Squared Poverty Gap Index

THE POVERTY GAP Index is a measure of poverty that calculates both the prevalence and the depth of poverty in a country. It is computed by calculating how far each poor individual is below the official poverty line as a percentage of the poverty line itself, and then averaging these proportional poverty gaps over the entire population. Persons above the poverty line are assumed to have a poverty gap of zero.

One problem economists raise concerning the Poverty Gap Index as a measurement tool is that it does not account for the distribution of income among the poor. All persons who fall below the poverty line are treated equally in calculating the index, regardless of how far below the line they fall. Thus, a change in the income of an utterly destitute person alters the Poverty Gap Index equally to a change in income for someone just below the poverty line cutoff. For this reason, some economists advocate the use of the Squared Poverty Gap Index to account for variations in income below the poverty line.

The Squared Poverty Gap Index is computed in a similar fashion to the Poverty Gap Index by calculating how far each poor individual is below the official poverty line as a percentage of the poverty line itself, except these proportional poverty gaps are squared before averaging over the population. In this manner, those persons who are further from the poverty line are weighted more heavily.

For example, suppose a country has 10 citizens and a poverty line of $1,000 per year. If one person has an annual income of $400 and a second person has an annual income of $600, while the remaining eight persons have incomes in excess of $1,000, then the simple Poverty Gap Index for the country is equal to .4 plus .6 divided by 10, or 10 percent. The Squared Poverty Gap Index is equal to .16 plus .36 divided by 10, or 5.2 percent.

Now suppose a policy change results in a transfer of $300 of income from the poorer individual to the richer one so that the new annual incomes are $100 and $900. While this clearly exacerbates poverty among the most poverty-stricken, it is not reflected in the Poverty Gap Index, which remains unchanged at 10 percent (.9 plus .1 divided by 10). The Squared Poverty Gap Index, however, rises to .01 plus .81 divided by 10, or 8.2 percent, reflecting the change in the income distribution.

As with other poverty measures, care must be taken in comparing the Squared Poverty Gap Index across nations since the official definition of poverty may differ [Page 1019]significantly from country to country. International agencies have attempted to correct for this deficiency by standardizing definitions of poverty.

The most commonly used standardized measure of poverty is the $1-a-day level, which corresponds to an annual income of $365 adjusted for inflation and international differences in costs of living (also known as purchasing power parity, or PPP). By the $1-a-day threshold, the Squared Poverty Gap Index for the developing world was 2.5 percent. This figure represents a significant decrease from past numbers largely because of reductions in the poverty in India and China. In 1981 and 1990, the Squared Poverty Gap Indexes for the developing world were 6.4 percent and 3.6 percent, respectively.

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