Poverty gap index

The most common method measuring and reporting poverty is the headcount ratio, given as the percentage of the population that is below the poverty line. For example, The New York Times in July 2012 reported the poverty headcount ratio as 11.1% of American population in 1973, 15.2% in 1983, and 11.3% in 2000.{{cite news|last=Edelman|first=Peter |author-link=Peter Edelman|url= https://www.nytimes.com/2012/07/29/opinion/sunday/why-cant-we-end-poverty-in-america.html |title=Poverty in America: Why Can't We End It?|date=July 28, 2012|work=The New York Times|access-date=2020-11-20}} One of the undesirable features of the headcount ratio is that it ignores the depth of poverty; if the poor become poorer, the headcount index does not change.{{cite book|last=Ravallion|first=Martin |author-link=Martin Ravallion|url=http://documents1.worldbank.org/curated/en/965061468739145705/pdf/multi-page.pdf|title=Issues in Measuring and Modeling Poverty|date=June 1996|series=Policy Research Working Paper|volume=1615 |place=Washington, D.C.|publisher=World Bank |access-date=2020-11-20}}

Poverty gap index provides a clearer perspective on the depth of poverty. It enables poverty comparisons. It also helps provide an overall assessment of a region's progress in poverty reduction and the evaluation of specific public policies or private initiatives.{{cite web|title=Indicators of Sustainable Development|publisher=United Nations Department for Policy Coordination and Sustainable Development|year=2004|url=http://esl.jrc.it/envind/un_meths/UN_ME.htm|access-date=2012-08-10|archive-url=https://web.archive.org/web/20120421005418/http://esl.jrc.it/envind/un_meths/UN_ME.htm|archive-date=2012-04-21|url-status=dead}}

The poverty gap index (PGI) is calculated as,

::$\{\backslash rm\; PGI\}\; =\; \backslash frac\{1\}\{N\}\; \backslash sum\_\{j=1\}^\{q\}\; \backslash left(\; \backslash frac\{z-y\_j\}\{z\}\; \backslash right)$

or

::

where $N$ is the total population, $q$ is the total population of poor who are living at or below the poverty line, $z$ is the poverty line, and $y\_j$ is the income of the poor individual $j$. In this calculation, individuals whose income is above the poverty line have a gap of zero.

By definition, the poverty gap index is a percentage between 0 and 100%. Sometimes it is reported as a fraction, between 0 and 1. A theoretical value of zero implies that no one in the population is below the poverty line. A theoretical value of 100% implies that everyone in the population has zero income. In some literature, poverty gap index is reported as $P\_1$ while the headcount ratio is reported as $P\_0$.{{cite book|title=Introduction to Poverty Analysis|chapter=Poverty Measures, Chapter 4|chapter-url=http://siteresources.worldbank.org/PGLP/Resources/povertymanual_ch4.pdf |place=Washington, D.C.|publisher=World Bank Institute|date=August 2005|archive-url=https://web.archive.org/web/20120710075646/http://siteresources.worldbank.org/PGLP/Resources/povertymanual_ch4.pdf|archive-date=2012-07-10}}

The poverty gap index can be interpreted as the average percentage shortfall in income for the population, from the poverty line.

If you multiply a country's poverty gap index by both the poverty line and the total number of individuals in the country you get the total amount of money needed to bring the poor in the population out of extreme poverty and up to the poverty line, assuming perfect targeting of transfers. For example, suppose a country has 10 million individuals, a poverty line of $500 per year, and a poverty gap index of 5%. Then an average increase of $25 per individual per year would eliminate extreme poverty. $25 is 5% of the poverty line. The total increase needed to eliminate poverty is US$250 million—$25 multiplied by 10 million individuals.

The poverty gap index is an important measure beyond the commonly used headcount ratio. Two regions may have a similar head count ratio, but distinctly different poverty gap indices. A higher poverty gap index means that poverty is more severe.

The poverty gap index is additive. In other words, the index can be used as an aggregate poverty measure, as well as decomposed for various sub-groups of the population, such as by region, employment sector, education level, gender, age, or ethnic group.

The poverty gap index ignores the effect of inequality between the poor. It does not capture differences in the severity of poverty amongst the poor. As a theoretical example, consider two small neighborhoods where just two households each are below the official poverty line of US$500 income per year. In one case, household 1 has an income of US$100 per year and household 2 has an income of US$300 per year. In second case, the two households both have annual income of US$200 per year. The poverty gap index for both cases is same (60%), even though the first case has one household, with US$100 per year income, experiencing a more severe state of poverty. Scholars, therefore, consider poverty gap index as a moderate but incomplete improvement over poverty head count ratio.{{Cite journal|title=Absolute versus Relative Poverty|last=Foster |first=James E. |author-link=James Foster (economist)|journal=The American Economic Review|volume= 88|number= 2|date=May 1998|pages= 335–341|jstor=116944|citeseerx=10.1.1.383.6488}}

Scholars such as Amartya Sen suggest poverty gap index offers a quantitative improvement over simply counting the poor below the poverty line, but remains limited at the qualitative level. Focusing on precisely measuring income gap diverts the attention from qualitative aspects such as capabilities, skills and personal resources that may sustainably eradicate poverty. A better measure would focus on capabilities and consequent consumption side of impoverished households.{{cite magazine|title=Who Is Poor?|last=Morrell |first=Dan |magazine=Harvard Magazine|date=January–February 2011|url=http://harvardmagazine.com/2011/01/who-is-poor|access-date=2020-11-22}} These suggestions were initially controversial, and have over time inspired scholars to propose numerous refinements.{{cite journal|title=A Sociological Approach to the Measurement of Poverty: A Reply to Professor Peter Townsend|last=Sen |first=Amartya |journal=Oxford Economic Papers|volume= 37|number= 4|date=December 1985|pages= 669–676|jstor=2663049 |doi=10.1093/oxfordjournals.oep.a041716}}{{cite journal|title=Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered|last=Takayama |first=Noriyuki |journal=Econometrica|volume= 47|number= 3|date=May 1979|pages= 747–759|jstor= 1910420|doi=10.2307/1910420}}{{cite journal|title=Three 'I's of Poverty Curves, with an Analysis of UK Poverty Trends|last1=Jenkins|first1=Stephen P. |last2=Lambert|first2=Peter J. |journal=Oxford Economic Papers | date=July 1997|volume= 49|issue= 3|pages= 317–327|jstor=2663596 |doi=10.1093/oxfordjournals.oep.a028611}}

The Foster–Greer–Thorbecke metric is the general form of the PGI. The $FGT\_\backslash alpha$ formula raises the summands to the power alpha, so that FGT0 is the headcount index, FGT1 the PGI and FGT2 the squared PGI.

Squared poverty gap index, also known poverty severity index or $P\_2$, is related to poverty gap index. It is calculated by averaging the square of the poverty gap ratio. By squaring each poverty gap data, the measure puts more weight the further a poor person's observed income falls below the poverty line. The squared poverty gap index is one form of a weighted sum of poverty gaps, with the weight proportionate to the poverty gap.

Sen index, sometimes referred to $P\_\{\backslash text\{SEN\}\}$, is related to poverty gap index (PGI).{{cite web|title=Poverty Measurement|last=Vecchi|first=Giovanni |publisher=World Bank|date=September 2007|url=http://siteresources.worldbank.org/PGLP/Resources/200709gv-03-povertymeasurement.pdf|archive-url=https://web.archive.org/web/20160303225039/http://siteresources.worldbank.org/PGLP/Resources/200709gv-03-povertymeasurement.pdf|archive-date=2016-03-03}} It is calculated as follows:

::$\{\backslash rm\; P\_\{\backslash text\{SEN\}\}\}\; =\; H*G\_z\; +\; PGI*(1-G\_z)$

where, $H$ is the head count ratio and $G\_z$ is the income Gini coefficient of only the people below the poverty line.

Watts index, sometimes referred to $W$, is related to poverty gap index (PGI). It is calculated as follows:

::$\{\backslash rm\; W\}\; =\; \backslash frac\{1\}\{N\}\; \backslash sum\_\{j=1\}^\{q\}\; \backslash ln\; \backslash left(\; \backslash frac\{z\}\{y\_j\}\; \backslash right)$

The terms used to calculate $W$ are same as in poverty gap index (see the calculation section in this article).

{{Update|section|date=November 2020}}

The following table summarizes the poverty gap index for developed and developing countries across the world.

• Foster–Greer–Thorbecke indices
• Gini coefficient
• Multidimensional Poverty Index
• Human Poverty Index
• Human Development Index
• Gender Development Index
• Gender Empowerment Measure
• Education Index

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{{Reflist}}

• [https://pip.worldbank.org/home Poverty and Inequality Platform]: World Bank's continuously updated database with poverty gap index and other poverty analysis tools
• [http://issuu.com/world.bank.publications/docs/9780821376133 Handbook on Poverty and Inequality]: A handbook with examples, features and limitations of poverty measures

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Category:Measurements and definitions of poverty