Including a Public Input in the Additive Two-Stage Network DEA Model: The Case of Quantitative Easing in Japan.

The traditional additive two-stage network DEA model under constant returns to scale has non-increasing decomposition weights (i.e. the weight assigned to the first stage is not less than the weight assigned to the second stage), which also has a direct impact on the stage efficiencies. Previous research has revealed that adding external input/s in the second stage provides the necessary conditions under which there can be a reversal in the decomposition weights for the two stages. In this paper we are investigating the case of an external public input in the second stage, which is shared across DMUs but not allocatable, and its effect on the decomposition weights. The empirical investigation is undertaken using a dataset of Japanese Regional Banks. Bank of Japan has a long tradition with quantitative easing as a monetary policy instrument that could help boost economic activity, avoid deflation, and overcome the problems of the liquidity trap. Given that quantitative easing provides all banks with liquidity, we model it as a constant input in the second stage of the model. This generalised structure of the model with an external single constant input in the second stage tend to produce results which do not suffer from the issues under investigation.