This chapter provides an in-depth explanation of three types of distance functions combined with parametric linear programming: the Output Distance Function (ODF), Input Distance Function (IDF), and Directional Distance Function (DDF), as well as the Meta-frontier Directional Distance Function (Meta-DDF) for addressing technological heterogeneity. It describes the mathematical forms, constraints, and applications of these methods, especially in environmental economics for estimating the shadow prices of undesirable outputs (e.g., pollution abatement costs). The chapter emphasizes the contexts in which each method is most suitable—for example, ODF is suited to periods of extensive growth, DDF is better for coordinated economic–environmental development, and Meta-DDF is appropriate for analyzing cross-group technological differences.

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Parametric Linear Programming Method

  • Ning Zhang,
  • Kerui Du

摘要

This chapter provides an in-depth explanation of three types of distance functions combined with parametric linear programming: the Output Distance Function (ODF), Input Distance Function (IDF), and Directional Distance Function (DDF), as well as the Meta-frontier Directional Distance Function (Meta-DDF) for addressing technological heterogeneity. It describes the mathematical forms, constraints, and applications of these methods, especially in environmental economics for estimating the shadow prices of undesirable outputs (e.g., pollution abatement costs). The chapter emphasizes the contexts in which each method is most suitable—for example, ODF is suited to periods of extensive growth, DDF is better for coordinated economic–environmental development, and Meta-DDF is appropriate for analyzing cross-group technological differences.