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Table 1 ML estimates for SFA parameters and for TE

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

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. βp -0.013 (0.063) -
Year βt -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) β1t 0.089 (0.035) -
(Labour × Labour) β22 0.124 (0.058) -
(Labour × Capital) β23 0.010 (0.015) -
(Labour × Year) β2t -0.018 (0.015) -
(Capital × Capital) β33 -0.013 (0.011) -
(Capital × Year) β3t 0.013 (0.009) -
(Year × Year) βtt 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 δt -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 + 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. (1) Adopted Model (Translog) (2) Preferred Model (Cobb-Douglas with no δ0 intercept).
  2. γ* is described in the text below.