Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty Martina Celidoni Department of Economics - University of Padua 2011 IARIW-OECD Conference on Economic Insecurity: Measurement, Causes, and Policy Implications November 22-23, 2011 1/ 20
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Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty
Decomposing the Foster-Greer-Thorbecke Index
of Vulnerability to Poverty
Martina CelidoniDepartment of Economics - University of Padua
2011 IARIW-OECD Conference onEconomic Insecurity:
Measurement, Causes, and Policy Implications
November 22-23, 2011
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Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty
Introduction
Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to
Poverty
Focus Risk is quite different in size, likelihood and frequency overtime. Different features correspond to differentimplications for the ability to cope with them as well as forpolicy (Dercon, 2001; similar idea in Morduch (2000))→ Need of more information.
This paper - Highlights vulnerability as a function of 3 contributingfactors (characteristics): expected incidence, expectedintensity and expected downward variability.
- Offers an empirical illustration using BHPS(intertemporal) and SHIW (across regions).
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Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty
The 3 Is of Poverty
The three Is of Poverty: Incidence, Intensity and Inequality
(Sen, 1976; Foster et al., 1984; Jenkins and Lambert, 1997)
Pα (y; z) =1
N
Q
∑h=1
[
z − yh
z
]α
, (1)
Pα=2 (y; z) = H[
I 2 + (1− I )2CV 2p
]
,
(2)
H = Q/N, (3)
I =1
Q
Q
∑h=1
[
z − yh
z
]
, (4)
CV 2p =
1
Q
Q
∑h=1
(µp − yh)2
µ2p
. (5)
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Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty
Decomposing vulnerability
The three vulnerability contributing factors
Expected Incidence, Expected Intensity and Expected Downward variability
◮ yhs vector of possible income values at t + 1 for the household h
◮ The vector yhs represents a permutation of yhs , so that the elements arenon-decreasingly ranked, i.e. for all yhs , y
h1 ≤ yh2 ≤ . . . ≤ yhSh
. . . ≤ yhN .
Vα=2,h (y; z) =Sh
∑s=1
ps
[
z − yhsz
]2
= EHh
[
EI 2h + (1− EIh)2ECV 2
h
]
, (6)
EHh =Sh
N(7)
EIh =Sh
∑s=1
p′s(z − yhs )
z, p′s =
1
Sh(8)
ECV 2h =
Sh
∑s=1
p′s(µ − yhs )
2
µ2, p′s =
1
Sh(9)
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Decomposing the Foster-Greer-Thorbecke Index of Vulnerability to Poverty
Decomposing vulnerability
An example
Examples of Poverty Gaps Pattern
Table: Vulnerability to poverty and its contributing factors