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The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)

Table 2 ML estimates of efficiency and its determinants

From: A meta-stochastic frontier analysis for energy efficiency of regions in Japan

  Group TFEE TGR
Group 1 (metropolitan area) Group 2 (rural area)
Input stochastic frontier
 Constant (β0) 12.574 (0.747) 21.59*** (19.087) 30.664*** (9.636)
 Log regional GDP (βY) 7.944 (1.572) 36.391*** (22.076) 0.143 (0.144)
 Log labor (βL) − 15.22** (− 2.369) − 17.73*** (− 9.737) 2.364** (2.453)
 Log capital (βK) 3.291 (1.223) − 22.349*** (− 30.167) − 6.104*** (− 7.252)
 Log GDP squared (βYY) 12.069*** (3.663) − 0.762*** (− 2.818) 1.265*** (2.72)
 Log labor squared (βLL) 4.157 (1.011) 0.775** (2.218) − 0.263 (− 0.735)
 Log capital squared (βKK) 0.776 (1.518) 0.977*** (11.643) 2.345*** (15.321)
 Log labor * Log capital (βLK) − 7.879** (− 2.280) − 0.214 (− 0.399) 0.586 (1.569)
 Log labor * Log GDP (βLY) − 5.267*** (− 4.888) − 0.634** (− 2.258) − 1.676*** (− 7.535)
 Log capital * Log GDP (βKY) 4.786*** (4.472) − 0.026 (− 0.078) − 0.521*** (− 2.679)
Equation of Inefficiency
 Constant (δ0) − 2.348 (− 1.054) 3.265*** (5.897)  
 Energy-intensive manufacturing industry share (δ1) 50.271*** (8.732) 26.058*** (24.443)  
 Non-energy-intensive manufacturing industry share (δ2) − 4.716** (− 2.570) − 0.48 (− 0.492)  
 Wholesale and retail trade industry share (δ3) 2.883 (1.326) 5.62*** (4.69)  
 Service activities industry share (δ4) 8.866* (1.864) − 2.43** (− 2.447)  
 Government services share (δ5) − 11.369 (− 1.458) − 16.575*** (− 14.573)  
 Population density (δ6) − 1.583e − 04** (− 2.275) 1.017e − 04 (0.278)  
 Income per capita (δ7) 8.736e − 05 (0.418) − 0.001*** (− 5.192)  
 Time (δ8) − 0.032 (− 1.616) 0.05*** (4.577)  
Sigma-squared (σ2) 0.134*** (5.968) 0.309*** (13.364) 0.349 (0.860)
Gamma (γ) 0.981*** (111.282) 1.000*** (26,240,861) 0.997*** (290.937)
Mu (μ)    − 0.867 (− 0.577)
Eta (η)    − 0.081*** (− 26.241)
Log likelihood 50.9903 3.218885 1116.932
Number of observations 208 403 611
Number of regions 16 31 47
  1. t values are in parentheses
  2. ***, **, and * Significant at the 1, 5, and 10% levels, respectively