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Analyzing Inequality

How to analyze inequality:

Compare inequality

Analyze inequality, growth and poverty

There are different ways to analyze inequality and present findings: first, by comparing inequality between different groups; second, by decomposing inequality to assess the major contributors to inequality; third, by analyzing inequality, growth and poverty and their relationship; and finally, by decomposing changes in inequality over time. This page briefly presents these alternative techniques.

Comparing Inequality

Many of the tools used in the analysis of poverty can be similarly used for the analysis of inequality. One could draw a profile of inequality, which would look at the extent of inequality among certain groups of households. This informs on the ‘homogeneity’ of the various groups, an important element to take into account when designing interventions.

Analysis of changes in inequality over time can also be carried out. One could focus on changes for different groups of the population to show whether inequality changes have been similar for all or have taken place, say, in a particular sector of the economy. In rural Tanzania, while rural incomes have increased substantially between 1983 and 1991, inequality increased (with a Gini coefficient increasing from 0.52 to 0.72), especially among the poor. This can be linked to important reforms which took place in the agricultural price policy, which has intensified inequalities, with the poor and less-efficient farmers unable to participate in the growth experienced by wealthier, more efficient farmers.

Another aspect of inequality analysis would be to compare the level of inequality in different dimensions. In a country where public health provision is well developed and reaches all strata of the population, one could expect to see lower levels of inequality in health outcomes than in income levels. This can be done by presenting measures of inequality for different dimensions, and comparing the value of the measures.

Analysis could also focus on the inequality of different consumption categories or income sources. In Egypt, it was found that agricultural income represented the most important inequality-increasing source of income, while non-farm income has the greatest inequality-reducing potential. The table below presents the decomposition and shows that while agricultural income only represents 25% of total income in rural areas, it contributes to 40% of the inequality

 Decomposition of income inequality in rural Egypt, 1997

For a discussion of the standard errors of inequality measures, which is useful for comparisons between estimates of inequality for different distributions, refer to Inequality: Methods and Tools (177kb PDF).

Decomposing income inequality

The common inequality indicators can be used to assess the major contributors to inequality, by different subgroups of the population and regions as well as by income source. In static decompositions, household and personal characteristics, such as education, gender, occupation, urban and rural, and regional location, are determinants of household income. If that is the case, then at least part of the value of any given inequality measure must reflect inequality between people with different educational levels, occupations, genders, and so on. This inequality is referred to as the ‘between-group’ component.

But for any such partition of the population, whether by region, occupation, sector or any other attribute, some inequality will also exist among people within the same subgroups; this is the ‘within-group’ component.  The Theil index and those of the Generalized Entropy class can be decomposed across these partitions in a additive way. Using the Theil coefficient, the within-area (within rural areas and within urban) contribution to inequality in Zimbabwe in 1995/1996 was 72 percent, while the between-area (between urban and rural areas) component was 28 percent. In other words, differences among residents living within rural or within urban areas were relatively much larger than differences between rural and urban areas. In many Latin American countries, the between-area component of inequality has a much higher share in explaining total inequality.

Of equal interest is which of the different income sources, or components of a measure of well-being, are primarily responsible for the observed level of inequality. For example, if total income can be divided into self-employment income, wages, transfers, and property income, one can examine the distribution of each income source. Raising one of the income sources by 1 percent, what would happen to overall inequality?

For a description of the formula, see Technical Note: Inequality Measures and their Decompositions.

Analyzing inequality, growth and poverty

Given that poverty is determined by the mean income or consumption and the inequality in income or consumption, it is feasible to simulate the impact of growth (an increase in mean income or consumption) and changes in inequality (an shift in the distribution across the population) on poverty. This type of analysis can be used for setting of targets for poverty reduction and to simulate the impact of various policy changes (which affect growth and/or distribution) on poverty levels. It is important to note that these techniques have important limitations, linked to the underlying strong assumptions. Thus, the tools presented in this section should be used with much caution.

The figure below illustrates graphically the difference between ‘growth’ effects and ‘inequality’ effects. The Figure presents the distribution function of income or consumption (i.e. the vertical axis shows us the percentage of households with incomes of different levels, represented on the horizontal axis). The vertical lines represent the means of the distribution and the poverty lines (set in this example at 50). The dotted lines which link the distributions to the horizontal axis represent the 5th and the 95th percentiles of the population, i.e. there are 5 percent of households with incomes below the left line and 5 percent of households with incomes above the right line. The arrows between these lines give a measure of inequality. The higher the dispersion between the 5th and the 95th percentile, the higher the inequality.

The figure on the left shows the impact of a uniform growth (where all individuals get an increase in income by 30), without any change in inequality. The entire distribution is simply shifted to the right. The figure on the right shows the impact of a decrease in inequality with constant mean (no growth). The two distributions have equal mean, but the “lower inequality” distribution has lower dispersion (distance between 5th and 95th percentile). The impact on poverty is measured by the share of households below the poverty line (i.e. the part of the distribution to the left of the line). In both cases, poverty is reduced. The purpose of this section is to distinguish between these two effects, in order to better understand past changes or to design various simulations of future poverty levels.

Effect of income/consumption growth and inequality changes on poverty levels.

Simulating the effect of growth and inequality on poverty

A single household survey with income and/or expenditure modules can be used to simulate the effect of growth and inequality on poverty. Such simulations can make different assumptions about inequality (it may remain constant, increase, or decrease), the sectoral distribution of growth (agriculture may be the engine of growth, in which case the population linked to agricultural activities would have a higher growth rate in personal incomes and expenditures than other groups), or the geographic distribution of growth.

Using 1993 as a baseline for Tanzania, the table below shows how per capita growth rates and changes in inequality would translate into changes in poverty over a 20-year period. With a zero real per capita growth rate and no change of inequality, the poverty rate would remain unchanged. A 1.5 percent sustained per capita growth rate with no change in the distribution of income (all household get a 1.5 percent income gain per year) would yield a substantial reduction in poverty. If inequality were to improve at the same time, the poverty reduction would be greatly accelerated, even with a similar growth level.

Poverty, Inequality, and Growth in Tanzania

The technique can be further refined to assess the impact of growth in different parts of the country, such as urban versus rural areas, or by different sectors of the economy.

Decomposing changes in poverty with two or more surveys

When successive surveys are available, it is feasible to find how much of observed changes in poverty over time can be attributed to changes in distribution and to changes in mean income or consumption. For example, lower poverty could result either from a general increase in the income of all households (without change in the income distribution) or from a decrease in inequality (redistribution from the rich to the poor without change in mean income or consumption). A change in poverty can always be decomposed into a growth component, a redistribution component, and a ‘residual’ component.

An example can be taken from rural Tanzania, which experienced a decrease in poverty but an increase in inequality. Decomposing changes in poverty incidence (headcount) and depth (poverty gap) reveals that while the poor benefited from growth over the period, the rich captured a much greater share of economic improvement. In fact, if the distribution of income hadn’t changed, the reduction in poverty incidence would have been much larger and the poverty gap would have also decreased. The table below presents the results of the analysis and show that, using a high poverty line, the head count would have decreased by 38% and the poverty gap by 24%. The changes in distribution (and interaction factors) resulted in a decrease in the head count of only 14% and in the poverty gap of only 2%.

Decomposition of changes in poverty in rural Tanzania, 1983-1991

For a description of the formula see Technical Note: Measuring Poverty and Analyzing Changes in Poverty Over Time.

This page is based on  Coudouel et al. (2002). Please refer to the document for further details and references. Please also refer to Inequality: Methods and Tools (177kb PDF) for a discussion of inequality measurement and decomposition. For a discussion of the relation between growth, poverty, and inequality, please consult the website on  Achieving Shared Growth.

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