This chapter introduces the application of Parametric Linear Programming (PLP) for evaluating technical efficiency. Unlike traditional DEA approaches, PLP leverages Stata’s Mata environment and specialized software such as LINGO to formulate and solve linear programming problems efficiently. The chapter outlines a structured PLP framework consisting of set establishment, data import, objective function specification, and constraint implementation. Key features include defining sets for inputs, outputs, and parameters, handling missing data, and constructing objective functions for output, input, and directional distance functions. Constraints ensure desirable properties like monotonicity, homogeneity, and symmetry. A detailed programming example demonstrates the estimation of group-specific efficiency using directional distance functions and the subsequent derivation of meta-frontier technical efficiency, accounting for inter-group technological heterogeneity. The chapter also presents Stata-based PLP implementation, allowing researchers to compute technical efficiency, shadow prices, and related metrics. Overall, the chapter provides a practical, stepwise guide for applying PLP in efficiency and productivity analysis. In this section, we provide a brief introduction to how Parametric Linear Programming (PLP) is used to solve technical efficiency problems. To enrich this section further, we not only present Stata coding instructions but also demonstrate the implementation using LINGO, a specialized linear programming software. LINGO allows users to describe complex optimization problems concisely and intuitively, making it easy to learn and implement, especially for beginners. Of course, LINGO also offers additional functionalities, but since they are not relevant to the focus of this book, we will not provide a systematic introduction here.

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Applications of Parametric Linear Programming Method

  • Ning Zhang,
  • Kerui Du

摘要

This chapter introduces the application of Parametric Linear Programming (PLP) for evaluating technical efficiency. Unlike traditional DEA approaches, PLP leverages Stata’s Mata environment and specialized software such as LINGO to formulate and solve linear programming problems efficiently. The chapter outlines a structured PLP framework consisting of set establishment, data import, objective function specification, and constraint implementation. Key features include defining sets for inputs, outputs, and parameters, handling missing data, and constructing objective functions for output, input, and directional distance functions. Constraints ensure desirable properties like monotonicity, homogeneity, and symmetry. A detailed programming example demonstrates the estimation of group-specific efficiency using directional distance functions and the subsequent derivation of meta-frontier technical efficiency, accounting for inter-group technological heterogeneity. The chapter also presents Stata-based PLP implementation, allowing researchers to compute technical efficiency, shadow prices, and related metrics. Overall, the chapter provides a practical, stepwise guide for applying PLP in efficiency and productivity analysis. In this section, we provide a brief introduction to how Parametric Linear Programming (PLP) is used to solve technical efficiency problems. To enrich this section further, we not only present Stata coding instructions but also demonstrate the implementation using LINGO, a specialized linear programming software. LINGO allows users to describe complex optimization problems concisely and intuitively, making it easy to learn and implement, especially for beginners. Of course, LINGO also offers additional functionalities, but since they are not relevant to the focus of this book, we will not provide a systematic introduction here.