Default in the Financial System: Reassessment of the Macroeconomic Factors of Zaniboni’s (2013) Thesis

Ceci Sales de Paula; Arthur Damasceno Vicente

DOI: 10.22167/2675-6528-202602773

Article derived from a Final Course Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

The study re-evaluated the dynamics of non-performing loans in the Brazilian financial system from 2019 to 2024, based on the methodological approach proposed by Zaniboni (2013). The research was quantitative, applied, and had an explanatory and predictive purpose, using time series econometric techniques. Non-performing loan data, represented by series SGS 21082, were obtained from the Central Bank of Brazil. Stationarity analysis was performed, which indicated a unit root at level and stationarity after first-order differencing. Subsequently, an ARIMA(0,1,1) model was specified and validated, and an ARIMAX model was estimated with exogenous variables previously selected by Zaniboni (2013). The ARIMA(0,1,1) model demonstrated consistent predictive performance and captured the dynamics of non-performing loans, with forecasts for 2024 showing good adherence and absence of systematic bias. The ARIMAX model achieved slightly superior performance to ARIMA, but the difference was small. The results suggested that non-performing loans maintain a strong dependence on their own historical dynamics, and the inclusion of exogenous variables did not provide a significant gain in predictive capacity.

Keywords: ARIMA; Default; Forecasting; Time series; Financial system.

1. Introduction

In an economy, credit plays a fundamental role, being understood as the delivery of a value upon the promise of payment (Silva, 2018). Among the various functions of credit, the social one stands out, allowing companies to increase their activity and individuals to obtain housing and other goods. Furthermore, credit stimulates consumption and facilitates the execution of projects when companies lack internal resources for full development (Silva, 2018).

However, credit granting is intrinsically associated with risk. There is always the probability that the promise of payment will not be fulfilled, leading the debtor to default (Silva, 2019). Given credit’s function as a provider of economic turnover and the possibility of credit risk culminating in default, it becomes essential to understand the influence, sensitivity, and correlation that macroeconomic indicators exert on credit risk. The relationship between macroeconomic variables and credit risk was proposed by Fridson et al. (1997), who identified a positive relationship between the real interest rate and the default of high-yield bonds (Zaniboni, 2013).

Monetary policy, as pointed out by the Central Bank of Brazil (BACEN, 2021), directly impacts the economy and the cost of credit, with changes in the Selic rate being passed on to the interest rate curve and affecting credit demand. In this scenario, updating the study conducted by Zaniboni (2013), which investigated the sensitivity of financial institutions’ credit risk to economic changes, becomes pressing. Zaniboni’s original thesis used data from 2007 to 2012, a period that encompassed the international economic crisis of 2008 and 2009. There was a hypothesis that the pre-crisis period presented excessive malleability of monetary policy (Paiva and Ferreira, 2022).

To evaluate the model in the current context, it is necessary to consider the period from 2019 to 2024, which includes the economic impacts of the COVID-19 pandemic and the subsequent credit recovery. The Central Bank of Brazil (BACEN, 2021) reported in its April 2021 Financial Stability Report an increase in credit risk, but at a slower pace for legal entities, suggesting the influence of emergency programs. Credit for individuals also resumed pre-pandemic growth. This work therefore aims to update the analysis by Zaniboni (2013), incorporating the impacts of the pandemic and the economic recovery period, seeking to verify whether, in a new macroeconomic context, the previously identified relationships remain statistically relevant.

The relevance of this study lies in the need to re-evaluate the impact of macroeconomic variables and the composition of the credit portfolio on the default of financial institutions in Brazil, considering the new economic scenario. Thus, the main objective of the present work is to re-evaluate the impact of the most relevant macroeconomic variables and the composition of the credit portfolio on the default of financial institutions in Brazil, according to the master’s thesis conducted by Zaniboni in 2013.

2. Material and Methods

This research was characterized as quantitative, of an applied nature, with an explanatory and predictive purpose, seeking to re-evaluate the relationship between macroeconomic variables and the default of the Brazilian financial system. The methodology adopted was based on Zaniboni’s (2013) dissertation, which employed univariate ARIMA and multivariate ARIMAX modeling.

The empirical data were secondary, obtained from the Time Series Management System (SGS) of the Central Bank of Brazil. The dependent variable was the default of the total credit portfolio of the National Financial System, represented by series SGS 21082. This indicator was selected to update the base of Zaniboni (2013), who defined default as the ratio between the balance in arrears exceeding ninety days and the total balance of contracts.

The analysis period covered the years 2019 to 2024. This temporal scope was chosen to update the analysis by Zaniboni (2013), which used data from 2007 to 2012, and to incorporate the economic impacts of the COVID-19 pandemic and the subsequent credit recovery in Brazil.

The explanatory variables were the eight selected by Zaniboni (2013), reused as an analytical starting point. They were grouped into credit portfolio, interest, and public sector debt. The transformations applied included three-month moving averages, year-on-year variation, and lags, according to the methodological logic of the reference study.

In the data treatment, all series were organized in monthly frequency and processed in Python language, using libraries such as pandas, numpy, statsmodels, and scipy. Consistency inspection of the bases, date verification, standardization of temporal indices, identification of missing values, and harmonization of the common interval between variables were performed.

The modeling was developed in two stages. In the first, a univariate ARIMA model was estimated. The stationarity of the series was verified by graphical inspection, analysis of the autocorrelation function (ACF), and unit root tests, such as the Augmented Dickey-Fuller (ADF) and KPSS (Gujarati, 2006; Fávero et al., 2009).

The level ADF test did not allow rejecting the null hypothesis of non-stationarity. Consequently, first-order differencing was applied to remove the stochastic trend and stabilize the series. After this transformation, the ACF of the differenced series showed rapid dissipation of autocorrelations, and the KPSS test did not reject the null hypothesis of stationarity, indicating that the series became integrated of order one (d=1).

The specification of the parameters p and q of the ARIMA(p, d, q) model was guided by the analysis of the autocorrelation and partial autocorrelation functions (Moura, 2011). A systematic estimation of multiple combinations of AR(p) and MA(q) parameters was performed through a grid search. The selection of the final model considered out-of-sample predictive performance, statistical significance of the parameters, and parsimony of the specification (Morettin and Toloi, 2006).

After selection, the econometric validation of the chosen specification was performed by analyzing the residuals. The autocorrelation function (ACF), the partial autocorrelation function (PACF), and the Ljung-Box test were examined to verify the absence of remaining serial autocorrelation. Models whose residuals exhibited white noise behavior were considered statistically adequate (Zaniboni, 2013).

In the second stage, a model with exogenous variables, named ARIMAX, was estimated, following the tradition of Zaniboni (2013). The objective was to re-evaluate the capacity of the previously selected explanatory variables to explain default in the recent period. For this, the Granger causality test was applied to verify the temporal precedence of the explanatory variables in relation to default (Zaniboni, 2013).

The explanatory variables were subjected to first-order differencing and z-score standardization. The selection of exogenous variables was conducted by combining relevant economic groups and a backward elimination procedure, keeping only statistically significant variables at the 10% level. The choice of the final model was based on the Akaike Information Criterion (AIC) and the evaluation of out-of-sample predictive performance, using metrics such as the sum of squared errors (SSE) and the mean absolute percentage error (MAPE). The ARIMA and ARIMAX models were compared considering statistical fit, parsimony of specification, residual behavior, and the coherence of coefficient signs and magnitudes with the literature. This comparison allowed us to verify whether the most explanatory factors from the previous decade maintained relevance in the recent macroeconomic context.

3. Results and Discussion

The reassessment of the non-performing loan dynamics in the Brazilian financial system, from 2019 to 2024, was conducted based on the methodology proposed by Zaniboni (2013), seeking to understand the influence of macroeconomic variables and the composition of the credit portfolio. The initial research results focused on the analysis of the non-performing loan series’ stationarity, a fundamental prerequisite for time series modeling. The graphical inspection of the series at level revealed a persistent behavior, with autocorrelations that decayed slowly, a pattern often associated with non-stationarity and the presence of a unit root, as discussed by Fávero et al. (2009) and Gujarati (2006).

To formalize this diagnosis, the Augmented Dickey-Fuller (ADF) test was applied to the series at level, resulting in a p-value of 0.13. This value did not allow the rejection of the null hypothesis of non-stationarity at the 10% significance level, corroborating the visual evidence and the correlogram analysis. Given this finding, the first-order differencing of the series was performed, a standard procedure to remove stochastic trends and induce stationarity, according to the time series literature (Fávero et al., 2009).

After differentiation, the ADF test was reapplied, and the p-value obtained was 0.09. Although close to usual significance levels, this value still did not allow for a conclusive rejection of the null hypothesis. To complement the analysis and strengthen the diagnosis, the KPSS test was used, which adopts stationarity as the null hypothesis. The KPSS results for the differentiated series did not reject the null hypothesis at the 10% level, indicating that the series, after the first differentiation, exhibited properties compatible with stationarity. The combination of these tests, with opposing null hypotheses, provided greater robustness to the diagnosis, confirming that the default series is integrated of order one, I(1), meaning it becomes stationary after a single differentiation.

The specification of the ARIMA model was guided by the identification of the series’ integration order, which proved to be I(1), implying the adoption of d=1. The definition of the autoregressive (p) and moving average (q) parameters was carried out through a systematic approach, which included the analysis of the autocorrelation function (ACF) and partial autocorrelation function (PACF), as well as the estimation of multiple combinations of AR(p) and MA(q) parameters. This methodology, aligned with the Box and Jenkins (1970) tradition, sought to identify the structure that best represented the temporal dependence of the series, avoiding the subjectivity of a purely visual selection (Moura, 2011; Gujarati, 2006).

The selection of the final model was not restricted to the visual inspection of autocorrelation functions, but considered an articulated set of criteria. Out-of-sample predictive performance, statistical significance of estimated parameters, and parsimony of specification were evaluated. To integrate these dimensions, metrics were normalized and aggregated into a final score, with weights of 0.5 for out-of-sample error, 0.3 for statistical significance, and 0.2 for model complexity. This combined approach, according to Morettin and Toloi (2006), ensures a more robust and consistent choice, prioritizing models that, in addition to good fit, exhibit stability and interpretability.

After applying these criteria, the ARIMA(0,1,1) model was selected as the most suitable specification to represent the dynamics of default. This model demonstrated the best performance in the overall ranking, indicating its ability to capture the temporal persistence of the series with a single differencing and a first-order moving average component. The absence of regular seasonal patterns in the autocorrelation functions of the original series justified the non-inclusion of seasonal components in the model, simplifying the structure and maintaining parsimony.

The validation of the ARIMA(0,1,1) model was performed through the analysis of residuals, which should behave as white noise for the model to be considered adequate. The Ljung-Box test, applied to the residuals, indicated high p-values for all lags analyzed (6, 12, 18, and 24), not allowing the rejection of the null hypothesis of absence of autocorrelation. This result suggests that the residuals do not present statistically significant temporal dependence, confirming that the series’ dynamics were adequately captured by the model (Zaniboni, 2013).

The graphical analysis of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the residuals reinforced this diagnosis, showing that the estimated coefficients remained within the confidence intervals, without relevant peaks or systematic patterns. This behavior is consistent with what is expected for residuals of a well-specified model, indicating that there is no remaining serial structure in the errors. The inspection of the integrated autocorrelation function (IACF) of the residuals also did not reveal hidden structural patterns, corroborating the absence of temporal dependence.

The predictive performance evaluation of the ARIMA(0,1,1) model was carried out by comparing the observed values with the fitted values in the training period (2019-2023) and with the forecasts for the test period (2024). In the estimation period, the model demonstrated high adherence to the historical series, capturing the main movements of default, including the sharp drop between 2020 and 2021 and the recovery observed until 2023. This ability to reproduce the series dynamics in the training period is an indicator of the model’s consistency (Zaniboni, 2013).

Regarding out-of-sample performance, the forecasts for 2024 showed relatively stable behavior, hovering around the most recent level of the series. The comparison between observed and predicted values indicated that the actual series oscillated around the estimated trajectory, with no evidence of systematic bias, which reinforces the model’s adequacy in terms of predictive capacity. Furthermore, the actual values remained within the estimated confidence intervals, although these intervals progressively widened along the forecast horizon, a phenomenon expected in time series that reflects the increasing uncertainty with the broadening of the horizon.

The second stage of modeling involved estimating an ARIMAX model, incorporating explanatory variables previously selected by Zaniboni (2013). The objective was to re-evaluate the relevance of these variables in the period from 2019 to 2024. To this end, the Granger causality test was applied, which seeks to verify whether past values of an explanatory variable contribute to predicting default. The results indicated that none of the tested variables presented a p-value lower than 10%, suggesting an absence of robust statistical evidence of Granger causality for the analyzed period.

Despite the absence of Granger causality, the decision was made to continue with ARIMAX modeling, in line with the objective of empirically re-evaluating Zaniboni’s (2013) set of variables. The ARIMAX model was structured as an extension of ARIMA(0,1,1), being estimated on the already first-order differenced default series. The explanatory variables were also differenced and standardized through z-score normalization, ensuring statistical compatibility. The selection of exogenous variables was carried out through a backward elimination procedure, keeping only those statistically significant at the 10% level.

The results of the ARIMAX model estimation indicated that the variable “14097 – Balance of credit operations of the National Financial System – South Region – Total – R$ (millions)”, after first-order differencing and standardization, was selected as statistically significant, with a coefficient of -0.0452 and a p-value of 0.0005. The moving average component of order 1 (MA, L1) also proved significant, with a coefficient of 0.4223 and a p-value of 0.0162. The model presented an Akaike Information Criterion (AIC) of -110.3154 on the training set and a coefficient of determination (R²) of approximately 28% on the differenced series, indicating a moderate but consistent level of explanation for macroeconomic series.

The adequacy of the ARIMAX model was evaluated by analyzing the residuals, which, as in the ARIMA model, did not show significant autocorrelation, as indicated by the p-values of the Ljung-Box test, which were greater than 5%. The distribution of the residuals was approximately normal, with the points on the Q-Q Plot close to the theoretical line. These results confirm that the ARIMAX model is adequately specified and that its residuals exhibit characteristics compatible with white noise, validating the estimated structure.

The evaluation of the ARIMAX model’s predictive performance for the test period (2024) also demonstrated good adherence to the observed series trajectory. Although the confidence intervals widen along the forecast horizon, the model was able to follow the movements of non-performing loans. This suggests that ARIMAX, by combining the historical trajectory of the series with the influence of selected macroeconomic variables, presents consistent predictive performance, even though the contribution of exogenous variables was limited in the context of Granger causality.

In the comparison between the ARIMA and ARIMAX models, out-of-sample forecast error metrics were used: the sum of squared errors (SSE) and the mean absolute percentage error (MAPE). The ARIMA model obtained an SSE of 0.1707 and a MAPE of 3.51%, while the ARIMAX presented an SSE of 0.1585 and a MAPE of 3.08%. These results indicate that the ARIMAX model demonstrated slightly superior performance to the ARIMA, with lower error values, suggesting a modest improvement in predictive accuracy with the inclusion of exogenous variables. However, the difference between the models was reduced, which points to the strong dependence of default on its own historical dynamics, a common characteristic in persistent macroeconomic series. The re-evaluation of Zaniboni’s (2013) variables in the new analyzed period, although it indicated a slight advantage for the ARIMAX, did not result in a significant alteration in the overall explanatory capacity of the series, suggesting that the internal dynamics of default remain a preponderant factor.

4. Conclusion

This study sought to re-evaluate the impact of macroeconomic variables and credit portfolio composition on the default of financial institutions in Brazil, from 2019 to 2024, following the methodological approach of Zaniboni (2013). It was found that the default series presented non-stationarity at level, becoming stationary after first-order differencing. Based on this finding, an ARIMA(0,1,1) model was specified and validated, which demonstrated consistent predictive performance and captured the default dynamics, with forecasts for 2024 showing good adherence and absence of systematic bias. The re-evaluation of Zaniboni’s (2013) set of exogenous variables using an ARIMAX model indicated that, although a credit balance variable in the South Region proved statistically significant, the Granger causality test did not show robust evidence of temporal precedence for any of the tested variables. Comparatively, the ARIMAX model achieved slightly superior predictive performance to the ARIMA, with lower errors, but the difference was reduced, suggesting that default maintains a strong dependence on its own historical dynamics.

The main contribution of this work lies in the updating and empirical validation of Zaniboni’s (2013) model for a new macroeconomic context, which included the impacts of the COVID-19 pandemic and the subsequent recovery. The results reinforce the understanding that the internal dynamics of default are a preponderant factor in its trajectory. However, a limitation of the study was the restriction to the set of exogenous variables previously selected by the original thesis, without an expansion of the scope of macroeconomic factors. For future studies, it is suggested to investigate new factors that can broaden the explanatory capacity of default, as well as explore methodologies that allow capturing non-linear relationships or more complex interactions between variables, in order to deepen the understanding of this phenomenon in the Brazilian financial system.

Bibliographic References

BCB – BANCO CENTRAL DO BRASIL. Relatório de Estabilidade Financeira, v. 20, n. 1, abr. 2021. Disponível em: https://www.bcb.gov.br/content/publicacoes/ref/202104/RELESTAB202104-refPub.pdf. Acesso em: 04 nov. 2025.

BOX, George E. P.; JENKINS, Gwilym M. Time series analysis: forecasting and control. San Francisco: Holden-Day, 1970.

Fridson et al., 1997 [Referência completa não encontrada no documento original]

FÁVERO, Luiz Paulo Lopes et al. Análise de dados: modelagem multivariada para tomada de decisões. Rio de Janeiro: Elsevier, 2009.

GUJARATI, Damodar N. Econometria básica. 4. ed. Rio de Janeiro: Elsevier, 2006.

MORETTIN, Pedro Alberto; TOLOI, Clélia Maria de Castro. Análise de séries temporais. 2. ed. São Paulo: Edgard Blücher, 2006.

MOURA, Fernando. Previsão do consumo de energia elétrica por setores através do modelo SARMAX. 2011. Dissertação (Mestrado em Administração) Faculdade de Economia, Administração e Contabilidade, Universidade de São Paulo, São Paulo, 2011. Disponível em: https://bdtd.ibict.br/vufind/Record/USP_a7799693921dd179f49d2a52fa6ae6ed. Acesso em: 04 nov. 2025.

PAIVA, Guilherme Leite; FERREIRA, Mauro Sayar. Uma nota sobre o canal de tomada de risco da política monetária com evidências para o Brasil. Revista Brasileira de Economia [Recurso Eletrônico], Rio de Janeiro, v.76, n.2, abr./jun. 2022. Disponível em: https://doi.org/10.5935/0034-7140.20220008. Acesso em: 04 nov. 2025.

SILVA, José Pereira da. Gestão e Análise de Risco de Crédito – 9ª edição revista e atualizada. 9. ed. Porto Alegre: +A Educação – Cengage Learning Brasil, 2018. E-book. p.57. ISBN 9788522126750. Disponível em: https://app.minhabiblioteca.com.br/reader/books/9788522126750/. Acesso em: 03 nov. 2025.

ZANIBONI, Natália Cordeiro. A inadimplência do sistema financeiro no Brasil explicada por meio de fatores macroeconômicos. 2013. Dissertação (Mestrado em Administração) Faculdade de Economia, Administração e Contabilidade, Universidade de São Paulo, São Paulo, 2013. Disponível em: https://www.google.com/search?client=safari&rls=en&q=ZANIBONI%2C+Natália+Cordeiro.+A+inadimplência+do+sistema+financeiro+no+Brasil+explicada+por+meio+de+fatores+macro econômicos.+2013.+Dissertação+(Mestrado+em+Administração)+—+Faculdade+de+Economia%2C+Administração+e+Contabilidade%2C+Universidade+de+Sã o+Paulo%2C+São+Paulo%2C+2013.&ie=UTF-8&oe=UTF-8. Acesso em: 01 abr. 2026.

Article originating from the Final Course Work of the Specialization in Data Science and Analytics of the MBA USP/Esalq

To learn more about the course, click here and access the MBX Academy platform