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

The objectivesof this study are to assessthe efficiency of the ecological footprint of seven G7 countries (Canada, France, Germany, Italy, Japan, the United Kingdom and the United States),and totest 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, theInput Orientation Slack-Based Data Envelopment Analysis (DEA) model was employed using threeinput variables (Investment by Asset, Labour Force Participation Rate and Total Energy Consumption) and twooutput 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 gatheredfromEnerdata.net, Global Footprint Network, and OECD. While the first stage of analysis design was conductedusing 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 4out of 7G7 countriesare efficient (Germany, Italy, the United Kingdom and the United States), while the remaining threecountries(Canada, France and Japan) were found to be inefficient. Besides, all fourefficient G7 countriesrankfirst,while Japanrankslast among the sevenG7 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 utilisingthe Slack-Based MeasureData Envelopment Analysisand ROC Analysis to address this knowledge gap.