Table 2 Summary descriptive measures of efficiency scores and goodness-of-fit (Akaike and Bayesian information criteria and Likelihood ratio test) by stochastic frontier model of health system efficiency using healthy life expectancy (HALE) at birth and at 65 years-old as outputs, in 2015 for 188 countries

Model 1

0.693

0.919

0.947

0.963

0.992

0.934

0.047

-511.6

-498.7

2.0 e-8

0.685

0.866

0.909

0.936

0.976

0.891

0.064

-279.7

-266.7

2.6 e-4

Model 2

0.684

0.910

0.946

0.963

0.993

0.929

0.051

-488.1

-475.2

0.9 e-8

0.666

0.861

0.903

0.930

0.975

0.885

0.068

-261.8

-248.9

1.1 e-4

Model 3

0.702

0.930

0.953

0.970

0.992

0.945

0.039

-574.5

-551.8

2.8 e-8

0.714

0.880

0.920

0.941

0.974

0.906

0.051

-305.8

-283.1

117.4 e-4

Model 4

0.710

0.936

0.957

0.973

0.994

0.948

0.037

-574.2

-503.0

18.1 e-8

0.686

0.873

0.918

0.949

0.981

0.905

0.058

-317.5

-246.3

12.3 e-4

Model 5

0.708

0.928

0.948

0.966

0.988

0.939

0.041

-539.3

-523.1

63.7 e-8

0.728

0.882

0.918

0.941

0.975

0.906

0.050

-297.8

-281.7

222.1 e-4