Japanese banking inefficiency and shadow pricing

We estimate Japanese banking inefficiency and the shadow price of problem loans by treating problem loans as a jointly produced undesirable by-product of the loan production process. Our method uses the directional output distance function of Färe et al. [R. Färe, S. Grosskopf, D.-W. Noh, W.L. Weber, Characteristics of a polluting technology: Theory and practice, Journal of Econometrics 126 (2005) 469–492] and seeks the maximum expansion of desirable outputs, such as loans and securities investments, and the simultaneous contraction in undesirable outputs, such as problem loans. The directional output distance function is estimated using data envelopment analysis and a parametric linear programming method. While the two methods give similar estimates of inefficiency, the shadow price estimates for the two methods diverge.