foster, absolute versus relative poverty

8/3/2019 Foster, Absolute Versus Relative Poverty

1/8

American Economic Association

Absolute versus Relative PovertyAuthor(s): James E. FosterSource: The American Economic Review, Vol. 88, No. 2, Papers and Proceedings of theHundred and Tenth Annual Meeting of the American Economic Association (May, 1998), pp.335-341Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/116944 .

Accessed: 30/08/2011 22:31

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The

American Economic Review.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=aeahttp://www.jstor.org/stable/116944?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/116944?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=aea


2/8

WHATS POVERTY NDWHOARE THEPOOR?REDEFINITIONOR THEUNITED TATES N THE1990'StAbsolute versus RelativePoverty

By JAMES E. FOSTER*Should poverty be measuredusing an "ab-solute" or a "relative" approach?This age-old question in poverty measurementis onceagain on the agenda,due to the ambitiouspro-posals of PatriciaRuggles (1990) and the Na-tional Research Council of the NationalAcademy of Sciences (Constance Citro and

Robert Michael, 1995) to alter the way U.S.poverty is measured.Their wide-ranging sug-gestions include a new "hybrid" approachtosetting the poverty threshold that, unlike thecurrent absolute method, is sensitive tochanges in the general living standard,butlesssensitive than a purely relative approach.Theproposals also recommendusing aggregatein-dexes of poverty beyond the usual "head-counts," such as well-known "gap" measuresand indicatorsof the distributionof resourcesamong the poor. Importantrelative notions ofpoverty enter at this "aggregation" step aswell. The effects of the various recommenda-tions on the trend and cross-sectional profilesof poverty are actively being explored (seee.g., David Betson and JenniferWarlick,1997;Thesia Gamer et al., 1997; David Johnson etal., 1997). At the same time it may prove use-ful to consider some of the conceptual mea-surement issues arising from the proposals.This is the direction takenin the present study.This paperevaluates the multiple notions ofrelative and absolute poverty that arise in

choosing poverty lines and in aggregatingthedata into an overall index of poverty. A gen-eral taxonomy is presented, and the questionof robust comparisons is addressed within thisgeneralframework. Special attention s paid todistinguishing between (i) the generalconceptunderlying the poverty line and (ii) the partic-ular cutoff chosen. The paper concludes witha discussion of "hybrid" poverty lines andtheassociatedparameter hat s likely to play a keyrole in futurediscussions: the income elasticityof the poverty line.

I. ElementsPoverty measurement is based on a com-parison of resources to needs. A person orfamily is identified as poor if its resources fallshort of the poverty threshold. The data on

families arethen aggregatedto obtainanover-all view of poverty.There aremany ways of defining resources,constructing thresholds, and aggregating theresulting data (see e.g., Ruggles, 1990; MartinRavallion, 1994; Citro and Michael, 1995).Virtually all partition the population intogroups of families (or resource-sharingunits)with similar characteristics, and I follow thisapproachhere. Let 0 denote the rawdata,con-taining information on resources received byfamilies, their demographicand other charac-teristics, and perhaps other data (e.g., con-sumption distributions) needed to constructpoverty thresholds. Let m be the number ofdistinct groups, with nk - nfk() being thenumber of families in groupk. Once a specificdefinition of family resources has been fixed,this yields a distributionof resources amongthe families in group k, denoted by the nk_dimensional vector xk = Xk ( ) . The povertythreshold for families in groupk is denotedbythe numberZk = zk(0); a family is identified

t Discussants: David S. Johnson, U.S. Bureau of LaborStatistics; Patricia Ruggles, U.S. Department of Healthand Human Services; BarbaraWolfe, University of Wis-consin; ChristopherJencks, HarvardUniversity.* Department of Economics, Vanderbilt University,Nashville, TN 37235. I thank the discussant, David S.Johnson, for his insightful commentary.Financial supportfrom the John D. and CatherineT. MacArthurFoundationthrough he Network on Inequality and Povertyin BroaderPerspective is gratefully acknowledged.335


3/8

336 AEA PAPERS AND PROCEEDINGS MAY 1998as poor if its resource level falls below Zk. Ex-actly how Zk is to be set (i.e., the "identifica-tion step" of AmartyaSen, 1976) is a key partof the present discussion.

As for the "aggregation step," most U.S.studies report poverty levels for the demo-graphic groups and then aggregate to obtainan overall level of poverty. Thus, they implic-itly take the poverty index to be "decompos-able" across the groups (on which more willbe said presently). With overall poverty aweighted sum of group poverties, the aggre-gation questionreduces to a choice of thepov-erty index P(x; z) to apply to a typical groupdistribution x and poverty line z. The mostcommon index is the head-count ratioH(x; z)= qln where q is the number of poor familiesin x given z, and n is the number of familiesin x. This index provides important nforma-tion on poverty (namely, the frequency of pov-erty among the population) but ignores otherrelevant information on the depth and distri-bution of poverty. Another importantkind of"partial index" is based on the sum of theincome gaps (z - xi) of poor families. These"gap indexes" add a second dimension of"depth" to poverty evaluations. A third di-mension is provided by indexes of inequalityamong the poor.While each partialindex conveys useful in-formation about some aspect of poverty (as-suming, of course, that the poverty thresholditself is meaningful), one must be careful inusing its unidimensional prescriptions as aguide to policy. For this and other reasons, ithas been argued (see e.g., Foster and Sen,1997) that an index combining all three di-mensions is more coherent in this role. Such"distribution-sensitive" indexes have beenused to great advantagein internationalcom-parisons and development studies (see e.g.,Ravallion, 1994).

II. Absolutesand RelativitiesThere are severalways in which relative andabsolute considerations enter into povertymeasurement. I offer a simple taxonomy in-cluding the threshold and equivalence-scalechoices in the identificationstep, andthe treat-ment of population, scale, and individualdep-rivation in the aggregation step.

A. ThresholdThe first and perhaps most important sensein which poverty measurement is absolute or

relative concerns the setting of the povertystandard.An absolute poverty line is a fixed(group-specific) cutoff level Za that is appliedacross all potential resource distributions. Incomparisons over time, for example, the stan-dard is unchanged even in the face of eco-nomic growth (although provisions are madefor changes in price levels);1 similarly, incomparisons across countries, fixed-thresholdcomparisons require an appropriateexchangerate. If the absolute standard s truly indepen-dent of the currentdata, though, how can onebe sure that the standard chosen is an appro-priate one? The poverty line is typically cal-ibrated in some initial period using, say,food-budget studies, and it is then carriedforth from year to year, irrespective ofwhether the same procedure applied to cur-rent data would yield the same result. In agrowing economy, the gap between the hy-pothetical recalibrated evel and the historicalstandardmay well be quite large. Such is thecase with the current U.S. poverty standard,and this is one of the criticisms that have beenleveled against it (see Citro and Michael,1995 pp. 2-3).In contrast, a relative approachuses currentdata to generatethe currentpoverty threshold.A relative poverty line begins with some no-tion of a standard of living r(x) for the distri-bution x, such as the mean, median, or someother quantile, and defines the cutoff as somepercentage a of this standard.The result is apoverty threshold Zr = ar(x) that varies one-for-one with the standardof living, in thata 1-percent increase in r is matchedby a 1-percentincrease in Zr, Examples include the "50 per-cent of the median" relative poverty line pro-posed by Victor Fuchs (1969) and the "50percent of the mean" threshold employed by

' There is a significant issue of whether resource shouldbe expressed in real terms and, if so, which cost of livingindex to use. This issue is ignored here for simplicity, butit is clearly another potentially important source of "rel-ativity" in the measurementof poverty.


4/8

VOL.88 NO. 2 WHAT S POVERTYAND WHOARE THE POOR? 337

Michael O'Higgins and Stephen Jenkins(1990).2Using a relative line does not amount tomeasuring inequality (although theorem 6 inFoster and AnthonyF. Shorrocks [1988a] pro-vides one important link) nor does it implythat poverty is by definition "always with us"(see Anthony Atkinson, 1975 p. 189). Andwhile many studies regardabsolute lines as be-ing especially low and relative lines as beinghigh, this is not necessarily the case. If livingstandardsarerising and thresholds are peggedat Za = Zr in some initial period, then Za < Zrfor all subsequent periods, but Za > Zr for allprevious periods, as emphasized by Citro andMichael (1995 p. 132). In any isolatedperiod,it is not possible to tell whether a given thresh-old z is relative or absolute, nor is the distinc-tion particularly important, since the samenumerical cutoff, however originally derived,must lead to the same level of poverty.The key distinction between absolute andrelative thresholds is not seen in the specificvalues obtainedat a given date,but in how thevalues change as the distribution changes.Thus, there is an importantdistinction to bemade between the general concept underlyingthe poverty threshold, and the specific cutoffselected. For comparisons involving extendedperiods of time, or very different standardsofliving, the former is likely to be the more im-portantissue (see also Ruggles, 1990 Ch. 3),while the latter choice (of cutoff) is largelyarbitrary (see Fuchs, 1969; Atkinson, 1975,1987; Foster and Shorrocks, 1988b). This in-evitable arbitrariness asts doubt on the mean-ing of the cardinalpoverty levels obtained atspecific cutoffs and leads to a considerationofthe robustnessof results to changes in the cut-off, a topic I will returnto below.

B. Equivalence ScaleA second entry point for relativities in pov-erty measurement is where poverty lines are

adjusted across demographic groups. One ap-proach is to applyrepeatedly the procedure orsetting poverty lines to each group separatelyand thereby arrive at m independent thresh-olds. However, as noted by Ruggles ( 1990 Ch.4), this can lead to odd (rnonmonotonic)be-havior of the poverty line as famiily sizechanges. An alternative approach sets the linein one reference group and then derives theremaining thresholds using an "equivalencescale" to account for the differing needs ofdifferent-sizedfamilies. The typical scale pro-vides the rate at which a dollar for one grouptranslates nto dollars for another. So if group1 is the reference, and Sk is the conversion ratefrom group 1 to group k, then Zk = 5k l be-comes the poverty line for group k.This sort of equivalence scale is relative inthat the transformation rom groupto group ismultiplicative, and consequently group pov-erty lines are proportionate o each other. An-other possibility raised by Charles Blackorbyand David Donaldson ('1994) is for variationsin family configuration o have an constant ab-solute effect so that, for example, adding an-otherchild is seen as an additional fixed (real)cost to the family, independentof the size ofthe base threshold. Relative equivalence scalespreserve the ratios of group poverty lines asthe base thresholdchanges; an absoluteequiv-alence scale preserves the absolute differ-ences. The two forms are indistinguishable ora single observationor if the reference thresh-old remains unchanged (as with an absolutepoverty line).

C. PopulationThe aggregation stage uses three notions ofabsolute and relative poverty in constructingpoverty indexes. First, a relative or per capitapoverty index is independentof thepopulationsize in the sense that "replicating" the popu-lation leaves the poverty value unaffected: forexample, P(x, x; z) = P(x; z). Such a mea-sureis based purelyon the relativefrequenciesof incomes in the income distribution.In con-trast, an absolute index is one whose valuerises in proportion to the number of replica-tions: for example, P(x, x; z) = 2P(x; z).The head-count ratio qln is relative in thissense while the head-count q is absolute. An

2There are importantmeasurement issues in selectingthe standardof living. Should it be the mean, the median,or some other representative ncome? Should it be fromthe entire population or some reference group? Should itbe for all expendituresor a significant subset? (For ref-erences, see Citro and Michael [1995].)


5/8

338 AEA PAPERSAND PROCEEDINGS MAY 1998absolute index can be converted to a relativeindex by dividing by n.

D. ScaleA second notion concerns the behavior ofan index when the poverty line and incomesare simultaneously altered. A relative orscale-invariant index is one that is un-changed when the poverty line and allincomes are multiplied by the same factor.An absolute or translation-invariant indexis independent of additions of the sameconstant to the poverty line and all in-comes (Blackorby and Donaldson, 1980).Thus, for example, the aggregate poverty

gap 1% I (z - xi) is an absolute index ofthis sort, while the normalized poverty gapl(z-xi )/z (which measures the povertygap in poverty line units) is relative. Thehead-count ratio is both absolute and relativein this sense (and is essentially unique in thisrespect [see Buhong Zheng, 1994]).E. Deprivation

Finally, the basic notion of deprivationthat underlies a given index may be relativeor absolute. If a family's poverty level de-pends purely upon its own characteristics, itsresource level, and its threshold, then the in-dex is based on a notion of absolute depri-vation. Foster and Shorrocks (1991) relatethis to decomposability of the index acrosspopulation subgroups (overall poverty is aweighted sum of subgroup poverties for anypartition) and also to a more fundamentalnotion of subgroup consistency (overallpoverty is increasing in subgroup povertylevels for any partition). The head-count ra-tio and the gap indexes are absolute in thissense, as is the index of Foster et al. (1984)which takes [(z - xi)/zI as the ith poorfamily's deprivation level. In contrast, Sen's( 1976) index is founded on the notion of rel-ative deprivation, since a family's depriva-tion level depends crucially on its relativeposition among poor families and thus in-corporates information beyond its own data.A discussion of the two approaches can befound in section A6 of Foster and Sen(1997).

III. RobustComparisonsThe above taxonomy presents several ave-nues for relative and absolute concepts to enter

into poverty evaluations, and many combina-tions are possible. For example, the currentmethod for evaluating U.S. poverty employsan absolute thresholdfor each group and a rel-ative or absolute equivalence scale (indeter-minate since poverty lines areunchanging) toidentify the poor; for the aggregation step ittypically uses the head-count ratio, a popula-tion relative index that is both absolute andrelative with respect to scale, and which isbased purely on absolute deprivation.The ag-gregate gap, which is absolute in all three di-mensions, is often used as an alternative ndex.Each combination of absolutes and relativeconcepts has many possible implementations(i.e., specific cutoffs, scales, and indexes)from which to choose. Inevitably, this entailsmaking choices for which there is little guid-ance (why 50 percentof the median insteadof49 percent?). It is important o note, however,that the decision need not be based on nor-mative or subjective considerations. Theselection from the arrayof possible implemen-tations could be purely arbitrary-made in theinterest of getting on with the analysis (on thisdistinction, see Sen [1980]).Given the inherent arbitrarinessn selectinga specification, it is importantto evaluate therobustness of any conclusions obtained. Incases where the numerical poverty levels areimportant, this may be as simple as testingother reasonable specifications and reportinghow the poverty level changes. Betson andWarlick (1997), for example, use 20-percentchanges in z to illustratethe cardinal sensitiv-ity of head-counts to the threshold. Alterna-tively, when rankingsof poverty levels are allthat matter, one has available a rather largecollection of tools to evaluate ordinal robust-ness (analogous to the well-known Lorenzcri-terion for inequality analysis), which covervariable thresholds, equivalence scales, andindexes (see e.g., Foster, 1984; Foster andShorrocks, 1988b; Atkinson, 1987, 1992).Virtually all approaches trace back to notionsof stochastic dominance from risk theory (seethe general discussion in Foster and Sen[1997]).


6/8

VOL.88 NO. 2 WHAT S POVERTYAND WHOARE THE POOR? 339Most results of this type are presented in aone-group framework with absolute thresh-olds; but in fact, the tools have far greater ap-plicability. As an illustration,suppose that the

base thresholdz1 and equivalence scale sk arerelative, the index P is based on a notion ofabsolute deprivation (hence decomposable)but otherwise relative, and the only questionis the specific cutoff a to be used in setting therelative poverty line. Suppose that for a spe-cific value of a, say, a - 50 percent, the re-source distribution (x, ... , xm) has greaterpoverty than (y', ... , yi). When can one besure that this will remain true for an entirerange of a values, say (0, ii ) where ii > 50percent? Let r be the standardof living under-lying the relative poverty line, and let rx andry denote the respective standards n the dis-tributions. Construct a new "equivalent" dis-tribution xik for demographic group k bydividing family resources by the equivalencescale sk, andthen replicatingby family size ink, so thatxk has one equivalentresourcelevelfor each person in group k. It is not difficultto show that for P satisfying the above prop-erties, the poverty level of the original distri-bution (x1 ..., xm) at the group-specificthresholdsz = skz is simply

Px 1 m; .Pi,..., ,mz)or the poverty in the equivalent distributiongiven group l's poverty line. If one furthernormalizes incomes by the standardof living,then the poverty level is given by

P(xI rx, ... , ?m/rx; a) .Consequently, the judgment that (x', ..., xm)has greater overty han y', ... ym) is in factrobust in a if

P(x/rx, ..,xmlr,,; a)>P(y r , ym/ry;)

foralla E (0, ).This last condition is in a form that allowsthe application of results in Foster andShorrocks (1988b) and Atkinson (1987). So,for example, the test for the head-count ratioH checks whetherthe two distributionsof nor-

malized equivalent incomes can be comparedusing first-degree stochastic dominance overthe range (0, c ), while the tests for the nor-malized gap index and theFoster et al. (1984)index use second- and third-degree stochasticdominance, respectively. Atkinson's (1987)results go beyond these results to considervariationsin poverty indexes and indicate, forexample, that if there is an unambiguouscom-parison for H (and hence first-degree stochas-tic dominance), then virtually any acceptableindex P will agree with this conclusion. Thisillustrates the power of the head-count ratio inthis context.

IV. HybridMeasurementMany of the categories in my taxonomy al-low for an intermediateposition to be chosenin place of a pure relative or absolute ap-proach.One particularlynterestingexample isthe "hybrid" poverty threshold that is centralto the proposal in Citro and Michael (1995),which is based on what lnight be termed a"partial" standardof living: rp s the medianexpenditure on certain basic goods. Thethresholdz = arp has the same structureas apurely relative cutoff (and in fact the robust-ness result applies equally well to it). How-ever, median expenditures on basic goods donot rise as fast as, say, median total expendi-tures, and it is this empirical fact that gives zits hybridnature.One could also imagine thresholds that arehybrid by construction, in thatthey depend di-rectly on an absolute and a relative standard.For example, consider a weighted geometricaverageof a relative hresholdr = ar andanabsolute threshold Za, namely, z =. zzI -pwhere 0 < p < 1. This formof hybridline hasthe property that a 1-percent increase in theliving standard r always leads to a p-percentincrease in the poverty line. In other words, pis the elasticity of the poverty line with respectto the living standard,or what Gordon Fisher( 1995) has termedthe income elasticity of thepoverty line. In general, p = (dzldr)(r/z) hasa natural nterpretationas a measure of the ex-tent to which a given threshold z is relative,with p = 0 correspondingto an absolute pov-erty line and p = 1 a fully relative one. Thepossibility of using a hybridstandardchanges


7/8


8/8

VOL.88 NO. 2 WHAT S POVERTYAND WHO ARE THE POOR? 341

O'Higgins, Michael and Jenkins, Stephen. "Pov-erty in the EC: Estimates for 1975, 1980,and 1985," in Rudolph Teekens andBernard M. S. van Praag, eds., Analysingpoverty in the European Community:Policyissues, research options, and data sources.Luxembourg: Office of Official Publi-cations of the European Communities,1990, pp. 187-212.Ravallion,Martin.Poverty comparisons. Chur,Switzerland:Harwood, 1994.Ruggles,Patricia.Drawing the line. Washing-ton, DC: UrbanInstitute Press, 1990.

Sen, Amartya K. "Poverty: An Ordinal Ap-proach to Measurement." Econometrica,March 1976, 44(2), pp. 219-31.

_-. "Description as Choice." OxfordEconomic Papers, November 1980, 32 (3),pp. 353-69._-. "Poor, Relatively Speaking." OxfordEconomic Papers, July 1983, 35(2), pp.153-69.Zheng, Buhong. "Can a Poverty Index BeBoth Relative and Absolute?" Econo-metrica, November 1994, 62(6), pp.1453-58.

foster, absolute versus relative poverty

Documents