How relevant is the choice of risk management control variable to non-parametric bank profit efficiency analysis? The case of South Korean banks

Adopting a profit-based approach to the estimation of the efficiency of South Korean banks over the 2007Q3 to 2011Q2 period, we systematically analyse, within a non-parametric DEA analysis, how the choice of risk management control variable impacts upon such estimates. This is in recognition of previous findings that such estimates are dependent on the choice of risk management control variable and the lack of guidance from such studies on the optimal choice of risk control variable. Using the model of Liu et al. (Ann Operat Res 173:177–194, 2010), we examine the dependency of the estimated efficiency scores on the chosen risk control variables embracing loan loss provisions and equity as good inputs and non-performing loans as a bad output. We duly find that, both for individual banks and banking groups, the mean estimates are indeed model dependent although, for the former, rank correlations do not change much at the extremes. Based on the application of the Simar and Zelenyuk (Econom Rev 25:497–522, 2006) adapted Li (Econom Rev 15: 261–274, 1996) test, we then find that, if only one of the three risk control variables is to be included in such an analysis, then it should be loan loss provisions. We also show, however, that the inclusion of all three risk control variable is to be preferred to just including one, but that the inclusion of two such variables is about as good as including all three. We therefore conclude that the optimal approach is to include (any) two of the three risk control variables identified. The wider implication for research into bank efficiency is that the optimal choice of risk management control variable is likely to be crucial to both the delivery of risk-adjusted estimates of bank efficiency and the specification of the model to be estimated.