Non-parametric data envelopment analysis (DEA) estimators based on linear programmingmethods have been widely applied in analyses of productive efficiency. Thedistributions of these estimators remain unknown except in the simple case of one inputand one output, and previous bootstrap methods...

The traditional approach to measuring allocative efficiency is based on input prices, which are rarely known at the firm level. This paper proposes a new approach to measure allocative efficiency which is based on the output-oriented distance to the frontier in a profit technical efficiency...