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Measuring Poverty and Wellbeing in Developing Countries$

Channing Arndt and Finn Tarp

Print publication date: 2016

Print ISBN-13: 9780198744801

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198744801.001.0001

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Absolute Poverty Lines

Absolute Poverty Lines

(p.10) 2 Absolute Poverty Lines
Measuring Poverty and Wellbeing in Developing Countries

Channing Arndt

Kristi Mahrt

Finn Tarp

Oxford University Press

Abstract and Keywords

Private consumption capabilities form only one facet of comprehensive living standards assessments, but they are an important facet whose measurement should be done well. Measurement is complex due to a multitude of methodological choices, which often interact with imperfect data and a desire for comparability through time. This chapter outlines ideas underpinning these choices with particular attention to the tensions between consistency and specificity. It also highlights a series of limitations associated with typical cost of basic needs approaches. Finally, it reaffirms that a ‘sensibly eclectic’ approach, employing multiple methods, is the best available mode for addressing these limitations. A first fundamental choice is whether to estimate an absolute poverty line at all. Consumption-based poverty metrics provide only a partial view into the welfare of individuals or households, which may or may not accord with other important facets of welfare.

Keywords:   poverty measurement, poverty line estimation, utility consistency, cost of basic needs, consumption

2.1 Introduction

A voluminous literature exists on the estimation of absolute poverty lines. In summing up this literature, one cannot do better than Martin Ravallion’s recent book The Economics of Poverty: History, Measurement, and Policy (Ravallion 2016). This book devotes nearly 150 pages to the issues associated with measuring welfare in general and the estimation of poverty lines in particular. It provides a succinct and accessible overview of what is known and what is not known in these broad domains, often with particular focus on measuring welfare in developing countries. There is little point in attempting to summarize or further condense this work. Instead, the focus in this chapter is to place the methods described in the present volume, as well as their practical application, within the broad canvas painted by Ravallion.

A first fundamental choice is whether to estimate an absolute poverty line at all. Ravallion (2016) goes to considerable lengths to emphasize that measuring welfare on the basis of consumption of private goods represents only one facet of welfare. As such, consumption-based poverty metrics provide only a partial view into the welfare of individuals or households, which may or may not accord with other important facets of welfare. For example, a population may uniformly prefer to sacrifice substantial private consumption to live in zones with better public services. Hence, on a broad-based metric of welfare that includes both public and private goods, subpopulations living in zones with poor public services should be considered worse off than those living in zones with better public services for identical levels of private consumption.

Serious difficulties in estimating the value of public services to individual households have largely precluded their inclusion in household consumption. These and other limitations are fully recognized and discussed in more (p.11) detail in section 2.3. Concomitantly, Ravallion’s (2016: 76) admonition ‘best current practice is sensibly eclectic, often using a combination of methods’ is fully endorsed.

While a focus on private consumption has limitations, any ‘sensibly eclectic’ approach almost surely includes consideration of private consumption. Private consumption is a very important facet of welfare, particularly in cases where levels are exceedingly low. There is a vast difference between choosing between going to the movies or not and choosing between adequately feeding yourself or your children. It is perfectly clear that substantial shares of the population in all of the case countries considered in Part II face the latter choice on a disturbingly regular basis. In these circumstances, the ability to rigorously document progress/stagnation/regress in expansion of consumption possibilities is highly desirable. And the conclusions so derived can have profound implications, not least for public policies.

Hence, there is, on the one hand, little doubt that private consumption capabilities form only one facet of a comprehensive assessment of living standards for a population. On the other hand, it is also clear that private consumption is an important facet whose measurement should be done well. Experience in this domain also strongly indicates that measuring private consumption possibilities is challenging. It involves a multitude of methodological choices and trade-offs. These choices often interact with imperfect data and a desire to maintain consistency with previous choices in order to generate comparable results through time. The remainder of this chapter outlines the ideas that underpin the choices made for the analysis of consumption poverty in the case studies in Part II of this book.

2.2 Absolute Poverty Lines and Utility

Poverty lines can be described as either absolute or relative thresholds for distinguishing the poor from the non-poor. Relative poverty lines measure poverty in relation to the wellbeing of the society. A well-known example of a relative poverty line is the European Union’s threshold of 60 per cent of median income. Absolute poverty lines identify those living below an arbitrarily fixed level of wellbeing. Absolute poverty lines are especially appealing in the context of developing countries where the focus remains on attaining minimum standards of living for large portions of the population.

Ravallion (1998) describes two steps in the process of defining absolute poverty lines. The first step involves specifying a reference level of utility representing a minimum standard of living. The second step involves identifying a money metric threshold between the poor and non-poor that is associated with the reference utility level. As utility is unobservable, the (p.12) threshold is associated with actual consumption, which is observable. Consumption of a bundle of goods generates, for given preferences, a set level of utility. If the goods comprising the bundle are freely available at given prices, then the cost of the bundle is easily established. An individual or household with the capability to spend the cost of the bundle can thus attain at least the reference level of utility.

Note that, while poverty lines are derived on the basis of consumption bundles and the associated opportunity cost to the household of acquiring the bundle (normally approximated by prevailing prices), poverty lines are, in this conception, fundamentally rooted to a reference level of utility. The associated bundles should therefore adhere to two desirable properties: consistency and specificity. Consistency demands that consumption bundles reflect a reference utility level that is fixed across spatial and temporal domains. The easiest way to ensure consistency of the bundles across space and time is to select the same bundle across all spatial and temporal domains. Specificity relates to the relevance of the bundles and associated poverty lines to local conditions.1

Almost invariably, there is tension between these two desirable properties even if one restricts attention uniquely to food consumption, which often represents half to three quarters of total private consumption of poor people in developing countries. A common tension arises purely from differences in relative prices. In developing countries, relative prices for basic foods frequently vary substantially across space and through time; and consumption patterns often vary accordingly with relatively inexpensive goods appearing more prominently in consumption patterns. A fixed bundle is consistent, in that it delivers the same utility level, but fails to account for substitution effects, thus violating specificity. As Ravallion (2016: 8) states, ‘as long as there is substitutability, the poverty bundles must vary with prices’.

The issues can be seen more formally with respect to an expenditure function derived from standard utility theory.



In equation (2.1), the reference utility level (uz) can be obtained at cost ziju given a vector of prices (pi) faced by household j in region i. Households may have varying characteristics, xij, such as the number and demographic composition of members, which influence the cost of attaining the reference (p.13) utility level. Equation (2.2) simply defines an associated least cost consumption bundle, qij, for reference utility level (uz), prices (pi), and household characteristics (xij). Because the bundle is least cost, any other bundle that provides reference utility level uz must cost at least as much as ziju for given prices and characteristics.

When substitution possibilities are present, the optimal consumption bundle (qij) varies with prices (pi) and so does the cost of attaining the reference utility level (uz). This cost is the appropriate poverty line, and the associated bundle is both consistent (constant utility level) and specific (adapted to the conditions of the region). As noted, large variations in relative prices are frequently observed across space and through time; and consumption patterns are generally responsive to these relative price differentials. Ignoring these differentials by selecting a single bundle either across space or through time is potentially highly problematic (Tarp et al. 2002). At the same time, the reference utility level (uz) is never observed and the fundamental preference parameters that underlie the expenditure function are extraordinarily difficult to estimate. Hence, alternative (more specific) bundles that reflect differential relative prices may also provide different levels of utility, violating consistency.

2.3 Cost of Basic Needs

At the outset of attempts to estimate consumption poverty, two principal approaches to deriving poverty lines were advanced: the food energy intake (FEI) approach (Dandekar and Rath 1971; Greer and Thorbecke 1985), and the cost of basic needs (CBN) approach (Ravallion 1994, 1998; Ravallion and Bidani 1994; Ravallion and Sen 1996; Wodon 1997). With time, the CBN approach has gradually predominated. CBN is in focus here.2

The CBN approach follows logically from the discussion in section 2.2. It estimates poverty lines based on the cost of attaining a reference utility level as represented by a bundle of goods. In the CBN approach as applied to the country cases considered here, the reference utility level is low, reflecting, as the name suggests, basic needs. In practice, the explicit goods bundle frequently contains only foods. This is so because prices of non-foods vary drastically with quality and/or are represented by broad categories in household surveys (e.g. clothing), rendering estimation of meaningful quantities impossible. Of course, foods vary in quality as well, but the variation in the quality of basic foods purchased by poor people is not as profound.

(p.14) The food bundle is ideally based on the consumption patterns of the poor (specificity) and is normally required to meet a pre-set minimum caloric requirement that may vary with demographics or other factors. Consistent with the discussion in section 2.2, food poverty lines measure the cost of acquiring the food bundle(s). Even if the bundles do not vary across space or time, their cost is generally obtained by evaluating the bundle at specific regional and temporal prices.

The food poverty line so obtained is then supplemented by a non-food poverty line, which can be viewed as a single aggregate non-food good. An attractive approach to estimating the non-food poverty line is to use the average non-food expenditure of those households with consumption at or near the food poverty line (Ravallion 1998). This approach follows from the observation that even very poor people allocate non-trivial resources to non-foods, such as housing, clothing, and transport. The non-food purchases of households whose total consumption is ‘near’ the food poverty line are defined as basic because these items are perforce displacing consumption on food and thus forcing the household to consume a basket of foods that is inferior to the CBN poverty line basket in quantity, quality, or both.

The poor are then identified as those with consumption levels below the total poverty line (the sum of the food and non-food poverty lines). From this point, the Foster, Greer, and Thorbecke (FGT) class of decomposable poverty measures (Foster et al. 1984) are typically calculated. The most famous and frequently deployed FGT measure is the poverty headcount, which simply states the percentage of the population that lives below the poverty line.

We have already discussed the tension between consistency and specificity; however, even if this tension is resolved entirely, the CBN methodology has features of which the analyst, as well as the consumer of poverty analysis, should be aware.

First, the CBN approach, as described in this section, seeks to measure the cost of attaining minimum basic needs, which is distinct from identifying whether households actually satisfy these basic needs. A caloric standard applied to the food bundle provides an anchor for setting the reference welfare level. It is not an indication that a given household in fact attains that nutritional standard (or other standards for that matter). A household with total private consumption greater than the CBN poverty line may choose to allocate resources such that it does not meet its nutritional needs, yet this household would still be deemed non-poor because it has the capability to meet basic needs through purchase of the CBN basket.

Second, largely due to data limitations, the standard CBN methodology makes no attempt to measure the allocation of resources within households. In a non-poor household, it is possible that the basic needs of only some household members, but not others, are met. Combined, these two features (p.15) raise the spectrum of households with children wherein the adults heavily consume alcohol, entertainment, and tobacco while providing completely inadequately for their children. Yet, these children would be considered non-poor as long as the total value of consumption (including the value of consumption on adult goods) is greater than the poverty line threshold.

At the same time, these two aspects of the CBN approach avoid paternalism. It may be considered paternalistic if a household is categorized as poor because the consumption allocations of the household do not conform to some externally imposed norms. The CBN approach avoids paternalism at the cost of potentially violating some widely held norms, such as that a member of a non-poor household whose basic needs are not being met due to unequal allocation of resources within the household should be categorized as poor.

Third, important classes of goods are excluded. As noted earlier, the focus is on private goods, ignoring publicly provided goods and services. If, for example, public services are better in urban than in rural areas, then the focus on private goods understates rural poverty relative to urban poverty, ceteris paribus. Some private goods are also ignored. Specifically, services generated within the household are generally not counted, largely because they are so difficult to value. If one member of a household spends considerable time providing services such as cooking, the whole household may be able to eat much better than their neighbour, who has the same level of private expenditure but allocates less time to home-produced services such as cooking.

Finally, and referencing equations (2.1) and (2.2) more generally, varying the poverty line as a function of household characteristics is possible in principle but forces difficult choices in practice. For example, are basic needs in terms of private consumption for children less than the basic needs of private consumption for adults? If each person counts the same, then the total consumption of the household can be divided by the number of people living in the household, irrespective of age, to arrive at a per capita measure. If not, an adult equivalent scale, which is a specific estimate of how much less children (and sometimes women) need to consume to meet basic needs as opposed to (male) adults, is required. This choice can substantially influence the estimated prevalence of child poverty, defined as children who live in households categorized as poor.

A second example relates to household economies of scale. A two-person household might attain a higher living standard than a one-person household with the same level of per capita expenditure. Most obviously, sharing a dwelling can provide better housing services for the same cost. Durable goods, such as a radio or cooking equipment, are (in principle) easily shared at low cost. And larger households might be able to buy food and other items in bulk at lower prices. As household size increases, these economies of scale (p.16) almost surely decline. Diseconomies of scale may appear at some point. However, rigorously estimating household economies of scale is exceedingly difficult.

In sum, while the CBN method is widely applied and broadly accepted as a guidepost to best practice in estimating absolute poverty lines, the methodology is not without its challenges. In many cases, the best solution is to adopt multiple approaches as noted earlier and as highlighted in Ravallion (2016). Answers to questions such as:

  • What do the anthropometric data say about the nutritional status of children?

  • Are public services available and of reasonable quality?

  • How sensitive are consumption poverty measures to the choice of adult equivalence scales and/or estimates of household economies of scale?

provide a more complete and nuanced picture and maintains the focus of the consumption poverty measure on the facet of welfare it is designed to measure—household-level private consumption. Given this focus, the key is to measure household-level private consumption correctly. To this end, we look at approaches for enhancing specificity while maintaining minimum consistency requirements in section 2.4.

2.4 Consistency and Specificity

Absolute Poverty Lines

Figure 2.1. Illustration of the implications of substitution effects

Source: Authors’ illustration

Figure 2.1 illustrates the advantages and drawbacks of attaining consistency via fixed bundles. The example focuses on changes in relative prices through time; however, the conclusions drawn from this example fully extend to the case when bundles are fixed across spatial domains. Consider a representative household in two time periods that consumes two goods c1 and c2 where preferences are fixed over time. The utility curve Uz represents the minimum welfare associated with the poverty line. Estimating the poverty line amounts to estimating the minimum cost of attaining the reference welfare level and therefore is represented by the budget line tangent to Uz at prevailing prices. As period one prices are reflected in the slope of the budget line M1, (c11,c21) is the optimal bundle that yields minimum welfare and therefore expenditure level M1 represents the period one poverty line.

Suppose relative prices change in period two, as reflected in the slopes of M2 and M2’. If the poverty analyst follows the practice of maintaining consistency by holding the period one consumption bundle fixed and evaluates it at period two prices, the cost of acquiring (c11,c21) is M2’, i.e. the fixed poverty line. Clearly, this is not an optimal solution and violates the property of (p.17) specificity in that it fails to allow for a response to the prices prevailing in period two. At the fixed poverty line, a utility-maximizing household would choose a consumption bundle associated with the higher utility curve, U. Therefore, with fixed bundles, the period one and period two poverty lines are associated with different utility levels. If in period two the reference household’s expenditure exceeds M2 but is equal to or less than the fixed poverty line, M2’, the household would be deemed poor. However, at expenditure levels in this range, the household would attain a utility level greater than the utility associated with the period one poverty line. At the constant welfare level, Uz, the reference household would opt to consume the flexible bundle (c12,c22) at a lower cost resulting in a lower utility-consistent poverty line, M2. In short, imposing the fixed bundle (c11,c21) in period two violates the property of specificity and in so doing overestimates the cost of acquiring the minimum welfare level.

It is important to highlight that this overestimation of the period two poverty line when holding the bundle from period one constant through time is a function of starting at a cost-minimizing consumption point in period one. However, if specificity is violated in estimating period one bundles and results in a non-optimal bundle, the impact of the bundle carried forward to period two is uncertain. To see this, let us think conceptually of a country with six relatively distinct spatial domains with differing price vectors for basic foods and (p.18) corresponding differences in consumption patterns. If we (for example) define a single national consumption bundle as the average consumption of households in the lower third of the nominal consumption distribution across all spatial domains, then we have a single (average) bundle that may not reflect consumption patterns in any of the domains. Assuming constant preferences across spatial domains, the chosen single bundle would provide some reference level of utility (e.g. it is consistent). If preferences permit substitution between goods, then, by standard cost minimization, households in region i could obtain the reference level of utility at a cost that is less than or equal to the cost of the chosen single bundle evaluated at region i prices.

However, the extent of this overestimation is unknown for any of the six regions. Because the single consumption bundle applied to each spatial domain may be substantially untethered from actual consumption behaviour in any domain, it is impossible to know, without further information, the implications of these overestimations for the regional poverty profile. Furthermore, if one moves forward in time to analyse a new household survey and one simply applies updated prices to the single chosen bundle from the previous survey, the biases due to the failure of specificity in the estimation of the change in poverty are entirely unknown at the national level or at any of the regional levels. This is so because the chosen single bundle potentially does not correspond with actual consumption patterns in any region in any period. As the extent of error may become smaller or larger when one moves across space or through time, the implications for poverty evolution are also unknown. This contrasts with Figure 2.1 which shows that maintaining a previously optimal bundle through time only has the potential to bias upward the estimated poverty rate.

As has been noted, a potential solution to the shortcomings of a single, fixed consumption bundle is to estimate multiple (flexible) bundles across time and space. This approach has been applied in many recent studies (see Tarp et al. 2002; Gibson and Rozelle 2003; Mukherjee and Benson 2003; MPF/IFPRI/PU 2004; Datt and Jolliffe 2005; Ravallion and Lokshin 2006). The use of flexible bundles increases specificity in ensuring that bundles reflect the consumption patterns of poor households in each domain. As seen in Figure 2.1, flexible bundles have the advantage of allowing consumers to respond to variations in relative prices by consuming relatively cheaper foods. If utility were observable, flexible bundles would also resolve the issue of utility inconsistency, as each poverty line would be anchored to Uz. However, in practice, utility is not observable. Without utility consistency, differences in poverty rates between domains could merely reflect differences in utility levels across poverty lines for each domain rather than differences in standards of living within domains. This potential loss of consistency underpins the choice of sticking with a single bundle.

(p.19) To come to grips with this issue, analysts have turned to revealed preference theory to test whether regional poverty lines are utility-consistent (Gibson and Rozelle 2003; Ravallion and Lokshin 2006). Spatial revealed preference conditions can be written:


where preferences are defined on I [i ∈ I] commodities; r, s represent indices for the set of spatial domains considered, R [r, s ∈ R]; and the variables p and q represent prices and quantities, respectively. The conditions compare the cost of a consumption bundle in a given domain, r, to the cost of a bundle from another domain, s, evaluated at prices observed in r. If the bundles represent the same level of utility and preferences are constant, a rational consumer would choose the least cost bundle. A failure of this condition indicates consumers opted to buy a more expensive bundle even though a cheaper combination was available. The chosen bundle is therefore revealed preferred. A rational consumer only chooses a higher cost bundle if it provides greater utility. Thus, a failure of revealed preference conditions indicates the consumption bundles do not provide a consistent level of utility.

Revealed preference conditions impose very mild conditions on the nature of the welfare function. All that is required is that consumers prefer more to less. For people living near absolute poverty, this is a banal assumption. In addition, the prices used must be a reasonable estimation of the opportunity costs to the consumer of the goods in the bundles that are being compared (societal opportunity costs are different). If a good is subsidized and freely available at the subsidized price, then the subsidized price is a very good approximation of the opportunity cost to the consumer. If the subsidized good is only available one day a week and requires waiting in line for hours in order to purchase it, then the subsidized price understates the opportunity cost to the consumer of purchasing the good. This latter situation pertains with some frequency in developing countries and requires that attention be paid to whether prices represent opportunity costs to the consumer in empirical analyses.

The use of revealed preferences to check for utility consistency also imposes assumptions about consumer preferences. Specifically, satisfaction of all revealed preference conditions implies that there exists a coherent preference set (assuming the representative consumer prefers more to less) that corresponds with the observed consumption behaviour. This coherent preference set becomes the reference against which all comparisons are made.

The fundamental assertion made when one applies revealed preference conditions to making welfare comparisons is that this reference preference set is reasonable. Indeed, in imposing revealed preference conditions, one is seeking to arrive at the best possible comparator for evaluating the welfare (p.20) derived from private consumption expenditure, particularly for households living ‘near’ the absolute poverty line. It is worth highlighting that, in comparing the welfare of household A to the welfare of household B, some observable reference is required. Bundles that reflect consumption patterns (specificity) and satisfy revealed preference conditions (consistency) would appear to be prime candidates to serve as the reference.

There are cases where preferences rather than prices clearly influence consumption patterns. For example, rather than prices, religious dietary restrictions may significantly influence the consumption patterns in a subset of regions. Box 2.1 considers the impact of regional climate variations on caloric needs as well as food preferences. In these and other cases, the question is not whether preferences are the same everywhere. Clearly, they are not. Nevertheless, the question remains: what reference comparator should be chosen in order to make welfare comparisons? Even when preferences clearly differ, there is still a good argument that bundles that reflect the specificities of distinct regions and satisfy revealed preferences are reasonable choices for the reference. These bundles essentially posit that there exists a preference set for a representative consumer whose consumption is unconstrained by dietary restrictions; who is equally content to consume any of the bundles; and who would choose to consume the bundle from region r at time t when faced with prevailing prices and having a budget set at the poverty line. In other words, arguments must be advanced that a better reference comparator is available.

(p.21) 2.5 Estimating Specific Utility-Consistent Poverty Lines

Revealed preference conditions are straightforward to apply to actual consumption bundles derived in poverty line estimation analysis. The conditions themselves are exacting and failures are frequently widespread. For instance, Ravallion and Lokshin (2006) apply revealed preference conditions to bundles from twenty-three spatial domains in Russia. The comparison matrix is thus 23×23. The diagonal of the matrix compares regions to themselves and can be ignored. There are thus 253 = 23*22/2 matched pairs defined as spatial domain A compared with spatial domain B and vice versa. Of these 253 possibilities, only six matched pairs satisfied revealed preference conditions. Similar results are found in Papua New Guinea by Gibson and Rozelle (2003) and in Mozambique and Egypt by Arndt and Simler (2010).

Arndt and Simler (2005, 2007, 2010) introduce a methodology based on information theory for resolving revealed preference violations. Using the cross-entropy criterion, they minimize the directed distance between the original consumption shares and estimated shares satisfying revealed preference conditions. The mathematical programme typically also ensures that the caloric content of the original consumption bundle is maintained. To satisfy revealed preferences, quantities likely need to be modified, thus altering composition of the food baskets.



qir are variables representing quantities consumed;sirent are variables representing food shares of the reference bundle;

sirorig are parameters representing initial food shares of the reference bundle;

i, i′ are indices of goods in the consumption bundles; and

r, s are indices of domains across space.

Subject to:

ipir*qisipir*qirr,sr s




The first constraint ensures that revealed preference conditions are satisfied across regions given prices, pir. The second constraint defines entropy budget shares, sirent, as a function of the modified quantities, qir. The third condition constrains the basket to attain caloric requirements (parameter cal), which are held constant across regions, by multiplying quantities by calories per unit (p.22) (e.g., grams) of each good (parameter calpgi). Temporal constraints are also possible to impose (Arndt and Simler 2010 and Chapter 4, section 4.2.4).

Arndt and Simler (2010) apply the maximum-entropy method to poverty lines in Mozambique and Egypt and discuss the philosophy of estimation under an information-theoretic approach. Briefly, the information-theoretic approach seeks to preserve, to the greatest degree possible, the information content inherent in the original budget shares (specificity) while ensuring that revealed preference conditions are satisfied (consistency). The procedure also ensures that the bundle provides a targeted level of calories in keeping with standard CBN practice.

2.6 Conclusion

Like it or not, there is no single set procedure for estimating absolute poverty lines. The CBN approach provides a series of valuable guideposts that are well rooted within consumer theory. But in actual practice, numerous choices must be made. This chapter has sought to explore the broad contours of some of the more fundamental choices with an extra dose of attention devoted to the long-running debate on reconciling consistency and specificity. Differing country circumstances will almost surely lead to different choices with respect to the overall approach. In addition, past choices often strongly influence current choices due to the desire to make relevant comparisons with earlier analyses. Chapter 4, the case studies in Part II, and the provided codes are meant to facilitate focus on the actual key choices and their implications.

This chapter began by emphasizing that private consumption represents only one facet of welfare, albeit an important one. We also highlighted in section 2.3 a series of limitations that are almost invariably associated with CBN-type approaches to welfare measures. And we reaffirmed the idea that the best mode for addressing these limitations is to employ multiple methods, particularly those better suited to providing insight where the typical CBN approach falls short. As a contribution to this end, Chapter 3 focuses on drawing conclusions from a series of indicators, each representing a facet of welfare, in a multidimensional framework. Hence, we now turn to broadening our conception of welfare.


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(1) A careful reading of Ravallion and Bidani (1994) and Thorbecke (2004) leaves open some ambiguity on the exact interpretation of the consistency and specificity properties between the two definitions provided. We will throughout employ the terms in the sense defined in this paragraph.

(2) The Pakistan case study contains an application of the FEI approach including comparisons to CBN results developed using a modified version of PLEASe.