Technical efficiency in the sheep dairy industry: an application on the Sardinian (Italy) sector

Agricultural and Food Economics

Table 1 ML estimates for SFA parameters and for TE

Variable	Parameter	Translog⁽¹⁾	Cobb-Douglas⁽²⁾
Frontier Model
Constant	β₀	2.888 (0.121)	1.161 (0.168)
Intermediate inputs	β₁	0.101 (0.148)	0.662 (0.036)
Labour	β₂	0.557 (0.162)	0.249 (0.037)
Capital	β₃	0.012 (0.044)	0.098 (0.023)
Private/ coop.	β_p	-0.013 (0.063)	-
Year	β_t	-0.114 (0.074)	0.011 (0.008)
(Inter. Inputs × Inter. inputs)	β₁₁	0.098 (0.022)	-
(Intermediate inputs × Labour)	β₁₂	-0.278 (0.160)	-
(Intermediate inputs × Capital)	β₁₃	0.049 (0.034)	-
(Intermediate inputs × Year)	β_1t	0.089 (0.035)	-
(Labour × Labour)	β₂₂	0.124 (0.058)	-
(Labour × Capital)	β₂₃	0.010 (0.015)	-
(Labour × Year)	β_2t	-0.018 (0.015)	-
(Capital × Capital)	β₃₃	-0.013 (0.011)	-
(Capital × Year)	β_3t	0.013 (0.009)	-
(Year × Year)	β_tt	0.008 (0.003)	-
Efficiency effects
Constant	δ₀	0.781 (0.328)	-
Age	δ₁	-0.344 (0.185)	-0.188 (0.121)
Intermediate inputs	δ₂	-0.299 (0.183)	-0.172 (0.152)
Labour	δ₃	-0.415 (0.251)	-0.363 (0.237)
Capital	δ₄	0.668 (0.454)	0.614 (0.365)
Year	δ_t	-0.026 (0.019)	-0.028 (0.020)
Variance parameters
$σ^{2} = σ_{u}^{2} + σ_{v}^{2}$	σ²	0.081 (0.054)	0.062 (0.041)
$γ = σ_{u}^{2} / (σ_{u}^{2} + σ_{v}^{2})$	γ	0.885 (0.085)	0.864 (0.104)
$γ * = γ / [γ + \frac{1 - γ}{π / (π - 2)}]$	γ*	0.954	0.946
Log-likelihood function		32.305	23.560
Mean TE		0.898 (0.090)	0.905 (0.091)
Returns to scale		1.022	1.009

⁽¹⁾ Adopted Model (Translog) ⁽²⁾ Preferred Model (Cobb-Douglas with no δ₀ intercept).
γ* is described in the text below.