Poverty gap index

Template:Short description Template:Use mdy dates 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.

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. Poverty gap index estimates the depth of poverty by considering how far the poor are from that poverty line on average.

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. It is expressed as a percentage of the poverty line for a country or region.

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. 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.

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.

Calculation

The poverty gap index (PGI) is calculated as,

$\mathrm{P}\mathrm{G}\mathrm{I}=\frac{1}{N}\sum _{j=1}^q\left(\frac{z-y_j}{z}\right)$

or

$\mathrm{P}\mathrm{G}\mathrm{I}=\frac{1}{N}\sum _{j=1}^N\left(\frac{(z-y_j).1(y_j<z)}{z}\right)$

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 $P_0$.

Features

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.

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.

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. These suggestions were initially controversial, and have over time inspired scholars to propose numerous refinements.

Related measures

The Foster–Greer–Thorbecke metric is the general form of the PGI. The $FG{T}_{\alpha }$ 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 $P_{\text{SEN}}$, is related to poverty gap index (PGI). It is calculated as follows:

${\mathrm{P}}_{\text{SEN}}=H*G_z+PGI*(1-G_z)$

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:

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

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

Poverty gap index by country

Template:Update 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)Template:Efn	Head count ratio (%)	Poverty gap index (%)	Year
Template:Flag	52	22.9	14.18	2020
Template:Flag	38	54.31	29.94	2000
Template:FlagTemplate:Efn	38	0.92	0.65	2010
Template:Flag	38	1.28	0.25	2008
Template:Flag	959	12.4	2.93	2010
Template:Flag	1024	6.6	1.81	2010
Template:Flag	38	0.43	0.14	2008
Template:Flag	38	43.25	11.17	2010
Template:Flag	38	0.1	0.1	2008
Template:Flag	930	8.8	1.80	2010
Template:Flag	38	12.21	5.52	1999
Template:Flag	38	47.33	15.73	2003
Template:Flag	38	10.22	1.81	2007
Template:Flag	38	15.61	8.64	2008
Template:Flag	38	0.04	0.02	2007
Template:Flag	38	31.23	11.04	1993
Template:Flag	350	3.91	3.62	2015
Template:Flag	38	44.6	14.66	2009
Template:Flag	38	81.32	36.39	2006
Template:Flag	38	22.75	4.87	2008
Template:Flag	38	9.56	1.2	2007
Template:Flag	1056	12.1	2.96	2010
Template:Flag	38	21.02	6.05	2001
Template:Flag	38	62.83	31.26	2008
Template:Flag	38	61.94	25.64	2002
Template:Flag	38	1.35	0.69	2009
Template:FlagTemplate:Efn	38	16.25	4.03	2005
Template:Flag	38	8.16	3.78	2010
Template:Flag	38	46.11	20.82	2004
Template:Flag	38	3.12	1.79	2009
Template:Flag	38	23.75	7.5	2008
Template:Flag	515	5.8	1.37	2010
Template:Flag	955	5.3	1.29	2010
Template:Flag	38	18.84	5.29	2002
Template:Flag	38	2.24	0.52	2010
Template:Flag	38	87.72	52.8	2005
Template:Flag	38	54.1	22.8	2005
Template:Flag	38	4.6	2.1	2010
Template:Flag	38	1.69	0.4	2008
Template:Flag	38	8.9	4.4	2009
Template:Flag	38	39	9.6	2005
Template:Flag	38	5.9	1.1	2009
Template:Flag	875	7.3	1.48	2010
Template:Flag	861	7.1	1.44	2010
Template:Flag	38	4.8	.9	2005
Template:Flag	38	33.6	11.7	2003
Template:Flag	918	11	3.67	2010
Template:Flag	38	15.3	4.6	2008
Template:Flag	38	28.6	9.9	2006
Template:Flag	720	12.6	3.36	2010
Template:Flag	38	13.5	4.7	2006
Template:Flag	38	43.3	15.	2007
Template:Flag	38	48.9	16.6	2002
Template:Flag	38	8.7	2.8	1998
Template:Flag	38	61.7	32.3	2001
Template:Flag	38	17.9	9.4	2009
Template:Flag	407	7.1	1.66	2010
Template:Flag	942	7.1	2.55	2010
Template:Flag	934	14.8	3.08	2010
Template:Flag	38	32.7	7.5	2010
Template:Flag	38	18.1	3.3	2010
Template:Flag	38	1.45	0.34	2005
Template:Flag	38	2.8	0.42	2007
Template:Flag	700	11.4	3.08	2010
Template:Flag	38	0.21	0.02	2004
Template:Flag	950	14.9	5.17	2010
Template:Flag	38	0.12	0.03	2010
Template:Flag	38	0.11	0.03	2009
Template:Flag	38	43.4	16.9	2005
Template:Flag	38	6.4	1.5	2008
Template:Flag	38	44	12.1	2002
Template:Flag	38	0.14	0.1	2008
Template:Flag	38	43.4	20.8	2003
Template:Flag	38	83.8	40.9	2007
Template:Flag	38	0.16	0.1	2008
Template:Flag	1511	8.1	1.62	2010
Template:Flag	38	0.29	0.04	2008
Template:Flag	38	81.3	43.3	2010
Template:Flag	38	73.9	32.3	2004
Template:Flag	38	1.48	0.14	2008
Template:Flag	38	50.4	16.4	2010
Template:Flag	38	23.4	6.8	2008
Template:Flag	192	18.4	6.97	2010
Template:Flag	38	31.2	16.3	2000
Template:Flag	38	0.39	0.08	2010
Template:Flag	38	0.12	0.08	2008
Template:Flag	38	2.5	.54	2007
Template:Flag	38	59.6	25.1	2008
Template:Flag	38	31.9	9.5	2004
Template:Flag	38	24.8	5.6	2010
Template:Flag	1168	7.7	1.61	2010
Template:Flag	803	10.8	3.63	2010
Template:Flag	38	11.9	2.4	2005
Template:Flag	38	43.6	12.4	2008
Template:Flag	38	68	33.7	2010
Template:Flag	1109	6.8	2.00	2010
Template:Flag	38	21	3.5	2008
Template:Flag	38	6.6	2.1	2010
Template:Flag	38	35.8	12.3	1996
Template:Flag	38	7.2	3.	2010
Template:Flag	38	4.9	1.3	2010
Template:Flag	38	18.4	3.7	2009
Template:Flag	338	14.6	5.20	2010
Template:Flag	512	12.9	3.74	2010
Template:Flag	38	0.41	0.19	2009
Template:Flag	61	14.3	5.09	2006
Template:Flag	38	63.2	26.6	2011
Template:Flag	38	28.2	7.9	2001
Template:Flag	38	33.5	10.8	2005
Template:Flag	38	0.26	0.17	2009
Template:Flag	38	53.4	20.3	2003
Template:Flag	368	8.1	2.07	2010
Template:Flag	38	13.8	2.3	2009
Template:Flag	809	14.6	5.26	2010
Template:Flag	749	14.1	4.51	2010
Template:Flag	38	7	1	2007
Template:Flag	38	19.8	5.5	2009
Template:Flag	38	15.5	5.9	1999
Template:Flag	38	40.6	16.	2010
Template:Flag	863	5.3	1.31	2010
Template:Flag	38	1.71	0.2	2004
Template:Flag	1148	8.7	3.37	2010
Template:Flag	38	6.6	1.2	2009
Template:Flag	38	67.9	28.1	2007
Template:Flag	38	0.37	0.05	2009
Template:Flag	38	37.4	8.9	2007
Template:Flag	38	38.7	11.4	2006
Template:Flag	38	4.2	1.1	2008
Template:Flag	38	1.35	0.28	2005
Template:Flag	211	17.5	5.76	2010
Template:Flag	38	24.8	7	1998
Template:Flag	38	38.01	12.2	2009
Template:Flag	38	0.06	0.04	2009
Template:Flag	1027	8.3	2.06	2010
Template:FlagTemplate:Efn	1232	17.1	6.55	2010
Template:Flag	38	0.2	0.07	2008
Template:Flag	38	6.6	3.7	2006
Template:Flag	38	16.9	3.8	2008
Template:Flag	38	17.5	4.2	2005
Template:Flag	38	68.5	37	2006

See also

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

External links

• Poverty and Inequality Platform: World Bank's continuously updated database with poverty gap index and other poverty analysis tools
• Handbook on Poverty and Inequality: A handbook with examples, features and limitations of poverty measures