Interactive effects between input and output technical inefficiencies

This paper derives a new set of results that provide corrective measures of overall technical inefficiency that either have been ignored or wrongly assumed in the literature. Using directional distance functions, we argue that overall technical inefficiency is not only a function of input and output technical inefficiencies as previous studies claim but also of the interaction between them. The derivation of the interactive effects between input and output technical inefficiencies (IEIOs) solves the arbitrary decomposition of overall technical inefficiency into input and output components. We also show that the IEIO depends on the choice of the directional vector and whether quantities and prices are taken into consideration. Using exogenous and endogenous directional vectors, we prove these results theoretically and empirically using the US commercial banking data set. Using Bayesian estimation with the monotonicity conditions imposed at each observation, we estimate input and output technical inefficiencies separately using directional input and output distance functions with the three commonly used directional vectors; the unit value, the observed input−output, and the optimal directional vectors. The overall technical inefficiency is estimated using systems of equations to incorporate the interactive effect equation and to address the endogeneity of inputs and outputs. Consistent with the theoretical results, we find significant evidence of the IEIO which has a negative effect on the overall technical inefficiency. This result is robust to alternative directional vectors and model specifications, suggesting that the adjustability of both inputs and outputs is required for the improvement of the efficiency of the US commercial banks.