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Comparingthreemethodsofstandarderrorestimationforpovertymeasures
where:
wi–thesurveyweightattachedtoi
thsampleunit(individual).
Thesecondindicator,namedRelativemedianpovertyriskgap(RMPG)
isdefinedasdifferencebetweenthemedianequivaliseddisposableincomeof
personsbelowtheat-risk-ofpovertythreshold(
MED
POOR
)andthethreshold
itself(ARPT),expressedasapercentageoftheat-risk-ofpovertythreshold.
RMPG
=
ARPT
ARPT
−
MED
POOR
(4)
Thirdindicatormeasuresinequalityofincomedistributionanditis
namedGinicoefficient(GINI).Thisistherelationshipbetweencumulative
sharesofthepopulationarrangedaccordingtothelevelofincomeandthe
cumulativeshareoftheequivalisedtotalincomereceivedbythem.Iftherewas
perfectequality(i.e.eachpersonreceivesthesameincome)theGini
coefficientwouldbe0%.AGinicoefficientof100%wouldindicatetherewas
totalinequalityandtheentirenationalincomewasinthehandsofoneperson.
TocalculatethisindicatorpersonshavetobesortedaccordingtoEQINCfrom
thelowesttothehighestvalue.Ifwidenotethesampleweightofaunitiinthe
ascendingincomesorteddistribution,thenwehave:
GINI
=
100
⋅
⎛
⎜
⎜
⎜
⎜
⎜
⎝
2
⋅
i
=
last
first
_
∑
_
person
person
⎛
⎜
⎜
⎝
⎛
⎜
⎜
⎝
w
i
=
last
i
first
⋅
EQINC
_
∑
_
person
person
w
i
⎞
⎟
⎟
⎠
i
⋅
⋅
i
=
last
first
first
person
_
∑
∑
_
_
person
person
person
(
_
w
w
i
i
i
⎞
⎟
⎟
⎠
⋅
−
EQINC
i
=
last
first
_
∑
_
person
person
i
(
)
w
i
2
⋅
EQINC
i
)
−
1
⎞
⎟
⎟
⎟
⎟
⎟
⎠
,
(5)
where:
wi–thesurveyweightattachedtoi
thsampleunit(individual).
NextmeasureofinequalityofincomedistributionisnamedS80/S20
incomequintileshareratio(S80/S20).Itistheratioofsumofequivalised
disposableincomereceivedbythe80%ofthecountry'spopulationwiththe
highestincome(topquintile)tothatreceivedbythe20%ofthecountry's
populationwiththelowestincome(lowestquintile).
S
80
/
S
20
=
i
i
EQINC
EQINC
∑
∑
i
i
≥
≥
w
w
Q
Q
i
80
i
80
EQINC
EQINC
i
i
,
where:
wi–thesurveyweightattachedtoi
thsampleunit(individual).
(6)
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