). But that does not mean that funding and efficiency does not matter at all. Indeed, efficient use of limited resources that aims at achieving human development could be considered as both a financial and social responsibility (Sen 2009) of countries and regions. In this study, we understand financial responsibility as the ability and political desire of public authorities to manage limited financial resources in a socially efficient manner, aiming at improving people's capabilities (Frericks and Höppner 2019). It is essential to consider financial responsibility; firstly, because in particular developing regions tend to have limited financial resources; and secondly, the willingness of financial transfers from other regions depends on the perception of efficient and effective use of their financial funds. If regions and their policy-and decision-makers make inefficient use of resources, the willingness of donors or taxpayers from other regions to help a particular region can decline (Timmons and Garfias 2015;Sousa et al. 2017), despite of a potential awareness of substantial human deprivations in the less developed regions.
Electronic copy available at: https://ssrn.com/abstract=3401374 Policy emphasis on "promoting human development" or "improving the efficiency of expenditures" are often discussed separately and sometimes even framed as antagonists. In practice, though, focus on human development and efficiency can be important allies. A higher level of human development can lead to a higher level of social efficiency, but per definition social efficiency can also contribute to human development and thus facilitate a virtuous cycle of human development expansion. Therefore, policy emphasis should arguably focus not only on human deprivation, but also merit the social efficiency and financial responsibility of converting financial resources into human development. It can be argued that a poor region that does a good job in translating limited financial resources into the best possible outcomes for the local population should be merited and prioritized for development funding. But how can such regions be identified, and thus social efficiency being incentivized?
Methods from Data Envelopment Analysis (DEA) can help to address this difficult question, because they allow us to measure both the social efficiency of regions and taking heterogenous human development strengths and weakness of regions into account. DEA uses methods from mathematical linear programming to measures the efficiency of decision units (e.g. in our case regions) to translate inputs (e.g. social expenditures and GDP) into the best possible output levels (e.g. in human development). DEA methods can be used to reveal the maximum number of social outputs that can be produced per unit of economic wealth and public expenditures by comparator countries or regions. Thus, DEA is perfectly suited to measure the social efficiency of regions converting financial resources into human development. This allows for a better identification of inefficiencies and bottlenecks of regions as well as facilitates learning from comparatively more efficient regions that achieve higher levels of human development with the same or less financial resources.
Electronic copy available at: https://ssrn.com/abstract=3401374 We apply DEA methods to the case of Brazil, because it is a country with stark socioeconomic contrasts, and thus substantial statistical variance, between more and less developed regions. Brazil is a country that suffers from heterogenous problems of multidimensional poverty and social inefficiencies across its vast territory. This heterogeneity makes it a perfect case to illustrate how methods from DEA can help to analyze different types of absolute human deprivation and social efficiency of regions. A valuable advantage of DEA is that it allows us to assign different weights to strengths and weakness of different regions in different dimensions of human development.
In sum, this article illustrates how considering both the absolute level of capabilities and deprivation, as well as how social efficiency allows for a more comprehensive analysis of the human development achievements of regions and helps to identify priority regions for public expenditure based on both their financial responsibility and need for help. To calculate indices on human development and social efficiency, we use regional data from the last Brazilian Census (2010). First, we calculate primary indexes to measure absolute performance and relative efficiency. Second, we create composite indicators combining social deprivation and social efficiency. Third, we create two indicators: a) the Capability Index Adjusted by Social Efficiency (CIASE), to rank regions according to social deprivation and social efficiency; and b) the Deprivation and Financial Responsibility based Prioritization Index (DFRP) to reveal poor regions that show high levels of efficiency. In order to ensure methodological homogeneity, we analyzed both the absolute and relative indices with DEA methods.
It can be argued that regions that show both high levels of human deprivation and high levels of social efficiency should be merited by public investment. Instead, reasons for relatively worse performance in social efficiency in comparison to the human development performance of a regions points to the need of in-depth studies on how these regions can use their financial resources more efficiently to reaching their human development potentials. This does not mean that a single analysis of absolute levels of human deprivation as well as social efficiency are not relevant anymore. Of course, profound levels of human deprivation and severe problems of social efficiency need to be addressed. Nonetheless a joint consideration of both absolute deprivation and social efficiency faciliates important new empirical insights, theoretical debates, and applied policy measures on how to promote human development under financial constraints. Moreover, it facilitates to identification of strengths, weaknesses and human development improvements potential of regions with poor, medium as well as high levels of human development.
The remainder of this article is structured as follows. Section 2 provides a literature review on absolute measures of human development as well as on social efficiency measures using methods from DEA. Moreover it discusses the social conditions and regional differences in Brazil. Section 3 introduces the data and our methods, including the creation of two new indicators. Section 4 presents the results, including a sensitivity analysis of the ranking positions Electronic copy available at: https://ssrn.com/abstract=3401374 of Brazilian mesoregions with respect to their DEA capability index (DCI), social efficiency index (SEI), Capability Index Adjusted by Social Efficiency (CIASE), and the Deprivation and Financial Responsibility based Prioritization Index (DFRP). Moreover, we discuss reasons for several case regions changing ranking positions in the respective indicators placing either more emphasis on absolute human developmetn values or social efficiency. Finally, Section 8 provides concluding remarks.

Absolute measures of human development and multidimensional poverty
According to the United Nations, human development is a process of enlarging freedoms for all human beings and depends on individuals' capabilities and freedom to achieve functions (Sen 1979(Sen , 1980(Sen , 1982(Sen , 1988Sen 1993, 2000;Robeyns 2005aRobeyns , 2005bRobeyns , 2006UNDP, 2016). To understand this phenomenon, the HDI is measured as the geometric mean of education, life expectancy and income (UNDP, 2016).
However, the HDI has received multiple criticisms. According to Sagar and Najam (1998), the HDI reflects a distorted world which is incapable of presenting a comprehensive view of human development dimensions. For Bilbao-Ubillos (2012), the HDI reflects an average, neglecting population groups that have not benefited from HDI achievements. There are several other issues of criticism and debate, such as the need of composite and qualitative educational measures, income logarithms and adequate normalization processes, as well as the need to consider additional human development dimensions like gender and income inequality, safety and homicides, democracy, environmental variables, refugees' living conditions, and discrimination (Herrero et al. 2010;Bilbao-Ubillos 20112012Nussbaum 2000;Fukuda-Parr et al. 2010;Domínguez et al. 2011;Kaufmann et al. 2008;Grimm et al. 2008;Seth 2009Seth , 2010. To address these limitations, several studies have developed new indexes. For instance, Ranis et al. (2006) Kaufmann et al. (2008) introduced the importance of political participation in human development. Grimm et al. (2008) developed a new method incorporating the income distribution effects on human development (based e.g. on the critique of Hicks 1997). Ravallion (2010) reformulated HDI with a cumulative function for education, income, and health, and Herrero et al. (2010) demonstrated that HDI's measurement can be improved.
A recent influential indicator is the Multidimensional Poverty Index (MPI), which looks beyond income to understand how people experience poverty in multiple and simultaneous ways Electronic copy available at: https://ssrn.com/abstract=3401374 (Alkire and Foster 2011;UNDP 2016). However, MPI also does not appraise financial responsibility and social efficiency. In sum, all of these indicators have focused only on the absolute levels of human development and deprivation. But these indicators do not consider the social efficiency of regions in translating financial resources into human development.

Social efficiency and relative measures of human development
Social efficiency quantifies how efficient regions are in converting economic wealth into social welfare (Mariano and Rebelatto 2014). The resulting ranking allows for a comparison of the social efficiency of regions. In contrast to human development indexes, the calculation of social efficiency requires the application of more complex methods, such as Data Envelopment Analysis (DEA) and stochastic frontier analysis. These techniques consider the role of public expenditures, using them as inputs to promote social development (Davies and Quinlivan 2006;Bilbao-Ubillos 2012;Wu et al. 2014). Furthermore, social efficiency takes into account the economy size and avoids subjective weighting choices.
Despite the growing literature on social efficiency (a structured literature review can be found in Mariano et al. 2015), there are not any studies, to our best knowledge, that combine absolute deprivation and social efficiency aspects. While previous studies focused on absolute deprivation and relative efficiency separately, we argue that both elements must be analyzed together. Moreover, federal governments face scarcity of financial resources, requiring authorities to distinguish regions that better merit receiving public investments.
To address both absolute deprivation levels and social efficiency simultaneously, we present here a combined indicator called Capability Index Adjusted by Social Efficiency (CIASE).
This indicator helps policy-makers to identify in areas with both high absolute levels deprivation and merit financial responsibility. We analyzed Brazil, because of its significant regional differences, with the North and Northeast being less developed, and the South and Southeast more developed (de Sousa e Ramos 2017; Monteiro and Lima 2017).

Using DEA to construct social indicators
Since 1993, DEA has been employed in social indicators research due to it having several advantages. For example, DEA addresses multidimensional efficiency problems, provides easy interpretation in a single index, and attracts the interest of decision makers (Saisana and Tarantola 2002;Nardo et al. 2005;Boncinelli and Casini 2014;Chaaban et al. 2016). In this technique, the weights are defined endogenously, which tackles some of the criticisms of the standard HDI (Sagar and Najam 1998;Wu et al. 2014;Chaaban et al. 2016).
Electronic copy available at: https://ssrn.com/abstract=3401374 Several human development indexes were derived from DEA. For Mariano et al. (2015), these indices are divided into two categories: (1) composite indices (absolute performance); and (2) social efficiency indices (relative performance). Studies that use this model to evaluate absolute performance are divided into two approaches: a) the Benefit of the Doubt (BoD) model, which contains outputs and a single input equal to 1 (Bougnol et al. 2010;Zhou and Zhou 2010;Bernini et al. 2013); and b) models including inputs and outputs that do not express a production relation (e.g. measuring per capita or cost-benefit indicators) (Boysen 2002;Murias et al. 2006;Guardiola and Picazo-Tadeo 2014;Mariano et al. 2015).
Many works used DEA to measure relative indices of human development. For instance, Mahlberg and Obersteiner (2001) used the Constant Return of Scale (CRS) model with weight restrictions to measure human development. Despotis (2005aDespotis ( , 2005b  Several other articles analyzed social efficiency with DEA methods. For instance, Despotis (2005a) constructed a social efficiency index for the countries and found that Canada, Sweden, Japan, the United Kingdom, New Zealand, Spain, and Greece were socially efficient. In an analysis restricted to Asia, Despotis (2005b) found that Fiji, Hong Kong, South Korea, Mongolia, Myanmar, Nepal, Philippines, Solomon Islands, Sri Lanka, and Vietnam were social efficient. Other works, such as Raab and Habib (2007) and Malul et al. (2009) measured efficiency using Gross Domestic Product, Gross National Product, Gini index, and gender performance to compared social efficiency across countries. Morais and Camanho (2011) calculated social efficiency using GDP per capita as the input and 29 indicators of quality of life as outputs. Mariano and Rebelatto (2014) applied DEA with weight restriction and tiebreaking methods in a global analysis of social efficiency.

The Brazilian challenges to development
Despite several studies measuring social efficiency, we did not find works simultaneously analyzing the social deprivations and efficiency values of regions in Brazil. This analysis is crucial because Brazil has managed to decrease poverty and inequality by increasing social expenditures, such as conditional cash-transfer programs, enabling more than 29 million Brazilians to leave poverty between 2003 and 2014 (World Bank 2018). However, Brazil continues to be a highly unequal and structurally heterogeneous country (Hartmann et al., 2019). Moreover, it continues to face bureaucratic, economic and political inefficiencies, and a large number of cases of corruption may undermine the efficiency and effectiveness of social expenditures (Osipian 2013;Sousa et al. 2017).
According to the Oxfam report (2017), corruption negatively impacts public expenditures on health, education, infrastructure and other projects funded by the government. For example, there are cases of corruption in many public services, such as school meal contracts, procurement of public health supplies, and private business linked to politicians and public enterprises (OXFAM, 2017). According to the Federal Court of Accounts (TCU), from R$ 100 billion to R$ 300 billion of public money were embezzled between 1970 and 2016. This amount corresponds to three times of the federal government expenditures on education in 2016 (OXFAM, 2017).
This means it is crucial to consider financial responsibility in Brazil, because corruption may negatively affect the Brazilian infrastructure and human development.
Brazil's infrastructure underperforms compared to other emerging economies, due to inefficiencies in the ports and rail system, which reduces its international competitiveness and its exports (Armijo and Rhodes 2017;Marchetti and Wanke 2017;Beuren et al. 2018). The public health and education systems are also criticized, due to inefficiency in the financial resources management and quality problems (Araujo et al. 2018). For example, the average performance of students in Brazil is significantly below the OECD average, placing Brazil internationally among the ten bottom positions in science (65 th ), reading (58 th ) and mathematics (63 rd  There are two social realities in Brazil according to the region in which a person lives. The less developed North and Northeast present regions like Maranhão, where only 32.7% of the population benefit from a garbage collection system, or Rondônia (54%) where half the population lives without a water supply system; or Piauí where only 8.3% of the population have access to a sewage system. In contrast, South and Southeast have better living conditions. For example, in São Paulo, the richest state of Brazil, almost the entire population has access to a garbage collection (98.8%), water supply (96.4%), and sewage system (93%) (IBGE 2019).
Despite the better living conditions and absolute indicators in São Paulo, some studies have argued that São Paulo is not efficiently spending its public money. According to Andrett et al. (2018), Sao Paulo's public health expenditures were inefficient in providing vaccination, basic care, hospitalizations, and outpatient care between 2005 and 2014. For Varela et al. (2010), only 6.41% of the municipalities from the State of São Paulo are efficiently spending public funds in primary health care. Furthermore, Coelho (2008) argues that the richest populations in the municipality of São Paulo tend to benefit more than the poorest from public spending in health.
In this sense, the inefficiency in public expenditures reveals how even in developed regions people can be affected by the lack of financial responsibility for human development and social efficiency.
To face this heterogeneity, Brazil has been developing social policies to reduce income inequality, food insecurity, housing deficit, and to raise the federal minimum wage (Saad-Filho 2015;Hall 2006;Rocha 2009;Campos and Guilhoto 2017;Maurizio and Vazquez 2016;Brito et al. 2017). However, since the recent corruption scandals, many Brazilians doubt the efficiency of public policies. The federal government has fewer funds, due to the Constitutional Amendment limiting public spending until 2027 (Emenda Constitucional 95/2016). This challenging scenario requires greater financial responsibility to convince Brazilians that social policies generate a higher quality of life.

Database
To evaluate human development and social efficiency in Brazil, we covered 5 main dimensions represented in 14 social variables from the latest Brazilian census (IBGE 2019). We justify the choice of Brazil due to the availability of a reliable and comparable census data (Chaaban 2009;Chaaban et al. 2016). This database captures information of 3,734 municipalities and represents 67.18% of all inhabitants of Brazil in 2010. The municipalities are divided into 129 mesoregions. According to IBGE (2017), a mesoregion is an area, within a federal state, which presents a form of geographic space organization defined by the following dimensions: the social process, natural environment, and the communication network. These three dimensions enable the space delimited as mesoregion to have a regional identity. This identity is a reality built up over time by the society that formed there.
To analyze relative efficiency, the DEA inputs were wealth (GDP) and public  Table 1.

Econometric validation
DEA is a non-parametric technique requiring econometric validation to prove causality (Charnes et al. 1978;Cook and Zhu 2014;Mariano et al. 2015). For this reason, we validate our data with fourteen econometric panels fixed effect models 2 . All variables were statistically significant, proving the impact of wealth and public expenditures on social dimensions, which validates the DEA procedure. The estimates are presented in Appendix I.
For the education dimension, we found that GDP and expenditures in education and culture have a positive impact on the number of literate people and the number of day care centers. For the housing conditions, GDP and expenditures in housing improve public services (electricity, sewage, and garbage collection), as well as decrease the housing deficit.
For the health dimension, GDP and public expenditures in health increase life expectancy and the number of vaccinated people. On the other hand, investing in health decreases the child mortality rate. Furthermore, the economic dimension shows that GDP and expenditures in education increase employment. In contrast, they reduce income inequality (Gini index and the number of extremely poor people).
For institutions, our findings suggest that democracy is positively impacted by GDP and expenditures in education. Homicides are reduced by investing in education. However, GDP increases the rate of homicides, which explains violence in richer Brazilian urban areas.

Measuring Data Envelopment Analysis (DEA)
Since the econometric results validate the relation between inputs and outputs, we DEA is a mathematical method based on linear programming developed by Charnes et al. (1978). This method measures the efficiency of Decision-Making Units (DMUs) with an empirical linear frontier. It reveals the maximum number of social outputs that can be produced per unit of wealth and public expenditures. Thus, it represents the production limit determined by the financial restriction of a region (Cook and Zhu 2014;Mariano and Rebelatto 2014).
According to Cook and Zhu (2014), each region can be ranked according to its efficiency, which varies between zero (no efficiency) and one (full efficiency). To reach the top ranking, DEA maximizes weights, focusing on the strengths of each region (Mariano et al. 2015). DEA models mainly differ according to the type of returns to scale and orientation. The hypothesis of the CRS model considers that outputs vary proportionally to inputs (Charnes et al. 1978). On the other hand, the VRS model identifies variation among inputs and outputs, proposing three frontier areas: a) increasing, where outputs grow proportionately more than inputs; b) constant, where there is proportionality between inputs and outputs; and c) decreasing, where outputs grow proportionally less than inputs (Banker et al. 1984). The advantage of VRS models is that it allows for the relative comparison among regions with different financial conditions, as shown in Table   2.
Electronic copy available at: https://ssrn.com/abstract=3401374  Mariano and Rebelatto (2014, p. 5) Where: jk x represents the amount of the wealth j of a region k; ik y represents the amount of the social dimensions i of a region k; j0 x represents the amount of the wealth j of the region; i0 y represents the amount of social variables i of the region; j v represents the weight of the GDP and public expenditures j for the region; i u represents the weight of social dimension i for the region; θ means the efficiency of the Brazilian region being analyzed; k λ is the contribution of the region k to the goal of the region; m is the quantity of analyzed social dimensions; n is the quantity of GDP and public expenditures analyzed; and w represents the scale factor.

=1
Subject to: Subject to: Subject to: w without sign restriction

Inverted Frontier
Many regions rank the same, thus they are tied, when applying a traditional DEA approach that puts emphasis on the strengths of regions. To solve this issue, tie-breaking techniques were developed, such as the Inverted Frontier (IF) method (Angle-Meza and Lins 2002).
The IF was initially proposed by Yamada et al. (1994) and used by Leta et al. (2005)  We compute the value γ equal to 0.5 to aggregate the classical and inverted boundary results (in Expression 1), which means that we used the average between the two boundaries. The choice for this value was due to the fact that it is the most commonly used in the literature, since it tends to be considered a neutral value. However, other values of γ could be even more appropriate for this problem. It would be consistent with the capability approach if the inverted border (which highlights the worse performance) had a greater weight than the classical frontier (which highlights the factors where the region stands out most). The reason for this is that the capability approach places great emphasis on setting minimum standards, so it is more important that the region does not perform very poorly on some variable(s) than it performs excellent only on a restricted number of variables. The study of the most appropriate γ value, however, is beyond the scope of this paper and requires also further in-depth theoretical discussion.  Table   3 presents a summary of all primary indicators. Third, with the help of the primary indexes, we created four composite indicators. The DEA Capability Index (DCI), which combines the standard (CIMFW) and the inverted frontier (DI). This absolute indicator allows us to evaluate each region according to their weakness and strengths as well as to reduce draws. The Social Efficiency Index (SEI) combines the SSE and ISE and considers the relative efficiency of each region. The SEI also evaluates social efficiency according to the weakness and strengths of each region.

Strategy to compare absolute deprivation, social efficiency and financial responsibility
Next, we created the Capability Index Adjusted by Social Efficiency (CIASE) to consider both absolute levels of deprivation and the financial responsibility. The CIASE represents a single index, combining the DCI and the SEI. For this reason, CIASE contemplates social deprivation, wealth and public expenditures together and ranks regions according to their social efficiency (Sen 2009). In a simple way, CIASE comes up with relevant information to rank regions and to generate policy recommendations (OECD 2008;Zhou et al. 2009).
We tested ten different combinations to evaluate which weights provides a better CIASE representation of the Brazilian regions. For this purpose, we combined DCI and SEI values from 0.1 to 0.9. It avoids a subjective weighting choice.
Finally, we created the Deprivation and Financial Responsibility based Prioritization Index (DFRP). The DFRP combines social efficiency (SEI) and social deprivation (DI). This indicator allows policymakers to decide which regions have the worse social deprivation and present great social efficiency. In sum, regions with higher DFRP can improve human development using their financial resources efficiently. Table 4 presents a summary of all composite indicators. Finally, all indicators followed the Min-max normalization method (expression 3), making them comparable (from zero to one).
Where: Min(x) and Max(x) are the minimum and maximum values of the sample.
In addition, our estimates were calculated with Matlab® and Stata®, and graphs were created with Origin® software.

Differences in absolute and relative performance
The DEA Capability Index (   On the other hand, some regions with social deprivation improved their ranking position in the social efficiency index. This is the case of East Goiano, which moved from 97 th to 9 th place (+88 positions). Other regions exhibit the same behavior, such as South-west Rio-Grandense (+87), South Amapá (+85), and Center South Mato-Grossense (+84).

Sensitivity analysis
In order to define what weights should be attributed to CIASE, we analyze the ranking permutations among the 9 models. Figure 2 presents the evolution of the weights between the absolute performance and social efficiency for each Brazilian mesoregion. While Model 1 (SEI=0.1; DCI=0.9) emphasizes absolute performance and Model 9 (SEI=0.9; DCI=0.1) strengthen social efficiency, the CIASE is found in Model 5 (α=0.5; β=0.5).  The CIASE tackles these divergences ordering regions according to both aspects. For example, the Macro Metropolitana Paulista ranked 65 th place and Metropolitan Fortaleza ranked 99 th place in the CIASE index. Moreover, a third group showed fewer ranking changes (e.g. Greater Florianópolis the 3 rd place). The next section discusses the CIASE contribution.

CIASE: a contribution to the financial responsibility analysis
By combining social deprivation, wealth and financial constraints of Brazilian mesoregions, the CIASE contributes to the financial responsibility concept. It provides a better understanding of how to allocate public funds to enhance human development, revealing which regions have more merit to receive public money and tackle their social deprivation.
For example, Campinas ranked 54 th in the DCI and 105 th in the SEI. Using the DCI, Campinas performs better than regions like East Goiano (97 th ), and Metropolitan Fortaleza (112 nd ). On the other hand, according to SEI, Campinas enhances worse collocation than these regions: East Goiano (9 th ), Metropolitan Fortaleza (59 th ). CIASE contributes to reveal a new ranking, which ranks East Goiano (49 th ) higher than Campinas (64 th ) and Metropolitan Fortaleza (99 th ). In other words, authorities could give credits to East Goiano (e.g. in form of prizes or increased public support from the federal government) because this region faces a worse social deprivation than Campinas and has greater financial responsibility compared to Campinas and Metropolitan Fortaleza.

Cases for discussion
It is important to answer why some regions are more efficient than others. There are several reasons, such as the way that a region uses its money, the human capital to manage public funds, and the public policies to develop better living conditions, for example, to provide basic sanitation, health programs, and infrastructure.
Firstly, a region can spend its funds better and more efficiently in order to generate more access to public services. Regions such as the South Amapá, Metropolitan Belém, and Paulista and provides 8.96% more basic sanitation to its population. In this sense, SEI captures this efficiency of translating financial resources into human development.
Furthermore, SEI shows that economic wealth by itself is not enough to provide human development. We found that regions that have a better fiscal management are also better at enhancing human development. Comparing the FIRJAN Fiscal Management Index 3 (IFGF) with our indicators, we found a correlation between IFGF and CIASE (0.54), DCI (0.56) and SEI (0.35). This correlation suggests that better management of public resources is associated with higher levels of absolute, relative and combined aspects of the human development performance . This region has universities and research institutes, national and multinational companies, hospitals with technological equipment, and a public transport system that is relatively better than in the rest of the country. The state of São Paulo is the richest in the country, with more public resources and GDP. However, when we analyze the generation of human development from wealth, the relative index (SEI) is only 0.351, which places this region on the position 108 th of the national ranking. Similarly, Campinas and Piracicaba, in the São Paulo countryside are located near the financial center of Brazil (São Paulo city), have research institutes, universities, and companies in the technological field. According to the DCI, the Campinas region ranks 54 th , yet it ranks only 105 th place when analyzing the SEI efficiency of public spending and local wealth. Although the region Piracicaba ranks 40 th in the DCI ranking and has important multinational companies (Griesse 2017) and public policy to professional qualification (Ferraz et al. 2018), Piracicaba has a worse SEI performance (67 th position).
Furthermore, Metropolitan Curitiba, where there is an important automobile cluster (Cruz and Rolim 2010), does not have good position in SEI ranking (96 th place), which is explained by previous studies on inequality (Lima and Bidarra 2019), housing (Monteiro 2015) and health (Aguilera et al. 2014).
In contrast, region Metropolitan Fortaleza, in the Northeast of the country, is ranked low in absolute terms (112 th ), and high in relative terms (59 th ). The main reasons for this are the public policies to improve educational attainment, to promote access to health in poor neighborhoods, and the number of illiteracies has declined because more people have attended school, which has also helped to the development of policies for health promotion  The Greater Florianopolis, an island in the South of Brazil, has a high absolute efficiency value and is ranked 22 nd out of 129 mesoregions, in terms of social efficiency is only ranked on 2 nd position. Reasons for this are arguably its lowest per capital murder and strongest middle class (Guerra et al. 2017), the infrastructure and economic diversification (Makowiecky and Carneiro Filho 2015;Yigitcanlar et al. 2018), the public universities and institutions to promote science and technology (Xavier 2010;Yigitcanlar et al. 2018), the knowledge-based economy and the innovation and scientific and technological promotion by local government (Esmaeilpoorarabi et al. 2016), the special program to vaccination (Kupek and Tritany 2009) and, the favelas localization, which guarantees facilities in day care centers, schools and hospitals (Yigitcanlar et al. 2018 In sum, DEA informed indicators may help in the complex task of allocating public expenditures more efficiently. In particular, they may help to increase human development in poor regions spending public money more efficiently.

Conclusions
In this study we evaluated how absolute and relative indicators can be used to interpret human development. By the means of methods from Data Envelopment Analysis, we found many changes in ranking position according to the indicator analyzed. Several regions with good absolute indicators showed worse performance in the relative ranking. On the other hand, some regions with worse social deprivation were socially efficient.
To our best knowledge, there are not yet any DEA inspired indicators yet that combine absolute and relative indicators. To fill this gap, we combine these two indicators and create the Capability Index Adjusted by Social Efficiency (CIASE). This indicator is important mainly in countries with heterogeneous regions like Brazil. CIASE allows for a new interpretation of human development achievements in Brazil, taking both absolute levels of deprivation and capabilities into account, as well as considering financial responsibility. In addition, CIASE deals with other types of research problems whenever there is a large difference between inputs and outputs (e.g. to compare public investments among countries, or to analyze sustainability among regions, or countries).
In order to identify which regions should receive higher public investments for human development, we have created the Deprivation and Financial Responsibility Based Prioritization Index (DFRP). This indicator takes into account the regions with the greatest social deprivation and presented financial responsibility. In this way, policy makers can use the DFRP to reallocate public resources in order to generate human development by spending public money efficiently.
We also presented some cases to discuss different strategies in Brazil mesoregions. Furthermore, to CIASE and DFRP, authorities must interpret these indicators carefully and evaluate the rankings accompanied by case studies.
However, some limitations can be found in this article. First, we did not consider the temporal evolution of human development. Second, our analysis is concentrated on global indicators. Third, we did not discuss which weights should and could be assigned to each social dimension.
We consider that future studies can analyze the evolution of human development in Brazil over the years, measure specific indexes for each dimension (education, health, basic sanitation, employment, and institutions), and discuss different weights of each dimension in a global index (e.g.health and education are more important than sanitation or institutions). Finally, a more indepth discussion of the ethical importance of social efficiency and its ability to sustain social policies is necessary. One relevant question for further research is to which extent public investment should focus on absolute deprivations, social efficiency, or a combination of both.
Policy measures need to address socially inefficiencies and invest in regions with high levels of human deprivation, but should probably also merit regions that do a good / efficient job. The precise resource allocation and ethical priority setting, though, requires further discussion and seems to be a promising path for future research on human development and social efficiency with relevance for public investment decisions.
Despite the limitations outlined above, our work reveals the need of simultaneously analyze social deprivation, social efficiency and financial responsibility in developing regions. In this regard, our study points to the possibilities of constructing new indicators that combine information on absolute levels of human development and the financial responsibility of regions. Our indicators point to the need of considering aspects of financial responsibility when (re)allocating wealth and public expenditures for human development improvements. Thus, CIASE and DFRP help to identify and promote the financial responsibility of regions in promoting human development. Employ. Gini Poor people Election Homicide logGDP 0.102*** 0.0824*** 0.259*** 0.149*** 0.706*** 0.732*** 0.0473*** -0.122*** 0.00820*** 0.167*** -0.0898*** -0.712*** 0.0545*** 0.200*** Electronic copy available at: https://ssrn.com/abstract=3401374