Nonparametric shadow pricing of non-performing loans: a study of the Chinese banking sector

A number of recent studies have modeled risk in banking by incorporating undesirable outputs such as non-performing loans into the banking production technology. However, most of the banking performance studies focus on the measurement of efficiency and productivity of financial institutions without considering the impact of non-performing loans on their profits. In this paper, we introduce a novel approach for modeling a bank's technology as a multi-stage production process. We use a nonparametric estimation framework to obtain the shadow prices of non-performing loans, which approximate the potential increase in a bank's profits following a reduction in its non-performing loans. We illustrate our approach using a panel of 55 Chinese banks from 2007 to 2020 grouped into four categories. Our results suggest that the city commercial banks' corresponding shadow price estimates have been among the highest in the sample, whereas the policy banks have had the best risk performance among the types of institutions we considered. We also demonstrate that the substantial disparities we observe among the different types of banks have been decreasing with time.