minTEVRS,λTEiVRS i = 1,...,76 (1)
subject to
4
- yim + ∑ yimλi ≥ 0 (2)
m=1
TEVRSxk -∑3 xkλ ≥0 (3)
i ik ik i
k=1
76
∑λi = 1 (4)
i=1
λi ≥ 0 (5)
whereyim represents m (=1,...,4) outputs for i (=1,...,76) observations, or decision making
units (DMUs), x ik represents k (=1,.,3) inputs for i (=1,.,76) observations, or DMUs, λi is a
nonnegative intensity variable over observations, and TEiVRS is the specific efficiency score to
be estimated for each of the 76 observations.
The second part of the empirical approach uses the estimated efficiency scores, Tlt VRS, as the
dependent variable in a regression analysis. This approach has been used in previous studies
of hospital efficiency (Kooreman, 1994; Ferrier and Valdmanis, 1996) and county council
efficiency (Gerdtham et al., 1999). The economic efficiency scores from the first part of the
empirical work is bounded between zero and one, meaning that the dependent variable in the
regression model is censored, and that ordinary least squares regression produces biased
estimates (see e.g. Maddala, 2001, p. 334). In order to address this problem, the following
Tobit regression model (Tobin, 1958) is estimated;
TE VRS = α + βι* ALTERit + β2* FSTATUSit + β3* REGIONit (6)
+ β4* QUALITYit + β5* POPDENSit + β6* OLDit
+ β7* CIRCULATORYit + β8* NERVOUS SYSTEMit
+ β9* PSYCHIATRICit + β10* NON-SOCIALISTit
+ β11* TRENDit + εit