<<

. 2
( 13)



>>

that are ˜clearly™ in their best interests. A clear model of human behaviour
is needed (one that goes beyond microeconomics); better explanations of
why poverty persists as part of broader processes of economic and social
change; more insight into how power is created, maintained, and challenged;
and more attention to how we can best learn from the new generation of
poverty reduction policies and practices. Woolcock illustrates his argument
with cases from Australia, Cameroon, and China. Each of these cases shows
how social relations are central to understanding responses to economic and
social change.
Fundamentally, Woolcock argues for a shift away within social theory from
what he terms ˜endless critiques™ and yet more ˜conceptual frameworks™ and
a more constructive engagement with the most pressing and vexing concerns
around chronic poverty. Much of development can be said to be about facili-
tating ˜good struggles™ in areas where there is no technical solution, but rather
progress is crafted by dialogue and negotiation.



22
Poverty Dynamics

1.5. Conclusion

In this volume the reader will encounter a rich menu of perspectives and
methodologies in some of the latest research on poverty. Our introduction
has provided the ¬rst course. Conceptually and methodologically poverty
dynamics are challenging but a number of clear conclusions emerge.
The ¬rst of these is about the duration of poverty. It is imperative to bring
time into analytical frameworks for measuring and understanding poverty.
There are many ways forward, including panel datasets (of which we need
many more, since they are still con¬ned to a small subset of countries) and
life history methods. Major conceptual problems do however remain. These
include the degree to which we do or do not place equal value on different
spells in poverty (time discounting).
Second, multidimensionality is essential. It is time to get out of the rut
of income/consumption measures. Poverty dynamics can look very different
when non-income measures are used, and these are critical as both a cross-
check on trends in income measures, as well as giving us a broader picture of
how well-being in all its dimensions is moving over time (essential if we are
to track the poverty impact of growth). Multidimensional, duration-adjusted
measures of poverty remain the next big challenge in measurement.
Third, interdisciplinary work is possible and desirable, despite the dif¬cul-
ties discussed in this chapter. In other words, the boundaries of our interdis-
ciplinary conversation are becoming clearer, and the points of commonality
and difference are now more sharply in focus. We need to encourage further
the trend towards combining qualitative and quantitative approaches in the
analysis of poverty dynamics. The present conversation about poverty dynam-
ics reveals a divide, between economists and other social scientists (sociology,
anthropology, politics, and geography). However, it also reveals that there is
a strong desire, and increasingly frequent attempts, to bridge this divide. We
hope that this volume will support that process, encouraging others to join in
the debate, and to tackle the conceptual and methodological hurdles that still
lie ahead.


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26
Part II
Poverty Dynamics
Poverty Measurement and Assessment
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2
Chronic Poverty and All That
The Measurement of Poverty over Time

C©sar Calvo and Stefan Dercon




2.1. Introduction

A vast literature has developed on the measurement of poverty. Poverty is
considered a state of deprivation, with a living standard below some minimal
level. Much debate has focused on ways to approach the underlying standard
of living. For example, in recent years much attention has been given to ¬nd-
ing appropriate ways to address the multidimensionality in assessing living
standards and poverty (Tsui, 2002; Bourguignon and Chakravarty, 2003). In
this chapter we focus on another issue often ignored in the standard poverty
literature: that the standard of living is not a static, timeless state, but a state
that evolves over time. The standard of living follows a trajectory, a path
with a history and a future. As a consequence, to assess poverty over time
for a particular individual or society, we could explore how we should assess
different trajectories of the standard of living, rather than just focusing on the
standard of living and poverty in each period, as if neither past nor future
poverty experiences had any bearing on the meaning of present hardship. In
this chapter, we provide some tentative steps to address this issue.
Both theory and empirical evidence provide reasons why careful attention
to time paths may be important. If we are interested in well-being over a
long time span, information about present outcomes can only be suf¬cient
in a very stable world, where individuals need not exert any effort to ensure
that their outcomes remain invariant. It is hard to think of such a scenario. In
practice, ¬rst, a myriad of reasons for ¬‚uctuations exist, and smoothing efforts
are often impossible, e.g. in the case of health, which cannot be transferred
from the present to the future, nor vice versa. While some storing technology
may be available for other well-being dimensions, the individual may still ¬nd
it hard to fully smooth away all variations, since such technology will rarely



29
C©sar Calvo and Stefan Dercon

be perfect. For instance, in the case of consumption, credit market failures
disallow some people to resort to high future consumption ¬‚ows in the face
of current hardship. Secondly, in a world with uncertainty, random shocks
may push outcomes above or below the expected time-invariant target. If
insurance mechanisms are imperfect, then the individual will be exposed to
the consequences of shocks she failed to foresee.
In this chapter, ¬‚uctuations are interesting in their own right. However,
this does not mean that their long-term effects on living conditions are
overlooked. Surely enough, ¬‚uctuations may turn into serious persistence: a
temporary shortfall may translate into a long period of low well-being, with
slow and uneven recovery, if at all. Also, in their quest for stability, households
may react to the threat of ¬‚uctuations by resorting to smoothing efforts with
some cost in terms of long-run growth. For instance, a street vendor may
prefer not to commit to items exhibiting great seasonality, even if they are
very pro¬table.
The issues arising as soon as we pay attention to time trajectories are thus
manifold. Policy implications also promptly crop up. For instance, this con-
cern can be directly linked to policy discussion related to concepts of ˜chronic™
poverty: we should be concerned with poverty that does not easily resolve
itself, that has a persistence attached to it. Obviously, this is a statement about
a future state, yet not just about one future period, but related to a permanent
escape or the lack of escape from poverty, persisting in different periods. In
order to assess different paths over time, means of ordering and/or valuing
these trajectories are required.
This chapter therefore explores issues related to the assessment of poverty
over a lengthy period of time for an individual. By ˜lengthy™ we mean that this
period can be decomposed into spells. In each spell, we observe the level of
the standard of living, which for simplicity we will call consumption. Each
spell is long enough for consumption ¬‚ows to be observed and measured. For
instance, we may think of a ¬ve-year period, with consumption data for each
single year. Let us use ˜spell™ to refer to the time units (indexed by t) where
consumption ¬‚ows ct are measured (in the example, one year), and ˜period™
to refer to that ˜lengthy™ stretch which we are interested in (i.e. all ¬ve years
together).
While, for the sake of concreteness, in this note we prefer to speak of
consumption, the discussion equally applies to any other dimension of well-
being, such as nutritional status. De¬ne poverty in a T-spell period as

PT (y1 , y2 , . . . , yT ),
where yt stands for consumption at spell t. Let z be the poverty line. We
assume this line to be time invariant for simplicity. Alternatively, if poverty
lines did vary over time, our analysis would still hold only if outcomes in every
spell were to be normalized with respect to their spell-speci¬c poverty lines.



30
Chronic Poverty and All That

Put differently, in our setting, consumption changes over time must re¬‚ect
variations in the ability of the individual to reach decent living standards,
above the minimum acceptable norm.
It would be wrong to suggest that the concerns addressed have no prece-
dents. A vast empirical literature has developed that assesses the ˜dynamics™
of poverty, by following the poverty status over time of particular individuals
or groups. For example, Baulch and Hoddinott (2000) summarize a number
of studies, using panel data, by counting ˜poverty spells™, whereby they mean
how often people are observed to be poor in a particular period, and also using
simple concepts of poverty mobility, based on poverty transition matrices,
identifying who moved in and out of poverty, and who stayed poor. The
best-known summarizing measure of poverty assessed over time is Ravallion™s
˜chronic poverty™ measure. This measure assesses chronic poverty as the level
of poverty obtained based on a Foster“Greer“Thorbecke measure, using the
average level of consumption over the entire period as the underlying stan-
dard of living measure (Jalan and Ravallion, 2000).
In this chapter, we will argue that these approaches are particular, certainly
suggestive, but still arbitrary choices among many different others that could
be made to make sense of poverty over a particular period. 1 We will present a
number of measures and document some of the speci¬c underlying normative
choices based on speci¬c alternative axioms. Our approach may be best moti-
vated by considering a few imaginary scenarios. First, let Figure 2.1a act as
a benchmark description of consumption ¬‚ows of a given individual. There,
each poverty-free spell is succeeded by hardship, which in turn lasts for only
one spell and is followed by a fresh episode of suf¬cient consumption. How
should this scenario compare to those in the other three charts? In Figure 2.1b,
the same pattern exists, except consumption is higher in non-poor spells,
whereas poor episodes remain just as bad. Should we say that period-long
poverty has lessened? This raises the issue of compensation of poverty spells by
non-poverty spells, and the ¬rst issue tackled below. As we will show, different
plausible measures of poverty of time take a different stance on this issue.
In static poverty measurement, across individuals, the issue barely arises by
using the focus axiom: the non-poor™s outcomes are considered as if they just
have reached the poverty line. When considering the poverty over time of a
speci¬c individual, this is not self-evidently resolved, as some may argue that
hardship at some point in life may be acceptable if it is followed by much
better outcomes in other periods. In our measures, we will show that how
such judgements can be incorporated.


1
Some of the concerns explicitly considered in this chapter related to compensation over
time and discounting are also discussed in a very different context, related to adjusting
poverty measures to handle differential mortality across a population, in Kanbur and
Mukherjee (2006).




31
C©sar Calvo and Stefan Dercon


c c




z z




2001 2002 2003 2004 2005 2006
2001 2002 2003 2004 2005 2006

a b

c c




z z




2001 2002 2003 2004 2005 2006 2001 2002 2003 2004 2005 2006

c d
Figure 2.1. Illustrative examples of poverty experiences


Next, compare 2.1a with 2.1c. As seen from 2006, the salient difference
lies now in the fact that poverty episodes were suffered further back in the
past. The alternation pattern is otherwise still in place. The question is then
whether the assessment of period-long poverty must pay the same attention
and attach the same weight to all isolated poverty spells, regardless of how
far in the past each occurred. This may be the case if the af¬‚iction of human
deprivation is seen as an irremediable loss, but on the other hand, its burden
can also be imagined to die out as time passes. This is a second issue explicitly
discussed: is there any case for using ˜discount rates™, judgements on the
relative importance of the present relative to the future or past?
The same question arises as we lastly take Figure 2.1d. Keeping Figure 2.1a as
the benchmark, 2002 and 2005 seem to swap consumption levels. However,
a new issue comes forth, since poverty spells are now contiguous, and the
individual faces a prolonged episode of poverty (2004“2006). Should the



32
Chronic Poverty and All That

70
180
160 60
140
50
120
40
100
80 30
60
20
40
10
20
0
0
1995
1999 1994 2004
1996 2004 1997
1997
1994 1999
1996
1995

a Abebe b Alemu

200
160
180
140
160
120
140
120 100
100 80
80
60
60
40
40
20
20
0 0
1995
1994 2004
1999 1997 1999
2004
1996 1996
1997
1994 1995

d Asfaw
c Tigist

Figure 2.2. Examples of poverty experiences from the Ethiopian panel data survey


distress of hardship compound over time, such that a three-spell episode of
poverty should cause greater harm than three isolated poverty spells? This
is the third question to tackle as we turn to our intent to propose poverty
measures over a lengthy period.
While these stylized examples show some of the choices involved, trajecto-
ries observed in actual data look messier. For example, take four trajectories
found in the Ethiopian rural household panel data survey, with six observa-
tions in the period 1994 to 2004. While these consumption levels may well
be measured with error, the patterns are not simple, and general judgements
about how to order these in terms of poverty over time are not self-evident.
For example, the household of Abebe (Figure 2.2a) appears to have been going
downhill in the last four years of the data, but has only one spell in poverty,
while Alemu (Figure 2.2b) has four poverty spells, but by the end of the period
has two years above the poverty line. Tigist and Asfaw™s families (Figures 2.2c
and 2.2d) both have spells below the poverty line, but at different times in the
sequence.
It is clear that many judgements will be required to summarize such trajec-
tories of the standard of living in one single index of intertemporal poverty.



33
C©sar Calvo and Stefan Dercon

This chapter aims to present a number of possible indices, even though its
main aim is to make some of these normative judgements explicit.
Foster (2007) in this collection has a related objective, but aims to explicitly
construct a class of measures of ˜chronic poverty™. Below we will highlight the
similarities with at least one of our own measures, but there is one crucial
difference worth commenting on now. His measure starts from the identi¬ca-
tion within the data of who is chronically poor, and then proceeds in ways
not dissimilar to ours. In his paper, a ˜chronic™ poor person is someone who
experiences at least a speci¬c percentage of poverty over time. His measure
of chronic poverty then values the depth and severity of poverty for such
persons, excluding the non-chronically poor. While internally fully consistent
and sensible, and a chronic poverty equivalent of the Foster“Greer“Thorbecke
measure, one key requirement is a judgement of a cut-off for classifying
someone as ˜chronic™ poor, irrespective of how far below the poverty line
this person is. By introducing a further threshold beyond the poverty line,
the result is that people with just over the required number of spells for
chronic poverty, but with all spells just below the poverty line, would be
considered chronically poor, while someone with marginally fewer but more
serious spells is counted as transitory poor. Our approach does not resolve this
issue at all”it just ducks it”by considering measures of ˜a poor life™, or more
precisely the extent, depth, and severity of ˜poverty over a period of time™,
using a means of weighing all poverty spells in one aggregate across time,
irrespective of the frequency of spells.
In the next section, we offer the basic set-up, discussing the key decision
needed regarding applying a focus on poverty, transformation of outcomes
and aggregation over time. In section 2.3, we present a number of core
axioms that may guide these choices, and the resulting choice of measures.
In section 2.4, a set of measures are presented, ordered by the particular
sequence in terms of applying focus, transformation, and aggregation. They
can be shown to satisfy (or not) some of the suggested axioms for intertem-
poral poverty assessment. The rest of the chapter will offer extensions. In
section 2.5, a discussion is introduced on the role of time preference, while
in section 2.6, the idea of sensitivity to prolonged poverty is introduced. In
section 2.7, we reintroduce risk and derive a forward-looking measure of the
threat of long-term poverty, building on our previous work on vulnerability.
Finally, in section 2.8, we offer some examples of how some of the measures
may be applied using data from Ethiopia.


2.2. Basic Set-up

Unless otherwise stated, and for most of the chapter, we will imagine the
world to be uncertainty free. All consumption levels are perfectly known,



34
Chronic Poverty and All That

regardless of the point we take in time. For instance, as seen from the ¬nal
spell, a backward-looking assessment of poverty throughout the period has
the bene¬t of hindsight, and no uncertainty clouds the view of past consump-
tion levels. Our assumption intends to put forward-looking assessments on a
similar standing, by granting the individual the gift of perfect foresight. To see
what this implies, imagine periods are seen (ex post) from their ¬nal spells and
ranked according to some intertemporal poverty measure, and also that some
ranking reshuf¬‚ing occurs if the standing point is brought forward (ex ante)
to their ¬rst spells. In our world, uncertainty cannot act as an explanation
for such reshuf¬‚ing, at least for now. In the ¬nal section of the chapter,
we will suggest an extension in which this perfect foresight is dropped and
uncertainty is reintroduced.
By assuming away uncertainty, we can focus both ex post and ex ante
analyses on our central question, which is to identify a metric for how much
suffering or deprivation was or will be endured over a particular period. This concern
must be distinguished from the current experience of suffering which may be
caused by a grim future (a sense of hardship to come), or by unhappy memories
of past deprivation. For instance, if we speak about poverty between 2007 and
2015, we will enquire how much poverty will be ˜accumulated™ by the end
of 2015 (and not how much future hardship impinges ex ante on well-being
in 2007). In this note, we think of period poverty as the cumulative result of
spell-speci¬c poverty episodes.
In the vein of the distinction between ˜identi¬cation™ and ˜aggregation™ in
the measurement of aggregate poverty (as in Sen), let us propose the following
three stages for our analysis:
r Focus. It is well known that all measures of aggregate poverty (e.g. Foster,
Greer, and Thorbecke, 1984) build on some form of focus axiom, whereby
outcomes above z are censored down to the poverty line itself, since
the poverty of the poor is not meant to be alleviated by the richness
of others. For instance, a society will not be said to be less poor simply
because the rich become richer, with no change in consumption levels
among the poor. Thus, it is this focus condition that ˜identi¬es™ the
relevant outcomes. Let this stage be related to a function f (u), such that
f (u) ≡ Min[u,zu ], where zu is the relevant poverty threshold, e.g. zu = z if
y = u.
r Transformation. To motivate this stage, recall the well-known Pigou“
Dalton condition, whereby aggregate poverty rises if consumption is
transferred from the very poor to the not-so-poor. In our case, we may
require period poverty PT to rise as a consequence of a transfer from a
poor spell to a not-so-poor spell, in the presumption that the drop in the
former will outweigh the gain in the latter. This however is a presumption
that cannot be taken for granted in our case, since the locations in time



35
C©sar Calvo and Stefan Dercon

of these two spells may matter and have not been determined yet. For
instance, the poorer spell may have occurred such a long time ago that its
loss in consumption may be meaningless. The ˜aggregation™ step turns to
such issues shortly.
Nonetheless, we can still say that for equally valued spells (in the way
that all individuals are equally valued by the Pigou“Dalton condition),
a transfer for the bene¬t of a not-poor spell should result in greater
intertemporal poverty PT . In practical terms, this implies that outcomes yt
must at some point be transformed by a suitable strictly convex function,
either before or after some correction for the value of their time location has been
made.
Let function g(u), with g (u) < 0 and g (u) > 0 account for the possibility
of this strictly convex transformation.
r Aggregation.Thirdly, spell-speci¬c inputs must combine into one single
measure of total, period-long poverty PT . To be clear, we deal here with
an aggregation over time spells, and not over individuals (as in the usual
poverty measures). Hence, aggregation methods may well differ from the
standard procedure. For instance, they will need to account for weight
differences across time spells, e.g. if we were to decide that spells further
back in the past should be paid less attention than more recent ones.
Let function AT (u1 ,u2 , . . . ,uT ) perform this aggregation. To keep the
convex, Pigou“Dalton-like transformation as a separate issue, let AT be
linear in each of its arguments. This restriction has no major drawback”
except for the transfer argument described above, there is no obvious
reason why changes in any spell should be allowed to have any bearing
on the effect on PT of further changes in that same spell.

How these three stages come together is a question with no unique answer.
Will we ¬rst apply focus, then transform and then aggregate over the entire
period, or will we change the order of these actions? As will be shown below,
this sequence matters. But which order we choose will depend on our view on
the set of desirable properties of a period-long poverty measure. To develop
this further, we will in section 2.4 give examples of the possible permutations
related to focus, transformation, and aggregation. In the next section, we will
¬rst discuss some possible desiderata.



2.3. Formalizing the Axioms

In this section, we offer a few possible axioms that can guide us in choosing
particular measures of individual, period-long poverty. The set of these axioms
is not exhaustive, in the sense that no combination of them determines
uniquely a particular family of measures. These desiderata will nevertheless



36
Chronic Poverty and All That

offer routes to decide among different permutations of focus, transformation,
and aggregation.
The ¬rst two axioms are quite general and hardly debatable.

Monotonicity in outcomes. Since consumption rises can under no circumstances
cause a rise in poverty, we impose

For d > 0, PT (y1 , y2 , . . . , yt + d, . . . , yT ) ¤ PT (y1 , y2 , . . . , yt , . . . , yT ) (2.1)

A narrower de¬nition speci¬cation is only possible if we decide when the
focus stage will enter. For instance, if the focus function f is allowed to come
¬rst, then we could go further and require

For d > 0 and yt < z, PT (y1 , y2 , . . . , yt + d, . . . , yT ) < PT (y1 , y2 , . . . , yt , . . . , yT )
(2.1 )
In words, this alternative version imposes that a consumption rise during a
poverty spell will reduce overall poverty. In (2.1), since focus has not yet been
enforced, yt < z is not enough to take for certain that the reduction in PT will
occur, and we can only rule out a rise in poverty.
Increasing cost of hardship. This axiom echoes the Pigou“Dalton condition,
whose exact translation to our setting would impose that a consumption
transfer from a very-poor spell to a not-so-poor spell should raise overall
poverty. However, we cannot readily resort to this formulation here, since
the time location of these spells must also be speci¬ed, unless we assume that
regardless of these locations, all spells are equally valued. While the Pigou“
Dalton assumption that all individuals (with equal consumption) receive
equal attention faces no major objection, here we must allow for the case
where some time spells receive greater weight than others.
An alternative formulation can build on the effect of consumption changes
at one single spell, and thus steer clear of the risk of committing to valua-
tions of changes in two different spells. The spirit of this condition remains
unchanged”consumption losses hit harder if consumption is already low to begin
with. We may phrase it as the increasing cost of hardship. Formally,

For d > 0 and yK < z, PT (y1 , . . . , yK , . . . , yT ) ’ PT (y1 , . . . , yK + d, . . . , yT )
> PT (y1 , . . . , yK + d, . . . , yT ) ’ PT (y1 , . . . , yK + 2d, . . . , yT ) (2.2)

Next, one may invoke an axiom providing the basis for comparison across
periods of different lengths. While ˜total™ poverty over a given T-span is
necessarily dependent on its length T, one may wish to speak of poverty at an
˜average™ spell, i.e. the spell-speci¬c poverty level which, if repeated in every
single spell of the period, would lead to the observed period-long poverty
level. To formalize this, let PT (y1 ,y2 , . . . ,yT ) increase proportionally to a k-fold
repetition of the period at hand, which we may write as



37
C©sar Calvo and Stefan Dercon

Full-period repetitions.

PkT (y1 , y2 , . . . , ykT ) = kPT (y1 , y2 , . . . , yT ), (2.3)

where yi+k(t’1) = yt for t = 1,2, . . . ,T and i = 1,2, . . . ,k.
In (2.3), we imagine that the complete period is lengthened by allowing the
¬rst spell to repeat k times before the outcome of the (initially) second spell
obtains, which then repeats k times before the third outcome occurs, and so
forth. Consider the following alternative formulation (2.3 ), where the whole
period unfolds and is then followed by an identical sequence of T spells, and
then by another, and so forth until it is repeated k times:

PkT (y1 , y2 , . . . , ykT ) = kPT (y1 , y2 , . . . , yT ), (2.3 )

where yt+k(i’1) = yt for t = 1,2, . . . ,T and i = 1,2, . . . ,k
The difference between (2.3) and (2.3 ) is trivial only if we impose two
assumptions which we shall discuss further on, namely that all outcomes are
equally valued, regardless of the time when they occur, and also that hardship
is assessed in each spell separately, e.g. with no chance for the immediately
preceding outcomes to matter. Otherwise, if either of these assumptions fails,
then a choice between (2.3) and (2.3 ) is required. Both assumptions are also
underlying the two remaining axioms of this section.
Note that this axiom is clearly akin to the population invariance axiom of
aggregate poverty measurement. It also plays a similar role here in contribut-
ing to a linear speci¬cation of the aggregation function AT . In the spirit of
Foster and Shorrocks (1991), we will approach linearity by imposing this full-
period repetitions axiom and also a ˜sub-period consistency™ axiom. The latter
is meant to impose Gorman separability and hence needs PT (y1 ,y2 , . . . ,yT ) to
be a transform of a linear combination of y1 , y2 , . . . , yT as long as T ≥ 3. The
axiom on full-period repetitions then generalizes this result to T ≥1.
To formalize, and further mirroring the aggregate poverty literature, allow
the period to be decomposed into (any) two sub-periods and focus on the
reaction of period-long poverty to changes in these sub-periods.
Sub-period consistency.
PT (y1 , y2 , . . . , yK , yK +1 , . . . , yT ) > PT (y1 , y2 , . . . , yK , yK +1 , . . . , yT ) (2.4)

if PK (y 1 ,y 2 , . . . ,y K ) > PK (y1 ,y2 , . . . ,yK ) and PT’K (y K +1 ,y K +2 , . . . ,y T ) = PT’K
(yK +1 ,yK +2 , . . . ,yT ).
If some sub-period exhibits a rise in poverty (while poverty remains unal-
tered in all other sub-periods), then PT must also rise for the entire period.
This sensitivity is what we mean by ˜consistency™. Its interpretation may gain
from noting that it restricts the ability of some spells (those from K +1 to T)
to impinge on the effect of other spells (from 1 to K ) on PT . We may see the
seed of a linear speci¬cation here, which however needs a stronger axiom to



38
Chronic Poverty and All That

be fully imposed. Such axiom can be phrased as ˜sub-period decomposability™,
whereby total period-poverty is a weighted sum of both sub-period poverty
indices.
Sub-period decomposability.
K
PT (y1 , y2 , . . . , yK , yK +1 , . . . , yT ) = PK (y1 , y2 , . . . , yK )
T
(T ’ K )
PT’K (yK +1 , yK +2 , . . . , yT )
+ (2.5)
T
Needless to say, this axiom is reminiscent of subgroup decomposability in the
aggregate poverty literature. Again, note both that timing is assumed to have
no bearing on the valuations of a given spell, and any information in the
sequence of poverty spells can be ignored: the valuation of a poverty spell is
unrelated to its history, such as whether the person was poor before or not”
sequences are quite freely broken into sub-pieces.
Even though this set of axioms is relatively limited, they are enough for a
clarifying discussion on some possible measures, linked to particular permu-
tations of the choices related to focus, transformation, and aggregation.



2.4. Choices as a Matter of Sequencing

We said that alternative PT speci¬cations follow from alternative sequencing
choices for three crucial stages (Focus, Transformation, and Aggregation).
Even though six orderings thereof are possible (FTA, TFA, FAT, TAF, AFT, and
ATF), in this section we only consider four of them, prior to giving the general
speci¬cation of the corresponding period-long poverty measures, as well as a
number of speci¬c examples. Four orderings are enough to characterize the
existing alternatives, since it can be easily shown that focus and transforma-
tion can swap positions with no practical consequence, provided aggregation
is not inserted between them. Thus, FTA exhausts all the insights in TFA, and
likewise AFT can stand for ATF.
Case 1: Focus“Transformation“Aggregation (FTA).

PT (y1 , y2 , . . . , yT ) ≡ AT (g ( f (y1 ) , f (y2 ) , . . . , f (yT ))) (2.6)

In this case, imposing ¬rst focus implies that consumption levels are immedi-
ately censored. Hence, this speci¬cation rules out compensations across time
spells, in the same spirit of the focus axiom in aggregate poverty measures,
which discards compensations across individuals. In our case, the intuition
could be phrased as follows: ˜poverty episodes cause shock and distress to
such an extent that they leave an indelible mark”no future or past richness
episode can make up for them.™



39
C©sar Calvo and Stefan Dercon

Under FTA, convexity is imposed next, before aggregation. Unsurprisingly,
the resulting families of measures are reminiscent of the well-known
Chakravarty (1983) and Foster, Greer, and Thorbecke (1984) measures of
aggregate poverty. To see this, consider in particular the ¬rst two of the
examples below, where ˜t ≡ Min[z,yt ] and aggregation allows for some time
y
t
adjustment, as by ‚ . For now, and for the rest of this section, we may take
this factor as given, until we turn to discuss it in section 2.4.
·
˜t
y
T
PT (y1 , y2 , . . . , yT ) = ‚T’t 1 ’ , with 1 < · and ‚ > 0. (2.7)
z
t=1

·
˜t
y
T
PT (y1 , y2 , . . . , yT ) = ‚T’t 1 ’ , with 0 < · < 1 and ‚ > 0. (2.8)
z
t=1


Measure (2.7) is a simple multi-period version of the FGT measure, where
aggregation has acted upon time spells, rather than individuals. Formula (2.8)
offers a similar idea for the Chakravarty measure. In terms of formal desider-
ata, FTA does rather well in capturing at least some of the basic desiderata.
Both Monotonicity and Increasing cost of hardship apply. Transformation ensures
the latter because it applies before aggregation, i.e. before all spell-speci¬c
outcomes merge into some form of total consumption, where no distinction
between poor and not-so-poor spells would be possible. Likewise, Sub-period
decomposability is also possible due to the fact that aggregation comes last,
so that the linearity of the ¬nal speci¬cation is not endangered”thus, total-
period poverty can be written as a weighted average of sub-period poverties.
This equally allows Full-period repetitions.
A limiting case of (2.7) is familiar, imposing ‚ = 1 and · = 0. It would result
in a period-long poverty measure that simply counts the number of spells
below the poverty line. But unlike (2.7), by imposing · = 0, it would fail both
the Monotonicity and the Increasing cost of hardship axioms. Nonetheless, the
simplicity of this speci¬cation makes it a useful starting point for summarizing
total-period poverty. It has been used among others by Baulch and Hoddinott
(2000), when counting poverty spells and its distribution across a population.
Measure (2.7) is probably the most straightforward and relevant for empir-
ical analysis. It aggregates individual period-by-period poverty spells into one
aggregate measure of poverty over a period of time consisting of T spells. It is
also close to the ideas behind Foster (2007) in this collection, with one crucial
difference: we do not restrict this measure to be zero for those who experience
a frequency of spells below the ˜chronic poverty™ threshold.
Case 2: Focus“Aggregation“Transformation (FAT).

PT (y1 , y2 , . . . , yT ) ≡ g (AT ( f (y1 ) , f (y2 ) , . . . , f (yT ))) (2.9)

A different set of families obtains if aggregation occurs before a convex trans-
formation is enforced. Since focus retains the ¬rst move, it is still true that



40
Chronic Poverty and All That

poverty episodes remain the crucial concern. We do not take into account
any outcomes above the poverty line: there is no weight attached to being
better off in good years. For example, Figures 2.1a and 2.1b will still be equally
valued and period-long poverty will still be the same for both cases. However,
in (2.9), the severity of poverty is paid attention to not in every single spell,
but only after all spell-speci¬c outcomes are summarized into one single value.
It is overall severity that matters.
Take the following few examples, which can read as a transformation of
some form of ˜present value of censored consumption™:
·
˜t
y
T
PT (y1 , y2 , . . . , yT ) = 1’ , with 1 < · and 0 < ‚.
T’t
(2.10)

z
t=1

Given the sequencing of the three stages, it is clear that Monotonicity still
holds, unlike Sub-period decomposability and Full-period repetitions, which must
be weakened down to Sub-period consistency. Finally, Increasing cost of hardship
also fails to hold, which may be undesirable on a number of accounts”very
bad poverty spells are brushed aside as long as, on average, poverty spells
are not too severe. This result, which clearly follows from the location of
transformation at the ¬nal position of the sequence, may explain why no
instances of this speci¬cation can be found in the literature. Nonetheless,
other cases where transformation also comes last do exist in the literature,
as we see next.
Case 3: Aggregation“Focus“Transformation (AFT).

PT (y1 , y2 , . . . , yT ) ≡ g ( f ( AT (y1 , y2 , . . . , yT ))) (2.11)

Here, transformation remains last, and even more importantly, focus is
removed from the ¬rst position. Note that this second choice implies that
some degree of compensation does occur across spells. As opposed to the view
underlying FTA and FAT, what matters here is not so much whether the
individual faced severe hardship at any particular point in time (regardless of
how she performs at other points). The main concern is rather that outcomes
realized in the rest of the period may not be high enough to compensate
for observed hardship episodes. In other words, poverty does not imply an
irremediable loss, since the case is also possible, where hardship does occur,
but high consumption in other spells does ˜save™ the period. Looking back at
our illustrative examples, Figure 2.1a has more poverty than Figure 2.1b.
Put it differently, (2.11) would be consistent with poverty assessed in rela-
tion to some form of intertemporal utility-based measure of poverty, whereby,
given instantaneous or direct utility in a particular spell, the present value of
these utilities is calculated as the sum of discounted direct utility, to which
then some benchmark norm is applied. While this is open to argument, it
does make somewhat unsatisfactory reading since period-long poverty can be
reduced by focusing on spells of already high consumption well above the



41
C©sar Calvo and Stefan Dercon

poverty line, say in the form of temporary opulence and feasts. Nevertheless,
some intuitive examples can be shown of measures in this case:
·
T T’t
yt
t=1 ‚
PT (y1 , y2 , . . . , yT ) = , with 1 < · and 0 < ‚.
1’Min 1, (2.12)
T T’t z
t=1 ‚
·
T T’t
yt
t=1 ‚
PT (y1 , y2 , . . . , yT ) = 1’ Min 1, , with 0 < · < 1 and 0 < ‚.
T T’t z
t=1 ‚
(2.13)

Since transformation comes last, Increasing cost of hardship fails to hold. More
strikingly, Sub-period consistency also does (which of course rules out Sub-period
decomposability as well). To see why, take the following example. Imagine
outcomes in a four-spell period changes from (8,8,8,40) to (4,4,8,40), with
z = 10. Poverty has risen in the sub-period comprising the ¬rst two spells
(while the rest of the period is unaltered), and yet poverty for the entire
period remains at zero. Again, the reason must be found in the fact that
compensations across spells are possible.
This may therefore seem an unappealing measure. However, one of the
most commonly used ˜measures of chronic poverty™, based on Jalan and
Ravallion (2000), is directly nested in this case, for ‚ = 1. The measure reduces
T
then toPT (y1 , y2 , . . . , yT ) = {1 ’ Min[1, t=1 yt /Tz}· , which is an FGT measure
of poverty applied to mean consumption in the period. It rests strongly on the
case for compensations across periods.
Case 4: Transformation“Aggregation“Focus (TAF).

PT (y1 , y2 , . . . , yT ) ≡ f (AT (g (y1 ) , g (y2 ) , . . . , g (yT ))) (2.14)

Again, removing focus from the ¬rst position does matter, since compensa-
tions are allowed. For instance in the following examples, the main compar-
ison takes place between the norm and some aggregation of the stream of
consumption ¬‚ows (say, its present value):
·
yt
T
PT (y1 , y2 , . . . , yT ) = Max 0, , with 1 < · and 0 < ‚.
T’t
1’ (2.15)

z
t=1

·
yt
T
PT (y1 , y2 , . . . , yT ) = Max 0, , with 0 < · < 1 and 0 < ‚
‚T’t 1’
z
t=1

(2.16)

Note that, in fact, these speci¬cations may allow PT = 0 even if yt < z for some
t”this may well be the case if yt is suf¬ciently above z in some other spells.
In terms of our desiderata, Increasing cost of hardship applies (since trans-
formation is enforced before aggregation), but again, Sub-period consistency
is dropped, along with Sub-period decomposability. In addition, Monotonicity
is risked, since cases where yt > z will display the troublesome feature of



42
Chronic Poverty and All That

greater positive gaps between yt and z raising both spell-speci¬c and period-
long poverty. Unsurprisingly, no instance of this speci¬cation exists in the
literature.
The result of this discussion is that a number of choices can be made in
terms of the sequence of aggregation, transformation, and the application
of a focus criterion, but only a relatively limited set is consistent with some
desiderata. For example, (2.7) and (2.8) or (2.12) and (2.13), building on
the Foster“Greer“Thorbecke and Chakravarty families of measure, have been
taken as acceptable candidates. A key issue is the extent of compensation
between spells that is allowed”a normative choice we can only point to.
However, the discussion opens avenues for applications and extensions. In
the next few sections, we will address three further issues: ¬rst, whether
there is any primacy of particular spells in our assessment of period-long
poverty. For example, should the last state be given any special weight, as
the end-point of our assessment? The second issue is whether there are any
normative issues related to the particular sequencing of spells”in particu-
lar, should any additional attention be paid to repeated spells and there-
fore prolonged periods of poverty? Finally, what would happen if we move
to forward-looking measures, which take into account that the world is
uncertain?


2.5. Equally Valued Spells

In all the examples thus far we have not been explicit about the choice of the
parameter ‚ beyond requiring that it is positive. The coef¬cient ‚ determines
the rate of time discounting: the weight we attach to consumption and
poverty spells in different periods. Standard economic analysis assesses the
value of some future ¬‚ow of a variable of interest (such as income or consump-
tion) by assuming the rate of time discounting to give nearby ¬‚ows a higher
T
weight. For instance, in (2.7), where PT (y1 , y2 , . . . , yT ) = t=1 ‚T’t (1 ’ ˜zt )· , as
y

seen from the outset at t = 1, we would require ‚ > 1, so that outcomes in the
distant future receive less attention. However, in our assessment of poverty
spells, we argue that in fact, the choice is not as self-evident. For example
taking ‚ = 1, meaning not to exert any discount, or even ‚ < 1, may be a
sensible decision, given our purposes.
While time discounting is made undisputed use of in most intertemporal
economic problems, it is not self-evident that it should apply when assessing
hardship spells. Severe hardship must cause some irremediable impact on
human life, or at least this seems to be the spirit underlying the whole of the
literature on poverty. Poverty episodes are spells of misfortune which cannot
be compensated for (in the spirit of FTA). Note how close this argument comes
to the rationale behind the cases above, where focus is given the ¬rst priority,



43
C©sar Calvo and Stefan Dercon

as opposed to those where the focus applies after some aggregation has been
performed and outcomes are allowed to compensate for one another across
spells, such as in the case of AFT. Even if some compensation were allowed for,
it would seem reasonable to require that compensation comes at least at some
serious cost. In any case, allowing some compensation is not an argument to
dismiss poverty spells, simply because they occur far away in the future. In
other words, discounting spells would sit uncomfortably with a concept of
period-long poverty.
There is a corollary in the literature on health measures. In the context of
the measurement of health, Anand and Hanson (1997) refuse to accept time
discounts in the calculation of DALYs:

We can see no justi¬cation for an estimation of the time lost to illness or death which
depends on when the illness or the calculation occurs. Suppose a person experiences
an illness today and another person, identical in all respects, experiences an illness of
exactly the same description next year. Discounting amounts to concluding that the
quantity of the (same) illness is lower in the latter case. This does not accord with
intuition or even with common use of language.


We are inclined to agree with this view. ˜A principle of universalism would
argue strongly for a common intrinsic valuation of human life, regardless of
the age at (or the time period in) which it is lived.™
An axiomatic formulation for this stance (‚ = 1) allows reshuf¬‚es across time
positions to occur with no bearing on total, period-long poverty. Timing does
not matter. Thus, we could impose
Symmetry over time positions.

PT (y1 , y2 , . . . , yT ) = PT (yÛ(1) , yÛ(2) , . . . , yÛ(T) ), (2.17)

where Û(u) is a one-to-one function whose co-domain is identical to its domain
(1,2, . . . ,T).
All the measures described before could be trivially adjusted to allow for
(2.17) by setting ‚ = 1.
But other arguments could be made. In evaluating trajectories, one may
well be tempted to value more the spells at the end of period rather those at
the beginning. Gradually drifting into poverty is then viewed as worse than
evolving from spells in poverty out of poverty, even if the number and extent
of spells in poverty may be equal in both cases. ˜All is well that ends well™ may
be a sentiment that could be re¬‚ected in our value judgements. An example
could be Figure 2.1d, compared to the reverse of this graph whereby the three
˜non-poor™ spells come at the end: the latter would then be considered better.
One way of introducing this in our evaluation of trajectories would be to
consider ‚ < 1: spells later on are given a higher weight. Other choices are



44
Chronic Poverty and All That

also possible: ‚ could become period dependent and particular periods in the
future could be given a much higher weight. 2


2.6. Axioms of a Sequence-Sensitive Speci¬cation

An arguably strong assumption is that some form of linearity is always present
in our measures of period-long poverty. To be more precise, note that our
2
aggregation fuction AT rules out any cross-effect across spells, i.e. ‚‚ysATt = 0.
‚y
This linearity is at the basis of the fact that the valuation of a poverty spell
is unrelated to its history, such as whether the person was poor before or
not. This is ensured by the linearity-related axioms above, but it can also be
summarized by an underlying axiom ensuring
Independence of other time spells.
PT (y1 , . . . yK ’1 , yK , yK +1, . . . , yT ) ’ PT (y1 , . . . yK ’1 , yK , yK +1, . . . , yT )
= PT (y1 , . . . yK ’1 , yK , yK +1, . . . , yT ) ’ PT (y1 , . . . yK ’1 , yK , yK +1, . . . , yT ) (2.18)

However, the case against such independence exists. Indeed, one may prefer
to imagine that prolonged, uninterrupted poverty is less acceptable than a
situation of equally frequent, but intermittent poverty episodes. For instance,
within a T = 3 period, two poverty episodes in a row may be harder to bear
than the same two poverty episodes with a recovery spell in between.
Of course, this is a normative issue. It may also be phrased on the grounds
of technology-related mechanisms, which we may even provide with the support
of some empirical evidence”e.g. body strength is progressively undermined
by continuous hardship and makes further poverty harder to bear, or more
plainly, low consumption comes hand in hand with asset depletion. However,
we prefer to say that prolonged poverty can be particularly bad per se. 3 The
quality of a human life may be eroded more harshly if poverty is sustained for
a lengthy string of spells.
In this case, we may de¬ne
Prolonged poverty.
PT (y1 , y2 , . . . , yK ’1 , yK + d, . . . , yT ) ’ PT (y1 , y2 , . . . , yK ’1 , yK , . . . , yT )
¤ PT (y1 , y2 , . . . , yK ’1 + e, yK + d, . . . , yT )
’PT (y1 , y2 , . . . , yK ’1 + e, yK , . . . , yT ), d, e ≥ 0.
for (2.19)
2
This sentiment is not unknown in the policy discourse, where targets are set: the
Millennium Development Goals have a well-de¬ned deadline”2015”and this deadline is
seemingly far more important than, say, outcomes in the preceding years.
3
Another way of putting this is that we assume here that our underlying standard of living
indicator comprehensively incorporates these concerns, so that there is no more information
on the spell-speci¬c standard of living required, for example on one™s asset position, once
the standard of living is known. Our concern with the sequence of poverty spells relates to
assessing the sequence of spell-speci¬c standard of living outcomes: repeated spells have an
additional welfare cost and there is information in the sequencing of spells.




45
C©sar Calvo and Stefan Dercon

This axiom implies that some form of path dependence exists. A change
in any given spell can only be assessed with knowledge of outcomes in
previous spells. In particular, greater poverty in a spell implies that a drop in
consumption in the following spell will hit harder. Our speci¬cation in (2.19),
however, can only be taken as a starting point, since it narrows the concept
of prolonged poverty down to a dependence only on the immediately pre-
ceding spell, whereas one may just as well allow spells further back to matter
likewise.
Note that this concern with prolonged poverty is not just one more form of
smoothing behaviour. In fact, it may actually run against such behaviour. For
instance, in the face of three consecutive spells where the consumption level
remains invariant and below the poverty line, PT (y1 ,y2 , . . . ,yT ) may drop if
the neat, smooth sequence is broken by raising the middle consumption level
above the poverty line, at the expense of a decrease in the other two spells. In
other words, individual preferences may or may not favour smoothing efforts,
and yet sensitivity of PT (y1 ,y2 , . . . ,yT ) to prolonged poverty persists all the
same. Our measure has a normative role, consisting in no more than reporting
the extent of poverty-related suffering over a stretch of time, quite regardless
of the features of the objective function of the individual.
For instance, take the following speci¬cation:
T
PT (y1 , y2 , . . . , yT ) = ‚T’t h (˜t , ˜t’1 ), with 0 < ‚
yy (2.20)
t=1

and where some standard value for ˜0 could be added as a convention to
y
prevent h(˜t , ˜t’1 ) from being unde¬ned for t = 1. One particular speci¬cation
yy
for this sequence-sensitive measure could be
’ ·
˜t
y ˜t’1
y
T
PT (y1 , y2 , . . . , yT ) = 1’ 1’ ,
T’t
(2.21)

z z
t=1

with 1 < ·, 0 < ‚ and 0 < ’ < 1
The measure in (2.21) can be seen as one example of a FTA measure: ¬rst
focus is applied, and then a transformation takes place, and ¬nally, aggrega-
tion over spells. This last stage includes however a new element, as it allows
the preceding spell to act as a weight. In particular, note that quite naturally
a poverty-free spell (˜t = z) does not add to period-long poverty, either in the
y
same spell or in the following one. However, if poverty does hit the individual,
then the resulting burden increases in the severity of hardship in the recent
past (since ’ > 0). And likewise, this new poverty episode impinges on the
weight of future deprivation. The restriction ’ < 1 simply aims to rule out the
case where in the assessment of hardship at time t, the poverty gap at t ’ 1
receives more attention than the actual gap at t.
Note that this speci¬cation imposes that ˜t and ˜t’1 must be seen as com-
y y
plements as we assess the contribution of poor consumption in spell t to total,




46
Chronic Poverty and All That

period-long poverty PT . In other words, whenever we assess the extent of con-
sumption shortfall in a particular spell, our valuation includes the memory
of the shortfall if any in the last period. There is a close similarity to the
literature on multidimensional poverty, where different attributes are assessed
in relation to each other. Just as in multidimensional assessment, the fact
that consumption (shortfalls) in any two spells must be combined into one
composite leaves the gate open to questions on whether they complement (or
substitute for) each other. In our case, complementarity is the only intuitive
answer, since it is the fear that poor previous consumption may compound
current hardship that motivates the Prolonged poverty axiom. The measure in
(2.21)”one of many possibilities”allows for this complementarity, ensuring
that poverty spells are valued higher in overall period poverty if they follow
after another poverty spell.


2.7. Vulnerability in a Dynamic World

The entire discussion thus far has considered poverty in a world with time,
but with no risk. When constructing a measure of poverty over time ex
post, building on past observed outcomes in the standard of living, then this
may be acceptable. Such a measure values actual realizations of a trajectory
of the standard of living. However, using the earlier analysis when looking
forward into the future to assess different paths of the standard of living, we
implicitly assume perfect foresight: we know the realization of the standard
of living without any uncertainty. In themselves, such exercises are useful:
for example, to compare trajectories under different policies or interventions.
But one striking feature of such assessment is that it is unlikely to be done in
a world of certainty, and risk should feature.
In Calvo and Dercon (2006), a measure of vulnerability as the ˜threat of
poverty™ has been derived. In particular, a set of desiderata has been proposed,
borrowing from the standard poverty literature, and incorporating axioms
that capture desirable properties stemming from the need to aggregate over
states of the world. In the annexe, an extract of this paper is given. The
intuition is to provide an aggregate over some transformation of outcomes
in all states of the world, whereby outcomes in each state are assessed relative
to the poverty line. This gives a metric of the threat of poverty, before uncer-
tainty has been resolved, and not of poverty itself. As Appendix 2.1 shows,
the desiderata include a focus axiom, symmetry over states, continuity and
differentiability, scale invariance, normalization, probability-dependent effect
of outcomes, a probability-transfer axiom between states, and risk sensitivity
(so increased risk raises vulnerability). If we impose an assumption of constant
relative risk sensitivity, then it is shown that the preferred vulnerability




47
C©sar Calvo and Stefan Dercon

measure will be the expected value of the Chakravarty measure of
poverty:
·
˜t
y
V(·) = 1 ’ E , with 0 < · < 1. (2.22)
z
E is the expected value operator, and · regulates the strength of risk
sensitivity”as · rises to 1, we approach risk neutrality. It is crucial to note
that, as de¬ned by (2.22), vulnerability becomes greater whenever uncertainty
rises, even if all in all expected outcomes remain unaltered. Thus, a normative
choice is made to ensure that risk per se is bad and compounds expected
hardship.
Note also that ˜t is a vector consisting of ˜it , censored outcomes for each
y y
state of the world i at time t. Although forward looking, this measure is
still essentially timeless: possible outcomes in timeless states are considered
before the veil of uncertainty is lifted and before a particular state has been
realized. Nevertheless, its desirable properties when constructing a measure of
the threat of poverty mean that it could be used as a candidate for period-by-
period outcomes before aggregation in an intertemporal measure of poverty.
In particular, consider a amended version of (2.8), which in itself was based
on the Chakravarty measure of poverty:
·
˜t
y
T
VT (y1 , y2 , . . . , yT ) = 1’ E , 1 < · and 0 < ‚
T’t
with

z
t=1
(2.23)
This can be considered a forward-looking and dynamic measure of vulnera-
bility, consistent with a form of ˜FTAA™-case, where allowing for uncertainty
requires that the ¬nal stage (after focus in each state and transformation) is
extended to a double exercise: aggregation ¬rst takes place over all states of the
world in each t, and then it operates over all periods of time. In each period, it
satis¬es set desiderata that appear reasonable when assessing poverty ex ante
in a risky world, as a metric of the threat of poverty. Even if the presence
of risk will affect the exact formulation of the intertemporal desiderata, it
appears clear that versions of the intertemporal axioms related to Monotonicity,
Increasing cost of transfers, and Sub-period decomposability apply as well.
In other words, we have a measure of forward-looking intertemporal
poverty, as a measure of the extent of the threat of poverty in the future,
providing a clear ordering of different possible trajectories for individuals.
It comes closer than any of its predecessors to providing a direct measure
of ˜chronic™ poverty, in that it does not just assess poverty in one period,
nor assess poverty in a risk-free world. It offers an exact way of ordering
very different and complex trajectories, including the threat of poverty and
deprivation implied ex ante for those whose trajectory in expectation contains
serious spells of severe deprivation, even if ex post they do not always become
realized.



48
Chronic Poverty and All That

2.8. An Example from Ethiopia

To illustrate the insights that can be gained from a variety of measures of
intertemporal poverty, we use data from rural Ethiopia. The Ethiopian Rural
Household Survey has collected data on about 1,450 households over the
course of ten years, in the form of six unequally spaced rounds. Here we
drop round 2, which was collected in the second half of 2004, as it was
collected in a distinctly different season and only about six months after
the ¬rst round of 2004. The result is data from 1994, 1995, 1997, 1999,
and 2004. We use data on consumption per capita, de¬‚ated to be expressed
in 1994 prices. The consumption aggregate is based on careful recording
of consumption from own production, purchased items, and gifts, and is
predominantly food, at about 75 per cent re¬‚ecting the relative poverty of
households in rural Ethiopia. The data is relatively highly clustered, from only
¬fteen communities, but reasonably well spread across the country. Round-by-
round attrition was low, although we focus in the rest of the analysis on 1,187
observations with complete information in all rounds. More details can be
found in Dercon and Krishnan (2000). Using a poverty line not dissimilar to
the national poverty line, at about US$8.50 per capita per month, we ¬nd that
the headcount of poverty declined in this period, from 48 per cent in 1994
and even 55 per cent in 1995, to 33 per cent by 1997 (an exceptionally good
harvest year) and 36 and 35 per cent in respectively 1999 and 2004. Still, there
is considerable churning, and combined with the gradual decreasing poverty
levels and possibly some problems of measurement error, we ¬nd that only
18 per cent of the households were never poor and 7 per cent were poor in all
rounds (Table 2.1).
Using these data, we calculated a number of different poverty measures
summarizing these poverty experiences, using 1,187 observations. First, and
for comparison, we calculated the squared poverty gap (the Foster“Greer“
Thorbecke measure with · = 2) in the base year, 1994, and the ¬nal year,
2004. We ¬nd that it almost halved from 0.120 to about 0.065. In terms

Table 2.1. Poverty episodes 1994 to 2004 (based on ¬ve
rounds)

Percentage of households (1)

Never poor 18
Poor once 22
Poor in 2 out of 5 rounds 23
Poor in 3 out of 5 rounds 16
Poor in 4 out of 5 rounds 14
Poor in all rounds 7

Source: Ethiopia Rural Household Survey (based on 1,187 observations
with data in all 5 rounds).




49
C©sar Calvo and Stefan Dercon

Table 2.2. Spearman rank correlation between different poverty measures

Sq Pov Sq Pov FTA AFT Seq FTA (7), FTA (7),
Gap 1994 gap 2004 (7) (12) FTA (22) (‚ = 0.85) (‚ = 1.15)

Sq Pov Gap 1994 (· = 2) 1
Sq Pov gap 2004 (· = 2) 0.166 1
FTA (7), (‚ = 1, · = 2) 0.690 0.462 1
AFT (12) (‚ = 1, · = 2) 0.553 0.468 0.689 1
Seq FTA (22) 0.662 0.371 0.824 0.715 1
(‚ = 1, · = 2, ’ = 0.90)
FTA (7), (‚ = 0.85, · = 2) 0.751 0.404 0.993 0.678 0.821 1
FTA (7), (‚ = 1.15, · = 2) 0.633 0.516 0.994 0.690 0.813 0.974 1

Source: Calculated from the Ethiopian Rural Household Survey by authors.



of intertemporal measures, we calculated measure (2.7) with · = 2, an FGT-
style measure in which the focus axiom is applied before transformation
and aggregation, so that no compensation is allowed between periods. We
also use the assumption of equal-valued spells, i.e. ‚ = 1. Although measure
(2.7) is not scaled by the number of periods, dividing it by 5 gives a direct
way to compare it with the period-by-period squared poverty gaps. Its scaled
mean value of 0.089 is consistent with the nature of the decline in poverty
in this period. Next, we calculated measure (2.12), effectively the Jalan and
Ravallion (2000) measure, a squared poverty gap measure based on mean
consumption in this period, allowing for compensation and equal-valued
spells (with · = 2 and ‚ = 1). Its mean value of 0.025 suggests how strong
the impact is of allowing for compensation, i.e. for aggregation before the
focus axiom is applied. Further, we calculated two indices of poverty, based
on (2.7) but relaxing the assumption of equal-valued spells, by focusing on
an index that values more recent years less than the past (‚ = 0.85) and
an index that values the present more than the past (‚ = 1.15). Finally, we
introduced sequence sensitivity, using measure (2.22), which values poverty
gaps only to the extent that one was poor in the previous year, using ’ = 0.90,
nesting it with the other cases by choosing · = 2 and ‚ = 1. The actual values
of these last three indexes cannot quite be compared with the other indices
shown.
For empirical relevance, we need to ask whether these different measures of
poverty give us any different messages about poverty. As these measures are
different non-linear transformations of underlying consumption measures, a
¬rst appropriate way to compare these measures would be to look at rank
correlations: do they order people differently? Table 2.2 gives Spearman cor-
relation coef¬cients for all these measures.
As could be expected, all measures are positively (signi¬cantly) correlated,
but some interesting differences emerge. Poverty in 1994 and in 2004 is




50
Chronic Poverty and All That

relatively weakly correlated, partly re¬‚ecting the overall decline. Among the
intertemporal measures, using the FTA (2.7) measure with different discount
rates does not appear to matter much for the ranking of households, with
high correlations with each other. Choices on the sequence of focus, transfor-
mation, and aggregation appears to matter most, with a correlation of about
0.69 between the AFT (2.12) and the FTA (2.7) measures with otherwise equal
values for · and ‚. Adjusting for the sequence of poverty outcomes matters,
but the correlation remains high with the other AFT measures. At least in these
data, choices on allowing for compensation appear to be most important,
while cross-section poverty estimates for a population may give the wrong
impression on intertemporal poverty outcomes and rankings.
Of course, much of this difference may be due to a different treatment of
measurement error in welfare outcomes, entailed by each of these intertempo-
ral poverty measures. More in general, the differences in poverty may be due
to individual speci¬c attributes hardly observable to a researcher. One way
of assessing whether our interpretation on the nature of poverty is different
across measures is by constructing a ˜poverty pro¬le™, a multivariate descrip-
tion of the correlates of poverty in these data, effectively whether we identify
different types of households to be poor using these different measures. This
is de¬nitely not an exploration of a causal relationship between any of the
factors identi¬ed and poverty”more careful analysis would be required”
but it can give some sense of whether different concepts of intertemporal
poverty result in different implications; for example, when trying to target
poor population on the basis of generic characteristics. Table 2.3 gives the
correlates of some of the different poverty measures used in Table 2.2: the
poverty gap in 1994, the FTA (2.7), the AFT (2.12), and the sequential FTA.
The last two FTA measures, with different discount rate, were not used as they
are very highly correlated with the FTA (2.7). As the poverty measures used are
all censored, we use a Tobit model with censoring at zero. Table 2.3 reports the
coef¬cients.
The correlates used include educational characteristics of the head (whether
completed primary education or more, and whether some primary education,
with the base group no education), land holding in hectares and per capita,
the sex of the head, demographic composition of the household (number
of male and female adults, children, and elderly), and a number of village
characteristics: the distance to the nearest town in kilometres, whether there
is a road passing the village that is accessible to trucks, buses, and cars, and
the coef¬cient of variation of rainfall in the village; and ¬nally, a few mean
village characteristics, such as the mean land holding per capita, and the
mean number of female and male adults per household (as there are sub-
stantial differences in land holdings and in demographic composition across
villages).




51
52




C©sar Calvo and Stefan Dercon
Table 2.3. Correlates of poverty measures (Tobit model)

Poverty gap 1994 AFT (7) FTA (12) Seq AFT (7)

’0.094 [2.35]—— ’0.054 [4.66]——— ’0.088 [3.36]——— ’0.025 [3.56]———
Head at least primary ed.
’0.075 [2.68]——— ’0.02 [2.39]—— ’0.013 [0.77] ’0.006 [1.29]
Head some primary
’0.046 [3.48]——— ’0.019 [4.89]——— ’0.03 [3.64]——— ’0.008 [3.42]———
ln land per capita (ha)
’0.068 [2.49]—— ’0.007 [0.83] ’0.005 [0.97]
Sex of the head is male 0.001 [0.04]
0.029 [3.13]——— 0.01 [3.32]——— 0.013 [2.24]—— 0.006 [3.95]———
No. of female adults
0.026 [2.69]——— 0.005 [1.84]— 0.004 [2.61]———
No. of girls 5“15 0.008 [1.37]
0.031 [2.18]—— 0.021 [4.83]——— 0.041 [4.74]——— 0.011 [4.42]———
No. of girls 0“5
’0.011 [0.50]
No. of females 65+ 0.037 [1.17] 0.004 [0.46] 0.009 [1.59]
’0.007 [1.11]
No. of male adults 0.015 [1.61] 0 [0.12] 0.001 [0.63]
0.039 [4.14]——— 0.014 [4.85]——— 0.02 [3.40]——— 0.006 [3.67]———
No. of boys 5“15
0.056 [3.80]——— 0.022 [4.88]——— 0.038 [4.26]——— 0.011 [4.45]———
No. of boys 0“5
’0.047 [0.96] ’0.006 [0.43] ’0.024 [0.76] ’0.008 [0.93]
No. of males 65+
0.021 [10.60]——— 0.006 [10.43]——— 0.013 [9.04]——— 0.004 [10.84]———
Distance to town (km)
0.006 [5.69]——— 0.002 [4.82]——— 0.003 [3.86]——— 0.001 [3.45]———
Coeff. variation rainfall
’0.22 [7.56]——— ’0.072 [8.66]——— ’0.164 [7.42]——— ’0.04 [7.75]———
Is road accessible trucks

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