Nonlinear effects of lending rates on credit risk in microfinance institutions: evidence from Peruvian municipal savings and credit banks

Technical Summary: Nonlinear Effects of Lending Rates on Credit Risk in Peruvian Microfinance Institutions

Problem Statement
Microfinance institutions (MFIs) in emerging economies operate under conditions of asymmetric information, where borrowers often possess limited financial transparency and unstable repayment capacities. While institutions must set lending rates to cover operational costs and expected risk, excessively high rates may trigger adverse selection and moral hazard. According to the theories of Stiglitz and Weiss (1981), higher interest rates can alter the composition of the borrower pool, attracting riskier individuals or encouraging riskier post-disbursement behavior, thereby deteriorating portfolio quality. Despite extensive literature linking credit risk to macroeconomic and bank-specific factors, there remains a gap in understanding whether a specific "optimal" lending rate threshold exists in microfinance, beyond which higher rates cease to compensate for risk and instead increase credit risk. This study addresses this gap by examining the nonlinear relationship between lending rates and credit risk within Peruvian Municipal Savings and Credit Banks (Cajas Municipales) during the 2021–2025 period.

Methodology
The study employs a quantitative, explanatory research design using a balanced panel dataset comprising ten Peruvian Municipal Savings and Credit Banks over five years (2021–2025), resulting in 50 annual observations. Data were sourced from the Superintendence of Banking, Insurance and Private Pension Funds (SBS) for financial indicators and the Central Reserve Bank of Peru (BCRP) for macroeconomic data.

The core econometric specification is a fixed-effects panel model designed to control for unobserved institutional heterogeneity (e.g., internal screening policies, regional coverage). The dependent variable, Credit Risk ($RC_{it}$), is measured as the ratio of overdue loans to direct loans. The primary explanatory variable is the Lending Rate ($r_{it}$), defined as the annual effective nominal interest rate applied to microcredit. To test for nonlinearity, the model includes a quadratic term ($r_{it}^2$).

The estimated equation is:
$$RC_{it} = \beta_0 + \beta_1 r_{it} + \beta_2 r_{it}^2 + \beta_3 gmf_{it} + \beta_4 csa_{it} + \beta_5 y_t + \beta_6 Dm_{it} + \mu_i + u_{it}$$

Where:

• $gmf_{it}$: Operational efficiency (Operating expenses / Financial margin).
• $csa_{it}$: Credit intensity (Direct loans / Total assets).
• $y_t$: GDP growth (macroeconomic control).
• $Dm_{it}$: Dummy variables for outlier observations.
• $\mu_i$: Institution-specific fixed effects.

The study utilizes diagnostic tests including the Jarque–Bera test for residual normality, Pesaran's CD test for cross-sectional dependence, and the Durbin–Watson statistic for autocorrelation. The optimal lending rate ($r^*$) is derived by setting the marginal effect of the lending rate on credit risk to zero ($\partial RC / \partial r = 0$). To assess the statistical uncertainty of this threshold, a cluster bootstrap procedure (10,000 replications) was performed at the institution level.

Key Results

1. Nonlinear Relationship: The estimation confirms a statistically significant U-shaped relationship between lending rates and credit risk. The linear coefficient for the lending rate is negative ($\beta_1 = -0.4497$), while the quadratic coefficient is positive and significant ($\beta_2 = 0.0077$, $p=0.024$). This indicates that credit risk initially decreases as rates rise (potentially compensating for risk) but eventually increases once a specific threshold is exceeded.
2. Optimal Lending Rate: The calculated optimal lending rate is 29.21% effective annual interest. The 95% bootstrap confidence interval for this threshold ranges from 24.51% to 36.53%.
3. Control Variables:
   • Operational Efficiency ($gmf_{it}$): Positively associated with credit risk ($\beta = 0.0581$), suggesting that higher operating costs relative to margins correlate with portfolio deterioration.
   • Credit Intensity ($csa_{it}$): Negatively associated with credit risk ($\beta = -0.0900$).
   • Economic Growth ($y_t$): Negatively associated with credit risk ($\beta = -0.0798$), confirming that favorable macroeconomic conditions improve repayment capacity.
4. Economic Simulation: A scenario analysis demonstrates the economic magnitude of exceeding the optimal threshold. Increasing the lending rate from the optimal 29.21% to 45.00% (holding other variables constant) raises the estimated credit risk from 4.98% to 6.90%, an increase of 1.92 percentage points.

Key Contributions and Significance
The primary contribution of this study is the empirical identification of a nonlinear, U-shaped relationship between lending rates and credit risk in the Peruvian microfinance sector. By integrating the asymmetric information framework of Stiglitz and Weiss (1981) with panel data evidence, the paper demonstrates that lending rates function not merely as a price mechanism but as a determinant of portfolio quality.

The study claims that there is a prudential limit to credit pricing. While rates below the optimal threshold may help institutions cover costs and risk, rates significantly above this level (e.g., 45%) fail to compensate for risk and instead actively deteriorate portfolio quality by increasing the probability of default. This finding provides evidence for credit pricing, risk management, and prudential supervision, suggesting that MFIs should avoid aggressive pricing policies that exceed the estimated threshold, particularly when serving borrowers with limited financial information and high vulnerability.

Limitations
The authors acknowledge that the analysis is based on annual data for a specific set of ten institutions over a five-year period. They suggest that future research could benefit from higher-frequency data (monthly or quarterly), dynamic estimation approaches (such as GMM) to address potential endogeneity, and comparative studies across other Latin American microfinance systems to determine if the estimated thresholds are specific to the Peruvian market or applicable more broadly.