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Table 2 Maximum likelihood estimates of the stochastic frontier models (n = 41)

From: Improving public hospital efficiency and fiscal space implications: the case of Mauritius

Ln (output) Parameter Cobb–Douglas function Translog function Multi-Output distance
Constant β0 5.274**** 2.904**** 6.539**
Ln (bed) β1 0.232**** 0.171 0.411
Ln (doctor) β2 0.618**** 11.756**** 13.629****
Ln (nurse) β3 0.165 −8.156**** −9.422****
Ln (non-medical staff) β4 0.228 *** 0.249 −0.311*
Ln (bed) × ln (doctor) β12   0.444 0.385*
Ln (bed) × ln (nurse) β13   0.600 1.052
Ln (bed) × ln (non-medical staff) β14   −0.433 − 0.409
Ln (doctor) × ln (nurse) β23   −4.62**** 1.107**
Ln (doctor) × ln (non-medical staff) β24   0.966 1.485****
Ln (nurse) × ln (non-medical staff) β34   −0.2 0.777
Ln (bed) × ln (bed) β11   −0.461 0.989**
Ln (doctor) × ln (doctor) β22   1.88**** 3.3785*
Ln (nurse) × ln (nurse) β33   4.343* 4.24
Ln (non-medical staff) × ln (non-medical staff) β44   −0.355 −1.005
Ln (outpatient/inpatient) β5    −2.85****
Ln (outpatient/inpatient) × ln (bed) β51    0.064
Ln (outpatient/inpatient) × ln (doctor) β52    1.084****
Ln (outpatient/inpatient) × ln (nurse) β53    0.677*
ln (outpatient/inpatient) × ln (non-medical staff) β54    −0.270
Ln (outpatient/inpatient) x ln (outpatient /inpatient)     0.010
Variance of technical inefficiency (sigma_u2) δu2 0.018 6.41 e − 06 5.04e-07
Variance of random error (sigma_v2) δv2 0.004 0.0017 .0013
Sigma square (sigma2) δs2 = δu2 + δv2 0.022 0.0017 .0013
Ln sigma square (lnsigma2) Ln (δs2) −3.780**** −6.35 −6.57
Variance ratio parameter (gamma) ϒ = δu2/δs2 0.79 0.0036 0.00015
Inverse logit gamma (ilgtgamma) = 0 ilgt ϒ 1.325 −5.600 −7.92
mu μ 0.045 −0.0949 −.0266
Wald Chi square (3) χ2 887.41 489 135
Number of observations N 41 41 41
Log likelihood   44 70 75
  1. * p < 0.08; ** p < 0.05; *** p < 0.01; **** p < 0.001