# Proportion of a country’s population who are poor

We need to have a mechanism to take into account the poverty level in a country. One possible candidate could be the average level of income in the country. Unfortunately, the average income does not do the job because it papers over the inequality in income among the population.

There are different measures of inequality that are potential candidates. One commonly used measure is the Gini coefficient. The most common geometric definition of the Gini coefficient is based on the Lorenz (or concentration) curve. It represents cumulative income share as a function of cumulative population share. If a population share is always exactly equal to a share in overall income then there is a situation of perfect equality. However, the Gini coefficient is not affected by a multiplicative factor. If everyone’s income increases ten-fold, the Gini coefficient is not affected. Technically, the Gini coefficient is a relative measure of inequality. To take a concrete example, Uganda and the United States have approximately the same Gini coefficient of income distribution. Both are around 38 percent. The lower the number, the more equal the income. Conversely, the higher the number is, the higher the inequality is going to be. Thus, a zero (percent) Gini coefficient means everybody in the economy has the same income. On the other hand, a 100 percent value Gini coefficient implies that one person has all the income in the country and everyone else has zero income. Of course, in real life, neither extreme is observable. In real life, it ranges from around 25 percent (for countries such as Belgium, Finland, and the Czech Republic) to over 60 percent (such as Brazil or Sierra Leone). Thus, the Gini coefficient would be meaningless as a measure of inequality that can be compared across countries at a given point in time.

A more appropriate measure of inequality is to include people who are poor in the country in absolute terms. One possibility would be to consider a threshold of some proportion of people who are below some absolute measure of poverty level. The rationale is simple. If there are many people below some absolute poverty level, they cannot afford to pay for adaptation or mitigation activities. A simple measure (available for most countries around the world) is the proportion of people in the country who live on USD 1 or less a day. So, the criterion would be the following: if the proportion of population (p) with USD 1 income exceeds some threshold t(p), then the country would automatically qualify. In symbols, if p > t(p), then a country automatically qualifies.

Thus, there are three possible criteria that could be used for determining the countries that qualify. The three are combined to arrive at a single criterion. If a country qualifies using any of the above threshold criteria, it should qualify. The following criterion, which includes all three measures using a compact notation, can be used: If maximum {r - t(r), pci - t(pci), p - t(p)} > 0, the country qualifies. This criterion ensures that: (1) if the emissions rate (r) is above the predetermined threshold (t(r)), then the country qualifies; (2) if the subsistence farmers in the population (pci) is above the predetermined threshold (t(pci)), then the country qualifies; and (3) if the proportion of population who are very poor (p) is above certain threshold (t(p)), then the country qualifies.

Although the measure above is useful, it is not entirely satisfactory. Suppose a country has all the above problems but it fails each threshold criterion by some amount and therefore fails to qualify. Clearly, we will need a method of “adding” each “score” to come up with an aggregate value that reflects the issue in all three dimensions. There are two ways of achieving this, which are discussed below.

Let max(r) be the country with the maximum emissions rate. Let max(pci) be the country with maximum proportion of subsistence farmers. Let max(p) be the country with the maximum proportion of people below USD 1 per day per capita income. We construct the following absolute index (Absolute Climate Sensitivity Index or Absolute CSI):

The rationale for the formula is as follows. If a country hits the maximum emissions rate, maximum subsistence farmers level and maximum number of poor people in the pool of all countries, the CSI will hit a maximum of 1. We can set a predetermined value of the Absolute CSI such that any country with the value of the index above that level would qualify.

Since this measure will never hit zero, some people might consider this measure unsatisfactory. We can adjust that by considering a modified version that measures different dimensions in relative terms. Thus, we construct the Relative Climate Sensitivity Index:

where, I(r) = [r - min(r)]/[max(r) - min(r)], I(pci) = [pci - min(pci)]/[max(pci) - min (pci)] and I(p) = [p - min(p)]/[max(p) - min(p)].

To see why we take such ratios, consider the first one: I(r). If, for a given country, the emissions rate r is the highest among all countries, then the index I(r) = 1. On the other hand, if the emissions rate r is the lowest among all countries, I(r) = 0. Similarly, if the proportion of subsistence farmers (pci) is the highest among all countries, then the index I(pci) = 1. On the other hand, if the proportion of subsistence farmers pci is the lowest among all countries, then the index I(pci) = 0. If the USD 1 a day population p is the highest among all the countries in question, then I(p) = 1, whereas if it is the lowest, then I(p) = 0. Thus, the relative CSI is a measure bounded by 0 and 1 as two extremes. By construction, the relative CSI could touch the limits for the best (in that case, it will touch 0) and the worst (in that case, it will touch 1) case scenarios. It should be noted that the worst outcome country in terms of Absolute CS Index may not be the worst outcome country in terms of the Relative CS Index. Thus, it is quite probable that in the list of all countries we will never observe the extreme value 1 for the Relative CS Index.

Similarly the best outcome country in the RCSI measure may not be the best outcome country in the ACSI measure. Thus, we might not observe the extreme value 0 in a sample of countries.

With the Relative CSI (RCSI), the criterion should specify a threshold (t): if the RCSI > t, the country should qualify under the composite measure for the most favorable level of treatment available. To incorporate this measure into our overall criterion, we propose the following:

If maximum {r - t(r), pci - t(pci), p - t(p), RCSI - t} > 0, then a country should qualify for the most favorable level of treatment.

The use of our index facilitates policies for sustainable economic growth in these types of countries. That process should eventually push them over the threshold value of the index so that they no longer qualify. Without such measures, these countries will be caught in a vicious circle and, therefore, will never generate the level of purchasing power needed to create a market where sustainable development becomes possible.

The index allows us to redress this balance of incentives through a mechanism that uses objective standards recognized by international bodies that represent all interested parties. It can be used to determine which countries should receive multilateral climate financing for adaptation and mitigation in a manner that takes into account the changing circumstances of countries over time.