檢視DEA方法中之資料特性

Abstract

資料包絡法(data envelopment analysis, DEA)是一種用來評估一組具同質性 (homogeneity)觀測資料之相對效率值的工具。源自生產經濟學(production economics)，DEA假設轉換投入成產出的生產技術(production technology)過程具凸性(convexity)，並藉此計算效率值。因此，受測資料具同質性與凸性是DEA的兩個基本假設；當所觀察樣本違反任一假設，所估計的效率值會與實際情形不一致、使分析結果偏差並造成錯誤的結論。 本論文提出藉觀察樣本資料的凸形輪廓(convex hull)特徵，以找出可能違反同質性假設的相異離群值。另一方面，亦提出藉檢視由樣本構成的包絡面(envelopment)上是否有凹陷，以推斷生產技術是否具凸性；此概念可進一步應用於視覺化高維度下生產技術的包絡面形狀，以獲得邊際規模變化的資訊。透過這兩種方法檢視樣本資料是否有違反基本假設，可有效確保DEA方法的正確性並獲得有效的結論。

Data quality is an important issue for all empirical studies including data envelopment analysis (DEA). Homogeneity and convexity are two fundamental assumptions for widely used DEA models such as BCC models (Banker et al., 1984) and CCR models (Charnes et al., 1978). This study presents two methods to examine data homogeneity and convexity for DEA studies, respectively. Relying on well-known “leave-one-out” idea, a quantitative metric on the volume and surface area of a convex hull is adopted and implemented to detect outliers, which is non-homogeneous to the rest of others, from a given data set. The deviations between convexity based and non-convexity based models can be used to infer the shape of the production technology and examine the data convexity.