Editing Gini coefficient (section)

== Limitations ==

===Relative, not absolute===
The Gini coefficient is a relative measure. The Gini coefficient of a developing country can rise (due to increasing inequality of income) even when the number of people in absolute poverty decreases.<ref>{{cite web|title=Dramatic Poverty Reduction in the Third World: Prospects and Needed Action|first=John W.|last=Mellor|publisher=International Food Policy Research Institute|date=2 June 1989|pages=18–20|url=http://pdf.usaid.gov/pdf_docs/PNABK503.pdf |archive-url=https://web.archive.org/web/20120803160551/http://pdf.usaid.gov/pdf_docs/PNABK503.pdf |archive-date=2012-08-03 |url-status=dead}}</ref> This is because the Gini coefficient measures relative, not absolute, wealth.

Gini coefficients are simple, and this simplicity can lead to oversights and can confuse the comparison of different populations; for example, while both Bangladesh (per capita income of $1,693) and the Netherlands (per capita income of $42,183) had an income Gini coefficient of 0.31 in 2010,<ref name=undp2010a>{{cite web|title=The Real Wealth of Nations: Pathways to Human Development (2010 Human Development Report – see Stat Tables)|pages=152–156|publisher=United Nations Development Program|year=2011|url=http://hdr.undp.org/en/reports/global/hdr2010/chapters/}}</ref> the quality of life, economic opportunity and absolute income in these countries are very different, i.e. countries may have identical Gini coefficients, but differ greatly in wealth. Basic necessities may be available to all in a developed economy, while in an undeveloped economy with the same Gini coefficient, basic necessities may be unavailable to most or unequally available due to lower absolute wealth.

===Mathematical limitations===
Gini has some mathematical limitations as well. It is not additive and different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets.

{| class="wikitable" style="float: right; margin-left:1em;"
|+ Table A. Different income distributions with the same Gini index<ref name="fao gini"/>
|-
! style=max-width:4em | Household group !! style=max-width:5em | Country A annual income ($) !! style=max-width:5em | Country B annual income ($)
|-
| 1 || 20,000 || 9,000
|-
| 2 || 30,000 || 40,000
|-
| 3 || 40,000 || 48,000
|-
| 4 || 50,000 || 48,000
|-
| 5 || 60,000 || 55,000
|-
| Total income || $200,000 || $200,000
|-
| Country's Gini || '''0.2''' || '''0.2'''
|}

Even when the total income of a population is the same, in certain situations two countries with different income distributions can have the same Gini index (e.g. cases when income Lorenz Curves cross).<ref name="fao gini"/> Table A illustrates one such situation. Both countries have a Gini coefficient of 0.2, but the average income distributions for household groups are different. As another example, in a population where the lowest 50% of individuals have no income, and the other 50% have equal income, the Gini coefficient is 0.5; whereas for another population where the lowest 75% of people have 25% of income and the top 25% have 75% of the income, the Gini index is also 0.5. Economies with similar incomes and Gini coefficients can have very different income distributions. Bellù and Liberati claim that ranking income inequality between two populations is not always possible based on their Gini indices.<ref name=Maio2007>{{cite journal|title=Income inequality measures|first=Fernando G.|last=De Maio|journal=Journal of Epidemiology and Community Health|year=2007|volume=61|issue=10|pages=849–852|doi=10.1136/jech.2006.052969|pmid=17873219|pmc=2652960}}</ref> Similarly, computational social scientist Fabian Stephany illustrates that income inequality within the population, e.g., in specific socioeconomic groups of same age and education, also remains undetected by conventional Gini indices.<ref>{{Cite journal |last=Stephany |first=Fabian |date=2017-12-01 |title=Who are Your Joneses? Socio-Specific Income Inequality and Trust |url=https://doi.org/10.1007/s11205-016-1460-9 |journal=Social Indicators Research |language=en |volume=134 |issue=3 |pages=877–898 |doi=10.1007/s11205-016-1460-9 |issn=1573-0921 |pmc=5684274 |pmid=29187771}}</ref>

===Income Gini can conceal wealth inequality===
A Gini index does not contain information about absolute national or personal incomes. Populations can simultaneously have very low income Gini indices and very high wealth Gini indexes. By measuring inequality in income, the Gini ignores the differential efficiency of the use of household income. By ignoring wealth (except as it contributes to income), the Gini can create the appearance of inequality when the people compared are at different stages in their life. Wealthy countries such as Sweden can show a low Gini coefficient for the disposable income of 0.31, thereby appearing equal, yet have a very high Gini coefficient for wealth of 0.79 to 0.86, suggesting an extremely unequal wealth distribution in its society.<ref>{{cite journal|title=Inequality Trends in Sweden 1978–2004|first1=David|last1=Domeij|first2=Martin|last2=Flodén|journal= Review of Economic Dynamics|volume=13|issue=1|year=2010|pages=179–208|doi=10.1016/j.red.2009.10.005|citeseerx=10.1.1.629.9417}}</ref><ref>{{cite web|title=Accounting for Swedish wealth inequality|first1=David|last1=Domeij|first2=Paul|last2=Klein|date=January 2000|url=http://fmwww.bc.edu/repec/es2000/0883.pdf|archive-url=https://web.archive.org/web/20030519155531/https://www.econometricsociety.org/meetings/wc00/pdf/0883.pdf|archive-date=May 19, 2003}}</ref> These factors are not assessed in income-based Gini.

===Country size and granularity bias===
Gini index has a downward-bias for small populations.<ref>{{cite journal|title=The Small-Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research|journal=The Review of Economics and Statistics|first=George|last=Deltas|date=February 2003|volume= 85|issue=1|pages=226–234|doi=10.1162/rest.2003.85.1.226|jstor=3211637|s2cid=57572560}}</ref> Counties or states or countries with small populations and less diverse economies will tend to report small Gini coefficients. For economically diverse large population groups, a much higher coefficient is expected than for each of its regions. For example, taking the world economy as a whole and income distribution for all human beings, different scholars estimate the global Gini index to range between 0.61 and 0.68.<ref name=fao2009 /><ref name=undp10 />
As with other inequality coefficients, the Gini coefficient is influenced by the [[granularity]] of the measurements. For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) for the same distribution. Philippe Monfort has shown that using inconsistent or unspecified granularity limits the usefulness of Gini coefficient measurements.<ref>{{cite web|title=Convergence of EU regions: Measures and evolution|first=Philippe|last=Monfort|publisher=European Union – Europa|page=6|year=2008|url=http://ec.europa.eu/regional_policy/sources/docgener/work/200801_convergence.pdf |archive-url=https://web.archive.org/web/20120803160544/http://ec.europa.eu/regional_policy/sources/docgener/work/200801_convergence.pdf |archive-date=2012-08-03 |url-status=live}}</ref>

===Changes in population===
Changing income inequality, measured by Gini coefficients, can be due to structural changes in a society such as growing population (increased birth rates, aging populations, emigration, immigration) and income mobility.<ref name=Kwok10>{{cite web|title=Income Distribution of Hong Kong and the Gini Coefficient|author=KWOK Kwok Chuen|year=2010|publisher=The Government of Hong Kong, China|url=http://www.eabfu.gov.hk/en/pdf/income.pdf|archive-url=https://web.archive.org/web/20101227043822/http://www.eabfu.gov.hk/en/pdf/income.pdf|archive-date=27 December 2010}}</ref>

Another limitation of the Gini coefficient is that it is not a proper measure of [[egalitarianism]], as it only measures income dispersion. For example, suppose two equally egalitarian countries pursue different [[immigration law|immigration policies]]. In that case, the country accepting a higher proportion of low-income or impoverished migrants will report a higher Gini coefficient and, therefore, may exhibit more income inequality.

===Household vs individual===
{| class="wikitable" style="text-align:center; float: right; margin-left:1em;"
|+ Table B. Same income distributions, but different Gini Index
|-
! style=max-width:4em | Household number !! style=max-width:5em | Country  Annual Income ($) !! style=max-width:5em |Household combined number !! style=max-width:5em |Country A combined Annual Income ($)
|-
| 1 || 20,000 || rowspan="2"  style="text-align: center;" | 1 & 2 || rowspan="2" style="text-align: center;" | 50,000
|-
| 2 || 30,000
|-
| 3 || 40,000 || rowspan="2"  style="text-align: center;" | 3 & 4 || rowspan="2" style="text-align: center;" | 90,000
|-
| 4 || 50,000
|-
| 5 || 60,000 || rowspan="2"  style="text-align: center;" | 5 & 6 || rowspan="2" style="text-align: center;" | 130,000
|-
| 6 || 70,000
|-
| 7 || 80,000 || rowspan="2" style="text-align: center;" | 7 & 8 || rowspan="2" style="text-align: center;" | 170,000
|-
| 8 || 90,000
|-
| 9 || 120,000 || rowspan="2"  style="text-align: center;" | 9 & 10 || rowspan="2"  style="text-align: center;" | 270,000
|-
| 10 || 150,000
|-
| Total Income || $710,000 ||  || $710,000
|-
| Country's Gini || '''0.303''' || ||'''0.293'''
|}
The Gini coefficient measure gives different results when applied to individuals instead of households, for the same economy and same income distributions. If household data is used, the measured value of income Gini depends on how the household is defined. The comparison is not meaningful when different populations are not measured with consistent definitions. Furthermore, changes to the household income Gini can be driven by changes in household formation, such as increased divorce rates or [[extended family]] households splitting into [[Nuclear family|nuclear families]].

Deininger and [[Lyn Squire|Squire]] (1996) show that the income Gini coefficient based on individual income rather than household income is different. For example, for the United States, they found that the individual income-based Gini index was 0.35, while for France, 0.43. According to their individual-focused method, in the 108 countries they studied, South Africa had the world's highest Gini coefficient at 0.62, Malaysia had Asia's highest Gini coefficient at 0.5, Brazil the highest at 0.57 in Latin America and the Caribbean region, and Turkey the highest at 0.5 in OECD countries.<ref>{{cite journal |last1=Deininger |first1=K. |last2=Squire |first2=L. |title=A New Data Set Measuring Income Inequality |journal=The World Bank Economic Review |date=September 1996 |volume=10 |issue=3 |pages=565–591 |doi=10.1093/wber/10.3.565 }}</ref>

Billionaire [[Thomas Kwok]] claimed the income Gini coefficient for Hong Kong has been high (0.434 in 2010<ref name=undp2010a />), in part because of structural changes in its population. Over recent decades, Hong Kong has witnessed increasing numbers of small households, elderly households, and elderly living alone. The combined income is now split into more households. Many older people live separately from their children in Hong Kong. These social changes have caused substantial changes in household income distribution. The income Gini coefficient, claims Kwok, does not discern these structural changes in its society.<ref name=Kwok10 /> Household money income distribution for the United States, summarized in Table C of this section, confirms that this issue is not limited to just Hong Kong. According to the US Census Bureau, between 1979 and 2010, the population of the United States experienced structural changes in overall households; the income for all income brackets increased in inflation-adjusted terms, household income distributions shifted into higher income brackets over time, while the income Gini coefficient increased.<ref name=uscb2011 /><ref name=cbo.p.10>[http://www.cbo.gov/doc.cfm?index=12485 Congressional Budget Office: Trends in the Distribution of Household Income Between 1979 and 2007]. October 2011. see pp. i–x, with definitions on ii–iii</ref>

{| class="wikitable" style="text-align:center; float: left; margin-right:1em;"
|+ Table C. Household money income distributions and Gini Index, US<ref name=uscb2011>{{cite web|title=Income, Poverty, and Health Insurance Coverage in the United States: 2010 (see Table A-2)|date=September 2011|publisher=Census Bureau, Dept of Commerce, United States|url=https://www.census.gov/prod/2011pubs/p60-239.pdf |archive-url=https://web.archive.org/web/20110923022827/http://www.census.gov/prod/2011pubs/p60-239.pdf |archive-date=2011-09-23 |url-status=live}}</ref>
|-
! style=max-width:6em | Income bracket (in 2010 adjusted dollars)!! style=max-width:4em | % of Population 1979 !! style=max-width:4em | % of Population 2010
|-
| Under $15,000 || 14.6% || 13.7%
|-
| $15,000 – $24,999 || 11.9% || 12.0%
|-
| $25,000 – $34,999 || 12.1% || 10.9%
|-
| $35,000 – $49,999 || 15.4% || 13.9%
|-
| $50,000 – $74,999 || 22.1% || 17.7%
|-
| $75,000 – $99,999 || 12.4% || 11.4%
|-
| $100,000 – $149,999 || 8.3% || 12.1%
|-
| $150,000 – $199,999 || 2.0% || 4.5%
|-
| $200,000 and over || 1.2% || 3.9%
|-
| Total Households || 80,776,000 || 118,682,000
|-
| United States' Gini on pre-tax basis || '''0.404''' || '''0.469'''
|}

===Instantaneous inequality vs lifetime inequality===
The Gini coefficient is unable to discern the effects of structural changes in populations.<ref name=Kwok10 /> Expanding on the importance of life-span measures, the Gini coefficient as a point-estimate of equality at a certain time ignores life-span changes in income. Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality simply because people generally have lower incomes and wealth when they are young than when they are old. Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of inequality when none exist, taking into account demographic effects. Thus a given economy may have a higher Gini coefficient at any timepoint compared to another, while the Gini coefficient calculated over individuals' lifetime income is lower than the apparently more equal (at a given point in time) economy's.{{Clarify|date=September 2022}}<ref name=blomq81>{{Cite journal |first=N. |last=Blomquist |s2cid=154519005 |year=1981 |title=A comparison of distributions of annual and lifetime income: Sweden around 1970 |journal=Review of Income and Wealth |volume=27 |issue=3 |pages=243–264 |doi=10.1111/j.1475-4991.1981.tb00227.x}}</ref> Essentially, what matters is not just inequality in any particular year but the distribution composition over time.

===Benefits and income in kind===
Inaccuracies in assign monetary value to [[income in kind]] reduce the accuracy of Gini as a measurement of true inequality.

While taxes and cash transfers are relatively straightforward to account for, other government benefits can be difficult to value. Benefits such as subsidized housing, medical care, and education are difficult to value objectively, as it depends on the quality and extent of the benefit. In absence of a free market, valuing these income transfers as household income is subjective. The theoretical model of the Gini coefficient is limited to accepting correct or incorrect subjective assumptions.

In subsistence-driven and [[informal economies]], people may have significant income in other forms than money, for example, through [[subsistence farming]] or [[barter]]ing. These forms of income tend to accrue to poor segments of populations in emerging and transitional economy countries such as those in sub-Saharan Africa, Latin America, Asia, and Eastern Europe. Informal economy accounts for over half of global employment and as much as 90 percent of employment in some of the poorer sub-Saharan countries with high official Gini inequality coefficients. Schneider et al., in their 2010 study of 162 countries,<ref>{{cite journal|first1=Friedrich|last1=Schneider|first2=Andreas|last2=Buehn|first3=Claudio E.|last3=Montenegro|s2cid=56060172|year=2010|title= New Estimates for the Shadow Economies all over the World|journal=International Economic Journal|volume=24|issue=4|pages=443–461|doi=10.1080/10168737.2010.525974|hdl=10986/4929}}</ref> report about 31.2%, or about $20 trillion, of world's [[Gross domestic product|GDP]] is informal. In developing countries, the informal economy predominates for all income brackets except the richer, urban upper-income bracket populations. Even in developed economies, 8% (United States) to 27% (Italy) of each nation's GDP is informal. The resulting informal income predominates as a livelihood activity for those in the lowest income brackets.<ref>{{cite book|title=The Informal Economy|publisher=International Institute for Environment and Development, United Kingdom|year=2011|url=http://pubs.iied.org/pdfs/15515IIED.pdf |archive-url=https://web.archive.org/web/20120803160544/http://pubs.iied.org/pdfs/15515IIED.pdf |archive-date=2012-08-03 |url-status=live|isbn=978-1-84369-822-7}}</ref> The value and distribution of the incomes from informal or underground economy is difficult to quantify, making true income Gini coefficients estimates difficult.<ref name=mfeld>{{cite web|title=Is income inequality really the problem? (Overview)|first=Martin|last=Feldstein|date=August 1998|publisher=US Federal Reserve|url=http://www.kc.frb.org/publicat/sympos/1998/S98feldstein.pdf|access-date=2 August 2012|archive-date=3 August 2012|archive-url=https://web.archive.org/web/20120803160558/http://www.kc.frb.org/publicat/sympos/1998/S98feldstein.pdf|url-status=dead}}</ref><ref name=tandw>{{cite book|title=Principles of Microeconomics: Global Financial Crisis Edition|first1=John|last1=Taylor|first2=Akila|last2=Weerapana|year=2009|isbn=978-1-4390-7821-1|pages=416–418|publisher=Cengage Learning }}</ref> Different assumptions and quantifications of these incomes will yield different Gini coefficients.<ref>{{cite journal|title=Income Inequality and the Informal Economy in Transition Economies|first1=J. Barkley Jr. |last1=Rosser|first2=Marina V.|last2=Rosser |first3=Ehsan|last3=Ahmed |s2cid=49552052 |journal=Journal of Comparative Economics|date=March 2000|volume= 28|issue=1|pages=156–171|doi=10.1006/jcec.2000.1645}}</ref><ref>{{cite web|title=Earnings inequality and the informal economy: evidence from Serbia|first1=Gorana|last1=Krstić |first2=Peter|last2=Sanfey |publisher=European Bank for Reconstruction and Development|date=February 2010|url=http://www.ebrd.com/downloads/research/economics/workingpapers/wp0114.pdf |archive-url=https://web.archive.org/web/20120803160550/http://www.ebrd.com/downloads/research/economics/workingpapers/wp0114.pdf |archive-date=2012-08-03 |url-status=live}}</ref><ref>{{cite report|title=The Size of the Shadow Economies of 145 Countries all over the World: First Results over the Period 1999 to 2003|first=Friedrich|last=Schneider|date=December 2004|ssrn=636661|hdl=10419/20729}}</ref>