Calculating the RCI from the Equity Calculator dataset
The Equity Reference Calculator sets a country’s fair share of the global climate effort in proportion to its Responsibility and Capacity Index, or RCI, which in turn is calculated from a country’s capacity and responsibility. Capacity for a given year is defined as the sum of the income of all individuals in the country, excluding the total income of everyone under a user-specified income level referred to as the development threshold. (Central to the calculation is the commonly used assumption that national income distributions can be modeled as lognormal distributions.[19] The lognormal distribution has been shown to provide a reasonable approximation of measured income distributions.[20] With this assumption, any national income distribution can be modeled with just a Gini Coefficient and the per-capita income.) The Calculator’s initial setting of for development threshold is $7500 per capita, PPP adjusted; so we will use that number in the following example. For people making more than $7500 annually, only their income above that threshold counts towards the national measure of capacity. Responsibility is calculated in a similar manner. Emissions are calculated from income based on a user-specified elasticity, which is initially set to one (i.e., all individuals in a country have emissions proportional to income); thus, all emissions are excluded for those whose incomes are under the development threshold, and emissions equivalent to $7500 of consumption at the national average carbon intensity are excluded for those with income over the threshold. Unlike the calculation of capacity, however, responsibility is calculated on a cumulative basis, starting at a user-specified initial year, so that responsibility in (say) 2015 is the sum of responsibility calculated in this way for each year from the specified start year to 2015. Capacity and responsibility are then expressed as a percentage of the global total, and combined into a single “Responsibility and Capacity Index” by taking a weighted average. In the Calculator, the Responsibility and Capacity weightings are initially set to be equal, but the calculator allows this to be user-specified, all the way from 100% Responsibility to 100% capacity.