Technical efficiency and productivity growth in public sector hospitals of Uttarakhand (India)

Abstract

This paper measures technical efficiency (TE) and total factor productivity (TFP) of 27 government hospitals of Uttarakhand (India) through data envelopment analysis based Malmquist Productivity Index for the period from 2001 to 2011. Technical efficiency change (TECh) and technical change (TECHCh) for each hospital are also estimated to identify sources of TFP growth. The results show that on average, TFP in the hospitals increased by a rate of 4.9 % per annum, with slightly higher growth observed in TE (2.6 %) than in technology (2.2 %). The study also reveals that TFP growth varies across regions and areas. On average, it has grown slightly faster in Garhwal region than Kumaon region. Further, it is observed relatively higher in the hospitals of plain/semi-plain areas than that of hill areas. It is observed that in some hospitals, TECh and TECHCh indices did not move in the same direction and therefore positive impact of one component on the TFP growth was largely cancelled by the negative impact of the other. The paper suggests that TFP in the public hospitals could be improved by reallocating the staff from inefficient hospitals to efficient ones; improving human capital base of inefficient hospitals; and investing in new medical technology.

Appendices

Appendix 1: Distance functions used to calculate MPIs

$$ \begin{gathered} \left. \begin{gathered} \left[ {D^{t} (X^{t} ,Y^{t} )} \right]^{ - 1} = \mathop {\text{Max}}\limits_{\phi ,\lambda } \phi \hfill \\ s.t.,\;\phi \;y_{r}^{t} - \sum\limits_{j = 1}^{n} {\lambda_{j}^{t} y_{rj}^{t} } \le 0,\quad \forall r = 1, \ldots ,s \hfill \\ \sum\limits_{j = 1}^{n} {\lambda_{j}^{t} x_{ij}^{t} } \le x_{i}^{t} \quad \forall i = 1, \ldots ,m \hfill \\ \lambda_{j}^{t} \ge 0\quad \forall j = 1, \ldots ,n \hfill \\ \end{gathered} \right\} \hfill \\ \phi \;{\text{is}}\;{\text{unrestricted}}\;{\text{in}}\;{\text{sign}} \hfill \\ \end{gathered} $$

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$$ \begin{gathered} \left. \begin{gathered} \left[ {D^{t + 1} (X^{t + 1} ,Y^{t + 1} )} \right]^{ - 1} = \mathop {\text{Max}}\limits_{\phi ,\lambda } \phi \hfill \\ s.t.,\quad \phi \;y_{r}^{t + 1} - \sum\limits_{j = 1}^{n} {\lambda_{j}^{t + 1} y_{rj}^{t + 1} } \le 0,\quad \forall r = 1, \ldots ,s \hfill \\ \sum\limits_{j = 1}^{n} {\lambda_{j}^{t + 1} x_{ij}^{t + 1} } \le x_{i}^{t + 1} \quad \forall i = 1, \ldots ,m \hfill \\ \lambda_{j}^{t + 1} \ge 0\quad \forall j = 1, \ldots ,n \hfill \\ \end{gathered} \right\} \hfill \\ \phi \;{\text{is}}\;{\text{unrestricted}}\;{\text{in}}\;{\text{sign}} \hfill \\ \end{gathered} $$

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$$ \begin{gathered} \left. \begin{gathered} \left[ {D^{t} (X^{t + 1} ,Y^{t + 1} )} \right]^{ - 1} = \mathop {\text{Max}}\limits_{\phi ,\lambda } \phi \hfill \\ s.t.,\phi y_{r}^{t + 1} - \sum\limits_{j = 1}^{n} {\lambda_{j}^{t} y_{rj}^{t} } \le 0,\quad \forall r = 1, \ldots ,s \hfill \\ \sum\limits_{j = 1}^{n} {\lambda_{j}^{t} x_{ij}^{t} } \le x_{i}^{t + 1} \quad \forall i = 1, \ldots ,m \hfill \\ \lambda_{j}^{t} \ge 0\quad \forall j = 1, \ldots ,n \hfill \\ \end{gathered} \right\} \hfill \\ \phi \;{\text{is}}\;{\text{unrestricted}}\;{\text{in}}\;{\text{sign}} \hfill \\ \end{gathered} $$

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$$ \begin{gathered} \left. \begin{gathered} \left[ {D^{t + 1} (X^{t} ,Y^{t} )} \right]^{ - 1} = \mathop {\text{Max}}\limits_{\phi ,\lambda } \phi \hfill \\ s.t.,\phi y_{r}^{t} - \sum\limits_{j = 1}^{n} {\lambda_{j}^{t + 1} y_{rj}^{t + 1} } \le 0,\quad \forall r = 1, \ldots ,s \hfill \\ \sum\limits_{j = 1}^{n} {\lambda_{j}^{t + 1} x_{ij}^{t + 1} } \le x_{i}^{t} ,\quad \forall i = 1, \ldots ,m \hfill \\ \lambda_{j}^{t + 1} \ge 0\quad \forall j = 1, \ldots ,n \hfill \\ \end{gathered} \right\} \hfill \\ \phi \;{\text{is}}\;{\text{unrestricted}}\;{\text{in}}\;{\text{sign}} \hfill \\ \end{gathered} $$

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Appendix 2

See Table 8.

Table 8 Descriptive statistics of input and output variables for the entire period (2001–2011)

Appendix 3

See Table 9.

Table 9 Full name of selected hospitals