Projecting human development and CO2 emissions
  We estimate cumulative CO2 emissions during the period 2000 to 2050 from developed and developing countries based on the empirical relationship between CO2 per capita emissions (due to fossil fuel combustion and cement production) and corresponding HDI. In order to project per capita emissions of individual countries we make three assumptions which are detailed below. First, we use logistic regressions to fit and extrapolate the HDI on a country level as a function of time. This is mainly motivated by the fact that the HDI is bounded between 0 and 1 and that it decelerates as it approaches 1. Second, we employ for individual countries the correlations between CO2 per capita emissions and HDI in order to extrapolate their emissions. This is an ergodic assumption. Third, we let countries with incomplete data records evolve similarly as their close neighbors (in the emissions-HDI plane, see Fig. 1 in the main text) with complete time series of CO2 per capita emissions and HDI. Country-based emissions estimates are obtained by multiplying extrapolated CO2 per capita values by population numbers of three scenarios extracted from the Millennium Ecosystem Assessment report. Finally, we propose a reduction scheme, where countries with an HDI above the development threshold reduce their per capita CO2 emissions with a rate that is proportional to their HDI. We estimate the minimum proportionality constant so that the global emissions by 2050 meet the 1000Gt limit. 
Lu\'is Costa, Diego Rybski, and J\"urgen P. Kropp
physics.soc-ph