Ecological Footprint Efficiency of G7 Countries: An Integrated Slack-Based Measure Data Envelopment Analysis and ROC Analysis

Abstract

The objectives of this study are to assess the efficiency of the ecological footprint of seven G7
countries (Canada, France, Germany, Italy, Japan, the United Kingdom and the United States), and to test the diagnostic performance of input and output variables in determining the efficiency status of the seven G7 countries. For these purposes, the study has a two-stage analysis design. In the first stage, the Input Orientation Slack-Based Data Envelopment Analysis (DEA) model was employed using three input variables (Investment by Asset, Labour Force Participation Rate and Total Energy Consumption) and two output variables (Ecological Footprint (undesirable) and Gross Domestic Product). In the second stage, ROC Analysis was conducted to assess the diagnostic performance of the input and output variables in determining the Efficiency Status of G7 countries. The dataset belongs to 2025 or the nearest year, and it is gathered from Enerdata.net, Global Footprint Network, and OECD. While the first stage of analysis design was conducted using the deaR package in the R project, the second stage was carried out using Inonu University Faculty of Medicine, Department of Biostatistics and Medical Informatics, Diagnostic Tests and ROC Analysis Software. According to the first stage of analysis design, it was determined that 4 out of 7 G7 countries are efficient (Germany, Italy, the United Kingdom and the United States), while the remaining three countries (Canada, France and Japan) were found to be inefficient. Besides, all four efficient G7 countries rank first, while Japan ranks last among the seven G7 countries. According to the second stage of analysis design, it was determined that i1: Investment by Asset input variable could distinguish the Efficiency Status with the cutoff points (21.723). Given that the ecological footprint efficiency of G7 nations has not been extensively investigated in current literature, this research is notable for utilising the Slack-Based Measure Data Envelopment Analysis and ROC Analysis to address this knowledge gap.