The Yin and Yang of banking: Modeling desirable and undesirable outputs

This paper introduces a novel by-production approach to modeling desirable and undesirable output production processes in the US banking sector. We utilize the structural proxy variable framework in which desirable outputs (different types of loans and other income-generating activities) are exogenous, which is a common practice in the banking literature. The undesirable output is non-performing loans (NPLs). To address the endogeneity of variable inputs (purchased funds and core deposits) in the production of desirable outputs, we employ an input distance function and rely on the bank's cost-minimizing behavioral assumption. We specify the undesirable output technology as a function of desirable outputs as well as other factors such as total non-transaction accounts, undivided profits, and capital reserves. Using US commercial bank data from 2001 to 2020, we find that bank productivity exhibits steady growth in desirable outputs. Banks prioritize reducing the overall productivity impact of NPLs post-crisis, shifting focus from pre-crisis service provision.