Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs

The paper focuses upon situations in which decision-making units carry out their production activities with some inputs or outputs unobservable (or possibly omitted), and when there are a priori known constraints on the relative significance of otherwise observable (or explicitly considered) inputs and outputs. For such settings, the paper proposes a modification that alters traditional construction of the production possibility set and isolates the role of the unobservable (or omitted) variables in production by means of restrictions on virtual inputs and outputs being converted into production trade-offs. In effect, the proposed procedure induces unit-specific production possibility sets that derive from production trade-offs framed for units assessed separately to reflect their specific observed production conditions. The modification is implemented within a weighted slacks-based measure with restricted direction of slacks in order to make technical efficiency measurement more informative and consistent with the operating conditions under which production activities are accomplished. These ideas are illustrated and models implemented in a case study of bank branch performance measurement.