Statistical Relation to Radial Efficiency Measures
A consideration arising in the context of output-specific efficiencies is the following: Assume that with positive probability we would observe complete specialization (i.e. m s = 1) of firms with regard to one output (indexed s) and this were true for all outputs. On the other hand we would never observe zero efficiency with regard to any of the outputs (i.e. d(ε s = 0) = 0 for all s = 1... S). Neither of the two assumptions seems particularly far fetched.
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