# Poverty gap index

The poverty gap index is a measure of the intensity of poverty. It is defined as the average poverty gap in the population as a proportion of the poverty line.[1]

The poverty gap index is an improvement over the poverty measure headcount ratio which simply counts all the people below a poverty line, in a given population, and considers them equally poor.[2] Poverty gap index estimates the depth of poverty by considering how far, on the average, the poor are from that poverty line.[3]

## Definition

The poverty gap index sometimes referred to as poverty gap ratio or pg index is defined as average of the ratio of the poverty gap to the poverty line.[4] It is expressed as a percentage of the poverty line for a country or region.[5]

### Significance

The most common method measuring and reporting poverty is the headcount ratio, given as the percentage of 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 year 2000.[6] 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.[7]

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 alleviation and the evaluation of specific public policies or private initiatives.[8]

## Calculation

The poverty gap index (PGI) is calculated as,[5]

${\displaystyle {\rm {PGI}}={\frac {1}{N}}\sum _{j=1}^{q}\left({\frac {z-y_{j}}{z}}\right)}$

or

${\displaystyle {\rm {PGI}}={\frac {1}{N}}\sum _{j=1}^{N}\left({\frac {(z-y_{j}).1(y_{j}

where ${\displaystyle N}$ is the total population, ${\displaystyle q}$ is the total population of poor who are living at or below the poverty line, ${\displaystyle z}$ is the poverty line, and ${\displaystyle y_{j}}$ is the income of the poor individual ${\displaystyle j}$. 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 ${\displaystyle P_{1}}$ while the headcount ratio is reported as ${\displaystyle P_{0}}$.[9]

## Features

The poverty gap index can be interpreted as the average percentage shortfall in income for the population, from the poverty line.[5]

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. Note that $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 the similar headcount ratio, but distinctly different poverty gap indexes. 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. ## Limitations 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 headcount ratio.[10]

Scholars such as Sen suggest poverty gap index offers 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.[11] These suggestions were initially controversial, and have over time inspired scholars to propose numerous refinements.[2][12][13][14]

## Related measures

The Foster-Greer-Thorbecke metric is the general form of the PGI. The ${\displaystyle FGT_{\alpha }}$ 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 ${\displaystyle P_{2}}$, 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.[9]

Sen index, sometimes referred to ${\displaystyle P_{\text{SEN}}}$, is related to poverty gap index (PGI).[2][15] It is calculated as follows:

${\displaystyle {\rm {P_{\text{SEN}}}}=H*G_{z}+PGI*(1-G_{z})}$

where, ${\displaystyle H}$ is the headcount ratio and ${\displaystyle G_{z}}$ is the income Gini coefficient of only the people below the poverty line.

Watts index, sometimes referred to ${\displaystyle W}$, is related to poverty gap index (PGI).[15] It is calculated as follows:

${\displaystyle {\rm {W}}={\frac {1}{N}}\sum _{j=1}^{q}\ln \left({\frac {z}{y_{j}}}\right)}$

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

## Poverty gap index by country

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

Poverty gap ratio for various countries[16][17]
Country Poverty
line
($/month)[18] Headcount ratio (%) Poverty gap index (%) Year Albania 38 0.62 0.19 2008 Angola 38 54.31 29.94 2000 Argentina[19] 38 0.92 0.65 2010 Armenia 38 1.28 0.25 2008 Australia 959 12.4 2.93 2010 Austria 1024 6.6 1.81 2010 Azerbaijan 38 0.43 0.14 2008 Bangladesh 38 43.25 11.17 2010 Belarus 38 0.1 0.1 2008 Belgium 930 8.8 1.80 2010 Belize 38 12.21 5.52 1999 Benin 38 47.33 15.73 2003 Bhutan 38 10.22 1.81 2007 Bolivia 38 15.61 8.64 2008 Bosnia and Herzegovina 38 0.04 0.02 2007 Botswana 38 31.23 11.04 1993 Brazil 38 6.14 3.62 2009 Burkina Faso 38 44.6 14.66 2009 Burundi 38 81.32 36.39 2006 Cambodia 38 22.75 4.87 2008 Cameroon 38 9.56 1.2 2007 Canada 1056 12.1 2.96 2010 Cape Verde 38 21.02 6.05 2001 Central African Republic 38 62.83 31.26 2008 Chad 38 61.94 25.64 2002 Chile 38 1.35 0.69 2009 China[20] 38 16.25 4.03 2005 Colombia 38 8.16 3.78 2010 Comoros 38 46.11 20.82 2004 Costa Rica 38 3.12 1.79 2009 Cote d'Ivoire 38 23.75 7.5 2008 Czech Republic 515 5.8 1.37 2010 Denmark 955 5.3 1.29 2010 Djibouti 38 18.84 5.29 2002 Dominican Republic 38 2.24 0.52 2010 Congo, Dem. Rep. 38 87.72 52.8 2005 Congo, Rep. 38 54.1 22.8 2005 Ecuador 38 4.6 2.1 2010 Egypt 38 1.69 0.4 2008 Estonia 38 8.9 4.4 2009 Ethiopia 38 39 9.6 2005 Fiji 38 5.9 1.1 2009 Finland 875 7.3 1.48 2010 France 861 7.1 1.44 2010 Gabon 38 4.8 .9 2005 Gambia 38 33.6 11.7 2003 Germany 918 11 3.67 2010 Georgia 38 15.3 4.6 2008 Ghana 38 28.6 9.9 2006 Greece 720 12.6 3.36 2010 Guatemala 38 13.5 4.7 2006 Guinea 38 43.3 15. 2007 Guinea-Bissau 38 48.9 16.6 2002 Guyana 38 8.7 2.8 1998 Haiti 38 61.7 32.3 2001 Honduras 38 17.9 9.4 2009 Hungary 407 7.1 1.66 2010 Iceland 942 7.1 2.55 2010 Ireland 934 14.8 3.08 2010 India 38 32.7 7.5 2010 Indonesia 38 18.1 3.3 2010 Iran 38 1.45 0.34 2005 Iraq 38 2.8 0.42 2007 Italy 700 11.4 3.08 2010 Jamaica 38 0.21 0.02 2004 Japan 950 14.9 5.17 2010 Jordan 38 0.12 0.03 2010 Kazakhstan 38 0.11 0.03 2009 Kenya 38 43.4 16.9 2005 Kyrgyzstan 38 6.4 1.5 2008 Laos 38 44 12.1 2002 Latvia 38 0.14 0.1 2008 Lesotho 38 43.4 20.8 2003 Liberia 38 83.8 40.9 2007 Lithuania 38 0.16 0.1 2008 Luxembourg 1511 8.1 1.62 2010 Macedonia 38 0.29 0.04 2008 Madagascar 38 81.3 43.3 2010 Malawi 38 73.9 32.3 2004 Maldives 38 1.48 0.14 2008 Mali 38 50.4 16.4 2010 Mauritania 38 23.4 6.8 2008 Mexico 192 18.4 6.97 2010 Micronesia 38 31.2 16.3 2000 Moldova 38 0.39 0.08 2010 Montenegro 38 0.12 0.08 2008 Morocco 38 2.5 .54 2007 Mozambique 38 59.6 25.1 2008 Namibia 38 31.9 9.5 2004 Nepal 38 24.8 5.6 2010 Netherlands 1168 7.7 1.61 2010 New Zealand 803 10.8 3.63 2010 Nicaragua 38 11.9 2.4 2005 Niger 38 43.6 12.4 2008 Nigeria 38 68 33.7 2010 Norway 1109 6.8 2.00 2010 Pakistan 38 21 3.5 2008 Panama 38 6.6 2.1 2010 Papua 38 35.8 12.3 1996 Paraguay 38 7.2 3. 2010 Peru 38 4.9 1.3 2010 Philippines 38 18.4 3.7 2009 Poland 338 14.6 5.20 2010 Portugal 512 12.9 3.74 2010 Romania 38 0.41 0.19 2009 Russia[21] 61 14.3 5.09 2006 Rwanda 38 63.2 26.6 2011 São Tomé and Príncipe 38 28.2 7.9 2001 Senegal 38 33.5 10.8 2005 Serbia 38 0.26 0.17 2009 Sierra Leone 38 53.4 20.3 2003 Slovakia 368 8.1 2.07 2010 South Africa 38 13.8 2.3 2009 South Korea 809 14.6 5.26 2010 Spain 749 14.1 4.51 2010 Sri Lanka 38 7 1 2007 Sudan 38 19.8 5.5 2009 Suriname 38 15.5 5.9 1999 Swaziland 38 40.6 16. 2010 Sweden 863 5.3 1.31 2010 Syria 38 1.71 0.2 2004 Switzerland 1148 8.7 3.37 2010 Tajikistan 38 6.6 1.2 2009 Tanzania 38 67.9 28.1 2007 Thailand 38 0.37 0.05 2009 East Timor 38 37.4 8.9 2007 Togo 38 38.7 11.4 2006 Trinidad and Tobago 38 4.2 1.1 2008 Tunisia 38 1.35 0.28 2005 Turkey 211 17.5 5.76 2010 Turkmenistan 38 24.8 7 1998 Uganda 38 38.01 12.2 2009 Ukraine 38 0.06 0.04 2009 United Kingdom 1027 8.3 2.06 2010 United States[22] 1232 17.1 6.55 2010 Uruguay 38 0.2 0.07 2008 Venezuela 38 6.6 3.7 2006 Vietnam 38 16.9 3.8 2008 Yemen 38 17.5 4.2 2005 Zambia 38 68.5 37 2006 ## See also ## References 1. ^ "Millennium Development Goal Indicators". United Nations. 2008. 2. ^ a b c Amartya Sen (March 1976). "Poverty: An Ordinal Approach to Measurement". Econometrica. 44 (2): 219–231. doi:10.2307/1912718. JSTOR 191271. 3. ^ Grusky and Kanbur (2006). Poverty and Inequality (Studies in Social Inequality). Stanford University Press. ISBN 978-0804748438. 4. ^ "Indicators for Monitoring the Millennium Development Goals" (PDF). United Nations, New York. 2003. p. 9. 5. ^ a b c "Poverty Measures" (PDF). The World Bank. 2009. 6. ^ Peter Edelman (July 28, 2012). "Poverty in America: Why Can't We End It?". The New York Times. 7. ^ Ravallion (June 1996). "Issues in measuring and modeling poverty". The World Bank. 8. ^ "Indicators of Sustainable Development". United Nations Department for Policy Coordination and Sustainable Development. 2004. 9. ^ a b "Poverty Measures, Chapter 4" (PDF). The World Bank. August 2005. 10. ^ James E. Foster (May 1998). "Absolute versus Relative Poverty". The American Economic Review. 88 (2): 335–341. JSTOR 116944. 11. ^ Dan Morell (Jan–Feb 2011). "Who Is Poor?". Harvard Magazine. 12. ^ Amartya Sen (December 1985). "A Sociological Approach to the Measurement of Poverty: A Reply to Professor Peter Townsend". Oxford Economic Papers, New Series. 37 (4): 669–676. JSTOR 2663049. 13. ^ Noriyuki Takayama (May 1979). "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered". Econometrica. 47 (3): 747–759. doi:10.2307/1910420. JSTOR 191042. 14. ^ Jenkins and Lambert (1997). "THREE 'I'S OF POVERTY CURVES, WITH AN ANALYSIS OF UK POVERTY TRENDS". Oxford Economic Papers. 49 (3): 317–327. doi:10.1093/oxfordjournals.oep.a028611. 15. ^ a b Giovanni Vecchi (September 2007). "Poverty Measurement" (PDF). The World Bank. 16. ^ "Poverty database". The World Bank. 2012. 17. ^ "OECD Factbook - 2010 (Poverty rates and gaps)". OECD. 2011. 18. ^ Note: this is on purchasing power parity basis, international dollar adjusted for inflation to 2005; To convert to$ per day income, divide by 30.4; for annual income multiply by 12.
19. ^ This data is for urban population only.
20. ^ This data is for rural population of China
21. ^ Mosley and Mussorov (April 2009). "Poverty and economic growth in Russia's regions" (PDF). University of Sheffield.
22. ^ The U.S. defines its poverty line on a dynamic basis and household size. As an example, for a family of 4 in a household, the poverty line was about \$1838 per month.