This document presents a framework for measuring intertemporal pro-poorness that accounts for individual income mobility over multiple time periods. It focuses on measuring poverty levels within and across individuals over their lifetimes, rather than just comparing aggregate cross-sectional poverty between two time periods. The proposed indices decompose the effects of growth on poverty into anonymous, mobility, and re-ranking components. An empirical application using EU-SILC data from 23 European countries between 2006-2009 finds the degree of intertemporal pro-poorness varied significantly across countries during the early phase of the economic crisis.

1. Intertemporal pro-poorness
Intertemporal pro-poorness
Florent Bresson*, Flaviana Palmisanoz
and Jean-Yves Duclos
*Universite d'Orleans, France, zUniversite du Luxembourg,
Universite Laval, Canada
33rd General Conference of the IARIW
6B: Multidimensionality and Growth Pro-poorness
Discussed by Roberto Zelli - Sapienza University of Rome

2. Intertemporal pro-poorness
Background, motivations and goals
The main objective of `pro-poor growth' literature is to consider the
extent to which poverty changes over time because of growth.
A number of dierent analytical tools have been developed to
quantify this eect (see, inter alia, Ravallion and Chen, 2003, Son,
2004, Duclos, 2009, Essama-Nssah, 2005, Essama-Nssah and
Lambert, 2009).
Ravallion and Chen: Rate of Pro-Poor Growth (RPPG) is the mean
growth rate for the poor (as distinct from the growth rate in the
mean for the poor).
Conditions of anonymity is satis

3. ed, but postulating anonymity
implies that these tools ignore individual income dynamics, that is
they ignore the mobility experience that can take place within the
overall growth process.

4. Intertemporal pro-poorness
Background, motivations and goals
A simple example: two periods, two dierent (income)
transformation processes A and B, four individuals, poverty line

5. xed
at z = 7:
A : (4; 6; 9; 9) ! (9; 9; 4; 6) ) RPPGA = 0
B : (9; 9; 4; 6) ! (9; 9; 4; 6) ) RPPGB = 0
Building on this criticism, recent contributions have argued that
welfare relevant judgments of the eect of growth should be based
on analysis endorsing a `non-anonymous' perspective (Grimm,
2007, Jenkins and Van Kerm, 2011, Bourguignon, 2011, Palmisano
and Peragine, forthcoming).
New approach stresses the link between the overall growth
process and the mobility experience that is generated.

6. Intertemporal pro-poorness
Background, motivations and goals
Main dierences between standard analysis of pro-poor growth vs
inter-temporal pro-poorness:
1 Anonymity vs Non-anonymity.
2 Comparison of aggregate cross-sectional poverty between two
periods of time vs looking at inter-temporal (or lifetime) poverty
)focusing on a multi-temporal perspective.
3 Positive measures vs explicitly welfare-based measures.
Mobility has at least two potential eects on social welfare
(Friedman, 1962):
+ve It generally helps to equalize the distribution of permanent incomes
as compared to the distribution of periodic incomes (i.e.
cross-sectional incomes), thus increasing social welfare.
-ve It generates variability at the individual level, because of the time
variability of individual incomes that mobility induces, thus reducing
social welfare if individuals are risk averse.

7. Intertemporal pro-poorness
Background, motivations and goals
Aim is to provide a pro-poor mobility measurement framework which
builds on an explicit ill-fare function able to account for both the
costs and the bene

8. ts of mobility across time and across individuals.
This function turns out to be equivalent to the poverty counterpart
of the `equally distributed equivalent income' of Atkinson (1970).
Empirical analysis conducted on 23 European countries over the
period 2005-2008.

9. Intertemporal pro-poorness
General measurement of pro-poorness in an intertemporal setting
- Let y(i) := (yi;1; : : : ; yi;t; :::; yi;T ) be the vector of individual i's
incomes across T periods and yt is a cross-sectional vector of
incomes at time t. The income pro

10. les yi is the ith row of the
n T matrix Y .
- Denote by z the poverty line and by ~yi;t := min (yi;t; z) the periodic
income censored at the poverty line.
- Over an individual's lifetime, poverty is measured by p
y(i); z
with
y(i); z
p
0 whenever 9t 2 f1; : : : ; Tg such that yi;t z and
y(i); z
p
= 0 otherwise (union approach).
- Total intertemporal poverty is measured by the index P(Y ; z).
- Pro-poor growth is based on ill-fare comparisons of the actual
income structure Y with a benchmark structure ^ Y characterized by
the absence of distributional changes:

11. Intertemporal pro-poorness
General measurement of pro-poorness in an intertemporal setting
Intertemporal
pro-poorness
evaluation function
IPP
P( Y ^ ; z); P(Y ; z)
,
where P( ^ Y ; z) is a measure of the benchmark ill-fare.
This function tells us whether ill-fare is higher or lower in the actual
income structure as compared to the benchmark.
It is assumed to satisfy a set of very intuitive and standard
properties.

12. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Speci

13. cations I
Speci

14. cation of the relationship between the two arguments of the
IPP:
IPP := P( ^ Y ; z) P(Y ; z): (1)
Speci

15. cation of the benchmark: the absence of any distributional
change implies the preservation of the status quo of the population.
) the benchmark is based on a hypothetical income structure
Y1 2
n in which every period's income distribution is the same as
the

16. rst period's.
Speci

17. cation of the periodic poverty measure used: based on the
normalized poverty gap gi;t := z~yi;t
z .

18. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Individual ill-fare I
g(i) := (gi;1; : : : ; gi;t; :::; gi;T ) be the corresponding vector of
normalized poverty gaps for individual i across T periods.
The poverty level of each individual i, over the T periods, is
measured by (FGT class of additively decomposable indices):
p

19. y(i); z
:=
XT
t=1
!tg

20. i;t with

21. 1; (2)
!t is a weighting function that captures the sensitivity of an
individual with respect to the speci

22. c period in which the deprivation
is experienced.
If !t !t+1 more importance is given to the poverty experienced
earlier in life, for instance in her childhood; if !t !t+1 more
importance is given to the poverty experienced later in life

23. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Individual ill-fare II

24. captures the intensity of periodic poverty. It can be interpreted as
a measure of aversion to inequality and variability in the
normalized poverty gaps, hence as a measure of aversion to
transient poverty.
For

25. = 1, (2) corresponds to the simple weighted average of the
individual i's poverty gaps across time (not sensitive to transfers that
equalize poverty gaps from one period to the other).
For

26. 1, instead, a sequence of income transfers that keeps the
weighted mean unchanged but reduces the intertemporal variability
of poverty gaps, decreases p

27. y(i); z
, thus making the index
`variability' sensitive.

28. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Individual ill-fare III
Use the poverty counterpart of the `equally distributed equivalent
income' for the measurement of social welfare and inequality. In this
context, the equally distributed equivalent (EDE) poverty gap
for individual i,

29. g(i)
, is given by:

30. g(i)
:= p1

31. p

32. y(i); z
=
XT
t=1
!tg

33. i;t
!1

34. : (3)
The EDE gap

35. g(i)
is the value of ill-fare that, if
experienced by individual i at each period of his lifetime,
would yield him the same average poverty over time as that
generated by the distribution of his periodic poverty.
Note that:

36. (g(i)) 1(g(i)
In the absence of distributional transformations, individual
intertemporal poverty will be equivalent to

37. g(i)
= 1
g(i)
.

38. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Social ill-fare I
Aggregation of individuals'

39. g(i)
in order to obtain a measure of
intertemporal social ill-fare corrected for the cost of transient
poverty:
P;

40. (Y ; z) :=
1
n
Xn
i=1

41. g(i)
; (4)
where 1 is a parameter of poverty aversion across individuals.
In order to obtain an aggregate measure of intertemporal poverty
sensitive to the equalization eect of mobility, we use again the
equally distributed equivalent methodology, obtaining the EDE in
the population, ;

42. (G), representing our measure of social
intertemporal poverty:
;

43. (G) :=
1
n
Xn
i=1

44. g(i)
!1
: (5)

45. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Social ill-fare II
Although the indices P;

46. and ;

47. are ordinally equivalent and so
can be used indierently for comparing any pair of distributions, we
prefer the last index since it has a simple and appealing
interpretation.
Indeed, the index ;

48. (G) is the level of intertemporal ill-fare
which, if assigned equally to all individuals and across all time
periods, would produce the same poverty level as that
generated by the intertemporal distribution G.
(It thus can be seen as an intertemporal generalization of the class of
ethical poverty indices introduced by Chakravarty (1983) for snapshot
monetary poverty).

49. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Social ill-fare III
Benchmark: in the absence of distributional transformation, the
benchmark distribution Y1 yields the benchmark deprivation matrix G1.
As noted for individual ill-fare, the parameter

50. is irrelevant for the social
evaluation of poverty. and the cross-sectional vector g1 can be substituted
for the whole benchmark matrix G1. More precisely, we have
;

51. (G1) = ;

52. (g1) = ;1 (g1) =: (g1) and our benchmark
intertemporal poverty measure becomes:
(g1) =
1
n
Xn
i=1
g
i;1
!1
; (6)
which is equivalent to initial cross-sectional poverty. More speci

53. cally,
equation (6) returns the EDE gap corresponding to the FGT index P
associated with the initial distribution of income.

54. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
The iso-elastic family of intertemporal pro-poorness indices I
The measure of intertemporal pro-poorness can be expressed as
follows:
IPP;

55. = (g1) ;

56. (G) : (7)
It complies with desirable properties: population invariance,
anonymity, scale invariance, continuity, subgroup consistency.
Monotonicity: increasing in the level of aggregate poverty and
decreasing in the level of aggregate intertemporal poverty.

57. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
The intertemporal pro-poorness of a two-period growth/mobility process:

59. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Decompositions I
Three additive decompositions of the Inter-temporal Pro-Poorness (IPP)
index:
1 It disentangles the impact of anonymous component of the growth
process and its mobility component:
IPP;

60. = (g1) (g1; g2) | {z }
AG
+ (g1; g2) ;

61. (g1; g2) | {z }
M
(8)
2 The second decomposition will be aimed at separating the
unitemporal eects of an income transformation process from the
multitemporal one (capturing the trading-o eects on poverty
between the costs and bene

62. ts of mobility):

63. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Decompositions II
IPP;

64. = !2 [P1 (g1) P1 (g2)] | {z }
Pc
+ !2 [c (g1) c (g2)] | {z }
cc
+ [!1c(g1) + !2c(g2)] c;

65. (g) | {z }
Mmc
1
n
Xn
i=1
c

66. (g(i))
| {z }
CV
(9)
3 It aims at incorporating the impact that mobility exerts on poverty
through the re-ranking it generates:

67. Intertemporal pro-poorness
A family of inter-temporal pro-poorness indices
Decompositions III
IPP;

68. =
;

69. (g1; g1) ;

70. g1; gI1
| {z }
I
+
;

71. g1; gI1
;

72. g1; gIR
1
| {z }
R
+
;

73. g1; gIR
1
;

74. (g1; g2)
| {z }
PG
: (10)

75. Intertemporal pro-poorness
Empirical illustration: main results
Data I
Panel component of the Eurostat `European Union Statistics on
Income and Living Conditions' (EU-SILC).
They consider the 2006 and 2009 waves (why not 2006{2009?).
Unit of observation is the household.
Income expressed at PPP rates and in constant prices of 2005,
adjusted for hh size using the OECD scale.
Relative poverty approach, with country-speci

76. c poverty lines

77. xed
at 60% of the median income in 2006 (2005?). Relative gaps for the
year 2008 are thus estimated using the same poverty line for each
country.

78. Intertemporal pro-poorness
Empirical illustration: main results
The IPP;

79. for 23 European countries, 2006{09

80. Intertemporal pro-poorness
Empirical illustration: main results
Main results I
The distribution of inter-temporal pro-poorness among countries is
quite dispersed.
It also depends on the normative relevance given to variability and
inter-individual inequality (

81. and ).
In an intertemporal pro-poorness perspective, the very early phase of
the crisis has impacted on each country-speci

82. c population with
dierent degrees of gravity.
For 13 out of 23 countries, encompassing all the southern countries,
the index is negative at least for one combination of and

83. .
Among them Cyprus and Denmark show the worst performance (the
index is always negative), followed by Spain and Sweden.
For =

84. = 1 Cyprus and Denmark are the only two countries with
negative intertemporal pro-poorness.
The remaining ten countries for which the index is always positive
are mostly represented by continental and eastern countries.

85. Intertemporal pro-poorness
Empirical illustration: main results
Main results II
For

86. ve new member countries (PL, CZ, HU, LV, SI) the 2006-2009
can be judged as an intertemporal poverty reducing process,
although the IPP value varies considerably with the values of the
parameters.
An exception is Norway that performs always better than the other
countries.
The analysis is much deeper since the three types of decompositions
introduced before are computed.

87. Intertemporal pro-poorness
Empirical illustration: main results
First decomposition: anonymous growth vs mobility within European countries, 2006{09

88. Intertemporal pro-poorness
Empirical illustration: main results
Second decomposition: Unitemporal vs multitemporal eect within European countries, 2006{09

89. Intertemporal pro-poorness
Empirical illustration: main results
Third decomposition: Inequality vs Reranking vs Growth within European countries, 2006{09

90. Intertemporal pro-poorness
Conclusion and remarks
Remarks I
Very interesting and innovative approach in evaluating pro-poorness.
Decomposition helps disentangling opposite eects on pro-poorness.
This family of measures should be used to complement and not to
substitute existing tools (which are more intuitive).
Empirical concerns:
Results strongly depend on the relevance that the social planner will
give to the costs and the bene

91. ts of mobility and on the interaction
between the two: M will be positive when aversion towards individual
poverty is stronger than aversion to individual temporal variability,

92. ; whereas it will be negative when the costs of variability are
higher than the bene

93. ts deriving from equalization, that is

94. .
Social planner! , each individual i !

95. i (assumption

96. i =

97. )?
To orientate the practitioner in the deluge of possible results ! need
of some suggestions/hints.
Ex: for = 1 and

98. = 3 very low variability around zero.
Why only two waves? Neglecting income variability in between.

99. Intertemporal pro-poorness
Conclusion and remarks
Remarks II
Dicult to follow households (wrt individuals) due to demographic
changes during the period of analysis.
International (cross-country) comparison: shouldn't we take into
account the dierent growth rates of the countries over the period?
(e.g. incorporating it in the benchmark..)
Ex: Norway exceptionally pro-poor: but average yearly growth rate
of Norway was higher than many other European countries!