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This study takes an average of these inefficiency components in formulations for the proposed intermediate model.
Because only a few studies used SFA, it was not possible to control for the model choices in SFA, such as functional form used for technology structure, distribution of inefficiency components, etc.
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On the other hand, this method cannot separate the inefficiency component from the noise.
It means that technical efficiency depends only on the inefficiency component under the control of the firm (u it ).
Our use of SFA was motivated by modelling flexibility and potential extensions to accommodate random effects and different distributions for the inefficiency component [ 44, 45].
Following [ 66], for each of our four models we estimated both the production function and the inefficiency component in a single stage.
The latter separates the residual into an inefficiency component (u i, positive departures from the (best practice) production frontier) and all other sources of model error (v i ), such as random shocks and measurement error [ 15, 36].
Primarily, the model assumes that both the symmetric error term (v) and the non-negative inefficiency component (u) are independent of each other and iid across observations [ 26, 28].
ξ i is a composite error term, representing the sum (or the difference) of the disturbance term (v i )—representing the measurement and specification error and the inefficiency component denoted by u i. Estimation of a stochastic frontier model requires a range of assumptions on the error components.
Hence, even if we stated earlier that the higher the PHARM, the better, we might find an inefficiency deterrent component in it that averts this kind of undesirable expenditure.
The error term e i in the regression model for a producing unit i is composed of two components: inefficiency and noise: e i = u i + v i [46].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com