Statistical Inference in Convexity of Production Technologies

• Main Authors: Wei-Ru, Chen, 陳威儒
• Other Authors: Wen-Chih, Chen
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/10645743810939822493

碩士 === 國立交通大學 === 工業工程與管理系所 === 96 === Production technology describes a process transforming various resources to different outputs. Production frontier represents the ideal situation of the transformation process. Convexity is one of the properties that a production technology generally satisfies, and it is used as the basic assumptions in many methods estimating the underlying but unknown production technology. For example, data envelopment analysis (DEA), first introduced by Charnes et al. in 1978, computes the efficiency of a record by estimating the production technology according to a set of records. Convexity is one of the important assumptions in most well known DEA models. In reality, however, the underlying technology may not follow convexity due to economics of scale and/or increasing returns to scale. Adopting the convexity assumption in these cases may leads to biased estimations and incorrect conclusions. This study investigates the shape of a production technology, particularly in scale. A statistical procedure is proposed to estimate and inference the underlying but unknown technology by a sample data set generated from itself. In addition, the inference results are visualized so that the shape of ideal technology frontier can be easily accessed for a decision makers. This work not only provides a way to examine the convexity of data for DEA studies. Understanding and visualizing frontier shape have broad applications such as decision aids for capacity planning.