Adaptive Dynamics of Bank Lending under Credit Risk: A Discrete-Time Modeling Approach

Abstract

This study constructs a discrete-time model to examine the dynamics of bank loans, deposits, and non-performing loans (NPL) in the presence of adaptive adjustment behavior. The model presumes that the banks progressively change lending and funding choices to target levels based on deposits, credit risk, and the policy rate. The initial step was linear specification, which can be characterized explicitly in terms of equilibrium and global stability. This was further extended to a nonlinear model where lending is risk-sensitive, becoming more cautious as risk increases. The models were estimated based on monthly data from commercial banks in Indonesia between October 2021 and June 2025. The quantitative results showed that the two models predict the major trends in the data, even though the nonlinear specification has a slightly better empirical fit. The sensitivity analysis showed that the accelerated rate of loan adjustment increased the rate of credit growth as well as the risk accumulation, while the sensitivity of the risks moderated the lending activity. On the contrary, stability and intermediary performance were improved by better NPL resolution. The suggested model provides a straightforward but efficient method of explaining the interplay of lending, funding, and credit risk within banking systems.

Keywords

• adaptive expectations
• banking dynamics
• discrete-time model
• non-performing loans
• nonlinear dynamics

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