The authors model the performance of DMUs (decision-making units) using the directional distance function within a two-stage framework. In the first stage of production, DMUs use inputs to produce an intermediate output. In stage 2, the intermediate output is used to produce final outputs. In contrast to DEA (data envelopment analysis) models, the two-stage directional model accounts for a network production structure and allows non-radial scaling of outputs and inputs. An empirical application of the method is provided for Japanese credit cooperative Shinkin banks. These banks use labor, physical capital, equity capital in a first stage to produce deposits, and then use the deposits to produce loans, securities investments, and other interest bearing assets in a second stage. The authors find evidence of greater inefficiency in the first stage of production than in the second stage of production. In addition, the findings indicate that models that ignore a network structure and measure performance using a black-box DEA model miss about 50% of total bank inefficiency when measured by the network model.