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Table 2 Maximum likelihood estimates of the stochastic frontier models

From: Measuring efficiency of governmental hospitals in Palestine using stochastic frontier analysis

Ln (output)

Parameter

Cobb–Douglas function

Translog function

Multi-output distance function

Constant

β0

8.601***

12.446***

11.49***

Ln (bed)

β1

0.621***

1.607*

−1.07

Ln (doctor)

β2

0.263**

2.351*

3.47**

Ln (nurse)

β3

−0.039

−0.360

0.31

Ln (non-medical staff)

β4

−0.031

−3.945*

−2.46

Ln (bed) × ln (doctor)

β12

 

−0.915**

−1.27***

Ln (bed) × ln (nurse)

β13

 

0.023

−0.51

Ln (bed) × ln (non-medical staff)

β14

 

0.452

1.58***

Ln (doctor) × ln (nurse)

β23

 

1.306***

1.58***

Ln (doctor) × ln (non-medical staff)

β24

 

−1.890***

−1.97***

Ln (nurse) × ln (non-medical staff)

β34

 

−1.203**

−1.01**

Ln (bed) × ln (bed)

β11

 

0.00004

0.27

Ln (doctor) × ln (doctor)

β22

 

0.663***

1.40***

Ln (nurse) × ln (nurse)

β33

 

0.137*

0.26

Ln (non-medical staff) × ln (non-medical staff)

β44

 

1.526***

1.19

Ln (outpatient/inpatient)

β5

  

−1.37

Ln (outpatient/inpatient) × ln (bed)

β51

  

−0.10*

Ln (outpatient/inpatient) × ln (doctor)

β52

  

0.07

Ln (outpatient/inpatient) × ln (nurse)

β53

  

−0.47

Ln (outpatient/inpatient) × ln (non-medical staff)

β54

  

−0.18

Ln (outpatient/inpatient) × ln (outpatient/inpatient)

β55

  

0.98**

Variance of technical inefficiency (sigma_u2)

δu2

0.128

0.086

0.284

Variance of random error (sigma_v2)

δv2

0.030

0.022

0.145

Sigma square (sigma2)

δs2 = δu2 + δv2

0.158

0.109

0.429

Ln sigma square (lnsigma2)

Ln (δs2)

−1.840***

−2.216***

−2.27***

Variance ratio parameter (gamma)

ϒ = δu2/δs2

0.807

0.792

0.662

Inverse logit gamma (ilgtgamma) = 0

ilgt ϒ

1.435*

1.338**

1.34**

mu

μ

0.563*

0.627**

0.671**

Wald Chi square (4, 14)

χ2

138.158***

285.563***

379.66***

Number of observations

N

132

132

132

  1. * p < 0.05; ** p < 0.01; *** p < 0.001
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