Table 2 Estimation of parameters

Constant

6.70 (0.000)***

 − 0.08 (0.725)

Inputs \(({x}_{j})\)

 Physician

0.54 (0.000)***

0.08 (0.600)

 Nurse

0.88 (0.000)***

0.76 (0.005)***

 OtherMedStaff

0.61 (0.000)***

0.37 (0.109)

 Bed

1.48 (0.000)***

Quadratic terms \(({{x}_{j}}^{2})\)

 Physicianxphysician

 − 0.10 (0.043)**

 − 0.26 (0.001)***

 Nursexnurse

 − 0.05 (0.653)

 − 0.90 (0.001)***

 OtherMedStaffxotherMedStaff

 − 0.27 (0.033)**

 − 0.22 (0.262)

 Bedxbed

 − 0.07 (0.649)

Cross products \((x_j\), \(x_k )\)

 Physicianxnurse

 − 0.11 (0.071)*

0.39 (0.001)***

 PhysicianxotherMedStaff

0.20 (0.001)***

 − 0.01 (0.872)

 NursexotherMedStaff

0.01 (0.913)

0.36 (0.043)**

 Bedxphysician

 − 0.13 (0.129)

 Bedxnurse

0.14 (0.417)

 BedxotherMedStaff

 − 0.16 (0.214)

Year dummies

 D₂₀₁₆

0.05 (0.004)***

0.00 (0.908)

 D₂₀₁₇

 − 0.03 (0.134)

 − 0.06 (0.026)**

 D₂₀₁₈

 − 0.02 (0.315)

 − 0.10 (0.001)***

 D₂₀₁₉

 − 0.06 (0.017)**

 − 0.15 (0.000)***

 D₂₀₂₀

 − 0.56 (0.000)***

 − 0.49 (0.000)***

 D₂₀₁₁

 − 0.37 (0.000)***

 − 0.35 (0.000)***

Inefficieny effects

 Constant

 − 3.05 (0.000)***

 − 1.02 (0.000)***

 TRH

1.33 (0.000)***

 − 1.73 (0.000)***

 CITY

0.87 (0.001)***

 − 1.86 (0.000)***

 POP

 − 6.43 (0.000)***

5.27 (0.000)***

 RATE

0.00 (0.994)

0.04 (0.224)

 D₂₀₂₀

0.21 (0.336)

0.25 (0.083)*

 D₂₀₂₁

0.24 (0.441)

0.69 (0.001)***

 Log Likelihood

 − 734.15

 − 2535.13

 LR Test

238***

864***