Productivity and quality changes in Greek public hospitals

Abstract

The objective of this paper is to estimate productivity changes after the inclusion of quality variables for a panel of Greek public hospitals during the period 2002–2007. We measure hospital productivity and quality changes through a non-parametric estimation of the quality adjusted Malmquist productivity index by using the percentage of survival after admissions as a proxy of hospital care services quality. Even though the empirical results indicate on average deterioration both in productivity and quality there is considerable variation among the sample hospitals.

Appendix: Linear programming problems

$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t} (x^{t + 1} ,y^{t + 1} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t + 1} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t} \ge 0, } } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t + 1} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots ,K} \\ \end{array} $$

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$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t + 1} (x^{t} ,y^{t} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t + 1} \ge 0,} } & { n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t + 1} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots ,K} \\ \end{array} $$

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$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t} (x^{t} ,y^{t} ,\alpha^{t} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t} \ge 0, } } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & { - \phi \alpha_{j}^{t} + \sum\limits_{k = 1}^{K} {z_{k} \alpha_{k}^{t} \ge 0, } } & {j = 1, \ldots ,J,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots K} \\ \end{array} $$

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Similar for [D ^t+1 _oc (x ^t+1, y ^t+1, α ^t+1)]⁻¹ = max ϕ

$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t} (x^{t + 1} ,y^{t + 1} ,\alpha^{t + 1} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t + 1} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t} \ge 0, } } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t + 1} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & { - \phi \alpha_{j}^{t + 1} + \sum\limits_{k = 1}^{K} {z_{k} \alpha_{k}^{t} \ge 0,} } & {j = 1, \ldots ,J,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots ,K} \\ \end{array} $$

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$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t + 1} \left( {x^{t} ,y^{t} ,\alpha^{t} } \right)} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}} .} & {x_{n}^{t} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t + 1} \ge 0,} } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t + 1} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & { - \phi \alpha_{j}^{t} + \sum\limits_{k = 1}^{K} {z_{k} \alpha_{k}^{t + 1} \ge 0,} } & {j = 1,..,J,} \\ {} & {z_{k} \ge 0, } & {k = 1,. \ldots K} \\ \end{array} $$

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