Village mean land p.c.

’0.039 [1.87]— ’0.024 [1.98]——

’0.049 [0.71]

Village mean male adults 0.052 [1.17]

0.397 [6.29]——— 0.188 [9.93]——— 0.178 [4.58]——— 0.095 [8.79]———

Village mean fem adults

’0.619 [7.90]——— ’0.212 [9.14]——— ’0.597 [10.33]——— ’0.152 [10.99]———

Constant

Observations 1125 1125 1125 1125

Absolute value of t statistics in brackets.— signi¬cant at 10%; —— signi¬cant at 5%; ——— signi¬cant at 1%.

Chronic Poverty and All That

Table 2.4. Percentage change in poverty index from marginal change in characteristics

AFT (7) FTA (12) Seq AFT (7)

’0.43 ’0.39 ’0.48

From no education to primary completed

’0.17 ’0.19 ’0.18

Doubling land per capita

’0.05 ’0.08 ’0.09

Reducing distance to town by one kilometre

’0.63 ’1.01 ’0.91

From bad or no road to road accessible for trucks/bus

Source: Calculated from results in Table 2.3.

The most striking insight from the table is that the differences between

the different intertemporal measures of poverty appear relatively small: in

any case, in terms of signi¬cance, the same variables appear to stand out,

with the expected signs: education, land, distance to towns, road access, and

weather variability. Demographic characteristics also matter but not the sex of

the head. Strikingly, even the pro¬le based on the 1994 squared poverty gap

offers broadly a similar set of correlates. Obviously, this does not mean that

the same people are being predicted as being poor across equations.

It is dif¬cult to interpret the differences in the size of the coef¬cients

across equations, as the left-hand side variables are rather different and

most are not directly comparable. To highlight better the different inter-

pretations across the regressions, we can compare the marginal effects rel-

ative to the mean of each left-hand size variable. In other words, we can

establish the percentage change on each poverty measure from a change

in one of the explanatory variables. The relevant marginal effects are not

the coef¬cients given in Table 2.3 as the zeros in the data can be given

direct meaning (a zero squared poverty gap is a zero squared poverty gap,

and not some unobserved negative poverty). The coef¬cients in Table 2.3

give the marginal effects relative to the underlying latent variable of the

statistical model which is assumed to take on negative values. Instead, we

use marginal effects based on the unconditional expected value, evaluated

at the mean of all explanatory variables. Expressing these as a percent-

age of the mean dependent variable for each poverty measure, we obtain

Table 2.4.

These results are suggestive, as there are some interesting differences in

the order of magnitudes of the relative marginal effects. The most striking

differences relate to the infrastructure variables: using the FTA (2.12) mea-

sure (i.e. allowing for compensation over time) suggests that living nearer

to towns or with better roads is associated with considerably lower poverty

than implied by the AFT (2.7). Education improvements are more strongly

related to the AFT measures, especially the measure that effectively only

counts repeated poverty episodes. In short, when using poverty measures over

time, the way aggregation over time is done will affect the characteristics

53

C©sar Calvo and Stefan Dercon

that will be especially highlighted in poverty pro¬les as correlated with lower

poverty. 4

2.9. Conclusions

This chapter has offered a discussion of a number of issues related to measur-

ing poverty over time. It has highlighted some of the key normative decisions

that have to be taken. In particular, we have highlighted the role of compensa-

tion over time (whether poverty spells can be compensated for by non-poverty

spells); the issue of the discount rate (whether each spell should be given an

equal weight); and the issue of the role of persistence (whether repeated spells

should be given a higher weight). We have offered a number of plausible

poverty measures, each with different assumptions regarding these key issues.

We have also shown how these insights can be used to construct a forward-

looking measure of vulnerability. Applying a number of these measures to data

from rural Ethiopia, it is shown that while correlations are high, there would

still be considerable differences in ranking households by poverty according

to different measures, especially those that have different views on the role

of compensation. Turning to a multivariate poverty pro¬le, it was shown that

while similar factors are signi¬cant, their relative importance in identifying

intertemporal poverty is different according to the measure used to summarize

poverty.

Appendix 2.1

A Family of Individual Vulnerability Measures (Based on

Calvo and Dercon, 2006)

Let individual vulnerability (V) be measured by V = v(z,p,y), where z is the poverty

line, and p and y are k-dimensional vectors, containing state-of-the-world prob-

abilities and outcomes, respectively”i.e. pi is the probability of the i-th state

occurring, with outcome yi . We impose yi ≥ 0. It may be easiest to think of

these outcomes as consumption levels in each possible state of the world, espe-

cially if poverty is de¬ned as usual as a shortfall in consumption. We remark

that we mean outcomes after all consumption-smoothing efforts have been deployed.

In other words, their variability across states is taken as a ¬nal word, with no

scope for reducing it further, e.g. by formal insurance, risk sharing, or precautionary

savings.

4

As is well known with poverty pro¬les, these results have only limited policy implica-

tions, as these correlates are not shown to be causal factors, and even if they were, the relative

cost of intervening in terms of infrastructure, land, or education would have to be taken into

account.

54

Chronic Poverty and All That

For each state, de¬ne ˜censored outcome™ ˜i by ˜i ≡ Min(yi ,z), and the ˜rate of

y y

coverage of basic needs™ xi by xi ≡ ˜i /z, so that 0 ¤ xi ¤1. Vectors y and x are de¬ned

˜

y

correspondingly. ei stands for a k-dimensional vector whose elements are 0, except for

the i-th one, which equals 1. We close our notation with vectors y and yc . Their ele-

˜

k

ments are all equal to y and ˜ c , respectively, which in turn are de¬ned by y = i=1 pi ˜i

y ˆ y

and v(z,p,˜) = v(z,p,˜ c ). Note that ˜ c can be written as a function ˜ c (z,p,˜ ) and will

y y y y y

shortly be called the risk-free equivalent to the set of prospects described by (z,p,y),

in the sense that it yields the same degree of vulnerability; y is the expected value

ˆ

of ˜i .

y

We propose eight desiderata. The ¬rst is the FOCUS AXIOM, which imposes v(z,p,y) =

v(z,p,˜). Our measure will thus disregard outcome changes above the poverty line.

y

If vulnerability is understood as a burden caused by the threat of future poverty, it

should not be compensated by simultaneous (ex ante) possibilities of being well off. In

consequence, high vulnerability is not necessarily tantamount to grim overall expected

well-being (as arguably in Ligon and Schechter, 2003), since the ˜promise™ of richness in

some states can raise welfare expectations, with no bearing on vulnerability.

Imagine that a farmer faces two scenarios: rain (no poverty) or drought (poverty).

Does she become less vulnerable if the harvest in the rainy scenario improves? Our

answer is ˜no™. Poverty is as bad a threat as before. It is as likely as before, and it is

potentially as severe as before.

According to this axiom, ˜excess™ outcomes yi ’ z > 0 are ˜wasteful™ and can be

ignored, as far as vulnerability is concerned. Taking this for granted, the remaining

axioms can be presented as follows:

SYMMETRY OVER STATES: v(z,p,˜) = v(z,Bp,B˜), where B is any k — k permutation matrix.

y y

All states receive the same treatment, and the only relevant difference between two

states of the world i and j is the difference in their outcomes (yi , y j ) and probabilities

( pi , p j ).

CONTINUITY AND DIFFERENTIABILITY. Function v(z,p,˜) is continuous and twice-

y

differentiable in y, for tractability and to preclude abrupt reactions to small changes

in outcomes.

SCALE INVARIANCE. v(z,p,˜) = v(Îz,p,Î˜) for any Î > 0. Our measure will not depend on

y y

the unit of measure of outcomes.

NORMALIZATION. Min ˜ [v(z,p,˜)] = 0 and Max ˜ [v(z,p,˜)] = 1. We impose closed bound-

y y

y y

aries to facilitate interpretation and comparability.

PROBABILITY-DEPENDENT EFFECT OF OUTCOMES. For “c < ˜i < z and pi pi = 0, /

y

v(z,p,˜)’v(z,p,˜+cei ) = v(z,p ,˜ ) ’ v(z,p ,˜ + cei ) if and only if pi = pi and ˜i = ˜i .

y y y y yy

Should ˜i change, the consequent effect on vulnerability is not allowed to depend on

y

the outcomes or probabilities of other states of the world”for a given pi , the change

in vulnerability depends only on ˜i . 5 In the opposite direction, the effect must be

y

5

A possible counterargument could run: ˜in fact, there could be some relief in considering that

one could have done much better had the odds been more fortunate™ (or to the contrary, ˜one may

rue having missed a better possible outcome, through no fault on one™s own part, and thus one™s

misery will be greater™). We ignore such counterarguments for the sake of tractability. In doing so,

we simply adhere to the common concept of poverty as mere failure to reach a poverty line, with

no regard for ˜subjective™ subtleties.

55

C©sar Calvo and Stefan Dercon

/

sensitive to the likelihood of that particular state of the world. Note that pi pi = 0

discards ˜impossible™ states ( pi = pi = 0).

¤ ≥

PROBABILITY TRANSFER. For every p j ≥ d > 0, v(z,p +d(ei ’e j ),˜) v(z,p,˜) if ˜i

y y y ˜.

y

¤j

≥

If ˜i is greater than or at least equal to ˜ j , then vulnerability cannot increase as a result

y y

of a probability transfer from state j to state i. Likewise, if ˜i is lower than or at most

y

equal to ˜ j , then vulnerability cannot decrease. Going back to the example of the farmer

y

facing rain and drought, we say that she becomes more vulnerable if a drought becomes

more likely, at the expense of the rainy scenario (or at least, her vulnerability does not

lessen as a result).

RISK SENSITIVITY. v(z,p,˜) > v(z,p,y). Vulnerability would be lower if the expected (cen-

y

sored) outcome ˆ were attained in all states of the world and uncertainty were thus

y

removed. In other words, greater risk raises vulnerability. 6 Thus we link up with our ¬rst

intuition about vulnerability, as a concept aiming to capture the burden of insecurity,

the fact that hardship is also related to fear of future threats.

Alternatively, resorting to the risk-free equivalent ˜ c , the same axiom could be

y

c /ˆ <1. Expected outcome is unevenly and ˜inef¬ciently™ spread across

expressed as ˜ y

y

states of the world, in the sense that a similarly low degree of vulnerability would result

from ˜ c < ˆ being secured in every state. ˜ c /ˆ re¬‚ects this ˜ef¬ciency loss™.

y y yy

CONSTANT RELATIVE RISK SENSITIVITY. For Í > 0, Í˜ c (z,p,˜) = ˜ c (z,p,Í˜). A proportional

y y y y

increase by Í in the outcomes of all possible states of the world leads to a similar pro-

portional increase in the risk-free equivalent ˜ c . While risk sensitivity ensures ˜ c /ˆ < 1,

y yy

we now require this ratio (or ˜ef¬ciency loss™) to remain constant if all state-speci¬c

outcomes increase proportionally.

As compared to the previous axioms, this ¬nal property seems less compelling. Still,

we ¬nd it attractive for its contribution both to narrowing down the families of accept-

able measures to only one, and to securing that risk sensitivities receive an appropriate

treatment. As for this second point, Ligon and Schechter (2003) were the ¬rst to point

out that some existing vulnerability measures hid some awkward assumptions, e.g. risk

sensitivity increasing in initial income, at odds with most empirical ¬ndings on risk

attitudes (e.g. Binswanger 1981).

Needless to say, we are avoiding here terms such as ˜risk aversion™ or ˜utility™. We

intend our choice of language to convey our view of vulnerability as distinct from

expected utility, if only to stress our departure from proposals where vulnerability

boils down to some form of bad ˜overall™ expectations (e.g. Ligon and Schechter,

2003). On the other hand, parallels should be obvious. In fact, the proof of the fol-

lowing theorem heavily draws on results from expected utility theory (mainly Pratt,

1964), necessarily with some departures due to the speci¬c traits of our vulnerability

concept. For this reason and for brevity, it is not provided, but it is available on

request.

THEOREM 1”If all the axioms above are satis¬ed, then

V(·) = 1 ’ E [x· ], with 0 < · < 1. (.24)

6

We implicitly de¬ne the increase in risk as a probability transfer ˜from the middle to the tails™,

in keeping with one of the Rothschild“Stiglitz senses of risk.

56

Chronic Poverty and All That

E is the expected value operator, and we recall xi ≡ ˜i /z is the rate of coverage of basic

y

needs, and 0 ¤ xi ¤ 1. We highlight the simplicity of this single-parameter family of

measures V(·) . 7 Of course, · regulates the strength of risk sensitivity”as · rises to 1, we

approach risk neutrality.

A few remarks are in place. First, for those facing no uncertainty and with known

xi = x— < 1 for all i, V(·) > 0. If vulnerability is about the threat of poverty, certainty of

being poor is but a dominant, irresistible threat. The concept is not con¬ned to those

whom the winds might blow into poverty or out from it. Vulnerability is about risk, but

not only about it.

Second, it is easy to prove that V(·) is equal to the probability of being poor only

if outcomes are expected to be zero in every state of the world where the individual

is poor. If vulnerability were measured as expected FGT0 (as in Chaudhuri and Jalan,

2002), then vulnerability would be overestimated. Ligon and Schechter (2003) have

pointed out the shortcomings of other FGT choices. 8

Finally, V(·) can still be assimilated into the expected-poverty approach to vulnerabil-

ity, provided poverty is measured as in Chakravarty (1983). In some sense, one of the

contributions of this chapter is to identify the Chakravarty poverty index as the best

choice if the poverty analysis moves from static poverty on to vulnerability.

References

Anand, S., and Hanson, K. (1997), ˜Disability-Adjusted Life Years: A Critical Review™,

Journal of Health Economics, 16: 685“702.

Baulch. B., and Hoddinott, J. (2000), ˜Economic Mobility and Poverty Dynamics in

Developing Countries™, introduction to special issue, Journal of Development Studies.

Binswanger, H. P. (1981), ˜Attitudes toward Risk: Theoretical Implications of an Experi-

ment in Rural India™, Economic Journal, 91(364): 867“90.

Bourguignon, F., and Chakravarty, S. R. (2003), ˜The Measurement of Multidimensional

Poverty™, Journal of Economic Inequality, 1(2): 1569“721.

Calvo, C., and Dercon, S. (2006), ˜Vulnerability to Poverty™, mimeo, Oxford University.

Chakravarty, S. R. (1983), ˜A New Index of Poverty™, Mathematical Social Sciences, 6: 307“

13.

Chaudhuri, S., and Jalan, J. (2002), ˜Assessing Household Vulnerability to Poverty

from Cross-sectional Data: A Methodology and Estimates from Indonesia™, Columbia

University Discussion Paper 0102-52.

Dercon, S., and Krishnan, P. (2000), ˜Vulnerability, Poverty and Seasonality in Ethiopia™,

Journal of Development Studies, 36(6): 25“53.

Foster, J. (2007), ˜A Class of Chronic Poverty Measures™, mimeo.

Greer, J., and Thorbecke, E. (1984), ˜A Class of Decomposable Poverty Measures™,

Econometrica, 52(3): 761“6.

and Shorrocks, T. (1991), ˜Subgroup Consistent Poverty Indices™, Econometrica,

59(3): 689“709.

7

For instance, if our last axiom (constant relative risk sensitivity) were replaced by constant

absolute risk sensitivity [Í + ˜ c (z,p,˜) = ˜ c (z,p,˜ + Í), for Í > 0], the less attractive measure V(‚) = 1

y y y y

--E[{e‚(1’x) ’ 1}/{e‚ ’1}], with ‚ > 0, would result.

8

More precisely, we should speak about expected individual poverty, as measured by the function

implicit in the corresponding aggregate FGT index, as in Foster, Greer, and Thorbecke (1984).

57

C©sar Calvo and Stefan Dercon

Jalan, J., and Ravallion, M. (2000), ˜Is Transient Poverty Different? Evidence from Rural

China™, Journal of Development Studies, 36(6): 82“99.

Kanbur, R., and Mukherjee, D. (2006), ˜Premature Mortality and Poverty Measurement™,

mimeo, Cornell University.

Ligon, E., and Schechter, L. (2003), ˜Measuring Vulnerability™, Economic Journal,

113(486): C95“C102.

Pratt, J. W. (1964), ˜Risk Aversion in the Small and in the Large™, Econometrica, 32(1/2):

122“36.

Tsui, K. (2002), ˜Multidimensional Poverty Indices™, Social Choice and Welfare, 19(1): 69“

93.

58

3

A Class of Chronic Poverty Measures

James E. Foster

3.1. Introduction

Traditional measures of poverty based on cross-sections of income (or con-

sumption) data provide important information on the incidence of material

poverty, its depth and distribution across the poor. However, they have little

to say about another important dimension of poverty: its duration. Empirical

evidence suggests that increased time in poverty is associated with a wide

range of detrimental outcomes, especially for children. 1 If so, then this would

provide a strong rationale for using a methodology for evaluating chronic

poverty that explicitly incorporates ˜time in poverty™. This chapter presents

a new class of chronic poverty measures that can account for duration in

poverty as well as the traditional dimensions of incidence, depth, and severity.

There are several methodologies available for measuring chronic poverty

using panel data. Two broad categories may be discerned, each with its own

distinctive strategy for identifying the chronically poor. 2 The components

approach, exempli¬ed by Jalan and Ravallion (1998), constructs an aver-

age or permanent component of income and identi¬es a chronically poor

person as one for whom this component lies below an appropriate poverty

line. 3 Variations in incomes across periods are ignored by this identi¬cation

process and by the subsequent aggregation step when the data are brought

together into an overall measure. The components approach to chronic

1

For example, longer exposure to poverty is associated with: increased stunting, dimin-

ished cognitive abilities, and increased behavioural problems for children (Brooks-Gunn and

Duncan, 1997); worse health status for adults (McDonough and Berglund, 2003); lower levels

of volunteerism when poor children become adults (Lichter, Shanahan, and Gardner, 1999);

and an increased probability of staying poor (Bane and Ellwood, 1986; Stevens, 1994). See

also the conceptual discussions of Yaqub (2003) and Clark and Hulme (2005).

2

This division is due to Yaqub (2000); see also McKay and Lawson (2002).

3

Examples of the components approach can be found in Duncan and Rodgers (1991),

Rodgers and Rodgers (1993), Jalan and Ravallion (1998), and Dercon and Calvo (2006), among

others.

59

James E. Foster

poverty measurement is not especially sensitive to the time a family spends in

poverty and, hence, may not be the best framework for incorporating duration

into poverty measurement.

A second approach to evaluating chronic poverty”called the spells

approach”focuses directly on the period-by-period experiences of poor fam-

ilies, and especially on the time spent in poverty. The identi¬cation of the

chronically poor typically relies on a duration cut-off as well as a poverty line:

Gaiha and Deolalikar (1993), for example, take the set of chronically poor

to be all families that have incomes below the poverty line in at least ¬ve

of the nine years of observations, hence have a duration cut-off of 5/9. As for

the aggregation step, most proponents of the spells approach use a very simple

index of chronic poverty based on the number of chronically poor. 4 While

the number (or percentage) of chronically poor may be an important statistic

to keep in mind, it is a rather crude indicator of overall chronic poverty. In

particular, it ignores the time a chronically poor family spends in poverty and

hence violates a ˜time monotonicity™ property that is especially relevant in

the present context. In addition, other key dimensions of poverty, namely its

depth and distribution, are utterly ignored by the index.

The present chapter adopts the general methodology of the spells approach.

Two distinct cut-offs are used for identifying the chronically poor”one in

income space (the usual poverty line z > 0) and another governing the

percentage of time in poverty (the duration line 0 < ™ ¤ 1). In other words, a

family is considered to be chronically poor if the percentage of time it spends

below the poverty line z is at least the duration cut-off ™. For the aggregation

step, this chapter presents a new class of chronic poverty measures based on

the P· family proposed by Foster, Greer, and Thorbecke (1984), appropriately

adjusted to account for the duration of poverty. All of the measures satisfy

time monotonicity and an array of basic axioms, while certain subfamilies

satisfy the multiperiod analogues of (income) monotonicity and the transfer

principle. Associated measures of transient poverty are de¬ned to account for

poverty that is shorter in duration. Each chronic poverty measure (and its

transient dual) satis¬es decomposability, thus allowing the consistent analysis

of chronic poverty by population subgroup. In particular, pro¬les of chronic

poverty can be constructed to understand the incidence, depth, and severity

of poverty in a way analogous to the standard static case.

The chapter proceeds as follows. Section 3.2 provides a brief overview of

poverty measurement in a static environment to help ground the discussion

of chronic poverty measurement. Section 3.3 introduces time into the analy-

sis. The identi¬cation and aggregation steps are speci¬ed and the new family

4

See for example The Chronic Poverty Report 2004“05, p. 9, which uses a simple headcount.

Duncan, Coe, and Hill (1984) and Gaiha and Deolalikar (1993) use the headcount ratio, or

the percentage of the population that is chronically poor.

60

A Class of Chronic Poverty Measures

of chronic poverty measures is de¬ned. Section 3.4 provides a brief application

of the technology to data from Argentina, while Section 3.5 concludes.

3.2. Traditional Poverty Measurement

Following Sen (1976), poverty measurement can be broken down into two

conceptually distinct steps: ¬rst, the identi¬cation step, which de¬nes the

criteria for determining who is poor and who is not; and, second, the aggrega-

tion step, by which the data on the poor are brought together into an overall

indicator of poverty. The identi¬cation step is typically accomplished by set-

ting a cut-off in income space called the poverty line and evaluating whether a

person™s resources are suf¬cient to achieve this level. There are several varieties

of poverty lines, each with its own information basis and method for updating

over time. Subjective poverty lines consider information from surveys that ask

participants how much it takes to get along. Relative poverty lines depend on

the current income standard in a given society: a common example sets the

poverty line at 50 per cent of the median income. Absolute poverty lines may

be purely arbitrary (such as the US$1 or US$2 per day lines used in World

Bank illustrations) or may be initially derived from consumption studies.

Note that in principle each type of line can be located at the low end or

the high end of conceivable cut-offs (e.g. a relative line at 1 per cent of the

median and an absolute line at US$15 per day); consequently, the use of an

absolute line does not identify a person as being ˜absolutely impoverished™.

Instead, the term ˜absolute™ typically refers to the fact that the poverty line

is to remain ¬xed during the time frame under consideration. In contrast, a

thoroughgoing relative (or subjective) approach will have a different poverty

line at each point in time as the income standards (or norms) change. 5 This

chapter assumes that an absolute poverty line has been selected and that it is

applicable at all time periods under consideration.

The aggregation step is typically accomplished by selecting a poverty index

(or measure). Each index is a method of combining the income data and the

poverty line into an overall indicator of poverty. Formally, it is a function

associating with each income distribution and poverty line a real number,

namely, the measured level of poverty. The simplest and most widely used

measure is the headcount ratio, which is the percentage of a given population

that is poor. It is sometimes helpful to view the headcount ratio as a speci¬c

population average; indeed, if every person identi¬ed as being poor is assigned

a value of ˜1™ while every person outside the set of the poor is assigned a

value of ˜0™, then the headcount ratio is simply the mean of the resulting ˜0“1™

vector.

5

One could also imagine alternative types of hybrid approaches to setting poverty lines

across space and time. See Foster and Sz©kely (2006).

61

James E. Foster

A second method of aggregation is given by the (per capita) poverty gap,

which is the aggregate amount by which poor incomes fall short of the

poverty line, measured in poverty line units, and averaged across the entire

population. It too can be seen as a population average, with those outside

the set of the poor being assigned a value of ˜0™, as before, and those inside

being represented by their normalized shortfall, or the difference between their

income and the poverty line, divided by the poverty line itself. In contrast to

the ˜all or nothing™ approach of the headcount ratio, the poverty gap uses the

normalized shortfall as a continuous measure of individual poverty and views

overall poverty as its average value across society. Consequently, it satis¬es a

standard monotonicity axiom for poverty measures, which requires poverty to

rise when the income of a poor person falls (ceteris paribus). The headcount

ratio does not.

A general method of aggregation suggested by Foster, Greer, and Thorbecke

(1984) proceeds as above, but ¬rst transforms the normalized shortfalls of the

poor by raising them to a non-negative power · to obtain the associated P·

measure. This approach actually includes both of the foregoing measures: P0

is the headcount ratio and P1 is the poverty gap measure. The squared gap mea-

sure P2 from this family takes the square of each normalized shortfall, which

has the effect of diminishing the relative importance of very small shortfalls

and augmenting the effect of larger shortfalls”and hence emphasizing the

conditions of the poorest poor in society. As a simple average of the squared

normalized shortfalls across the population, P2 satis¬es the transfer axiom,

which requires poverty to rise whenever a poor person transfers income to a

richer poor person. All the P· measures satisfy a range of basic axioms as well

as a property linking subgroup and overall poverty levels that has been used

extensively in the empirical literature: Decomposability requires overall poverty

to be the weighted average of subgroup poverty levels, where the weights are

the population shares of the respective subgroups. While there are several

other poverty measures in common use, this chapter will focus on the P· class

in general and the three measures P0 , P1 , and P2 , in particular, in developing

a new class of chronic poverty measures. 6

3.3. The Measurement of Chronic Poverty

A main premiss of chronic poverty evaluation is that poverty repeated over

time has a greater impact than poverty that does not recur. This section

discusses how poverty measurement can be altered to take into account the

6

Other measures can be found in Sen (1976), Clark, Hemming, and Ulph (1981),

Chakravarty (1983), for example; see also Foster and Sen (1997), Zheng (1997), and Foster

(2006).

62

A Class of Chronic Poverty Measures

additional dimension of time in poverty. The ¬rst part begins with some

important de¬nitions and notation.

3.3.1. Notation

The basic data are observations of an income (or consumption) variable for a

set {1, . . . ,N} of individuals at several points in time. 7 Let y = (yit ) denote the

matrix of (non-negative) income observations over time, where the typical

entry yit is the income of individual i = 1, 2, . . . ,N in period t = 1, 2, . . . , T. We

adopt the convention that y is a T — N matrix (having height T and length N),

so that each column vector yi lists individual i™s incomes over time, while each

row vector yt gives the distribution of income in period t. It will prove helpful

to use the notation |y| = È t yit to denote the sum of all the entries in a given

matrix, and to de¬ne an analogous notation for vectors (hence |yi | = t yit is

the sum of i™s incomes across all periods while |yt | = i yit is the total income

in period t). It is assumed that incomes have been appropriately transformed

to account for variations across time and household con¬gurations so that

a common poverty line z can be used to establish who is poor in each

period.

It is sometimes useful to express the data in terms of (normalized) shortfalls

rather than incomes. Let g be the associated matrix of normalized gaps, where

the typical element git is zero when the income of person i in period t is z

or higher, while git = (z ’ yit )/z otherwise. Clearly, g is a T — N matrix whose

entries are non-negative numbers less than or equal to one. When an entry

git is equal to zero, this indicates that the person™s income is at least as large

as the poverty line and hence is not in poverty; when an entry is positive,

this indicates that the person™s income falls below the line, with git being a

measure of the extent to which that person is poor. 8 We can similarly de¬ne

the matrix s of squared normalized shortfalls by squaring each entry of g; i.e.

the typical entry of s is sit =(git )2 .

Counting-based approaches to evaluating poverty ignore the extent of the

income gap and instead only take into account whether the gap is positive or

zero. It is therefore helpful to create another matrix h by replacing all positive

entries in g with the number ˜1™. Thus the typical entry hit of h is ˜0™ when the

income of person i in period t is not below z, and ˜1™ when yit is below z. One

statistic of interest in the present context is the duration of person i™s poverty,

or the fraction of time the person is observed to have an income below z.

Denote this by di and note that it can be obtained by summing the entries in

7

The income variable can be any single-dimensional, cardinally meaningful indicator of

well-being. In the present case, where per-period values are not transferable across time, this

may be more consistent with consumption than with income, per se.

8

In this chapter a person with an income of z is not poor; the alternative assumption (that

z itself is a poor income level) could be adopted with a slight change in notation.

63

James E. Foster

hi (the i-th column of h) and dividing by the number of periods; i.e. di = |hi |/T.

In essence the duration is analogous to a headcount ratio, but de¬ned for a

given person over time, not across different people within the same period of

time.

This chapter™s approach to chronic poverty will be based on the percentage

of time a person spends in poverty. Toward this end, it will be useful to derive

matrices from g (and also from s and h) that ignore persons whose duration

in poverty falls short of a given cut-off ™ ≥ 0. Let g(™) (and s(™) and h(™) ) be

the matrix obtained from g (respectively s and h) by replacing the i-th column

with a vector of zeros when di < ™. In other words, the typical entry of g(™),

namely git (™), is de¬ned by g it (™) = git for all i satisfying di ≥ ™ while git (™) = 0 for

all i having di < ™ (with the analogous de¬nition holding for s and h).

As the duration cut-off ™ rises from 0 to 1 the number of non-zero entries

in the associated matrix falls, re¬‚ecting the progressive censoring of data

from persons who are not meeting the poverty duration requirement. The

speci¬cation ™ = 0 would not alter the original matrices at all, so that g(0) = g,

s(0) = s, and h(0) = h. Every poverty observation would be included, regardless

of a person™s duration in poverty. At the other extreme, the cut-off ™ = 1

ensures that any person who was out of poverty for even a single observation

would have a column of zeros; in other words, g(1), s(1), and h(1) consider a

person who fell out of poverty for one period indistinguishable from a person

who was always out of poverty.

As in the static case, the measurement of chronic poverty can be divided

into an identi¬cation step and an aggregation step. There are many potential

strategies for identifying the chronically poor, but all have the effect of select-

ing a set Z of chronically poor persons from {1, . . . ,N}. The aggregation step

takes the set Z as given and associates with the income matrix y an overall

level K (y; Z) of chronic poverty. The resulting functional relationship K is

called an index, or measure, of chronic poverty.

3.3.2. Identifying the chronically poor

What can panel data reveal that cross-sectional observations cannot? By fol-

lowing the same persons over several periods, they can help discern whether

the poverty experienced by a person in a given period is an exceptional

circumstance or the usual state of affairs.

With panel data, there are several income observations linked to each

individual, and this in turn leads to a wide array of potential methods for

deciding when a person is chronically poor. One approach employed by Jalan

and Ravallion (1998) bases membership in Z on a single comparison between

the poverty line z and a composite indicator of the resources an individual

has available through time. The speci¬c income standard employed by Jalan

and Ravallion is Ï(yi ) = |yi |/T, the average or mean income over time; hence

64

A Class of Chronic Poverty Measures

their method identi¬es as chronically poor any person whose mean income is

below the poverty line. As noted above, this approach is not particularly sen-

sitive to the duration of poverty. Nonetheless, it may make good sense when

incomes are perfectly transferable across time and, accordingly, consumption

can be completely smoothed. Anyone with an average income below z would

in the best case be poor for every period; while a person with a mean of z

or above could be out of poverty in every period. However, the assumption

of perfect transferability may be dif¬cult to sustain, particularly for poorer

individuals; and if per-period incomes are even slightly less than perfectly

substitutable, this procedure could easily misidentify persons. 9

At the other extreme is the ˜spells™ approach to identifying the chronically

poor, which bases membership in Z upon the frequency with which one™s

income falls below the poverty line. So, for instance, one might require a

person to be poor 50 per cent of the time or more, before identifying the

person as chronically poor. A higher cut-off (say 70 per cent of the time or

more) would probably lead to a smaller set of persons being identi¬ed as

chronically poor, while a lower cut-off (such as 30 per cent) would probably

expand the set. Note, though, that this approach also contains within it an

implicit assumption”that there is no possibility of transferring income across

periods. Indeed, it is not entirely clear why a person with a tremendous

amount of income (or expenditure) in period one, who is just barely below

the poverty line in the remaining periods, would be considered chronically

poor, as may be required under this approach. Nonetheless, if (1) the poverty

line is considered to be a meaningful dividing line between poor and non-

poor and (2) the observed data on income (or consumption) in each period

faithfully re¬‚ects the constraint facing the person in the given period, then

identifying chronic poverty with suf¬cient time in poverty makes intuitive

sense.

This chapter uses a dual cut-off ˜spells™ approach to identifying the chron-

ically poor: The ¬rst cut-off is the poverty line z > 0 used in determining

whether a person is poor in a given period; the second is the duration line

™ (with 0 < ™ ≥ 1) that speci¬es the minimum fraction of time that must

be spent in poverty in order for a person to be chronically poor. Given the

income matrix y and the poverty line z, the matrix h depicts the poverty

spells for each person, and this in turn yields di , the fraction of time that

person i is observed to have an income below z. Then, given ™, the set of

chronically poor persons is de¬ned to be Z = {i : di ≥ ™}, or the set of all persons

in poverty at least ™ share of the time. Since Z depends on z and ™, the poverty

index can be written as a function K (y; z, ™) of the income matrix and the pair

of parametric cut-offs. The next section constructs several useful functional

forms for K (y; z, ™).

9

The case of imperfect substitutability is considered by Foster and Santos (2006).

65

James E. Foster

3.3.3. Chronic poverty and aggregation

The ¬rst question that is likely to arise in discussions of chronic poverty is:

How many people in a given population are chronically poor? The answer

comes in the form of the headcount Q(y; z, ™) de¬ned as the number of per-

sons in Z. This statistic is often highlighted in order to convey meaningful

information about the magnitude of the problem; however, when making

comparisons, especially across regions having different population sizes, the

headcount ratio H(y; z, ™) = Q(y; z, ™)/N is commonly used, where N is the

population size of y. The measure H focuses only on the frequency of chronic

poverty in the population and ignores all other aspects of the problem, such

as the average time the chronically poor are in poverty, or the average size of

their normalized shortfalls.

An example will help illustrate these concepts. Consider the income matrix

⎡ ¤

3 9 7 10

⎢7 3 4 8⎥

⎢ ⎥

y=⎢ ⎥

⎣ 9 4 2 12 ¦

832 9

where the poverty line is z = 5 and the duration line is ™ = 0.70. The associated

matrices of normalized poverty gaps, g, and of poverty spells, h, are given by

⎡ ¤

⎡ ¤

1000

0.4 0 0 0

⎢0 1 1 0⎥

⎢0 0.4 0.2 0 ⎥ ⎢ ⎥

⎢ ⎥

h=⎢ ⎥

g=⎢ ⎥

⎣0 1 1 0¦

⎣0 0.2 0.6 0 ¦

0110

0 0.4 0.6 0

Summing the entries of h vertically and dividing by T = 4 yields the dura-

tion vector d = (d1 , d2 , d3 , d4 ) = (0.25, 0.75, 0.75, 0) and hence we see that

Q(y; z, ™) = 2 and so H(y; z, ™) = 0.5; in this population, half of the persons

(namely numbers 2 and 3) are chronically poor.

Now consider a thought experiment in which person 3 in the above

example receives an income of 3 rather than 7 in period 1, and hence the

normalized gap in that period becomes 0.40 and the entry in h becomes one.

Then person 3 would still be chronically poor, but would have a poverty

duration of d3 = 1.0 rather than 0.75. What would happen to H? Clearly, it

would be unchanged even though a chronically poor person has experienced

an increment in the time spent in poverty. In other words, H violates an

intuitive time monotonicity axiom: if the income in a given period falls for a

chronically poor person in such a way that the duration in poverty rises, then

the level of chronic poverty should increase. 10 It can be argued that, while

H conveys meaningful information about one aspect of chronic poverty, and

10

See Foster (2007) for a precise statement of this axiom.

66

A Class of Chronic Poverty Measures

hence is a useful ˜partial index™, it is a bit too crude to be used as an overall

measure. 11

There is a very direct way of transforming H into an index that is sensitive

to changes in the duration of poverty. Consider the matrix h(™) de¬ned above,

which leaves a column unchanged if the person is chronically poor, and

otherwise replaces the column with zeros. Let di (™) = |hi (™)|/T denote the

associated duration level of person i, so that di (™) = di for each chronically

poor person and di (™) = 0 otherwise. Then the average duration among the

chronically poor is given by D(™) = (d1 (™) + · · · + dN (™) )/Q. This is a second par-

tial index that conveys relevant information about chronic poverty, namely,

the fraction of time the average chronically poor person spends in poverty.

Combining the two partial measures yields an overall index that is sensitive

to increments in the time a chronically poor person spends in poverty as

well as to increases in the prevalence of chronic poverty in the population.

De¬ne the duration-adjusted headcount ratio K 0 = H D to be the product of

the original headcount ratio H and the average duration D or, equivalently,

K 0 = (d1 (™) + · · · + dN (™) )/N.

K 0 offers a different interpretation of our thought experiment from the one

provided by H. Return to the original situation in which person 3 is not poor

in period 1. For ™ = 0.70, the relevant h(™) matrix is given by

⎡ ¤

0000

⎢0 1 1 0⎥

⎢ ⎥

h(™) = ⎢ ⎥

⎣0 1 1 0¦

0110

and the respective column averages are given by d1 (™) = d4 (™) = 0 and d2 (™) =

d3 (™) = 0.75. The headcount ratio is H = 0.50 while the mean duration is

D = 0.75 so that the duration-adjusted headcount ratio K 0 is initially 0.375.

Now when person 3™s income in period 1 becomes 3 rather than 7, the fraction

of time spent in poverty rises to 1 for that person, while the mean duration

among all chronically poor rises to 0.875. Consequently, even though H is

unchanged, K 0 rises to about 0.438, with this higher overall level of chronic

poverty being due to person 3™s increased time in poverty.

The above example also shows that K 0 = Ï(h(™) ) = |h(™)|/(T N); in words, K 0

is the mean of the entries in matrix h(™) or, equivalently, the total number

of periods in poverty experienced by the chronically poor, as given by |h(™)|,

divided by the total number of possible periods across all people, or TN. In

the above example, it is easy to see that the mean of the sixteen entries in

h(™) is 6/16 = 0.375, and hence this is the duration-adjusted headcount index

K 0 . Notice that if a chronically poor person were to have an additional period

in poverty, this would raise an entry in the matrix h(™) from zero to one,

11

See the discussion of partial indices in Foster and Sen (1997).

67

James E. Foster

thereby causing the average value K 0 to rise, as noted above. In other words,

K 0 satis¬es the time monotonicity axiom.

There is no doubt that K 0 is less crude than H as an overall measure of

chronic poverty. However, it too may not fully re¬‚ect the actual conditions of

the chronically poor. The matrix h(™), upon which K 0 is based, is unaffected by

changes in incomes (or normalized gaps) that preserve the signs of the entries

of g(™), even if the magnitudes of the entries in g(™) change dramatically.

For example, if the income of person 3 in period 2 were decreased from 4

2

to 2, so that the normalized gap g 3 rose from 0.2 to 0.6, the corresponding

entry in h would obviously be unchanged (namely, h2 = 1), and hence K 0

3

would remain the same. So a chronically poor person is now much poorer in

period 2, and yet this fact goes unnoticed by the duration-adjusted headcount

measure. This is a violation of the (income) monotonicity axiom, which states

that if a chronically poor person™s income is below the poverty line in a given

period, lowering that income further should increase the measured level of

chronic poverty. 12

What is missing from this measure of chronic poverty is information on

the magnitudes of the normalized gaps. Consider the matrix g(™) de¬ned above

whose non-zero entries are the normalized gaps of the chronically poor. The

number of non-zero entries in g(™)”and hence h(™)”is |h(™)|, while the sum of

the non-zero entries in g(™) is |g(™)|. The ratio |g(™)|/|h(™)| indicates the average

size of the normalized gaps across all periods in which the chronically poor

are in poverty. The resulting average gap G(™) = |g(™)|/|h(™)| provides exactly the

type of information that would usefully supplement the adjusted headcount

ratio. De¬ne the duration-adjusted poverty gap index K 1 = K 0 G to be the product

of the duration-adjusted headcount ratio K 0 and the average gap G or, equiv-

alently, K 1 = HDG, the product of the three partial indices that respectively

measure the prevalence, duration, and depth of chronic poverty.

This chronic poverty index provides a third perspective from which to view

our numerical example. Given the duration cut-off ™ = 0.70, the matrix g(™)

associated with the original situation in which person 3 has an income of 4

in period 2 is given by

⎡ ¤

00 0 0

⎢ 0 0.4 0.2 0 ⎥

⎢ ⎥

g(™) = ⎢ ⎥

⎣ 0 0.2 0.6 0 ¦

0 0.4 0.6 0

The respective sum of entries is |g(™)| = 2.4 while the number of periods in

poverty is |h(™)| = 6, and hence the average gap is G = 0.40. Given H = 0.50

and D = 0.75 from before, the resulting level of the duration-adjusted poverty

gap measure is K 1 = 0.15. Now suppose that the period 2 income of person

12

See Foster (2007) for a rigorous statement of this axiom.

68

A Class of Chronic Poverty Measures

3 falls from 4 to 2. Clearly H and D are unaffected by this change, and so

K 0 would likewise be unchanged. However, the average gap G would rise to

about 0.47, and hence the duration-adjusted gap would now be K 1 = 0.175,

re¬‚ecting the worsened circumstances for person 3. K 1 rises as a result of the

income decrement since it satis¬es the monotonicity axiom.

The duration-adjusted gap measure has a simple expression as the mean of

the entries of the matrix g(™), so that K 1 = Ï(g(™) ) = |g(™)|/(T N). In words, K 1

is the sum of the normalized shortfalls experienced by the chronically poor,

or |g(™)|, divided by T N, which is the maximum value this sum can take. 13

While K 1 is sensitive to magnitude of the income shortfalls of the chroni-

cally poor, the speci¬c way the gaps are combined ensures that a given sized

income decrement has the same effect on overall poverty whether the gap is

large or small. One could argue that a loss in income would have a greater

effect the larger the gap, in which case the square of the normalized gaps,

rather than the gaps themselves, could be used. For example, suppose that the

initial level of income is 4 and the poverty line is 5, so that the normalized

gap is 0.20 and the squared (normalized) gap is 0.04. Decreasing the income

by one unit will increase the squared gap to 0.16, an increase of 0.12. Now

suppose that the initial level of income is 2, so that the normalized gap is 0.60

and the squared gap is 0.36. The unit decrement would raise the squared gap

to 0.64, which represents a much larger increase of 0.28. Using squared gaps,

rather than the gaps themselves, places greater weight on larger shortfalls.

Consider the matrix s(™) whose non-zero entries are the squared normal-

ized gaps of the chronically poor. The number of non-zero entries is |h(™)|

so that the average squared gap over these periods of poverty is given by

S(™) = |s(™)|/|h(™)|. If this partial index is used instead of G(™) to supplement

the duration-adjusted headcount ratio, the resulting chronic poverty index

would place greater weight on larger shortfalls. The resulting duration-adjusted

FGT measure K 2 = K 0 S is a chronic poverty analogue of the usual FGT index

P2 (just as K 0 and K 1 respectively correspond to P0 and P1 of the same

class). K 2 has a straightforward expression as the product of partial indices

K 2 = HDS and as the mean of the entries of the matrix s(™) of squared gaps

K 2 = Ï(s(™) ) = |s(™)|/(TN). It is the sum of the squared (normalized) gaps of the

chronically poor, divided by the maximum value this sum can take.

Referring once again to the numerical example, the matrix of squared gaps

is given by

⎡ ¤

00 0 0

⎢ 0 0.16 0.04 0 ⎥

⎢ ⎥

s(™) = ⎢ ⎥

⎣ 0 0.04 0.36 0 ¦

0 0.16 0.36 0

TN is the value of |g(™)| that would arise in the extreme case where all incomes were 0.

13

69

James E. Foster

and hence K 2 = Ï(s(™) ) =(1.12)/16 = 0.07. Now recall that the income of

3

person 2 in period 3 is y2 = 4, so that a unit decrement in income causes

the squared normalized gap to rise from 0.04 to 0.16, and raising K 2 by

3

about 0.008. In contrast, a unit decrement from y3 = 3 raises the squared

normalized gap from 0.16 to 0.36, and lifting K 2 by about 0.013. With K 2 ,

the impact of a unit decrement is larger for lower incomes than for higher

incomes.

Analogous reasoning demonstrates that K 2 is sensitive to the distribution

of income among the poor. Let i and j be two chronically poor persons with

income vectors yi and y j . Suppose that their income vectors are replaced with

yi = Îyi + (1 ’ Î)y j and y j = (1 ’ Î)yi + Îy j , respectively, for some Î µ (0,1/2].

This represents a uniform ˜smoothing™ of the incomes of persons i and j,

with the value Î = 1/2 yielding the limiting case where yi = y j = (yi + y j )/2

is a simple average of the two vectors. A transformation of this type is a

multidimensional analogue of a progressive transfer (among the poor) and

it is easy to show that K 2 will not rise; indeed, if their associate normalized

gap distributions gi and g j were not initially identical, K 2 would fall as result

of the progressive transfer. 14 In the numerical example, if the income vectors

of persons 2 and 3 are replaced by the average vector (with Î = 1/2), then

K 2 falls from 0.07 to about 0.54. In contrast, this smoothing of incomes

affects neither the average duration of poverty, nor the average shortfall

among the chronically poor, and hence K 0 and K 1 are entirely unaffected. The

property requiring such a transformation to lower chronic poverty is called

the transfer axiom. 15 The measure K 2 satis¬es this axiom while K 0 and K 1 both

violate it.

The general approach to constructing chronic poverty measures can be

applied to obtain analogues of all of the indices in the FGT class. For any · ≥

0 let g · (™) be the matrix whose entries are the · powers of normalized gaps for

the chronically poor (and zeros for those who are not chronically poor). 16 The

duration-adjusted P· measures are the general class of chronic poverty measures

de¬ned by K · (y; z, ™) = Ï(g · (™) ) = |g · (™)|/(TN); in other words, K · is the sum

of the · power of the (normalized) gaps of the chronically poor, divided by

the maximum value that this sum could take. It can be shown that time

monotonicity is satis¬ed by all K · ; monotonicity is satis¬ed by K · for · > 0;

and the transfer axiom is satis¬ed by K · for · >1.

The K · measures satisfy a wide range of general properties for chronic

poverty measures, some of which are direct analogues of the static poverty

14

See Kolm (1977) and Tsui (2002). The condition g i and g j rules out the case mentioned

by Tsui (2002) where the two chronically poor persons are poor in the same periods and have

the same incomes below the poverty line.

15

See Foster (2007) for a rigorous de¬nition of this axiom.

16

For · = 0, the entries of the matrix are more precisely de¬ned as the limit of the entries

of g · (™) as · tends to 0.

70

A Class of Chronic Poverty Measures

axioms and others more explicitly account for the time element in chronic

poverty. 17 One axiom that deserves special mention due to its importance in

empirical work is the following:

Decomposability. For any distributions x and y we have

N(x) N(y)

K (x, y; z,™) = K (x; z, ™) + K (y; z, ™).

N(x, y) N(x, y)

According to this property, when a distribution is broken down into two sub-

populations, the overall chronic poverty level can be expressed as a weighted

average of subgroup chronic poverty levels, with the weights being the respec-

tive subgroup population shares. 18 All the measures in the K · class satisfy

decomposability and hence are well suited for the analysis of chronic poverty

by population subgroup.

For each measure of chronic poverty K · , a corresponding measure of tran-

sient poverty can be de¬ned to account for spells of poverty among those

who are not chronically poor. Applying K · to a cut-off of ™ = 0 removes all

the restrictions concerning the duration of poverty. The resulting quantity

K · (y; z, 0) = Ï(g· ) takes into account every spell of poverty for all persons,

including those who are not chronically poor, and, in fact, is the overall (or

average) level of measured poverty (using P· ) across the T periods. In con-

trast, K · (y;z,™) limits consideration to the shortfalls of the chronically poor,

and hence the difference R· (y; z, ™) = K · (y; z, 0) ’K · (y; z, ™) is an intuitive

measure of transient poverty. The shares of overall poverty that are chronic

K · (y; z, ™)/K · (y; z, 0) and transient R· (y; z, ™)/K · (y; z, 0) are helpful tools for

understanding the nature of poverty over time, and are used in the empirical

application below.

3.4. An Empirical Illustration

In this section, the new chronic poverty measures are applied to panel data

from Argentina™s Encuesta Permanente de Hogares carried out by Instituto

Nacional de Estadísticas y Censos (INDEC), covering 2,409 households during

the four waves of October 2001, May 2002, October 2002, and May 2003. The

income variable used is equivalent household income, calculated by dividing

total household income in each period by the number of equivalent adults

(using the equivalent adult scale provided by INDEC). 19 The Instituto also

provides a separate poverty line for each region and each period in order to

17

The ¬rst group of axioms includes anonymity, replication invariance, focus, and subgroup

consistency; the second includes time anonymity and time focus. See Foster (2007).

18

This expression can be generalized to any number of subgroups by repeated application

of the two-subgroup formula.

19

In periods where an income is missing or zero for a given household, the methodology

of Little and Su (1989) is followed, which calculates an imputed income using the household™s

incomes at other dates and other household incomes at the same date. In the few cases where

71

James E. Foster

Table 3.1. Chronic poverty in Argentina: estimated levels for various measures

and durations

Measure

H K0 K1 K2

™ = 0.25 0.61 0.44 0.21 0.124

™ = 0.50 0.50 0.42 0.20 0.122

™ = 0.75 0.40 0.37 0.19 0.116

™ = 1.00 0.27 0.27 0.15 0.096

% Chronica 66.3 83.1 90.7 93.5

% Transient 33.7 16.9 9.3 6.5

a

The duration cut-off is ™ = 0.75. Since there are four periods, ™ = 0.25 yields the same values

. .

as overall poverty, and Percentage Chronic can found by dividing the third row by the ¬rst row.

Percentage Transient is 100 minus Percentage Chronic.

capture spatial variations in the cost of living as well as in¬‚ation over time.

Normalized gaps for a household are found by subtracting the equivalent

income from the appropriate poverty line and dividing this difference by the

same line. Since there are T = 4 periods, there are four relevant duration cut-

offs ™, namely, 0.25, 0.50, 0.75, 1.00. Table 3.1 provides the resulting levels of

chronic poverty for each of the measures H, K 0 , K 1 , and K 2 , at each of the

four duration cut-offs.

Notice that for each index, the measured level of chronic poverty rises as the

duration requirement ™ falls. For ™ = 1, the headcount and duration-adjusted

headcount have the same value since the average duration in this special case

is precisely 1. In general, for ¬xed ™ the value of H is higher than that of K 0 ,

which in turn is higher than K 1 , and so forth, re¬‚ecting the mathematical

properties of the measures. However, it is important to remember that actual

poverty comparisons should only be made using the same poverty measure

and with the same duration cut-off.

The ¬rst row provides the chronic poverty level when the duration in

poverty is at least 0.25, and for K · this is clearly the same as the level when

the minimum duration is 0. This latter level K · (y; z, 0) is precisely the static

poverty level that would arise if the data from all periods were merged into

a single distribution and evaluated by P· , or equivalently, t P· (yt ; z)/T, the

average static poverty level across all periods. Now given a minimum duration

of ™ = 0.75, the difference between this overall poverty level K · (y; z, 0) and the

chronic poverty level K · (y; z, ™) is the level of transient poverty, R· (y; z, ™) as

de¬ned above. 20 The ¬nal two rows provide the percentage of overall poverty

due to chronic poverty and transient poverty respectively for ™ = 0.75 given

the household reports zero income in all four periods, an income equal to the lowest social

welfare transfer was assumed.

20

For H, overall poverty is the limit of H(y; z, ™) as ™ tends to zero; this also equals the value

at ™ = 0.25.

72

A Class of Chronic Poverty Measures

Table 3.2. Chronic poverty pro¬le for Argentina

Measurea

Pop. share (%) K0 % contrib. K1 % contrib. K2 % contrib.

GBA 12 0.18 8.3 0.10 8.0 0.065 8.1

NE 15 0.44 25.2 0.26 26.3 0.174 27.1

NW 22 0.34 28.4 0.19 28.1 0.120 27.4

C 28 0.22 23.5 0.13 24.1 0.085 24.6

MW 11 0.24 10.0 0.13 9.6 0.080 9.1

S 12 0.10 4.6 0.05 4.0 0.029 3.6

Total 100 0.27 100.0 0.15 100.0 0.096 100.0

a

Duration cut-off is ™ = 1.00. Percentages may not sum to 100% due to rounding errors.

each measure. It is interesting to note that as the poverty measure changes

from H to K 0 to K 1 to K 2 , the share of chronic poverty becomes larger

while the share of transient poverty falls. For K 2 the chronic poverty share

is 93.5 per cent, suggesting that the transient poverty spells generally do not

involve large shortfalls.

Table 3.2 provides a pro¬le of chronic poverty in each of the six regions

of Argentina, namely, Greater Buenos Aires (GBA), the North-East (NE), the

North-West (NW), the Center of the country (C), the Midwest (MW), and the

South (S). In this example, chronically poor means poor in all four periods;

hence the duration cut-off is ™ = 1. The ¬rst column in the table gives the pop-

ulation shares of the six regions. The second, fourth, and sixth columns pro-

vide the regional chronic poverty levels for K 0 , K 1 , and K 2 , respectively; while

the third, ¬fth, and seventh columns give the percentage contribution of each

region to total poverty (or the population share times the regional poverty

level over the total poverty). Notice that the North-East has only 15 per cent

of the population, yet accounts for at least 25.2 per cent of the chronic poverty

in Argentina; in contrast, the South has 12 per cent of the total population,

but only contributes 4.6 per cent or less to total chronic poverty.

3.5. Conclusions

This chapter has presented a new family K · of chronic poverty measures based

on the P· measures of Foster, Greer, and Thorbecke (1984). Each measure has

an intuitive interpretation as a ˜duration-adjusted P· measure™ and can be

readily calculated as the mean of a particular matrix. All the measures satisfy

a series of general axioms for chronic poverty measures, and an additional

set of axioms that are applicable to measures based on a spells approach

to chronic poverty. Within the class, there is a range of measures satisfying

a monotonicity axiom, and a smaller subset satisfying a transfer axiom.

73

James E. Foster

In particular, K 2 , the duration-adjusted analogue of the usual P2 measure,

satis¬es all of the properties discussed in this chapter. The usefulness of the

class of chronic poverty measures has been illustrated using panel data from

Argentina.

One powerful criticism of the general framework for evaluation used here is

that, being limited to a single income variable, it cannot utilize data on other

dimensions of relevance to poverty and well-being. The approach is indeed

restrictive, and when panel data containing information on other capabilities

become more widely available, multidimensional measures of chronic poverty

will need to be developed. Of course, there remain serious dif¬culties in

formulating effective multidimensional poverty measures, even in the sta-

tic context. The identi¬cation step for multidimensional poverty depends

crucially on assumptions about substitutability across different dimensions;

and the aggregation step has seemingly endless possibilities for bringing

the various dimensions of deprivation into a single coherent index. The

problem of measuring multidimensional chronic poverty is not likely to be

solved anytime soon.

The measurement approach presented in this chapter is based on a very sim-

ple treatment of time in poverty: an earlier period in poverty is given the same

weight as a later period in poverty. Indeed, such a position could be justi¬ed

using the traditional ˜no discounting™ argument of Ramsey (1928). However,

other plausible alternatives exist. For example, one might argue that greater

weight should be placed on income received in earlier periods, as is typically

done by discounting (see Rodgers and Rodgers, 1993, or Dercon and Calvo,

2006). This could be justi¬ed ex ante where there may be greater perceived

or actual value from receiving income earlier. However, when viewed from an

ex post perspective, there may also be good reason to view earlier incomes as

having less weight (see, for example, the discussion in Ray and Wang, 2001).

An additional problem with discounting (one way or the other) is deciding

what to discount: the income received by the chronically poor person, the

utility level, or some function of the gap. And if the discounting procedure

delivers a different ordering depending on the base period for evaluation, this

could certainly make the procedure less attractive.

There are other aspects of the above approach that might be altered. Some

have argued that continuous spells of poverty should have larger weight in the

evaluation of chronic poverty. As noted by Mckay and Lawson (2002), there

are signi¬cant data problems from trying to implement this using panel data.

Another perspective might consider placing greater weight on observations

from a chronically poor person who is in poverty longer. This could indeed be

done either via a new functional form or through dominance orderings over

time, but this will have to await future work.

74

A Class of Chronic Poverty Measures

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76

4

Measuring Chronic Non-Income

Poverty—

Isabel Günther and Stephan Klasen

4.1. Introduction

In recent years, the research agenda on poverty in developing countries has

moved beyond static assessments of poverty levels to consider dynamic tra-

jectories of well-being over time. The main reason for this shift in emphasis

was the recognition that there is considerable mobility of well-being over

time and that only a share of the poor are affected by persistent (or chronic)

poverty, while a much larger share of the total population experiences tran-

sient poverty, or vulnerability to poverty.

Since the two groups were found to be quite different in terms of their

characteristics and in terms of their needs regarding policy interventions, the

research community has developed two largely distinct research agendas, one

focusing on chronic poverty, the other focusing on vulnerability to poverty.

The research agendas complement one another, with chronic poverty focus-

ing on poverty traps and poverty persistence and vulnerability focusing on

risks and shocks and poverty dynamics.

The distinction between chronic and transient poverty is usually closely

linked to conceptualizing poverty in the monetary dimension. This is largely

related to the fact that the stochastic nature of the income-generating process

is well recognized in economics for decades, going back to Friedman™s Perma-

nent Income Hypothesis, which already made a distinction between perma-

nent and transitory incomes (Friedman, 1957). In line with that hypothesis,

consumption is used as the preferred welfare indicator in many applications

in developing countries as it is believed to be a better re¬‚ection of long-term

—

We would like to thank Bob Baulch, Stephan Dercon, Michael Grimm, David Hulme,

Stephen Jenkins, John Mickleright, an anonymous referee, and participants at a workshop in

Manchester for very useful comments on a ¬rst draft of this chapter.

77

Isabel Günther and Stephan Klasen

or permanent incomes. 1 In this sense, low consumption (i.e. consumption

below a poverty line) is seen as a re¬‚ection of a chronic inability to generate

suf¬cient incomes to leave poverty, even though households might temporar-

ily escape income poverty.

But empirically it has been shown that in developing countries also house-

holds™ consumption ¬‚uctuates greatly, in fact often not much less than

income. This could be for three reasons. First, households, particularly poor

households, are not able to smooth their consumption due to a lack of assets

and access to credit and/or insurance markets (e.g. Townsend, 1995; Deaton,

1997). Second, ˜permanent™ incomes of households change as a result of per-

manent shocks affecting the lifetime earning paths of individuals, thus forcing

households to re-optimize their consumption decisions. Last, consumption

(and/or incomes) is measured with error and thus much of the ¬‚uctuation is

spurious and related to these errors. 2

To ¬gure out which households are facing permanently low consumption,

i.e. are chronically poor, and which households are ˜only™ transitory poor and

which households (currently non-poor) are facing a high risk of becoming

poor is thus a very important and at the same time quite dif¬cult task and it

is not surprising that a large literature has dedicated itself to this subject. And

with the help of an increasing number of panel data in developing countries,

dynamic assessments of consumption, i.e. an analysis of chronic poverty as

well as vulnerability to poverty, have indeed become more feasible in an

increasing number of countries, thus underpinning the analysis of poverty

dynamics.

At the same time, this exclusive emphasis on incomes in the assessment

of chronic poverty and vulnerability has clear limitations and shortcomings

(see also Hulme and McKay, 2005), as it is well recognized that income (or

consumption) is an inadequate indicator of well-being. If we conceptualize

well-being from a capability perspective, income is but one (and for some

capabilities a rather poor) means to generate capabilities such as the ability

to be healthy, well educated, integrated, clothed, housed, and the like (see

Sen, 1995, 1999; Klasen, 2000); nor do equal incomes translate into equal

capabilities for different individuals, due to the heterogeneity of people in

translating incomes into well-being. It is therefore preferable to study well-

being outcomes directly (e.g. capabilities or functionings; see Klasen, 2000 3 )

1

There are other reasons to prefer consumption to incomes as a welfare measure in

developing countries. See Deaton (1997) and Deaton and Zaidi (2002).

2

This is a dif¬cult issue to sort out with the type of panel data available for developing

countries which typically have only two or three waves and thus do not allow the applica-

tion of common methods to control for measurement error (such as instrumental variable

techniques).

3

In principle, it is preferable to study capabilities to understand the choices people have

at their disposal. In practice, we usually can only observe functionings and thus most studies

are analysing functionings instead of capabilities (e.g. Klasen, 2000).

78

Measuring Chronic Non-Income Poverty

rather than study a speci¬c well-being input. However, there have been few

attempts to integrate the insights from the static analysis of non-income

dimensions of well-being into a dynamic setting and thus investigate chronic

poverty and vulnerability from a non-income perspective. In addition, apart

from the conceptual advantage of studying chronic poverty from a non-

income perspective, there are several advantages (but also limitations) from

a measurement perspective to studying non-income chronic poverty, which

we discuss in more detail below.

The purpose of this chapter is to try to conceptualize chronic poverty

and hence also poverty dynamics from a non-income perspective and then

illustrate ways to explore this topic empirically. Section 4.2 discusses the

potentials as well as limitations of conceptualizing chronic poverty in a non-

income perspective. Section 4.3 presents a ¬rst approach to empirically mea-

sure chronic non-income poverty, focusing on critical functionings related

to health and education, using a panel survey of Vietnam from 1992/3 and

1997/8. Section 4.4 shows the results of this application. Section 4.5 concludes

with highlighting open issues and suggestions for further research.

4.2. Conceptualizing Chronic Non-Income Poverty

It is clear that in principle it should be useful to study chronic poverty in

non-income dimensions (using for example applications of Sen™s capability

approach) as it would allow us to track well-being outcomes rather than simply

track an important well-being input (income) over time. Thus it would allow

us to measure well-being itself rather than only a proxy of it. The same

theoretical reasoning to prefer non-income to income indicators to measure

well-being as in a static framework certainly applies in a dynamic well-being

framework (see e.g. Sen, 1985). In addition, there are some speci¬c advan-

tages (and limitations) of studying poverty using non-income indicators that

emerge particularly in a dynamic poverty framework.

4.2.1. Potentials

Analysing non-income poverty dynamics would ¬rst of all allow an assess-

ment of the relationship between income and non-income chronic and

transitory poverty. Identifying those households where the two approaches

converge would identify those households who are chronically poor from a

multidimensional perspective and thus possibly most deprived and arguably

most deserving of support. This would enrich our assessment of dynamic well-

being. Conversely, where the two approaches fail to converge in identifying

the chronic poor, we would learn more about the dynamic relationship

between income and non-income poverty. This is directly interesting for

79

Isabel Günther and Stephan Klasen

policy purposes as policy makers are interested in reducing income and non-

income poverty and thus knowing the temporal relationship between the

two, e.g. whether improvements in income will eventually improve health

outcomes (but only with a lag), or vice versa, is critical.

The measurement of non-income poverty dynamics might also shed some

new light on the causes of the less than perfect correlation between income

and non-income dimensions of poverty in a static framework (see e.g. Klasen,

2000). In particular, the lack of correlation at one point in time might be

related more to different dynamics of the two well-being approaches, rather

than the lack of a contemporaneous causal relation between the two. More

precisely, for example in a two-wave panel, static assessments of poverty

in both periods could yield the same result regardless of whether income

and non-income dimensions are used. However, the two (income and non-

income) approaches could also agree in the static assessment of poverty in

the ¬rst period, but differ in the dynamics between the ¬rst and second

periods, suggesting that different drivers affect these dynamics. Similarly, the

two approaches could agree in the static assessment of poverty in the second

period, but differ in the dynamics, and thus would not agree in the static

assessment of poverty in the ¬rst period. Last, the two approaches might also

disagree on classifying households in both periods but agree on the dynam-

ics over time. Thus analysing income and non-income poverty dynamics

simultaneously we are able to separate static and dynamic disagreements in

identifying the poor. 4 If we only examined the two periods separately, we

would either ¬nd a lack of overlap in the ¬rst period or a lack of overlap

in the second period. But we would not be able to tell whether this is due

to different dynamics between two periods or whether there is a permanent

disagreement between the two approaches to identifying the poor.

However, even if it turned out that chronic income and non-income

poverty dynamics are highly correlated, there could still be practical advan-

tages focusing on the measurement of non-income poverty, as many indi-

cators of non-income deprivation (e.g. education or housing) are easier to

measure and less prone to measurement error than income (or consumption)

measures. 5 In fact, at times it may be useful to use non-income measures

of well-being as instruments to correct poorly measured incomes (and or

consumption).

A second measurement advantage is that information on past dynamics

of non-income well-being are often easier to get and more reliable than

information on past income series”even when using cross-sectional surveys.

For example, it is easier to get reliable information about the educational

4

If we had more waves, we could also say more about the temporal relationship between

the two variables by explicitly examining leads and lags.

5

See, for example, Zeller et al. (2006) for an example of a short-cut approach to poverty

measurement using non-income indicators.

80

Measuring Chronic Non-Income Poverty

history of a person than that person™s income history. Moreover, some current

non-income indicators can already provide some information about historical

trends in access to critical functionings. For example, the height of an adult

re¬‚ects past nutritional status and the current grade enrolled for a child

at a certain age reveals important aspects of that child™s past educational

history.

In addition, many capabilities/functionings (e.g. education and health) can

be measured at the individual level while income/consumption poverty can

only be assessed at the household level, due to the presence of household-

speci¬c public goods which are impossible to attribute to individual members