Estimating indirect allocative inefficiency and productivity change

Building on the method used in previous indirect production studies, we construct an indicator of indirect output allocative inefficiency. Our indicator equals the difference between a revenue-constrained directional input distance function and a directional input distance function that depends on outputs, rather than revenue. The indicator measures the overuse of inputs that occurs when firms do not choose a revenue maximizing mix of outputs. Adding a time dimension allows productivity change to be measured. In an empirical illustration of our method we find that Japanese banks use, between 2% and 7%, too many inputs because bank outputs are inefficiently allocated.