Ranking Invariant Efficiency Measures of Healthcare Units
38 Pages Posted:
Date Written: February 13, 2021
Public service spending is an important issue with great economic, social and political ramifications. Consequently, correct measurements with respect to productivity evaluation of such expenditures is of paramount significance. Case in point: public healthcare budget allocations are often based on past performance. Motivated by evaluating public healthcare units from a non-parametric production efficiency perspective and the computational irregularities this may entail, we present refined bounds for the crucial non-Archimedean infinitesimal (aka epsilon). In non-parametric efficiency models the epsilon plays a key role as a multiplication factor to the sum of input and output slacks in the objective function, equivalently, it is used as a lower bound for the input and output weights in productivity multiplier models. Selecting a value for epsilon is non-trivial since: it has to be sufficiently small to guarantee the envelopment model is bounded (or the multiplier model feasible) yet large enough to provide managerial insight and not to cause computational problems; is highly context specific, depending on the input and output metrics; sensitive to underlying assumptions with respect to constant or variable returns-to-scale; and may lead to drastically different relative efficiency rankings. To guarantee the relative ranking of the evaluated units remain consistent we provide two bounds for the epsilon. The first, positive efficiency guarantee, ensures the obtained efficiency measures are always well-defined, and the second, ranking invariance guarantee, is a refinement such that the relative efficiency rankings remain consistent. We illustrate our bounds and their implications using data from twelve public healthcare centers.
Keywords: Production Efficiency Measures; Healthcare Productivity; Unique Efficiency Ranking; Data Envelopment Analysis; Non-Archimedean.
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