
Cobb–Douglas function

Translog function



(equation 1)

(equation 2)



Coefficient

Standard error

Coefficient

Standard error


ln Number of physicians

0.384***

0.019

2.898***

0.304

ln Number of beds

0.665***

0.034

−0.525**

0.211

Hospital standardized mortality ratio

−0.208***

0.022

−0.172***

0.020

ln Number of physicians (squared)
  
0.438***

0.108

ln Number of beds (squared)
  
0.691***

0.115

ln Number of physicians x ln number of beds
  
−0.711***

0.118

Efficiency score

0.610
 
0.586
 
Log likelihood

−66.852
 
−88.115
 
Likelihood ratio test value

365.405***
 
322.880***
 
 ***p < 0.01 **p < 0.05.
 The results obtained with the TFEM show that all explanatory variables in the Cobb–Douglas function (equation 1) were statistically significant, and all sign directions were as expected. The inputs, the number of physicians and the number of beds, were both positive and statistically significant. The coefficient of the HSMR was significantly negative, suggesting that low mortality rates (or high quality of care) decreases output. The translog model (equation 2) yielded results similar to those obtained with the Cobb–Douglas model (equation 1).