The complex relationship between credit and liquidity risks: a linear and non-linear analysis for the banking sector

The study investigates whether credit risk (CR) and liquidity risk (LR) in banks are reciprocally linked and whether these relationships are linear or exhibit threshold-driven non-linearities. Motivated by the central role of banks in financing Tunisia’s economy and the importance of CR and LR for bank profitability and stability, the authors hypothesize (i) a bidirectional relationship between CR and LR and (ii) the existence of optimal levels (thresholds) of each risk that alter the impact on the other. Using Tunisian banks (2000–2018), the study seeks to quantify the linear relationships via SUR and identify potential non-linear, threshold effects via PSTR, thereby informing risk management and regulatory policy in Tunisia’s bank-centric financial system.

Prior research broadly recognizes CR and LR as key risks affecting bank performance and stability. Empirical findings on their linkage are mixed: many studies report a positive relationship (e.g., Cai and Zhang, 2017; He and Xiong, 2012; Magwedere and Marozva, 2022), while others find negative or insignificant effects (Cai and Thakor, 2008; Wagner, 2007; Imbierowicz and Rauch, 2014). The literature also distinguishes linear from non-linear analyses. Non-linear work (e.g., Pop et al., 2018; Boussaada et al., 2022; Djebali and Zaghdoudi, 2020) documents threshold effects in LR–NPL dynamics, typically examining only one direction (LR→NPLs). However, no prior study jointly examines both linear and non-linear relationships in both causal directions (CR↔LR). This gap motivates the present study to analyze bidirectional, linear and non-linear interactions and identify thresholds for both risks.

Data: Panel of 10 systemically important Tunisian banks (top by assets, loans, deposits) from 2000–2018. Bank-level financials are from banks’ annual reports via the Tunisian Professional Banking and Financial Institution Association; macroeconomic data (GDP growth, inflation) are from the World Bank WDI. Variables: CR is measured by the ratio of non-performing loans to gross loans (NPLs). LR is proxied by loans-to-deposits ratio (LTD). Bank-specific controls: diversification (DIV: noninterest income ratio), capital (EQTA: equity/total assets), size (SIZE: ln total assets), profitability (NIM: net interest margin). Macroeconomic controls: GDP growth (GDPG) and inflation (INF). Linear analysis: A Seemingly Unrelated Regression (SUR) system with two equations is estimated to capture reciprocal effects: (1) LR equation with NPLs and controls; (2) CR equation with LTD and controls. Precondition for SUR (correlated disturbances) is tested via residual correlation matrix and Breusch–Pagan test. Non-linear analysis: Panel Smooth Transition Regression (PSTR), an extension of Hansen’s PTR, models regime-dependent coefficients as smooth functions of a transition variable. Two PSTR specifications are estimated: (i) CR as dependent with LR (LTD) as transition variable to detect LTD threshold affecting CR; (ii) LR as dependent with CR (NPLs) as transition variable. Linearity is tested using LM/Wald, LM(F), and LR tests. The number of regimes (thresholds) is selected via LMw and LMF tests, favoring a single-threshold model in both directions. Threshold values and smoothness parameters are estimated, and regime-specific effects (below/above thresholds) are interpreted.

Descriptive statistics indicate mean LTD=116.6% (SD=35.23; min 63.56; max 259.71) and mean NPLs=14.40% (SD≈8.8; min 0.50; max 48.02). Pearson correlations show low collinearity among regressors. SUR results (Table 5): - LR equation (dep. LTD): NPLs positively and significantly increases LTD (coef=1.297, p<0.01). EQTA (−2.996, p<0.01), SIZE (−0.052, p<0.05), NIM (−8.898, p<0.01), GDPG (−0.053, p<0.01) significantly reduce LR; INF positive but marginal (p≈0.086); DIV not significant. - CR equation (dep. NPLs): LTD positively and significantly increases NPLs (coef=0.082, p<0.01). NIM (−2.413, p<0.01) and GDPG (−0.016, p<0.01) significantly reduce CR; INF increases CR (0.027, p<0.01); EQTA, SIZE, DIV not significant. Residual correlation across equations is significant (ρ≈0.167; BP test p=0.021), supporting SUR. Non-linearity and thresholds (Tables 6–8): Linearity is rejected in both directions (p≤0.05 for LTD as dependent; p≤0.01 for NPLs as dependent). A single-threshold PSTR is supported. Estimated optimal thresholds: LTD=102% (LR threshold affecting CR) and NPLs=9.87% (CR threshold affecting LR). Smoothness parameters are modest (γ≈0.9 and 1.4), indicating stable PSTR fits. PSTR regime effects (Table 9): - Effect of LR on CR: Below LTD<102%, effect is negative and significant (coef≈−2.524, t≈−2.73). Above LTD>102%, effect turns positive but not significant (coef≈1.323, t≈1.33). - Effect of CR on LR: Below NPLs<9.87%, effect is negative and significant (coef≈−0.440, t≈−8.13). Above NPLs>9.87%, effect is positive and significant (coef≈0.442, t≈7.07). Controls in PSTR: EQTA and NIM reduce both risks (EQTA: −5.204 for CR; −0.688 for LR; NIM: −3.063 for CR; −1.195 for LR), GDPG reduces both risks (stronger for CR), INF significantly raises CR but not LR; SIZE and DIV remain insignificant. Policy-relevant estimates: Thresholds are below sample means (mean LTD≈116.6%; mean NPLs≈14.4%), implying elevated risks at observed averages and suggesting stricter LR and CR management targets.

The findings confirm a bidirectional linkage between credit and liquidity risks: higher NPLs increase LTD and higher LTD increases NPLs in linear models, indicating risk amplification loops. However, the PSTR results reveal that this nexus is regime-dependent. When risk indicators are maintained below identified thresholds (LTD<102% and NPLs<9.87%), the CR–LR relationship becomes stabilizing (negative and significant), implying that prudent levels of one risk help mitigate the other. Exceeding thresholds reverses the effect to positive, with statistically significant amplification notably for CR→LR, underscoring that elevated credit risk materially worsens liquidity conditions. These insights address the research question by demonstrating both causality directions and the existence of optimal risk levels that change the sign and significance of interactions. The results are highly relevant for bank risk management and regulation in bank-centric economies like Tunisia, guiding policies to avoid regimes where risk interactions become mutually reinforcing.

This study jointly examines linear and non-linear, bidirectional relationships between credit risk (NPLs) and liquidity risk (LTD) for 10 major Tunisian banks (2000–2018) using SUR and PSTR. Key contributions include: (i) documenting positive two-way linear effects between CR and LR; (ii) identifying threshold effects in both directions, with optimal thresholds at LTD=102% and NPLs=9.87%; and (iii) showing that below these thresholds the CR–LR linkage is negative (stabilizing), whereas above them it becomes positive, significantly so for CR→LR. Bank capital, profitability, and GDP growth consistently reduce both risks; inflation raises CR; bank size and diversification are not robust determinants. Policy recommendations include keeping LTD below ~100–102% (suggesting revising the current 120% regulatory cap) and reducing NPLs below ~9.87% through better screening, collateralization, and risk management. Future research should broaden samples and adopt additional LR measures (e.g., LCR, NSFR) to enhance generalizability and robustness.

The sample is limited to 10 Tunisian banks, constraining external validity and generalizability. Liquidity risk is measured solely by the loans-to-deposits (LTD) ratio; incorporating Basel III metrics such as the Liquidity Coverage Ratio (LCR) and Net Stable Funding Ratio (NSFR) could refine LR assessment. Future work should expand the bank sample within Tunisia and consider cross-country comparisons, and include additional LR proxies to test robustness.