Estimating indirect allocative inefficiency and productivity change

Abstract

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.

Keywords:

• DEA (data envelopment analysis)
• indirect allocative inefficiency
• directional distance functions
• productivity change
• Japanese banking

Acknowledgements

We are grateful to Kazuyuki Sekitani and two anonymous referees for their constructive comments. This research is partially supported by the Grants-in-aid for scientific research, fundamental research (A) 18201030 and (B) 19310098, the Japan Society for the Promotion of Science.

Notes

1 Färe et al (1994) and Camanho and Dyson (2005, 2008) provide examples, extensions, and empirically estimated direct data envelopment analysis (DEA) allocative efficiency measures.

2 A table of optimal outputs that are the solution to the revenue-constrained Shephard input distance function are available from the authors upon request.

3 Simar and Wilson (2002) apply their method to test whether a production technology is globally constant returns to scale versus the alternative that the technology is variably returns to scale.

4 Banker (1996) suggests that when the distribution of technical inefficiency is unknown, researchers should employ a Kolmogorov–Smirnov test to investigate hypotheses regarding alternative assumptions concerning returns to scale.