Socio-Economic Impact of the Brumadinho Landslide: A Hybrid MCDM-ML Approach

Abstract

Most humanitarian logistics research focuses on immediate response efforts, leaving a gap regarding the long-term socio-economic impacts of post-tragedy financial aid. Our research investigates the Brumadinho landslide tragedy in Minas Gerais, Brazil, analyzing the effectiveness of financial aid in fostering sustainable recovery and resilience in affected communities. We employ a hybrid multi-criteria decision-making (MCDM) and machine learning model to quantitatively assess the socio-economic impact on affected municipalities. Using social responsibility indices from official state government datasets and data from the PTR transparency initiative—a financial aid program determined by the Judicial Agreement for Full Reparation and operationalized by FGV Projetos, which allocates USD 840 million for the reparation of damages, negative impacts, and socio-environmental and socio-economic losses—our analysis covers all municipalities in Minas Gerais over 14 years (10 years before and 4 years after the tragedy). We determine a final socio-economic performance score using the max entropy hierarchical index (MEHI). Additionally, we assess the efficiency of the PTR financial aid in affected municipalities through examining MEHI changes before and after the transfers using a difference-in-differences (DiD) approach. Our findings reveal both direct and indirect impacts of the tragedy, the efficacy of financial aid distribution, and the interplay of various socio-economic factors influencing each municipality’s financial health. We propose policy recommendations for targeted and sustainable support for regions still coping with the long-term repercussions of the Brumadinho landslide.

1. Introduction

The rupture of a tailings dam results in significant social, economic, and environmental impacts, including loss of life, extensive property damage, and the release of toxic substances into ecosystems [1,2]. In Brazil, the 2019 rupture of the B1 tailings dam in Brumadinho, Minas Gerais, released approximately 12 million cubic meters of iron ore tailings into the Paraopeba River watershed, causing widespread devastation [3,4,5,6,7]. This tragedy highlighted critical issues of negligence and inadequate safety measures by Vale S.A., resulting in legal actions and calls for stricter mining regulations. In response, compensation, financial aid, and environmental recovery funds were provided by the Brazilian government and Vale S.A. to support victims and affected communities [8,9].

The long-term socio-economic recovery of affected regions poses a significant challenge, as efforts to mitigate the impacts on local economies, including agriculture, tourism, and small businesses, often fall short [10]. This study aims to fill a crucial gap in the existing literature by examining the long-term socio-economic impacts of post-tragedy financial aid, specifically in the context of the Brumadinho landslide tragedy.

Effective tragedy management encompasses activities undertaken before, during, and after a tragedy, spanning both preparatory and responsive phases [11]. Pre-tragedy efforts often involve risk management strategies [12], while emergency response entails interventions during the tragedy to mitigate its adverse effects [13,14]. These activities may include rescuing and evacuating victims, meeting basic needs, ensuring protection, managing displaced persons, and establishing necessary infrastructure and facilities. Post-tragedy efforts focus on rehabilitation, reconstruction, and revitalizing community economies [11,15].

Addressing economic losses and infrastructure damage in communities is facilitated through the provision of financial aid and compensation to tragedy victims. While these resources support responsive phases, they can also complicate service delivery systems. Previous studies, such as those by Gajewski et al. [16] and Myomin and Lim [17], have examined the challenges and dynamics of financial aid and compensation programs in different contexts, revealing issues of resource allocation, equity, accountability, and coordination.

Most humanitarian logistics research focuses on immediate response efforts, leaving a gap regarding the long-term socio-economic impacts of post-tragedy financial aid [14,18,19,20]. Limited literature exists on the socio-economic recovery and how financial aid influences the socio-economic landscape of affected areas [21,22,23,24]. Our research addresses this gap by investigating the Brumadinho landslide tragedy, analyzing the effectiveness of financial aid in fostering sustainable recovery and resilience in affected communities.

This research applies a hybrid multi-criteria decision-making (MCDM) and machine learning approach to assess the socio-economic impact on affected municipalities in Minas Gerais. By leveraging social responsibility indices from official state government datasets and data from the PTR transparency initiative—a financial aid program determined by the Judicial Agreement for Full Reparation and operationalized by FGV Projetos, which allocates USD 840 million for reparation—we analyze the long-term effects on socio-economic indicators over 14 years (10 years before and 4 years after the tragedy).

The combination of MCDM and machine learning provides a robust framework for analyzing socio-economic impacts, offering deep insights by leveraging the strengths of both quantitative decision-making and predictive modeling approaches [25,26,27,28,29,30,31]. The hierarchical application of the TOPSIS model for each major socio-economic dimension allows for a nuanced assessment, while information entropy weights enhance the objectivity of the analysis [32,33,34]. Additionally, LASSO regression and transfer entropy methods are employed to identify significant predictors and explore dynamic interrelations among socio-economic dimensions [35,36,37,38].

Our study addresses three key questions: (i) whether financial aid and compensation to Brumadinho tragedy victims reshaped the socio-economic indicators of affected communities, using a difference-in-differences design; (ii) if a hybrid MCDM–machine learning approach can capture the socio-economic impacts of financial aid and compensation; and (iii) whether the combination of MCDM and machine learning provides suitable information for policy decision support. By systematically analyzing these aspects, our research aims to provide actionable insights and policy recommendations for targeted and sustainable support for regions still coping with the long-term repercussions of the Brumadinho landslide tragedy.

2. Materials and Methods

This research applies a hybrid MCDM–machine learning approach to capture the socio-economic impacts of the financial aid and compensation provided to the affected municipalities in Minas Gerais. The implementation of this approach involved four sequential analytical stages and presents several advantages and novelties, which are further discussed below, over previous models employed in the literature.

2.1. Data

First, data cleaning and cubic splines (see Section 3.1) were used to revisit the socio-economic indices of Fundação João Pinheiro (FJP) with respect to the municipalities of Minas Gerais. Not only are all of them measured on a biannual basis, requiring the use of interpolation techniques to set them into a monthly basis in order to construct a comprehensive panel from the financial aid data, but, also, some indices were discontinued, while others were created over the 10-year period of analysis. We used software R Studio version 4.4.0. The data cleaning process yielded the following resulting indices shown in Figure 1, grouped into eight major dimensions: social assistance, finances, health, security, education, urbanization and sanitation, environment, and employment and income.

Second, TOPSIS—a well-known MCDM model (see Section 3.2)—was employed in a hierarchical aggregative fashion over each dimension, as depicted in Figure 2. In each of the eight dimensions, information entropy (IE) weights (see Section 3.3) for each constituent index were used to determine a final socio-economic performance or score of a given dimension, namely, the max entropy hierarchical index (MEHI). The MEHIs for each dimension were entered into another TOPSIS model with their respective IE weights, ultimately yielding a monthly total MEHI for each municipality over the course of time. The total MEHI was used in the machine learning models as a dependent variable to be further regressed against a series of dummy, trend, and financial aid variables.

Third, prior to the LASSO regression analysis (see Section 3.5), the transfer entropy method (see Section 3.4) was applied to the partial MEHIs computed for the eight socio-economic dimensions (see Figure 1 and Figure 2) in order to unveil the eventual cause–effect or feedback relationships among them. Splitting the IE weights before and after the landslide tragedy—and, hence, computing two distinct partial MEHI datasets to be tested—it was possible to explore whether these socio-economic dimensions were moving together in a feedback process in the affected municipalities, their neighbors, and in the non-affected municipalities of Minas Gerais. As feedback processes in social-economic indicators are a key issue in sustainable development, transfer entropy allows for the identification of improvement opportunities by pinpointing detached socio-economic dimensions from the others or cause–effect relationships that might be dysfunctional.

Feedback processes in socio-economic indicators are crucial for sustainable development, as they help to identify and address areas that may be lagging or disconnected from overall progress. Transfer entropy, a measure of information transfer between variables, has been proven to be effective in pinpointing these issues, as mentioned above. Through analyzing the flow of information, researchers can detect improvement opportunities and implement targeted interventions to enhance socio-economic resilience and sustainability [39,40]. This approach ensures that policy measures are both data driven and adaptive, fostering a more holistic and responsive development strategy.

Fourth, using LASSO regression (see Section 3.5) while focusing on the socio-economic impacts of a tragedy such as the Brumadinho landslide requires several considerations with respect to the municipalities serving as references for the affected, neighboring, and non-affected municipalities. As such, the choice of Brumadinho, Belo Horizonte, and Uberlândia as reference points for affected municipalities, neighboring municipalities, and non-affected municipalities, respectively, was based on a mix of geographical, socio-economic, and impact-related criteria [41]. The rationale for choosing these municipalities as references is discussed in the following.

Affected Municipality: As the site of the tragedy, Brumadinho is the primary subject of analysis for direct impacts. Including it as a reference allows for the assessment of immediate and direct socio-economic changes due to the event. It also serves as a benchmark for comparing the extent of impact. Analyzing changes in socio-economic indicators in Brumadinho provides a clear before-and-after picture of the tragedy’s effect.

Neighboring Municipality: Belo Horizonte is geographically close to Brumadinho, which means that it could have experienced indirect effects or ripple effects from the tragedy. These effects might include changes in economic activity, migration patterns, or shared environmental resources. Besides, as the state capital and a major urban center, Belo Horizonte’s inclusion helps to analyze how urban areas might differently absorb or mitigate the impacts of nearby tragedies, compared to more rural or directly affected areas like Brumadinho.

Non-affected Municipality: Uberlândia can act as a control group within the study. Being geographically distant and not directly affected by the tragedy, its socio-economic changes (or lack thereof) provide a baseline against which to measure the specific impacts on Brumadinho and its neighbors. Yet, as one of the largest and most economically significant cities in Minas Gerais, with the second highest population and GDP in Minas Gerais (IBGE, 2021), Uberlândia’s socio-economic trends can reflect broader state-wide or national trends, further helping to isolate the specific impacts of the Brumadinho tragedy.

While the specific choice of the control municipality does not fundamentally alter the overall conclusions of this study, it serves a crucial role as a reference point for policymakers and stakeholders. For instance, by comparing the socio-economic trajectories of the affected and neighboring municipalities to those of a non-affected, economically significant city like Uberlândia, decision-makers can gain a clearer understanding of the unique challenges and opportunities faced by each region. This comparative analysis facilitates the development of tailored recovery strategies that consider the diverse needs and characteristics of different municipalities, ultimately leading to more effective and equitable policy interventions.

LASSO regression is particularly adept at reducing the complexity of models by penalizing the absolute size of the coefficients, effectively selecting only the most relevant variables (in this case, financial aid, trend, and dummies for municipality types) for predicting the outcome (total MEHI).

To estimate the monthly values of the IMRS indicators of the João Pinheiro Foundation, nth-order splines were employed. A spline of order n is a piecewise function composed of polynomials of degree n joined smoothly at certain points called knots. These polynomials are selected such that the spline function is continuous and smooth up to its (n − 1)th derivative.

The general equation of a cubic spline can be expressed as follows:

$$\mathrm{S}\left(\mathrm{x}\right)={\mathrm{a}}_{\mathrm{i}}+{\mathrm{b}}_{\mathrm{i}}\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{i}}\right)+{\mathrm{c}}_{\mathrm{i}}{\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{i}}\right)}^2+\dots +{\mathrm{k}}_{\mathrm{i}}{\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{i}}\right)}^{\mathrm{n}},$$

(1)

where:

x_i are the knots.

a_i, b_i, c_i, …, k_i are the coefficients of the cubic polynomials, which vary in each interval defined by the knots.

In this study, a 10th-order spline was used to estimate the monthly values. This means that polynomials of degree 10 were fitted to the data, allowing for a highly flexible and accurate representation of the monthly IMRS indicator data.

2.2. TOPSIS

Over the past three decades, there has been significant research and application of multi-criteria decision-making (MCDM) methods in the fields of business analytics and engineering, including methods such as the AHP [42,43], Promethee [44,45], Electre [46], Dematel [47], Vikor [48,49], and Uta [50].

TOPSIS is one of the methods utilized in multi-criteria decision-making (MCDM) approaches, particularly when the criteria for selecting the most suitable method are pre-defined externally [51,52,53,54,55,56,57]. Its core principle involves selecting an alternative that is simultaneously closest to the positive ideal solution and farthest from the negative ideal solution [58,59]. Specifically, the positive ideal solution aims to maximize benefits while minimizing costs, whereas the negative ideal solution seeks to minimize benefits while maximizing costs [60,61].

TOPSIS utilizes purely analytical methods based on Euclidean distance functions on normalized vectors of positive (outputs) and negative (inputs) criteria. However, it is essential to note that the weights in TOPSIS need to be pre-defined by the decision-maker before the analysis [57]. The TOPSIS technique is built on an evaluation matrix consisting of m alternatives and n criteria, with the intersection of each alternative and criteria given as xij. Therefore, one obtains a matrix (x_ij)_m×n. This matrix (x_ij)_m×n should first be normalized from a regulated matrix R* = (r_ij), as demonstrated in Equation (2).

$$r_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{\sum _{i=1}^m{x}_{ij}^2}}},i=\mathrm{1,2},\dots ,m and j=\mathrm{1,2},\dots ,n.$$

(2)

After normalization, the weighted normalized decision matrix for efficiency assessment should be calculated, observing Equation (3):

$$W={\left(w_{ij}\right)}_{mxn}={\left(w_j{r}_{ij}\right)}_{mxn},$$

(3)

where w_j is the weight given to criteria j and ∑(j = 1)ⁿ w_j =1.

Once the weighting criteria are defined, the worst alternative (the negative ideal assessment unit) A_a and the best alternative (the positive ideal assessment unit) A_b can be obtained using Equations (4) and (5):

$$A_a=\left\{\begin{array}{c}〈\min \left(w_{ij}|i=\mathrm{1,2},\dots ,m\right)|j\in J_{+}〉,\\ 〈\max \left(w_{ij}|i=\mathrm{1,2},\dots ,m\right)j\in J_{-}〉 \end{array}\right\}=\left\{{\alpha }_{aj}|j=\mathrm{1,2},\dots ,n\right\},$$

(4)

$$A_b=\left\{\begin{array}{c}〈\max \left(w_{ij}|i=\mathrm{1,2},\dots ,m\right)j\in J_{+}〉,\\ 〈\min \left(w_{ij}|i=\mathrm{1,2},\dots ,m\right)|j\in J_{-}〉\end{array}\right\}=\left\{{\alpha }_{bj}|j=\mathrm{1,2},\dots ,n\right\},$$

(5)

where J₊ = {j|j ∈ positive} and J₋ = {j|j ∈ negative}, which are the sets of positive (benefit) and negative (cost) attributes, respectively.

Given the best and the worst alternatives, the distance d_ia between the target alternative i and the worst condition A_a can be calculated using Equation (6):

$$d_{ia}=\sqrt{\sum _{j=1}^n{\left(w_{ij}-{\alpha }_{aj}\right)}^2},i=\mathrm{1,2},\dots ,m,$$

(6)

and the distance d_ib between alternative i and the best condition A_b is obtained using Equation (7):

$$d_{ib}=\sqrt{\sum _{j=1}^n{\left(w_{ij}-{\alpha }_{bj}\right)}^2},i=\mathrm{1,2},\dots ,m,$$

(7)

where d_ia and d_ib are the Euclidean distances from the target alternative i to the worst and best conditions, respectively.

Then, the similarity of alternative i to the worst condition (the inefficient best condition) should be computed, as follows:

$${\mathit{S}}_{\mathit{i}}={\displaystyle \frac{{\mathit{d}}_{\mathit{i}\mathit{a}}}{\left({\mathit{d}}_{\mathit{i}\mathit{a}}+{\mathit{d}}_{\mathit{i}\mathit{b}}\right)}},$$

(8)

where 0 ≤ S_i ≤ 1, i = 1, 2, …, m.

S_i = 0 if and only if the alternative solution has the worst condition, while S_i = 1 if and only if the alternative solution has the best condition.

According to Jahanshahloo, Lotfi, and Davoodi [62], S_i represents the efficiency scores for each alternative; that is, for each bank of the sample, over the course of time, as determined by the decision-making criteria. Finally, the alternatives should be ranked according to S_i (a higher value of S_i indicates a better solution with respect to higher efficiency levels within the environment), thereby enabling subsequent assessment of the impact of the contextual variables.

2.3. Entropy Weights

Information entropy serves as a metric for quantifying uncertainty, particularly in probabilistic contexts [63]. Within our research framework, we leverage information entropy to assess the level of randomness and dispersion inherent in each group of socio-economic indicators pertinent to our study. By computing the information entropy for each original socio-economic indicator within distinct categories relevant to our analysis, such as demographic regions or economic sectors, we aim to discern the degree of heterogeneity present within each category.

The magnitude of information entropy directly correlates with the level of randomness or dispersion within a given category, signifying greater heterogeneity. Through this approach, we introduce a novel methodology for evaluating the inherent diversity within a specified locus of analysis in relation to each socio-economic indicator under consideration. This allows us to gain insights into the heterogeneity across different dimensions of our study, facilitating a comprehensive understanding of the socio-economic landscape.

In step 1, it is assumed that there are j original socio-economic indicators, ranging from 1 to n, related to i units (1, …, m) within a specified dimension k. These elements make up the decision-making matrix Dij(k) for each socio-economic indicator j of each municipality i under group k (in this research k = 2, encompassing the datasets before and after the landslide tragedy), as follows:

$$Dij\left(k\right)=\left[\begin{array}{c}{d}_{11\left(k\right)}\\ d_{21\left(k\right)}\\ \dots \\ d_{m1\left(k\right)}\end{array}\begin{array}{c}{d}_{12\left(k\right)}\\ d_{22\left(k\right)}\\ \dots \\ d_{m2\left(k\right)}\end{array}\begin{array}{c}\dots \\ \dots \\ \dots \\ \dots \end{array}\begin{array}{c}{d}_{1n\left(k\right)}\\ d_{2n\left(k\right)}\\ \dots \\ d_{mn\left(k\right)}\end{array}\right].$$

(9)

In step 2, the matrix Dij(k) is transformed into a decision-making matrix Rij(k) via normalization, in order to obtain the weight of each socio-economic indicator:

$$Rij\left(k\right)=\left[\begin{array}{c}{r}_{11\left(k\right)}\\ r_{21\left(k\right)}\\ \dots \\ r_{m1\left(k\right)}\end{array}\begin{array}{c}{r}_{12\left(k\right)}\\ r_{22\left(k\right)}\\ \dots \\ r_{m2\left(k\right)}\end{array}\begin{array}{c}\dots \\ \dots \\ \dots \\ \dots \end{array}\begin{array}{c}{r}_{1n\left(k\right)}\\ r_{2n\left(k\right)}\\ \dots \\ r_{mn\left(k\right)}\end{array}\right].$$

(10)

Here, the sum of each column is equal to 1; or, in other words, the decision-making matrix Rij(k) satisfies the equation:

$$\sum _{i=1}^m{r}_{ij\left(k\right)}=1,k=\mathrm{1,2}.$$

(11)

In step 3, column vectors (A₁, A₂, …, A_n) of the normalized decision-making matrix Rij(k)—namely, the socio-economic indicator—are treated as a probabilistic distribution of information. Therefore, the information entropy E_ij(k) of the jth socio-economic indicator obtained from the kth group is defined as:

$$E_{ij\left(k\right)}=-{\displaystyle \frac{1}{\ln m}}\sum _{i=1}^m{r}_{ij\left(k\right)}\ln r_{ij\left(k\right)},k=1,2 \mathrm{for} \mathrm{all} j$$

(12)

where 0 ≤ E_ij(k) ≤ 1 and a value of 1 signifies maximal entropy.

2.4. Transfer Entropy

The flow of information among socio-economic indicators, denoted as variables i and j, is quantified by integrating Shannon entropy [64] and Kullback–Leibler distance [65], assuming a Markov process with k and l levels of factors, respectively [39]. Given the probability distributions p(i) and p(j) for socio-economic indicators i and j, along with their joint probability p(i,j), the flow of information from indicator j to indicator i is computed using the following equation, proposed by Dimpfl and Peter [66]:

$$T_{J\to I}\left(k,l\right)=\sum _{i,j}p\left(i_{t+1},i_t^{\left(k\right)},j_t^{\left(l\right)}\right)·\log \left({\displaystyle \frac{p\left(i_{t+1}|i_t^{\left(k\right)},j_t^{\left(l\right)}\right)}{p\left(i_{t+1}|i_t^{\left(k\right)}\right)}}\right).$$

(13)

This equation quantifies the deviation from the generalized Markov process $p\left(i_{t+1}|i_t^{\left(k\right)}\right)=p\left(i_{t+1}|i_t^{\left(k\right)},j_t^{\left(l\right)}\right)$ at the marginal conditional distribution odds-ratio $\log \left({\displaystyle \frac{p\left(i_{t+1}|i_t^{\left(k\right)},j_t^{\left(l\right)}\right)}{p\left(i_{t+1}|i_t^{\left(k\right)}\right)}}\right)$.

Similarly, the flow of information from indicator i to indicator j is assessed, enabling the determination of causation direction between different socio-economic indicators based on the net information flow. This net flow is calculated as the difference between the flows from i to j, and vice versa. The statistical significance of the net information flow between socio-economic indicators is determined through bootstrapping of the inherent probability distributions for each factor or level in each criterion, enabling repeated execution of this Markov process.

2.5. Lasso Regression

LASSO (least absolute shrinkage and selection operator) operates independently from the linear model, employing an alternative method to determine the coefficients, denoted as β₀, β₁, …, β_p. This method zeroes out certain coefficients when the tuning parameter (penalty) exceeds a certain threshold [67]. Consequently, LASSO models tend to be more interpretable than linear models, as they focus on a subset of predictors. Various approaches exist for selecting an optimal value of the tuning parameter. Equation (14) presents the LASSO model utilized in our research to identify a subset of variables related to the socio-economic indicators within the analysis related to the Brumadinho tragedy, aiming to elucidate their impacts on the recovery and long-term socio-economic well-being of affected communities.

$$Minimize\left(\sum _{i=1}^n{\left(y_i-{\beta }_0-\sum _{j=1}^{21}{\beta }_j{x}_{ij}\right)}^2+\lambda \sum _{j=1}^{21}\left|{\beta }_j\right|\right),$$

(14)

where y is the MEHI efficiency vector, x is the matrix containing contextual variables, β₀ is the intercept of the linear model, and β_j is the regression coefficient of variable j. In this study, we propose the following model:

$$MEH{I}_{total}=f\left(\mathit{ln}PTR,trend,tren{d}^2,tragedy, affted,neighbors,municip.\right),$$

where lnPTR is the natural logarithm of the value paid for given municipality; the variables trend and trend² represent the short- and long-term temporal evolution of the MEHI that each municipality presents, respectively; the tragedy variable is binary and marks the time after the event in Brumadinho; and the variables affected, neighbors, and municipality are dummies that mark the fixed effects for each individual municipality as well as the groups of municipalities affected by the rupture and their neighbors. As we use three dummies in the model, the municipalities of Brumadinho, Belo Horizonte, and Uberlândia were chosen as references for affected, neighboring, and non-affected municipalities, respectively.

To determine the confidence intervals for the coefficient of variable β_j, a bootstrap method with 1000 replications was implemented. The 95% lower and upper limits from the confidence interval are calculated using the 2.5% and 97.5% quantiles, respectively.

Table 1. Pseudocode for the bootstrapped LASSO regression.

LASSO Regression Bootstrap Algorithm
	Inputs:
		B: Number of Bootstraps
		D: Dataset
	Output:
		LASSO Regression Confidence Interval
		LASSO Regression Median Estimate
1	For each bootstrap replication from 1 to B:
2		Draw a bootstrap sample D* of size N from D.
3		Estimate LASSO Regression coefficients on D*.
4		Combine the estimated coefficients into a result set.
5	For each j coefficient:
6		Calculate the 50% Quantile. (Estimate)
7		Calculate the 2.5% Quantile. (Lower Bound)
8		Calculate the 97.5% Quantile. (Upper Bound)
9	End.

presents pseudocode outlining the procedure.

2.6. Differences in Differences

Finally, we assess the efficiency of the PTR financial aid implemented in the municipalities affected by the Brumadinho landslide tragedy by examining how each dimension of the MEHI behaves before and after the program. The most suitable method for this comparison is the difference-in-differences (DiD) approach [68,69]. By utilizing this method, we can determine whether the municipalities that received financial aid experienced improvements in their MEHI indicators across the following dimensions: education, employment and income, environment, finances, health, security, social assistance, and urbanization and sanitation.

To conduct this analysis, we used the MEHI indicator as the dependent variable and created conditions for the pre- and post-tragedy periods to serve as independent dummy variables. This allowed us to assess the impact of the PTR financial aid on each of the eight MEHI dimensions in the affected municipalities [70].

2.7. Assumptions and Limitations of the Hybrid MCDM-ML Model

The hybrid MCDM-ML approach utilized in this study offers a robust framework for analyzing complex socio-economic phenomena. However, like all models, it operates under certain assumptions and has inherent limitations that warrant consideration.

2.7.1. Assumptions

The LASSO regression component of our model assumes a linear relationship between the predictors and the total MEHI. While we have employed transformations and diagnostics to assess potential non-linearity, it is important to acknowledge that some degree of non-linearity may still be present. Additionally, the model assumes no omitted variable bias, implying that all relevant factors influencing the MEHI have been accounted for. However, unmeasured variables like individual resilience and community social capital could potentially play a role in socio-economic outcomes, and their exclusion may introduce some degree of bias.

2.7.2. Limitations

The biannual frequency of certain indicators necessitates interpolation for monthly analysis, introducing potential uncertainty. Finally, the findings of this study are context-specific to the Brumadinho tragedy and the socio-economic and cultural landscape of Minas Gerais and Brazil. Generalizing the results to other disaster contexts requires caution, as the effectiveness of financial aid and recovery efforts can vary considerably based on regional and cultural factors. Despite these limitations, the hybrid MCDM-ML approach demonstrates its value in providing a nuanced understanding of the socio-economic impacts of the Brumadinho tragedy and the effectiveness of the financial aid program. By acknowledging these limitations, this research contributes to a more transparent understanding of the complex dynamics involved in disaster recovery and highlights potential avenues for future research.

3. Results and Discussion

This study analyzes socio-economic indicators across all municipalities in Minas Gerais. While the study includes data from all municipalities, we focus primarily on the period between 2010 and 2023, due to the limited availability of reliable data before 2010. This timeframe ensures that the analysis is based on accurate and reliable information, leading to more precise conclusions about social dynamics and trends in these regions.

Figure 3 shows the flowchart of the hybrid MCDM-ML framework employed in this study, outlining the specific research questions addressed by each methodological step.

3.1. Descriptive Statistics

Table 2. Descriptive Statistics of the final FJP indices used in the research (see Figure 1).

MEHI Dimension	Social-Economic Index	Direction	Min	Max	Median	Mean	SD	CV	Skewness	Kurtosis	IE
Education	Education quality index (5th grade elementary)	+	0.00	1.23	0.56	0.56	0.10	0.18	−0.04	0.41	0.30
Education	Education quality index (9th grade elementary)	+	0.00	0.98	0.37	0.37	0.08	0.21	0.22	0.51	0.30
Education	Per capita expenditure (education)	+	0.00	869.08	51.45	63.90	44.98	0.70	3.56	23.89	0.22
Employment and income	Employment rate (formal sector)	+	2.28	141.81	18.66	21.25	12.63	0.59	2.66	13.72	0.28
Employment and income	Gross value added per capita	+	0.00	141,616.96	648.26	1493.89	3652.84	2.45	13.64	311.18	0.08
Employment and income	Per capita income (formal sector)	+	0.68	402.73	15.52	21.03	21.41	1.02	5.63	53.88	0.21
Environment	Agricultural coverage	−	0.00	194.53	68.54	62.59	19.99	0.32	−0.87	0.09	0.30
Environment	Native flora vegetation coverage	+	0.00	99.91	26.82	32.54	18.44	0.57	0.95	0.15	0.35
Environment	Urban infrastructure coverage	−	0.00	82.44	0.30	1.21	4.61	3.80	10.27	137.97	0.08
Finances	GDP per capita	+	0.00	118,881.29	1183.40	1758.46	2907.10	1.65	15.89	391.12	0.11
Finances	Net current revenue per capita	+	0.00	4123.58	222.65	285.86	212.64	0.74	3.49	22.48	0.22
Finances	Net taxes	+	0.00	1,174,530.04	521.97	7417.92	49,262.23	6.64	15.37	279.72	0.04
Finances	Per capita expenditure (legislative)	−	0.00	129.23	8.46	10.61	7.68	0.72	2.79	15.25	0.24
Finances	Per capita expenditure (total)	−	0.00	4464.09	232.00	296.40	215.45	0.73	3.67	26.90	0.21
Finances	Personnel expenditure in relation to net current revenue	−	0.00	6.74	4.20	4.13	0.45	0.11	−1.24	4.80	0.27
Health	Aging index	−	7.10	181.09	48.47	53.27	18.81	0.35	1.33	2.40	0.30
Health	Per capita expenditure (health)	+	0.00	858.36	56.21	70.48	49.38	0.70	2.81	16.01	0.24
Security	Inhabitants per police officer	−	0.00	4845.05	633.46	694.49	350.21	0.50	2.26	12.13	0.27
Security	Rate of violent crimes	−	0.00	2341.81	104.61	148.04	161.96	1.09	4.55	33.23	0.23
Social assistance	Disabled beneficiaries of the BPC	+	0.00	25,529.48	100.57	290.11	894.14	3.08	16.24	362.06	0.08
Social assistance	Elderly beneficiaries of the BPC	+	0.00	28,415.72	53.48	217.46	938.06	4.31	18.65	443.41	0.06
Social assistance	Families benefited by Bolsa Família	+	0.00	269,819.38	728.69	1472.03	4270.72	2.90	25.63	1092.95	0.04
Social assistance	Municipal decentralized management index (Bolsa Família)	+	0.00	101.55	0.92	22.17	33.96	1.53	1.15	−0.45	0.20
Social assistance	Per capita expenditure (social assistance)	+	0.00	161.41	5.42	6.90	6.70	0.97	7.25	103.51	0.19
Social assistance	Social assistance reference centers	+	0.47	34.21	1.00	1.36	1.57	1.15	12.17	215.37	0.06
Urbanization and sanitation	Per capita expenditure on infrastructure	+	0.00	1679.49	24.46	35.63	41.90	1.18	8.92	188.78	0.14
Urbanization and sanitation	Population density	+	0.00	7687.20	22.78	68.94	324.96	4.71	15.83	313.62	0.05
Urbanization and sanitation	Urbanization rate	+	22.01	104.96	75.10	73.74	15.57	0.21	−0.49	−0.29	0.36
Urbanization and sanitation	Vehicle density	+	0.00	8470.14	9.31	34.91	230.69	6.61	24.32	696.38	0.03

+/− respective impact sign (or direction; i.e., + or −) on overall performance (or building the respective MEHI partial index), as required by the TOPSIS model. All data came from Fundação João Pinheiro (FJP). Retrieved from https://fjp.mg.gov.br/ (accessed on 2 April 2024).

reports the descriptive statistics of the socio-economic indices for all investigated municipalities over the course of the investigation period, their respective dimension, and their respective impact sign (or direction; i.e., + or −) on overall performance (or building the respective MEHI partial index), as required by the TOPSIS model. These indices were normalized before entering the TOPSIS model in order to mitigate scale effects. Readers should refer to FJP’s website (https://imrs.fjp.mg.gov.br/consultas (accessed on 2 April 2024)) for a detailed description of each index, how each of them was collected and measured, and their respective unit of measurement.

The direction signs (+ or −) for each socio-economic index within the TOPSIS model reflect the assumed relationship between the index and the overall socio-economic development or well-being of a municipality. These directions are crucial for accurately assessing the composite socio-economic performance of municipalities within each MEHI dimension. In the following, we describe the rationale for determining the direction of each index, providing respective references whenever existing or applicable.

3.1.1. Education

(1)

Education quality index (5th and 9th grade elementary): Positive (+), as higher scores directly indicate better educational outcomes, which are fundamental for socio-economic development [71].

(2)

Per capita expenditure (education): Positive (+), as higher investments in education per capita are generally associated with better educational facilities, resources, and outcomes [72].

3.1.2. Employment and Income

(1)

Employment rate (formal sector): Positive (+), as higher formal employment rates are indicative of better job availability and economic stability [73].

(2)

Gross value added per capita and (3) per capita income (formal sector): Positive (+), as these indices represent the economic productivity and income levels of the population, with higher values signifying better economic health [74].

3.1.3. Environment

(1)

Agricultural coverage: Negative (−), as excessive agricultural land coverage might imply deforestation or loss of natural habitats [75].

(2)

Native flora vegetation coverage: Positive (+), as higher levels of native vegetation are crucial for environmental sustainability and biodiversity [76].

(3)

Urban infrastructure coverage: Negative (−), as extensive urbanization can lead to environmental degradation and reduced green spaces [77].

3.1.4. Finances

(1)

GDP per capita, (2) net current revenue per capita, and (3) net taxes: Positive (+), as they reflect the economic prosperity and financial health of municipalities [78], (4 and 5) per capita expenditure (legislative and total), and (6) personnel expenditure in relation to net current revenue: Negative (−), as higher expenditures in these areas, relative to the overall financial resources, might indicate inefficiency or over-spending [79].

3.1.5. Health

(1)

Aging index: Negative (−), as a higher proportion of older population might indicate future challenges for healthcare and social services [80].

(2)

Per capita expenditure (health): Positive (+), as higher health spending per capita is typically associated with better healthcare access and outcomes [81].

3.1.6. Security

(1)

Inhabitants per police officer and (2) rate of violent crimes: Negative (−), as lower police coverage and higher crime rates are detrimental to social well-being and community safety [82].

3.1.7. Social Assistance

(1)

The six indices related to social assistance benefits and expenditures: Positive (+), as they reflect the extent and effectiveness of social support systems, which are crucial for vulnerable populations [83].

3.1.8. Urbanization and Sanitation

(1)

Per capita expenditure on infrastructure, (2) population density, (3) urbanization rate, and (4) vehicle density: Positive (+), as these indices generally signify better urban development, infrastructure, and accessibility, contributing to higher living standards [84].

3.2. Socio-Economic Development Overview of Minas Gerais

Figure 4 depicts the information entropy weights for each socio-economic index within each of the eight partial MEHIs. We recall that these weights were computed for the totality of Minas Gerais municipalities, thus reflecting an overall perspective of the socio-economic development of this state, both before and after the Brumadinho landslide tragedy. Higher weights denote high heterogeneity across municipalities for a given index (i.e., greater data dispersion). The observed heterogeneity and homogeneity across different socio-economic dimensions in Minas Gerais reflect a complex mosaic of development challenges and achievements.

Areas with high heterogeneity, such as urbanization rate, education quality, and employment rate, underscore the pressing need for targeted policies to address disparities in urban development, educational outcomes, and employment opportunities [71,73]. These disparities suggest that, while some municipalities are progressing rapidly, others lag significantly behind, necessitating tailored interventions to bridge these gaps.

Meanwhile, the relative homogeneity in other areas, such as vehicle density and per capita health expenditure, suggests that some level of basic infrastructure and services is more uniformly available across municipalities [81,84]. This uniformity indicates that foundational services and infrastructure are relatively well distributed, providing a baseline of development that can be built upon.

However, the disconnect between certain homogeneous inputs (e.g., per capita expenditure on education and health) and heterogeneous outcomes (e.g., education quality, aging index) highlights inefficiencies or mismatches between resource allocation and actual needs or performance. This finding indicates that while some resources may be distributed evenly, their utilization or impact varies significantly, necessitating a more nuanced approach to policy formulation and implementation. Effective policies must not only ensure equitable distribution of resources but also address the specific contexts and challenges faced by individual municipalities to enhance overall socio-economic development [85,86].

In its turn, Figure 5 reports on the distributional profiles of the eight MEHI dimension scores across municipalities in Minas Gerais and depicts a picture of a state with both opportunities and challenges for the whole period under analysis. While certain areas such as security show relative uniformity and satisfactory performance, other critical dimensions such as urbanization, social assistance, health, employment, and education exhibit significant disparities or general under-performance. This analysis suggests that a multi-faceted approach to policymaking is necessary. For instance, considering dimensions with high heterogeneity or skewed distributions (e.g., urbanization and sanitation, social assistance, environment, employment, and income), targeted interventions are needed to address the specific needs of under-performing municipalities.

On the other hand, for dimensions with relatively symmetrical distributions but low median scores (e.g., health, education), state-wide reforms and investments are crucial to raise the overall level of performance of Minas Gerais municipalities (see Figure 6), which is considerably low (around 0.10) with a few exceptions that are discussed later. Readers may find the comparison between Total MEHI and the overall FJP’s socio-economic index interesting, where the effect of decorrelating the individual constituent indices using the information entropy weights is noticeable.

Notwithstanding, social assistance analysis warrants careful consideration. The presence of two peaks in the distribution suggests distinct groups of municipalities: one with lower and another with higher social assistance scores. This bimodality likely reflects a division between urban and rural areas, or between municipalities with varying levels of access to and quality of social services. Urban areas, often characterized by better infrastructure and greater access to resources, tend to have higher social assistance scores. In contrast, rural areas may struggle with inadequate social services, leading to lower scores. The relatively low median indicates that, overall, social assistance needs to be strengthened across the state. This general deficiency in social assistance could contribute to the bimodality observed in the Total MEHI distribution, as areas with insufficient social support cannot achieve socio-economic performance comparable to those with robust social services.

Strengthening social assistance programs is crucial to mitigating these disparities and promoting more equitable socio-economic development across all municipalities [83]. An enhanced focus on social assistance would not only address immediate needs but also facilitate long-term resilience and socio-economic stability, ultimately reducing the observed bimodal distribution and contributing to a more balanced overall development.

Finally, Figure 7 and Figure 8 show the information entropy weights for MEHI dimensions within total MEHI and the temporal evolution of total MEHI between 2020 and 2013, respectively. The decreasing order of importance based on information entropy weights (see Figure 7)—environment, security, employment and income, social assistance, education, health, urbanization and sanitation, and finances—indicates the varying degrees of heterogeneity across these dimensions. On the other hand, the increasing spread of density plots over time, particularly from 2017 onwards (see Figure 8), along with fluctuations in median values from 2011 to 2015 and a subsequent increase, may suggest that the underlying causes of these phenomena are threefold.

First, the hierarchy of entropy weights suggests that environment and security exhibit the highest heterogeneity across municipalities, indicating significant disparities in environmental management and safety conditions. This is followed by employment and income, social assistance, and education, which are critical for economic stability and social well-being but also show considerable variability. Health, urbanization and sanitation, and finances present lower heterogeneity, suggesting more uniformity in these areas across the state, although still showing room for improvement.

Second, the increasing heterogeneity, evidenced by more spread-out density plots from 2017 onwards, suggests a widening gap in socio-economic conditions across municipalities. This could be due to several factors, such as: (a) uneven economic growth or decline, with some areas benefiting more from positive national economic trends or suffering more from negative ones; (b) increased heterogeneity in the environmental dimension, reflecting varying impacts of climate change, deforestation, or environmental policies on different municipalities; and (c) growing disparities in security, which could be attributed to localized issues or the effectiveness of policing and community safety programs.

Third, the decrease in median values from 2011 to 2015 followed by an increase may mirror broader economic trends in Brazil, such as the impact of the global economic downturn, fluctuations in commodity prices, and specific local policies implemented by the Minas Gerais government. Brazil faced a significant recession during this period, impacting employment, income, and investment levels, which could explain the reduced socio-economic performance. As a major exporter, Brazil’s economy—particularly in resource-rich states such as Minas Gerais—is sensitive to changes in global commodity prices, influencing employment, income, and government revenues. Responses by the Minas Gerais government to these challenges, including fiscal adjustments, social programs, or infrastructure investments, may have contributed to the observed changes in median values.

Together, our findings emphasize the importance of continuous monitoring and adaptive policymaking to address the diverse and evolving needs of municipalities in Minas Gerais. Effective policies must not only ensure equitable distribution of resources but also address the specific contexts and challenges faced by individual municipalities to enhance overall socio-economic development [85,87].

In summary, analyzing the aggregated socio-economic conditions and trends within Minas Gerais before delving into the specific impacts of the Brumadinho landslide tragedy on affected, neighboring, and non-affected municipalities provides context, sets a baseline for comparison, and helps in understanding the broader socio-economic fabric into which the tragedy is woven, thus facilitating the analysis and discussion of the results presented in the following sections.

For example, identifying temporal trends in socio-economic development across Minas Gerais enables researchers to distinguish between the effects attributable to the tragedy and those resulting from broader economic or social trends. For instance, if there was a pre-existing trend of increasing economic disparity or environmental degradation, it is essential to factor this into the analysis of post-disaster impacts. On the other hand, Minas Gerais is characterized by significant socio-economic diversity among its municipalities. A state-wide analysis highlights these disparities, offering insights into the varied vulnerabilities and capacities of municipalities to respond to and recover from disasters. Finally, given the high heterogeneity in environmental and security conditions across the state, as indicated by the entropy weights, understanding these aspects is crucial. This contextualizes the environmental impact of the tragedy and the security response, providing a comprehensive picture of how these pre-existing conditions may have influenced recovery efforts.

3.3. Transfer Entropy Results

This section discusses the endogeneity analysis results for the eight MEHI dimensions of Minas Gerais state and selected municipalities, both before and after the landslide tragedy. The transfer entropy results were cross-checked with those obtained through traditional Granger causality tests. Transfer entropy and Granger causality are both techniques used to infer directional relationships or causal influences between time-series data [88,89,90]. They come from different theoretical backgrounds and have their unique assumptions, advantages, and disadvantages. Transfer entropy does not assume linear interactions between variables, making it suitable for complex systems where interactions might be non-linear [91]. Furthermore, transfer entropy assumes that the system can be represented as a Markov process, where the future state depends only on the current state and not on the sequence of events that preceded it. On the other hand, the Granger causality test assumes that the causal relationship between variables can be described through linear models [92], which may not hold for systems with non-linear dynamics. It also requires the time-series data to be stationary, meaning that their statistical properties (e.g., mean and variance) do not change over time [93].

3.3.1. Analysis for Minas Gerais State in Aggregate

The results for the Granger causality tests performed on each pair of the eight MEHI dimensions, considering Minas Gerais state in aggregate, revealed significant feedback relationships among all MEHI dimensions (see Appendix B). These results were also verified for each of the more than 850 municipalities considered in isolation. While it seems appealing, at first sight, that the eight socio-economic MEHI dimensions are evolving together in a feedback process (rather than in isolation or under dysfunctional cause–effect relationships), the heterogeneous scenario previously discussed may be hiding non-linear effects among MEHI dimension pairs that are not fully captured through Granger causality tests.

Figure 9 shows the transfer entropy results for the eight MEHI dimensions, taking Minas Gerais in aggregate, before and after the landslide. The feedback among pairs of MEHI indicators is less noticeable and more cause–effect relationship pairs were found, with particular attention to the finance’s indicator, which is detached from employment and income and from social assistance. Possible explanations for this phenomenon may be related to the economic weakening of Minas Gerais state, together with Brazil as a whole, where public finances and labor productivity cannot meet adequately demands from other social areas, possibly reflecting the reallocation of resources and funds and/or other governmental priorities.

Precisely, Figure 9 outlines changes in the relationships between various socio-economic MEHI dimensions. For instance, before the tragedy there were directional relationships (X->Y) from social assistance to finances, environment, and security, indicating that changes in social assistance metrics had a predictive influence on these dimensions. This also suggests that social assistance programs and policies might have been a driving force influencing economic stability, environmental policies, and safety measures within municipalities before the landslide. This could reflect a socio-economic environment where interventions aimed at social welfare had broader impacts, possibly due to integrated policy approaches or the significant role of social programs in local economies and communities. However, after the tragedy, the relationships from social assistance to finances and environment are no longer present, while the relationships with education and urbanization and sanitation persisted. The disappearance of such relationships post-tragedy could indicate a shift in how social assistance impacts or is correlated with these areas. This might be due to changes in policy focus, resource reallocation, or shifts in socio-economic priorities following the disaster.

It is also worth mentioning that the mutual influence (X<->Y) between finances and employment and income, before the landslide, suggests a strong interdependence between the financial health of the state and employment rates/income levels. This mirrors broader economic trends, where fiscal policies and employment conditions are closely linked. Nevertheless, this mutual influence disappeared after the tragedy. A possible explanation for this phenomenon may be related to the fact that, during the period surrounding the Brumadinho tragedy, Brazil faced significant economic challenges, including recessionary pressures and fluctuations in commodity prices due to post-impeachment policies and the COVID-19 pandemic. The observed shifts in socio-economic relationships could reflect responses to these broader economic conditions, with implications for employment, income distribution, and social welfare policies. In fact, the changes in employment, income, and governmental finances relationships also suggest adjustments in social and economic policies in response to both the tragedy and the broader economic environment; this includes potential shifts in funding from social assistance programs to more direct disaster response efforts or reallocations between different socio-economic priorities.

3.3.2. Analysis for Minas Gerais State in Aggregate

Appendix C reports the transfer entropy analysis results for selected municipalities, including Brumadinho, Betim, Belo Horizonte, Juiz de Fora, Uberlândia, Extrema, and Piranguinho. This intentional selection of municipalities not only reflects the distinct conditions of locations affected, neighbored, and non-affected by the tragedy but also different paths of economic development and/or stagnation that should provide counter-factual evidence regarding how the socio-economic indicators of Brumadinho could have been affected in the post-tragedy scenario, possibly due to the inflow of additional financial aid resources. This rationale for this selection is provided below.

Brumadinho (Directly Affected): As it is the epicenter of the tragedy, analyzing Brumadinho offers insights into the immediate and direct socio-economic impacts of the disaster. The focus is on understanding how financial aid and other resources contributed to recovery and whether these interventions spurred socio-economic improvement beyond the pre-disaster conditions.

Betim (Neighboring Municipality): This is included as a neighboring municipality that likely experienced indirect effects of the tragedy. While not directly impacted, Betim might have seen changes in economic activity, population movements, or environmental impacts related to the disaster. Its inclusion helps to assess the ripple effects of the tragedy and subsequent aid on surrounding areas.

Belo Horizonte: As the state capital and a major urban center, it serves as a crucial reference for evaluating the broader urban impact and the capacity of larger cities to absorb and mitigate the effects of nearby disasters.

Juiz de Fora and Uberlândia (Non-Affected Municipalities with Significant Economic Activity): These cities represent economically significant non-affected municipalities. They provide a baseline for comparing the socio-economic performance of Brumadinho in the post-tragedy period in the absence of such an event. Both cities have diverse economies and have undergone unique paths of development, making them ideal for counterfactual analysis.

Extrema and Piranguinho (Non-Affected Municipalities with Distinct Economic Paths): Extrema is known for its rapid economic development, driven by its strategic location and investment into logistics and industrial sectors. Analyzing Extrema can offer insights into how targeted economic strategies contribute to socio-economic resilience and growth. Piranguinho, while smaller and less economically diversified than Extrema, is included to represent municipalities that have experienced different economic stagnation or slower growth, thus providing a contrast to both the directly affected area and the rapidly developing municipalities, offering a broader perspective on the variability of socio-economic development across Minas Gerais.

Before the tragedy, the socio-economic relationships in Brumadinho were characterized by a relative absence of defined transfer entropy relationships in the analyzed dimensions. This suggests a more isolated or less interactive set of socio-economic variables, where changes in one area (e.g., social assistance) did not strongly predict or influence changes in another (e.g., finances, environment, security). Such a scenario could indicate either a balanced system that does not require frequent adjustments, or a lack of integration and responsiveness between different socio-economic sectors. However, the aftermath of the tragedy marked a significant shift in the socio-economic relationships within Brumadinho, as evidenced by the emergence of feedback loops (X<->Y) and direct influences (X->Y or X<-Y) across various dimensions. Notably, the establishment of feedback loops in critical areas such as finances, environment, and security with social assistance, and vice versa, highlights a more interconnected socio-economic environment.

The emergence of feedback loops suggests that, in the post-tragedy period, there was a greater interdependency between various socio-economic sectors. This could be due to integrated recovery efforts, where interventions in one area (e.g., financial aid) were designed to support broader objectives, including environmental restoration and social security improvements. Furthermore, the shift towards more defined relationships indicates that Brumadinho’s socio-economic system became more responsive and adaptive after the tragedy. This adaptiveness is crucial for recovery, allowing the municipality to address immediate needs and lay the groundwork for long-term development. Finally, the introduction of financial aid and resources likely played a significant role in transforming these socio-economic relationships. Financial interventions may have catalyzed new dynamics between social assistance programs and other areas, such as employment, health, and urbanization, aiming to rebuild and improve upon the pre-tragedy conditions.

3.4. LASSO Regression Results

The bootstrapped LASSO regression results are reported in

Table 3. Results for the bootstrapped LASSO coefficients.

Variables	Coef	Lower CI	Upper CI	Significance
(Intercept)	0.215545	0.210778	0.219706	*
PTR_Amount	0.000473	0.000384	0.000553	*
Trend	−0.000721	−0.000730	−0.000713	*
Trend2	0.000004	0.000004	0.000004	*
Tragedy	0.001650	0.001354	0.001948	*
Affected	−0.046451	−0.051073	−0.041443	*
Neighborhood	0.280816	0.274345	0.287747	*

Significant at * p < 0.05; CI: 95%.

and Figure 10. The reader should recall that total MEHI, a composite socio-economic performance index derived from our hierarchical MCDM model, was considered the dependent variable. This integration of MCDM-derived metrics into ML models exemplifies the hybrid nature of our approach. The optimal penalty parameter was found to be zero in the 10-fold cross-validation approach, thus indicating that these results are comparable to those derived using OLS and that no independent variable was discarded. Precisely, Table 3 reports the coefficients for the PTR_Amount (financial aid), trend and trend squared, a dummy temporal variable marking the beginning of the tragedy, a dummy for affected municipalities (Brumadinho as reference), another for neighborhood (Belo Horizonte as reference), and others (Uberlandia as reference). All coefficients were found to be significant at the 0.0001 level. Figure 10 depicts selected coefficients for the municipalities (only part of them are reported for the sake of simplicity), grouped into four quadrants related to location and significance. Only four rich municipalities located in the Triangulo Mineiro region, with strong agribusiness activity, small population, and high GDP per capita, were found to be non-significant.

The positive coefficient for financial aid implies that increases in financial aid are associated with improvements in total MEHI scores. This relationship underscores the effectiveness of financial aid in enhancing the socio-economic conditions of the municipalities, particularly in the aftermath of the tragedy. In turn, the negative coefficient for the trend variable suggests a general decline in total MEHI scores over time. This could reflect broader economic or social challenges faced by the region over the analyzed period, independent of financial aid or the direct impacts of the tragedy. However, the positive coefficient for the square of the trend variable indicates a non-linear relationship, where the initial decline in Total MEHI scores may decelerate or reverse over time. This suggests a potential long-term recovery or improvement in socio-economic conditions after an initial period of decline.

On the other hand, the positive coefficient for the tragedy dummy variable indicates a significant increase in Total MEHI scores following the onset of the tragedy. This could reflect the mobilization of resources, including financial aid and other forms of support, in response to the disaster, leading to a temporary boost in socio-economic conditions. With respect to location, the negative coefficient for the affected municipalities, with Brumadinho as the reference, suggests that being directly affected by the tragedy has a significant negative impact on Total MEHI scores compared to Brumadinho. This highlights the severe socio-economic repercussions of the disaster on the directly affected areas. Finally, the positive coefficient for municipalities in the neighborhood of the tragedy, with Belo Horizonte as the reference, suggests that neighboring areas may have experienced socio-economic benefits or less severe impacts, when compared to the directly affected municipalities. This could be due to a variety of factors, including the redistribution of economic activities or the concentration of recovery efforts.

The non-significance of the coefficients for four rich municipalities in the Triangulo Mineiro region, characterized by strong agribusiness activity, small population, and high GDP per capita, suggests that the socio-economic impacts of the tragedy and subsequent financial aid were not uniform across all areas. The unique economic structures and possibly stronger socio-economic foundations of these municipalities may have insulated them from the disaster’s impacts or influenced the effectiveness of financial aid differently compared to other regions.

Overall, this analysis reveals the complex interplay between financial aid, temporal dynamics, and the varied impacts of a major disaster on municipal socio-economic conditions, highlighting the importance of tailored recovery strategies that consider the specific needs and characteristics of different municipalities to effectively address the aftermath of such tragedies. The hybrid MCDM-ML approach employed in this study has been instrumental in uncovering these nuanced relationships, going beyond traditional analyses to reveal key findings that would have otherwise remained hidden. For example, the hierarchical TOPSIS model allowed for a comprehensive assessment of well-being across multiple dimensions, while transfer entropy exposed feedback loops between socio-economic factors. Additionally, the application of LASSO regression enabled the isolation of the most critical predictors of socio-economic outcomes, offering insights into the specific factors that most significantly influence the recovery process. It is important to note that municipalities with strong industrial and logistic economic activities, such as Betim and Extrema, tended to outperform their peers and the references for their groups.

3.5. DiD Results

Finally, we present the DiD results for assessment of the efficiency of the PTR financial aid implemented in the municipalities affected by the Brumadinho landslide tragedy, through examining how each dimension of the MEHI behaves before and after the program. We ran DiD using software R Studio version 2022.12.0. Figure 11 illustrates the correlation between each MEHI dimension and the conditions used in the model.

At first glance, it is evident that the environment and urbanization and sanitation dimensions experienced positive impacts under both conditions. This can be attributed to municipal and state efforts to rebuild cities and restore ecosystems and preservation areas following the landslide tragedy. Additionally, the income transfer program had a positive effect on the social assistance MEHI dimension, indicating that targeted efforts were made to support vulnerable populations, thereby improving the six indices that comprise this dimension.

It is also important to note that the MEHI dimensions related to employment and income and security did not change significantly after the landslide tragedy or following the implementation of the income transfer program. The security dimension, which includes rates of violent crimes committed and the number of inhabitants per police officer, remained unchanged despite expectations of a potential deterioration. Economic hardship and scarcity often lead to increased competition for resources and a rise in crime rates; however, as the entire community was relocated to a new site, the ratio of inhabitants per police officer remained relatively constant, thereby maintaining police effectiveness at similar levels.

An interesting outcome was observed in the education dimension. Although the income transfer program did not have a statistically significant effect on this dimension, a positive impact was noted post-tragedy. This could be due to the necessary improvements in providing education to relocated students from severely affected areas, which increased the three indices comprising this dimension, which are all related to per capita education expenditures.

Similarly, the health dimension showed comparable results to the education dimension. The income transfer programs alone did not statistically affect this dimension, but a noticeable increase was seen in the post-tragedy period. Comprising per capita health expenditure and the aging index, it is assumed that increased spending in this field had a positive impact. This increase was driven by the need to provide medical assistance to relocated individuals and the establishment of emergency hospitals in affected areas. The heightened medical aid provided to tragedy victims persisted for many months, boosting this index.

Conversely, the finances dimension was the only MEHI dimension that exhibited a decline post-tragedy and in municipalities receiving income transfer programs. As most indices in this dimension are calculated on a per capita basis, the exodus of people from affected cities led to a decline. Specifically, the GDP per capita index worsened as economic activity in these municipalities nearly ceased, contributing to the low index rates observed.

The MEHI dimension of environment, as anticipated, demonstrated a positive effect following the tragedy and within the affected municipalities. This dimension encompasses the coverage of agricultural areas, urban infrastructure, and native flora vegetation. All of these indices presented an increase after the tragedy, due to concerted efforts to rebuild ecosystems, revitalize agricultural systems, and resume economic activities related to the primary sector. Similarly, the urbanization and sanitation indices exhibited positive effects under both conditions. Post-tragedy, and in municipalities that received the income transfer program, there was a notable increase in the indices comprising this dimension. This outcome aligns with expectations, as urbanization rates typically increase when there is a necessity to rebuild affected cities. Additionally, this index includes vehicle and population density metrics, which were not expected to increase. However, the substantial urbanization and per capita expenditure on infrastructure evidently offset these factors, resulting in the positive effect observed. This indicates the extensive efforts undertaken to reconstruct the municipalities affected by the tragedy. The significant investments in infrastructure and urban development underscore the commitment to restoring the affected areas, thereby enhancing the overall MEHI dimension of urbanization and sanitation. These improvements reflect the comprehensive approach adopted to address the immediate and long-term needs of the communities impacted by the landslide.

The social assistance dimension, which encompasses six distinct indices, also exhibited a positive effect following the landslide tragedy and within the municipalities that benefited from the income transfer program. These indices are intricately related to income transfer initiatives, such as the Bolsa Família program, a conditional cash transfer program on schooling outcomes of children aged 6–17 years. Consequently, a positive effect was anticipated, given that income maintenance was a central priority in the policies implemented. The observed positive impact on the social assistance dimension underscores the effectiveness of targeted income support programs in mitigating the adverse effects of the tragedy. Through providing financial stability to the affected populations, these programs played a crucial role in alleviating economic distress and supporting the livelihoods of the most vulnerable groups. The comprehensive approach adopted in the design and implementation of these income transfer programs ensured that essential needs were met, thereby contributing to the overall well-being and recovery of the affected communities.

Moreover, the data indicate that the concerted efforts to maintain income levels through these programs had a significant and measurable impact on the various components of the social assistance dimension. This finding highlights the importance of robust social safety nets for tragedy response and recovery, as they provide a vital mechanism by which individuals and families can be supported during times of crisis. The positive outcomes observed in this dimension reflect the success of the income transfer programs in addressing immediate needs, while also laying the groundwork for long-term recovery and resilience.

Overall, the application of the DiD approach provided a robust framework for evaluating the effectiveness of PTR financial aid in enhancing various aspects of human development in municipalities recovering from the Brumadinho landslide.

4. Conclusions

This study investigated the socio-economic impacts of the PTR (Programa de Transferência de Renda) financial aid program implemented after the Brumadinho landslide tragedy in Minas Gerais, Brazil. We employed a hybrid multi-criteria decision-making (MCDM) and machine learning approach to quantitatively assess the socio-economic impacts in affected municipalities. Using social responsibility indices from official state government datasets and data from the PTR transparency initiative, this research analyzed the effectiveness of financial aid in fostering sustainable recovery and resilience in the affected communities over a span of 14 years (10 years before and 4 years after the tragedy).

It should be noted that FGV Projetos plays a pivotal role in the PTR financial aid program, providing critical expertise and strategic guidance to ensure the program’s successful implementation. As a reputable consulting arm of the Fundação Getulio Vargas, FGV Projetos brings its extensive experience in socio-economic research and project management to the forefront, facilitating effective resource allocation and monitoring. The involvement of FGV Projetos ensures that the financial aid reaches the intended beneficiaries—over 132,000 affected individuals—with transparency and efficiency. Leveraging data-driven insights and robust analytical frameworks, FGV Projetos helps to maximize the program’s impact, fostering socio-economic recovery and resilience in the Brumadinho community in the aftermath of the devastating dam collapse.

4.1. Key Findings

This study addressed three key research questions and reached the following conclusions:

1. Reshaping Socio-Economic Indicators: Financial aid and compensation provided to Brumadinho tragedy victims significantly altered the socio-economic indicators of affected communities. Our difference-in-differences analysis indicated positive impacts on dimensions such as social assistance, urbanization and sanitation, and environment, showing improvements in these areas in the post-tragedy period.

2. Hybrid MCDM–Machine Learning Approach: The hybrid approach effectively captured the socio-economic impacts of financial aid and compensation. The hierarchical application of the TOPSIS model and the integration of information entropy weights provided a nuanced assessment of socio-economic dimensions, while the LASSO regression and transfer entropy methods helped to identify significant predictors and dynamic interrelations.

3. Policy Decision Support: The combination of MCDM and machine learning offered valuable information for policy decision support. Our findings highlighted the interplay between various socio-economic factors and the impacts of financial aid, providing a comprehensive framework for targeted and sustainable support strategies.

4.2. Managerial and Policy Implications

Based on the key findings, several policy recommendations are proposed:

1. Enhanced Social Safety Nets: Strengthening social assistance programs across all municipalities is crucial. This can be achieved by expanding coverage, improving efficiency, and investing in digital infrastructure to streamline aid distribution. Providing vocational training and employment opportunities will help beneficiaries achieve financial independence and reduce reliance on aid programs.

2. Targeted Urban Development: Addressing disparities in urbanization and sanitation requires targeted investments into infrastructure, prioritizing municipalities with lower urbanization rates and inadequate facilities. Incorporating green spaces and sustainable construction practices will enhance environmental quality and resilience against future disasters.

3. Educational and Health Investments: Increasing funding and improving resource utilization in education and health sectors are essential. Investing in teacher training, curriculum development, primary healthcare services, and expanding access to medical facilities will enhance the overall socio-economic conditions.

4. Environmental Management and Restoration: Implementing robust environmental management and restoration policies, including reforestation projects and conservation efforts, will restore and protect ecosystems. Promoting environmental education and community involvement will build local capacity for sustainable environmental management.

5. Economic Diversification and Employment: Promoting economic diversification and job creation through support for small- and medium-sized enterprises (SMEs) and entrepreneurship will stimulate local economies. Establishing partnerships for skill development and employment will foster inclusive and sustainable economic growth.

By implementing these recommendations, municipalities in Minas Gerais can enhance their socio-economic resilience, promote equitable development, and ensure sustainable recovery from the Brumadinho landslide tragedy. Regions facing similar challenges can significantly enhance their socio-economic resilience. The strategies outlined can help promote equitable development, ensuring that all communities benefit from recovery efforts. Sustainable recovery measures will not only address immediate needs but also build long-term capacity to withstand future crises. This approach can serve as a model for other municipalities globally, demonstrating the importance of integrating socio-economic and environmental considerations in disaster response plans. Additionally, the focus on equity can help bridge gaps between different socio-economic groups, fostering a more inclusive recovery process. Policymakers can adapt these recommendations to their specific contexts, tailoring interventions to local needs and conditions. By prioritizing resilience, equity, and sustainability, communities can better navigate the complexities of recovery from natural disasters, ensuring a more robust and inclusive path forward.