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where <math>N</math> is the total population, <math>q</math> is the total population of poor who are living at or below the [[poverty threshold|poverty line]], <math>z</math> is the poverty line, and <math>y_j</math> is the [[income]] of the poor individual <math>j</math>. In this calculation, individuals whose income is above the poverty line have a gap of zero.
where <math>N</math> is the total population, <math>q</math> is the total population of poor who are living at or below the [[poverty threshold|poverty line]], <math>z</math> is the poverty line, and <math>y_j</math> is the [[income]] of the poor individual <math>j</math>. 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 <math>P_1</math> while the head count ratio is reported as <math>P_0</math>.<ref name=wb0805>{{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}}</ref>
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 <math>P_1</math> while the headcount ratio is reported as <math>P_0</math>.<ref name=wb0805>{{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}}</ref>


==Features==
==Features==
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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.
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 head count ratio. Two regions may have the 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 an important measure beyond the commonly used headcount ratio. Two regions may have the 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 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==
==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 head count ratio.<ref>{{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}}</ref>
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.<ref>{{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}}</ref>


Scholars such as [[Amartya 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 [[economic inequality|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.<ref>{{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}}</ref> These suggestions were initially controversial, and have over time inspired scholars to propose numerous refinements.<ref name=sen/><ref>{{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}}</ref><ref>{{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}}</ref><ref>{{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}}</ref>
Scholars such as [[Amartya 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 [[economic inequality|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.<ref>{{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}}</ref> These suggestions were initially controversial, and have over time inspired scholars to propose numerous refinements.<ref name=sen/><ref>{{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}}</ref><ref>{{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}}</ref><ref>{{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}}</ref>


==Related measures==
==Related measures==
The [[Foster–Greer–Thorbecke indices|Foster–Greer–Thorbecke metric]] is the general form of the PGI. The <math>FGT_\alpha</math> formula raises the summands to the power alpha, so that FGT0 is the head count index, FGT1 the PGI and FGT2 the squared PGI.
The [[Foster–Greer–Thorbecke indices|Foster–Greer–Thorbecke metric]] is the general form of the PGI. The <math>FGT_\alpha</math> 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 <math>P_2</math>, 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.<ref name=wb0805/>
'''Squared poverty gap index''', also known poverty severity index or <math>P_2</math>, 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.<ref name=wb0805/>

Revision as of 22:42, 25 November 2024

The poverty gap index is a measure of the degree of poverty in a country. It is defined as extent to which individuals on average fall below the poverty line, and expresses it as a percentage of the poverty line.[1]

The poverty gap index is an improvement over the poverty measure head count 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 the poor are from that poverty line on average.[3]

The poverty gap index sometimes referred to as 'poverty gap ratio' or 'pg index' is defined as an 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 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.[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 reduction and the evaluation of specific public policies or private initiatives.[8]

Calculation

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

or

where is the total population, is the total population of poor who are living at or below the poverty line, is the poverty line, and is the income of the poor individual . 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 while the headcount ratio is reported as .[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. $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 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.

Limitations

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.[10]

Scholars such as Amartya 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]

The Foster–Greer–Thorbecke metric is the general form of the PGI. The 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 , 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 , is related to poverty gap index (PGI).[2][15] It is calculated as follows:

where, is the head count ratio and is the income Gini coefficient of only the people below the poverty line.

Watts index, sometimes referred to , is related to poverty gap index (PGI).[15] It is calculated as follows:

The terms used to calculate 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
Country Poverty
line
($/month)[a]		 Head count
ratio
(%)		 Poverty
gap
index
(%)		 Year
 Albania 52 22.9 14.18 2020
 Angola 38 54.31 29.94 2000
 Argentina[b] 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 350 3.91 3.62 2015
 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[c] 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[16] 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[d] 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

Notes

  1. ^ 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.
  2. ^ This data is for urban population only.
  3. ^ This data is for rural population of China.
  4. ^ 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 $1,838 per month.

References

  1. ^ "Poverty Gap". stats.areppim.com. Retrieved June 3, 2023.
  2. ^ a b c Sen, Amartya (March 1976). "Poverty: An Ordinal Approach to Measurement". Econometrica. 44 (2): 219–231. doi:10.2307/1912718. JSTOR 1912718.
  3. ^ Grusky, David B.; Kanbur, Ravi, eds. (2006). Poverty and Inequality. Studies in Social Inequality. Stanford, California: Stanford University Press. p. [page needed]. ISBN 978-0-8047-4843-8.
  4. ^ Indicators for Monitoring the Millennium Development Goals (PDF). New York: United Nations. 2003. p. 9.
  5. ^ a b c "Poverty Measures" (PDF). World Bank. 2009. Archived from the original (PDF) on July 10, 2012.
  6. ^ Edelman, Peter (July 28, 2012). "Poverty in America: Why Can't We End It?". The New York Times. Retrieved November 20, 2020.
  7. ^ Ravallion, Martin (June 1996). Issues in Measuring and Modeling Poverty (PDF). Policy Research Working Paper. Vol. 1615. Washington, D.C.: World Bank. Retrieved November 20, 2020.
  8. ^ "Indicators of Sustainable Development". United Nations Department for Policy Coordination and Sustainable Development. 2004. Archived from the original on April 21, 2012. Retrieved August 10, 2012.
  9. ^ a b "Poverty Measures, Chapter 4" (PDF). Introduction to Poverty Analysis. Washington, D.C.: World Bank Institute. August 2005. Archived from the original (PDF) on July 10, 2012.
  10. ^ Foster, James E. (May 1998). "Absolute versus Relative Poverty". The American Economic Review. 88 (2): 335–341. CiteSeerX 10.1.1.383.6488. JSTOR 116944.
  11. ^ Morrell, Dan (January–February 2011). "Who Is Poor?". Harvard Magazine. Retrieved November 22, 2020.
  12. ^ Sen, Amartya (December 1985). "A Sociological Approach to the Measurement of Poverty: A Reply to Professor Peter Townsend". Oxford Economic Papers. 37 (4): 669–676. doi:10.1093/oxfordjournals.oep.a041716. JSTOR 2663049.
  13. ^ Takayama, Noriyuki (May 1979). "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered". Econometrica. 47 (3): 747–759. doi:10.2307/1910420. JSTOR 1910420.
  14. ^ Jenkins, Stephen P.; Lambert, Peter J. (July 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. JSTOR 2663596.
  15. ^ a b Vecchi, Giovanni (September 2007). "Poverty Measurement" (PDF). World Bank. Archived from the original (PDF) on March 3, 2016.
  16. ^ Mosley, Paul; Mussurov, Altay (April 2009). "Poverty and Economic Growth in Russia's Regions" (PDF). Sheffield Economic Research Paper Series. University of Sheffield. ISSN 1749-8368.
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