. 2023 Oct 10;9(10):e20573. doi: 10.1016/j.heliyon.2023.e20573

Table 4.

Estimated stochastic frontier models (dependent variable: Infant survival rate).

Variable	Kumbhakar (1990)	Battese and Collie (1995)	True Fixed Effects	True Random Effects
Production function
Health spending	0.0360***	0.0594***	1.7493***	0.0289***
Health spending	(0.0109)	(0.0108)	(0.6481)	(0.00573)
Health spending squared	−0.00339***	−0.00482***	−0.1711***	−0.00245***
Health spending squared	(0.000998)	(0.00114)	(0.0638)	(0.000546)
Education	0.0173	0.0211***	−0.1794	0.0584***
Education	(0.0128)	(0.00582)	(0.11532)	(0.00343)
Employment		0.0271***	0.7684**	0.0446***
Employment		(0.00707)	(0.35816)	(0.00345)
Share of population aged 65+		0.0108	0.0346	−0.0231***
Share of population aged 65+		(0.00666)	(0.0690)	(0.00357)
Constant	6.832***	6.603***	NA	6.680***
Constant	(0.0305)	(0.0395)		(0.0231)
Model parameters
Sigma u ( $σ_{u}$ )	0.167***	1.515**	2.225***	0.006***
Sigma u ( $σ_{u}$ )	(0.0383)	(0.8398)	(0.4358)	(0.0009)
Sigma v ( $σ_{v}$ )	0.005***	0.008***	0.091***	0.002***
Sigma v ( $σ_{v}$ )	(0.0005)	(0.0018)	(0.0072)	(0.0006)
Lambda ( $λ$ )	33.95***	189.16***	24.33***	2.570***
Lambda ( $λ$ )	(0.0381)	(0.8393)	(0.6743)	(0.0013)
Theta ( $θ$ )	N/A	N/A	N/A	−0.038***
Theta ( $θ$ )				(0.0015)

Clustered robust standard errors in parentheses; ***p < 0.01, **p < 0.05, *p < 0.1.