Outliers/Most Influential Observationsin Variable Returns to Scale Data Envelopment Analysis

Abstract

Background/Objectives: Outliers are extreme observations which deviate significantly from the normal observations. Their presence distorts the end results of scientific study. In Data Envelopment Analysis (DEA), most influential observations are outliers. Identification of outliers and their deletion is important in DEA problems. Deletion of an extreme observation results in contraction of the production possibility set. Methods/Analysis: This study identifies outliers as these extreme observations whose absence results in significant contraction of the production possibility set. Data Envelopment Analysis is based on solving linear programming problems to assess the efficiency scores of Decision Making Units (DMUs). The present study can estimate efficiency scores of DMUs with and without outliers. Deletion of outliers provides smaller targets to the inefficient DMUs. Findings: For identification of outliers super efficiency, problems can be solved for extremely efficient DMUs, which results in the largest dimension of the contracted Production Possibility Set (PPS). The present study provides many dimensions of the contracted PPset, solving Banker, Charnes and Cooper (BCC 1984) linear programming problems. Sum of these dimensions can be viewed as histogram that closely envelops the contracted Production Possibility Set. Larger is the sum of all dimensions, more influential is the decision making unit. To identify outliers in DEA in this study a statistical test is outlined. Application/Improvements: The methodology outlined can be used for DMUs competing with each other in a competitive environment employing similar inputs to produce similar outputs.