reductions in inequality that make the poorer better off will likely increase the ability of vulnerable populations to adapt and thus limit the welfare implications of climate change. Reducing inequality can also matter for mitigating climate change. If countries reduce inequality, they require less growth to end poverty, and as economic growth is a major driver of greenhouse gas emissions, inequality reductions imply that fewer emissions would be needed to end poverty (Wollburg r al. 2023).

_Social cohesion._ Inequality influences social cohesion. Higher inequality has been associated with greater political instability, including a greater risk of violence (World Bank 2011), and lower ability for countries to respond to economic shocks (Berg & Ostry 2011). Notions of economic fairness and perceptions of inequality also impact individual behavior (Brunori et al. 2013, Niehues 2014).

# **3.** **<mark>Choice of inequality measure</mark>**

Classifying countries as high inequality requires choosing a specific measure of inequality on which to group countries. The new World Bank indicator uses the Gini index as the measure of inequality. Several other inequality measures exist, each with their own benefits and shortcomings. Here we will look at a subset of measures and summarize the advantages and disadvantages of the Gini vis-à-vis these measures.

Concretely we consider five measures of inequality: the Gini index, the mean log deviation, the Theil index, Kuznets ratios, and quantile ratios, all of which are defined in Box 1. We evaluate these inequality measures along four criteria: whether they are commonly used, easy to explain, Lorenz consistent, and subgroup decomposable. Table 1 summarizes the conditions satisfied by the five inequality measures considered.

## **Box 1: Definitions of a subset of inequality measures**

_<mark>The Gini index</mark>_ <mark>is a measure of inequality ranging from 0 to 100 (or 0 to 1), where 0 indicates perfect equality and 100 perfect inequality (Gini 1912, Ceriani & Verme 2012). The Gini index is commonly defined through a Lorenz curve, which plots the cumulative income or consumption share for a country on the vertical axis against the cumulative population share on the horizontal axis. The Gini index is twice the area between the 45-degree line (which reflects perfect equality) and the observed Lorenz curve. Mathematically, the Gini coefficient is the average transfer needed to make two people in a country equal, expressed relative to the country’s mean income or consumption ( x ): G G =</mark> 1 ∑ ∑ �, where is the number of people in a country. ii=1 jj=1 ii jj 2xx̅NN<sup>2</sup> �xx −xx NN _<mark>The mean log deviation and the Theil index</mark>_ <mark>belong to the class of Generalized Entropy inequality measures (Shorrocks 1980), which were derived from their fulfillment of a range of desirable theoretical properties, these being subgroup decomposability, anonymity, the population principle, the transfer principle, and scale invariance. The various general entropy measures differ by how large weight they place on inequality at the bottom of distributions vis-à-vis inequality at the top of</mark> 1 distributions. The mean log deviation is given by ∑ ~~,~~ while the Theil index is given 1 NN xx̅ ∑ ~~.~~ NN ii=1 llGG xxii NN xxii xxii _<mark>Kuznets ratios</mark>_ NN ii=1 xx̅ llGG xx̅ <mark>measure the share of income going to the top quantiles divided by the income going to the bottom quantiles. The greater the ratio, the higher inequality. One example of a Kuznets ratio is the share of income going to the top 10% divided by the income share of the bottom 40%, also known</mark> as the Palma ratio (Palma 2011).

_<mark>Quantile ratios</mark>_ <mark>measure income ratios at particular quantiles, such as the income of the 90</mark><sup>th</sup> <mark>percentile divided by the income of the 10</mark><sup>th</sup> <u><mark>percentile.</mark></u> 3