Executive Summary

February 06, 2026

Correlation between economic time series and credit life insurance in Brazil

Elisabete Apis Oliani; Gian Carlo Decarli

Summary prepared by the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege focused on synthesis and writing.

This work aimed to identify and quantify the impact of variations in the Índice de Preços ao Consumidor Amplo (IPCA) and the unemployment rate on the evolution of credit life insurance premiums in Brazil, from January 2014 to October 2024. The investigation sought to determine the existence, temporal scales, and lags of this relationship, analyzing the sector’s sensitivity to economic shocks. The research is justified by the relevance of credit life insurance as a risk mitigator, making the understanding of its determinants crucial for the strategic decisions of insurers and financial institutions.

Credit protection insurance is a financial protection mechanism that guarantees debt settlement in events such as unemployment, disability, or death. According to the National Confederation of Insurers (CNseg, 2024), this modality reduces the risk of default for creditors and provides security to the credit taker. Its importance was highlighted during the COVID-19 pandemic, when it consolidated as a counter-cyclical instrument in a scenario of economic uncertainty and income drop, mitigating credit risk for the financial system (Silva and Vasconcelos, 2022).

The Brazilian macroeconomic context, with inflationary oscillations and fluctuations in the labor market, pressures the financial health of families. The expansion of credit to individuals, while boosting consumption, has increased household fragility to economic shocks (Montani Martins, 2025). The rise in the cost of credit and income compression affect the consumer’s ability to pay and risk perception. The unemployment rate is a strategic variable, as its increase can, theoretically, stimulate the search for insurance that covers income loss, a hypothesis that differs from studies focused solely on claims (Silva and Chan, 2015).

The analysis of economic time series presents challenges such as non-stationarity and long-range autocorrelation, which limit the effectiveness of traditional correlation methods like the Pearson correlation coefficient (Morettin and Toloi, 2018). To overcome these limitations, this research employs econophysics techniques: Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA). DFA, proposed by Peng et al. (1994), quantifies long-term memory in a single series. DCCA, an extension by Podobnik and Stanley (2008), analyzes the covariance between two non-stationary series. To quantify the strength and direction of the relationship, the ρDCCA coefficient (Zebende, 2011) is used, which normalizes the covariance and ranges from -1 to +1. The combination of these tools allows for a robust investigation of the interdependencies between the studied variables.

The research adopts a quantitative approach, with time series analysis via DFA, DCCA, and ρDCCA, suitable for non-stationary data (Zebende, 2011; Podobnik and Stanley, 2008). The study followed the steps of the CRISP-DM process (Chapman et al., 2000). The data sources were IPCA (API of the Central Bank of Brazil), the unemployment rate (PNAD Contínua/IBGE), and the direct premium revenue for credit insurance (SUSEP). All series cover the period from January 2014 to October 2024, totaling 130 monthly observations. Data preparation involved harmonizing the series, with no missing values identified. Modeling applied DFA and DCCA functions, considering lags of one, three, and six months for the macroeconomic variables, to investigate market response time. The implementation was carried out in Python (version 3.10.12) on Google Colaboratory, using libraries such as Pandas and NumPy and custom functions for DFA, DCCA, and ρDCCA.

To normalize the correlation measure, Zebende (2011) introduced the ρDCCA coefficient, defined as the ratio between the DCCA covariance function and the product of the fluctuation functions of each individual series, obtained via DFA. The value of ρDCCA(n) ranges between -1 and +1; values close to zero indicate absence of correlation, positive values indicate direct correlation, and negative values indicate inverse correlation. For the interpretation of intensity, this study adopted the classification of Zebende et al. (2018): weak correlations for ρDCCA values between 0 and ±0.333, medium between ±0.333 and ±0.666, and strong above ±0.666.

The analysis of the results began with the observation of the historical evolution of each series. The IPCA showed high volatility, with monthly peaks of 1.62% (March 2022) and episodes of deflation, such as -0.68% (July 2022), characterizing a process with rapid fluctuations. In contrast, credit life insurance premiums showed a clear upward trend, increasing from approximately R$ 600 million per month in 2014 to over R$ 1.6 billion in 2024. The unemployment rate presented an inverted “U” cyclical pattern, starting from about 7% in 2014, reaching a peak of approximately 14% in 2017, and returning to levels close to 7% in 2024, revealing a medium-term cycle.

The application of DFA analysis revealed the internal temporal dependence structures of each series. For the IPCA, the fluctuation function F(n) grew at an accelerated rate on intermediate scales (30 to 90 months), confirming that the series has long-term memory. For credit life insurance premiums, the F(n) function showed continuous exponential growth, indicating a strong growth trend and pronounced temporal memory. The unemployment rate also showed a consistent advance in fluctuations with increasing scale, reflecting the gradual nature of labor market adjustments and the presence of prolonged cycles.

The cross-correlation analysis (ρDCCA) between IPCA and lender insurance premiums showed to be practically null on short-term scales (up to 24 months). On intermediate scales (36 to 84 months), a weak to moderate positive correlation emerged, with the ρDCCA coefficient reaching a peak of approximately 0.40 on scales between 90 and 102 months. Lag analysis revealed that the strongest association occurs with a three-month lag. This result suggests that persistent inflation, by impacting the cost of living, may positively influence the demand for protection, but the relationship is not immediate. The drop in the coefficient on very long scales (above 114 months) may be attributed to edge effects of the methodology or the aggregation of different macroeconomic regimes. Inflation, therefore, appears to act more as a contextual factor than as a primary driver of sales.

The correlation between the unemployment rate and credit life insurance premiums also proved to be null on short-term scales. A positive correlation emerged on intermediate scales, but the intensity was consistently weak, with a peak ρDCCA around 0.33 (borderline between weak and moderate ratings) on scales between 90 and 102 months. Lag analysis indicated that the association becomes more visible with lags of three to six months. This longer response time is consistent with the chain of economic events; changes in the labor market influence consumer confidence and credit policies. The positive, albeit weak, correlation suggests that periods of increased unemployment may stimulate demand for protection, but other factors, such as credit supply, likely play a more dominant role.

The integrated reading of the results shows that credit life insurance, in the analyzed period, exhibited low sensitivity to monthly inflation and unemployment shocks. The relationships with these variables only become statistically visible in medium to long-term horizons (above three years) and, even so, the intensity of the correlation remains in the weak to moderate range. This suggests that the premium growth trajectory is sustained by more structural dynamics of the credit market and the insurance sector, such as customer base expansion and commercial strategies, with macroeconomic conditions acting as a modulating, but not determining, background.

From a methodological point of view, the study confirmed the adequacy of DFA and DCCA techniques for analyzing non-stationary time series, identifying relationships that would be obscured by traditional methods. The ability to assess correlations at multiple time scales and with different lags provided a granular view of the interactions. The research contributes to the literature by applying econophysics methodologies to the Brazilian credit insurance sector, offering a new perspective on the determinants of demand for credit insurance.

The conclusions of this research indicate that the direct influence of inflation and unemployment on the evolution of credit protection insurance premiums in Brazil, between 2014 and 2024, was limited, manifesting mainly in longer time horizons and with lags. The positive association, of weak to moderate intensity, suggests that macroeconomic conditions act as a contextual factor, but not as the main driver of the sector’s dynamics. The growth trajectory of credit protection insurance appears to be more influenced by factors intrinsic to the credit market and the insurance industry. As a limitation, the study focused on only two macroeconomic variables. Future investigations could incorporate other variables, such as the interest rate (Selic), consumer default, and credit supply, or segment the analysis by different insurance branches.

Despite the limitations, the findings offer practical implications for insurers and risk managers. The product’s low sensitivity to short-term shocks indicates resilience, but the correlation over longer horizons reinforces the need to monitor the macroeconomic scenario in medium and long-term strategic planning. Understanding the time lags can aid in calibrating pricing models and anticipating demand changes. It is concluded that the objective was achieved: it was demonstrated that the variations in IPCA and the unemployment rate showed predominantly weak correlations with the premiums of credit life insurance, with the most notable associations emerging only at intermediate time scales and with lags of three to six months.

References:
Banco Central do Brasil. (2024). Índice Nacional de Preços ao Consumidor Amplo [IPCA] Série Histórica. Accessed December 29, 2024, from https://api. bcb. gov. br/dados/serie/bcdata. sgs.433/dados? formato=csv&dataInicial=01/01/2000&dataFinal=29/12/2024
Chapman, P. (2000). CRISP-DM 1.0: Step-by-step data mining guide. SPSS Inc.
Confederação Nacional das Seguradoras [CNSEG]. (2024). 10 reasons to contract loan insurance. Available at: https://cnseg. org. br/conteudos/10-motivos-para-voce-contratar-um-seguro-prestamista. Accessed: Nov. 03, 2024.
Guedes, E. F.; Zebende, G. F. (2019) DCCA cross-correlation coefficient with sliding windows approach. Physica A: Statistical Mechanics and its Applications, Amsterdam.
Instituto Brasileiro de Geografia e Estatística [IBGE]. (2023). Índice Nacional de Preços ao Consumidor Amplo – IPCA. Available at: https://www. ibge. gov. br/estatisticas/economicas/precos-e-custos/9256-indice-nacional-de-precos-ao-consumidor-amplo. html?=&t=o-que-e. Accessed: Jan. 07, 2025.
Instituto Brasileiro de Geografia e Estatística [IBGE]. Unemployment. Available at https://www. ibge. gov. br/explica/desemprego. php. Accessed Jul 26, 2025.
Martins, N. M. (2025). Household financial fragility in Brazil (2005–2023). Journal of Economic Issues, 59(1), 174–194. https://doi. org/10.1080/01603477.2024.2378744. Accessed Sep. 05, 2025.
Morettin, P. A., & Toloi, C. M. (2018). Análise de séries temporais (3rd ed.). Edgard Blücher.
Peng, C.-K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., & Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Physical Review E, 49(2), 1685–1689. Accessed: Sep. 05, 2025.
Podobnik, B., & Stanley, H. E. (2008). Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series. Physical Review Letters, 100(8), 084102. Accessed: Sep. 05, 2025.
Sebrae Previdência. (2024). Interest rate hike: understand how it affects finances. Available at: https://www. sebraeprevidencia. com. br/planejar-dicas/156/Alta-de-juros:-entenda-como-ela-afeta-as-fin%C3%A7as. Accessed: Nov. 05, 2024.
Silva, F. L., & Chan, B. L. (2015). Análise da Demanda e Sinistralidade do Seguro Prestamista. In Aportes ao Desenvolvimento da Economia Brasileira (pp. 233-254). Blucher. Available at: https://pdf. blucher. com. br/openaccess/9788580391237/12. pdf. Accessed: Nov. 05, 2024.
Silva, R., & Vasconcelos, F. (2022). Crédito e risco em tempos de crise: o papel do seguro prestamista. Revista Brasileira de Risco e Seguro.
Superintendência de Seguros Privados [SUSEP]. (2024). Insurance database: Premiums and Claims. Available at: https://www2. susep. gov. br/menuestatistica/ses/principal. aspx. Accessed: Dec. 24, 2024.
Zebende, G. F. (2011). DCCA cross-correlation coefficient: A new method to measure the cross-correlation of two non-stationary time series. Physica A: Statistical Mechanics and its Applications, 390(4), 614-618.
Zebende, G. F., Brito, A. A., Silva Filho, A. M., & Castro, A. P. (2018). DCCA applied between air temperature and relative humidity: An hour/hour view. Physica A, 494, 17-26. https://www. sciencedirect. com/science/article/pii/S0378437117312748. Accessed: Sep. 05, 2025.

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

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