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DevelopmentEconomics

Office of the Vice President Public Disclosure Authorized The May 1991 WPS 684

The Value

Public Disclosure Authorized of Intra-household Survey Data for Age-based NutritionalTargeting Public Disclosure Authorized

LawrenceHaddad and Ravi Kanbur

Public Disclosure Authorized The design of niutritioniintervenltionis can be very' susceptible to the level of aggregation of available informationi.

I hc Poc y, Research, aid lxieia! AfIfirs Coin( lcx dsLinhuics IPRF 9Aorking l'arcrv ti, di-emiate Licthe nditng Ofof s rk in progrcss aid to crncourag OiC exchaige o0fideds amiong lidlik stalf diadall others intCerstedin docsloprnenr issues Ihese parvirs san) the lieiics of the authors, reflect ofII dicir %icA ss dnd shr.u:d he ustd and cit,d according!) Ihc rfidndigs.iInerpre-'1t1oli. ald ciulsirns ate! tlCe authors own. Ihc) should not he anthtecd to dhc World lanIk. its Bfoard of Diretors itr aninaptuert- r ans of its niembhr coomriic. Policy,Research, and External Affairs

DevelopmentEconomics

WPS 684

This paper - a product of thc Rescarch Advisory Staff, Office of the Vicc Prcsidcnt, Devclopmncit - is part of a larger effort in PRE to understand the dcsign of povcrty alleviation policies. Copies are available free from the World Bark, 1818 H-Street NW, Washinlgton,DC 2(A33. Plcase contaict Janc Sweeney, room S3-026. extension 31021 (29 pages, with figures and tables ).

Age is a good indicator f( identifying at-risk * How useful is it to kinow thc caloric reallo- population groups for intervenitionsthat focus on cation outcome if age is used as a targeting prevention rather than cure. But whaitis the ideal instrumcint? upper age limit for tar-getingintcrvcintionls to minimize undernutrition>? Age proved to be a good indicator of under- nutrition wheniresearchers had data on individual Within the framework of upper-limit indica- nutrition and on the intra-lhouscholdallocation of tor targeting, Haddad and Kanlburaddrcssed calories. certain questions: Age was apparently less uselul aIs a targetinig * How far wrong can one go using only instrument when only houseihold-level dala on household-level data on nutrition? calorie adequacy were used. TIlhccnors in age- based targeting were theefoire significanit. * How valuable is thc extra infotmnationone gets from costlier intra-household surveys on Food sharing rcndered age trulYless useful nutrition? as a targeting instrumcnt because oflecakaige within thc houseihold. Calories tarmted to the * How far wrong can one go by neglecting the younger household members cnd up reaching the intra-houschold repercussions of nutritionazl older individuals. interventions - for example, supplemeintsto a child being nullified by equivalent reductions in food to the chiildin the home?

The PRE Working Paper Series disseminates ihc findings of work under As\iTin the Bank's Polii-, Research. and Emtemal AffairsConiplex. Anobjectiveofthe series is.Iog.ttlicscfind ingsoutquickl\.cv cn ifprescntation, are lesc than. fully p1\lished. The nindings, intcrpretatiorts, and conclusions in ihcse papers do not necessa.rily represcrit official Bank polic'y.

I'ro(luced by the PRE l)icssmination Center TABLEOF CONTENTS

1. Introduction...... 1 2. Upper-LimitIndicator Targeting: Theory ...... 3 3. OptimalAge CutOffs for NutritionalTargeting: An Applicationto PhilippineData ...... 7 4. The Valueof Intra-HouseholdInformation ...... 9 5. Intra-HouseholdAllocation, Leakage and the Implicationsfor Targeting...... 11

6. Conclusions ...... 14

* The authors would like to thank the International Food Policy Research Institute for access to the data, and Pete Mitchell for hf programming assistance. 1. INTF-JCTION Nutritionalinterventions exist in manydeveloping countries. Theyare of courseto be foundas emergencyrelief programs after disastersor famines,but regularsupplementary feeding programs are alsowidespread. A key questionfor theseprograms is targeting. Sinceresources are limited,some method has to be adoptedof making surethat nutritional supplements are givento thosewho needit most. The mosteffective method is to evaluatethe nutrientshortfall from a givenstandard for eachindividual and to supplyexactly this amount of supplementand no more. But suchfine targeting is not possibleon the ground,and practitionersrely on moreeasily observable indicators.Examples of suchmethods are levelsand trendsin anthropometricindicators such as weight-for-height,weight-for-age, and upperarm circumference.However, if the interventionis fccussed specificallyon preventionrather than cure, age is acknowledgedto be one of the betterways of identifyingat-ri:k population groups (Kennedyand Alderman1986).' Acceptingthat age may fulfillthe roleof a usefultargeting indicator,this still leaves open the exactnature of its use. In manycases programs use an upperae Jimnitfor eligibility (Pfeffermannand Griffin 1989, Beaton and Ghassemi1982, Timmons et.

1 How easyis it to assessan individual'sage in culturesnot dominatedby calendars?Enumerators concerned with accurate age measurementsunder these circumstances are trainedto constructa detailedcalendar of localevents based on, for example,climatic auid cropcycle highlights (UN 1986). -2-

al. 1983).2What should this upper age lint be, if the objectiveis to minimizeundernutrition with given resources for the provisionof nutritionalsupplements? It willbe recognizedthat the abovequestion is partof the generalclass of indicatortargeting problems, as developedby Akerlof (1978).We referto it as the problemof unoer-liMitindicatgr irgiUtng. The firstobjective of thispaper is thusto developa framework for upper-limitindicator targeting, and to illustrateit for the case of age-basednutritional interventions using individual level, intra- householdsurvey data from the Philippines.Although the dataused provideonly an approximationto individualnutritional achievements withinthe household,most surveys in developingcountries do not provideeven this information. How farwrong can onego withonly householdlevel data on nutrition?The secondobjective of thispaper is thereforeto providea quantitativeestimate of the valueof the extrainformation that the costlierintra-household survey provides, whenthe objective is to designoptimally targeted nutritional interventions.There is, however, a recognitionin the nutrition literaturethat such interventions cannot be seenindependently of the natureof the intrahouseholdnutritional allocaticn, since a supplementto a childcan be nullifiedby an equivalentreduction in

2 Infantsin the age range6-36 months are especiallyhighly targetedas (1)they are vulnerableto undernutrition(low energy densityweaning foods for example),and infection(the move from breastfeeding to weaningfoods, and increasedtoddler mobility for example)and (2)the functionalconsequences of poorhealth are more severefor thisage group. .3-

feedingat home (Alderman1990). The thirdobjective of the paperis thereforeto providea quantitativeassessment of how farwrong one goesby neglectingthe intrahouseholdrepercussions of a nutritional intervention.We start,howevpr, with some basic theory on indicator targeting.

2. UPPER-LINITINDICATOR TARGETING: THEORY Let0 denotea measureof nutritionaladequacy (for example, the calorieadequacy ratio for an individual)and t the age of an individual.Let f(0,t)be the Jointdensity of the two variablesin the population.If z measuresa normativelygiven "adequate level for0, (e.g.z - 1 for calorieadequacy), then a measureof the extent of undernutritionin the populationis givenby

P. = f AA'f(t )dot (1) 00 z

It willbe recognizedthat this measure of undernutritionis analogousto the measureof povertyput forwardby Foster,Greer, and Thorbecke(1984). Variants of it havebeen discussed in the context of undernutritionby Kakwani (1989) and Ravallion (1990). This will be the workhorseof our analysisof nutritionaltargeting-the object of policywill be to reducethe valueof Pa as givenby (l). The magnitudeof a reflectsvalue judgements on the viewtaken about the depthof undernutrition.When e - 0 thisdepth is ignoredand the PO -4- essentiallymiasures the fractionof populationthat is underno"rished.When a - 1, P1 is the aggregatenutrition gap, suitablynormalized. As a increasesabove 1, P. givesgreater and greaterweight to thosewith lowest nutritional achievement. Most of our empiricalanalysis will concentrate on the valuesa - 09 1 and 2 as capturingthis range of valuejudgements. Beforeintroducing policy, notice that P. can be rewrittenusing the factthat

f(,,t) = a(*It) h(t) (2) wherea(0 I t) is the conditionaldensity of 0 givent and h(t)is the marginaldensity of t in the population.Using (2), (') becomes

Ps f (f -ZAv a(*tt)d#3 h(t)dt 0 0

(3)

co f Ps (t) h(t) dt 0

In otherwords, total undernutrition is simply the sumof undernutritionat each age level, weighted by the proportioitof populationat thatage level. We sapposethat the policymaker has a totalamount of nutritionalsupplement B to dispense.If eachindividual 0 couldbe -5-

observedcostlessly the policyprogram would be easy-simplyfind thosefor whom0 is lessthan z and administerthe rightamount of y supplement.But on the groundthis is impos.'Nleto do and other criteriaare used. One suchcriterion is an tpperage limitT such thatonly those with age lessthan or equalto T receivethe supplement.If thereexists a householdsurvey that allows us to estimatethe bivariatedensity f(o,t), this could be usedto choose the optimalvalue of T, suchthat Pe is minimizedfor the givenamount of rasourcesB. But how? We haveto specifyhow the supplementis distributedto thosewho meetthe criterion.The simplestmodel, and alsothe mostpracticable method,is to distributethe supplementequally among those 'let throughthe door" on the criterion thattheir age be lessthan or equal to T. There are H(T)individuals of age lessthan or equalto T whereH(-) is the cumulativedistribution of the densityh(.). Thus eachindividual who satisfiesthe criterion getsan amountB/H(T) and the new levelof undernutritionis given by

T z-B/H(t) P, (B,T) * f [Z -, a(* ! t)] h(t)dt (4) as z |f f Zt a (4 1 t) Ih (t) dt -6-

The centralquestion is whathappens to Pe (B,T)when T changes forgiven B. Differentiating(4) with respect to T we get:

d.(BT)6 a , Bh(T) f P- B(,T I t)h(t)dt d-r Z [H(T)]2 (5

+ [ Pe(B,T I t) - P, (O,T I T) ]h(t)

The two termson the righthand side of (5)capture the conflicting effectson undernutritionwhen the upperage limitis increasedat the margin,so thatmore people are drawninto the net. Thesenew people get a supplementso theirnutrition improves-this is the secondterm on the righthand side of (5). Butwith the new peoplethere is less to go around,anJ thosealready in the net loseout. This intra- marginal'effect is capturedby the firstterm on the righthand side of (5). As shownin Kanbur(1987), the impactof a smalldecrease in

transferon Pi is proportionalto P,.1 and thisterm consists preciselyof expressionsof thistype. Furtherinsight into (5) can be derivedby specializingto the caseof a - 1. Then(5) becomes

T dPj1 (B,T) _ 2. Bh(T) T~ BrIthtd 6 dT z (H(T) 2 o (6)

+ [P1 (B,T I T) - P1 (O,T I T)lh(T)

Furthermanipulation on P, (B,TI T) and P, (O,TI T) leadsto -7-

dPj (B,T) 1 .B * h(T) lp (B,T I t sT) - Po (B,T I T)| dT zH (T)0 z (7) h fT z3 a t!) do z_B/H (T) )

From(7), the impactof a changein T on undernutritionas measured by P, de.)nds on two factors.First, there is theextent to whichthe incidenceof undernutritionfor thosewith age lessthan or equalto T exceedsor fallsbelow the incidenceof undernutritienfor thoseat age T. Second,there is the extentof originalundernutrition of thoseof age T who stopbeing undernourished with the intervention. Whilethe secondterm is somewhatconvoluted, the firstterm is intuitive--itis the differencebetween the marginal and the infra- marginalincidence of undernutritionfor givenT. The optimalvalue of the age cut-offoccurs when (5) is zero. Denotethis by T*. But it can be seenthat this leads to a complex equationfor T thatcannot be solvedin closedform. A numerical analysisis required,and we now turnto thatin the contextof a specificdata set.

3. OPTIMALAGE CUT OFFSFOR NUTRITIONALTARGETING: AN APPLICATION TO PHILIPPINEDATA The dataset usedhere comes from a householdsurvey in the Philippines.The dataand methodsof collectionare descriuedfully in Boulsand Haddad(1990). The datacontain information on nutrition among448 householdsin the southernPhilippine province of Bukidnon, .80 collectedand averagedover four rounds to accountfor seasonalityand otherfluctuations. The distinctivefeature of thedata Is thatthe foodintake of eachindividual in the householdwas obtained.The 24- hourrecall method was used(for an evaluationof thismethod, see Bouisand Haddad,1990). Thisintake can be convertedinto calories usingstandard conversion factors. !n addition,we can calculatethe calorierequirement for eachindividual baWed on 32 age-gender- pregnancystatus categories. For thisreason, the dataare to he viewedas illustrativerather than definitive measures nf individual- levelnutrient adequacy. 3 The calorieadequacy ratio, the ratioof intaketo requirement,is our measureof undernutritionin this application,and we use a calorieadequacy ratio of one as our benchmark(i.e. z - 1, in termsof the formulaein the previous section).We willrefer to thisas a "povertyline", although it is clearthat in our applicationit is an 'adequatenutrition line". The foodenergy deficit in our sample,namely the sum of the individualdifference between intake and requirement,is 1,048,631 caloriesfor the 2880individuals in the 448 households.4As in the previoussection, let 0 be an individual'scalorie adequacy ratio. If we did not haveindividual level data, we wouldbe forcedto assigna householdscalorie adequacy ratio to eachindividual in that household.Donate this variable by 4 . Figure1 showsthat the mean

3 For a fineranalysis, individual energy requirements would in additionbe basedon bodyweight and activity patterns.

'4 All programmesfor Tables 1, 2, 4 and Figures1-7 were written in MicrosoftFortran version 3.1. -9-

of 0 in an age groupIncreases, by and large,with age, but thatthe mearof 4 , doesnot. This insensitivityof * to age is alsobrought out by figure2. Herepoverty indices as givenby equation(1' are calculatedfor each age grouping based on 0 and P'ain,Pl. age is a sensitivepredictor of P,(O)but not Pi(4 ). Thisinsensitivity of 4 and itstransforms drives many of our resultsin the following

section.The sensitivityof X to agemay suggesta primafacie case for an upperage limitto caloriesupplements through feeding programs and the like. But whatis the optimalage cut off? Figure3 showsthe behaviorof P^ (B,T) as a functiz*.of T for

variousvalues of B witha set at 1. The top lineis for B * 0, which obviouslyshows no effecton P. of changesin T. The lowestline is when8 - 1 millioncalories, Just abou. the amountnecessary to eliminAtethe energydeficit if it couldbe targetedonly to those withdeficits. But whenthis is not possible,the curveshows the bestthat can be achievedwith age-bas!d targeting. As the upperage limitof eligibilityincreases, from low valuesof T, undernutrition falls. Thusthe marginaleffect of bringingmore people into the net dominatesthe infra-marginaleffect of spreadingresources more thinly overthe existingbeneficiaries. However, as figure3 shows, eventuallythis balance is reversed,and there is an optimalT. We callthis our scenario1. How doesthe optimalT, T, dependon a and B, the parametersof the problem?Table I presentsvalues of the optimalupper age eligibilityfor variousvalues of a and B and figure4 plotsthis surface.It is seenthat, by and large,T* increasesin a and in B. -10-

The factthat T increasesin B is intuitive- whenthere are more resources,mors people can be optimallybrought into the net. The factthat T* increasesin a is relatedto a greaterdepth of undernutritionat the mdarginrather than infra-marginally. At lower age eligibilitiesthere are so fewwho qualifyfor supplementthat thosewithin the net are pushedfar above the povertyline, therefore

thereis no inframarginalundernutrition, and as a increases, undernutritionat themargin is weighedmore heavily, and the optimal T is reachedat higherages.

4. THE VALUEOF INTRA-HOUSEHOLDINFORMATION The analysisof the previoussection is basedon a surveythat collectsinformation on individualnutrition within the household. Bt;tmost surveys available to plannersin developingcountries collect foodconsumption information only at the householdlevel. The usual methodof proceedingis ths;ito calculatea measureof household calorieade uacy,and to attributethis to eachindividual in the household.Intra-household inequality is thereforeignored. Intra-householdinformation on nutritionis costlyto collectand it wouldbe usefulto knowthe benefitsfrom its collection.In particular,how usefulis it in targeting?With our data set,we can providean answerto thisquestion. As before,let O be the true individualcalorie adequacy ratio and denote by $ the individual calorieconsumption adequacy ratio when each individual is simply allocatedthe household'scalorie adequacyratio. Withoutinformation on individualintakes, we wouldbe forcedto use the bivariate -11- distributionof $ and t, to calculatethe optimalupper age eligibility.We callthis our scenario2. Denotethe optimalvalue of T as t . Thusall those with age lessthan V willget nutrition supplementB/H( ' ). Undernutritionwith this supplement is given by expression(4) with T - Figure5 comparesthe behaviorof Po(B,T)and P.s(B,T)as a functionof T for 2 valuesof B at a - l. It is clearthat TI and V can be verydifferent. In general,the Ps*curves are flatterand lowerthan the P, curves.Intuitively, the flatnessis a reflection of the flatnessof the $ and Pm#lines evaluated within each age group (seefigures 1 and 2). The suppressionof intrahouseholdinequality as representedby $ resultsin age beinga muchpoorer correlate with observedundernutrition and hencea poorertargeting instrument. The marginalundernutrition reduction effect dominates the inframarginal effectuntil much higher levels of T are reached.In addition,the lownessof the Pg4 curvereflects the shallowness of observed , at all age groups,once intrahousehold inequality is suppressed. The differencebetween P. (B,T) andP* (B, ) is the differencein undernutritionwhen the wronginfonmation is used. A measureof thisdifference in calorieterms can be derivedas follows. If B. is the solutionof the followingequation:

P64#(B,T) (B,l -12-

thedifference between B. andB representsthe extracalories (or equivalentgain5)that would be neededto achievethe samelevel of undernutritionreduction with the 'wrong'age cutoff,t! , as was achievedwith the correct age cutoff,T'. Table2 presentsequivalent gainsfor variousvalues of B anda. The coststo not havingaccurate individuallevel calorie adequacyinformation upon which to identify r, whenexpressed as percentagesof theoriginal interventions, can exceed30%. The caloriecosts are substantialprecisely because actual calorie adequacyis stronglyassociated with age, and suppressionof intrahouseholdcalorie information deprives us of a usefultargeting instrument.

5. INTRA-HOUSEHOLDALLOCATION. LEAKAGE AND THE INPLICATIONSFOR TARGETING The analysisso far has assumedzero sharing of the calorie interventionthat the eligibleindividual brings into the household. Eitherbecause the interventionis dividedwithin the household,or throughreductions in non-interventioncalorie intake of the eligible member,it is highlyunlikely that intervention calories add, one-for one,to the totalcalories consumed by theeligible individual. What are the implicationsfor the age-basedtargeting of calorieleakage fromthe eligibleindividual to his or her fellowhousehold members? Doesit stillmake sense? In general,this depends on the extentto whichthere is intrahouseholdcalorie allocation away from the

5 Fora relateduse of the equivalentgain concept, see Ravallion(1989). -13- targetedgroup (TG), i.e. children. These tradeoffs are represented in Table3. Casenumbers 4 and 3 representscenarios 1 and 2 respectively, and case8 representsthe thirdscenario, food sharing. If within- householdfood sharing is substantialbut intrahouseholdfood allocationsare skewedaway from those with the lowestcalorie adequacies,age-based targeting is not feasible.Calories directed to theyounger housahold members end up in the handsof the older individuals. Specifically,our dataset allowsus to providean answerto the question'how useful is it to knowthe caloriereallocation outcome if age is usedas a targetinginstrument?'. As before,let O be the true calorieadequacy ratio, and leteach eligible individual receive B/H(T)calories. Now, however, the individualshares the calories withthe other household members. The arbitraryrule imposed here is thatthe ith individual'spre-intervention share of household calories,w,, is unaffectedby the intervention.6Thu the ith individualin the householdreceives (B/H(T)).w, calories. The upper age eligibilityat whichundernutrition in the entiresample is minimizedis denotedby T;. Figure6 showsthe behaviorof P#oc(B,T) as a functionof T for variousvalues of B witha set at 1. As with previousfigures, the marginal/inframarginal relationship exists althoughit is not as smooth.In theprevious scenarios individuals

6 Thisrule can be justified,however, by referenceto certain principlesof bargainingtheory; see Selten (1978). For an analysis of intra-householdbargaining over nutritional and otherresources, seeHaddad and Kanbur(1990b). -14-

couldonly receive less calories as the netwidened. In this scenario,however, individuals already in the interventioncan receive Mu caloriesas the eligibilityage is increased(if, for example, theirhouseholds contain two childrenquite close in age). Thus P,O,(B,T),the undernutritionindex, can go up and thendown. Figure7 comparesthe behaviorof Po+(B,T),Pa,(B,T) and P#(B,T) as a functionof T at B-i and a-I. It is clearthat T , can be verydifferent from T and t . Whenthe threefunctions are comparedon the samevertical scale, we can see thatP0C (B,T) is the flattestand lowestof the th,eelines. The fLnt_M is becausethe originalsampling design required eachrural household in the Philippinessurvey contain at leastone preschooler.Each household immediately receives calories even when the upperage eligibilityis only2. Thereforeage is onlya good targetinginstrument if poorhouseholds contain more young children and intrahouseholdallocations are not skewedaway from them. The sameanalysis with a moredemographically representative sample containingolder, richer households with no childrenwould produce a morecurved PO(B,T). The 1qLpilin of the lineresults from (1) the objective functionwe havechosen to minimize:undernutrition across all individualsin the sample,and (2)the largeabsolute calorie interventionsthat are reachingadults who are closeto the poverty linecompared to smallercalorie interventions reaching children who are far belowthe povertyline. If we had placedlarger weights in -15-

the objectivefunction on the alleviationof infantundernutrition, the curvewould be higher. The differencebetween P#O(B,Tc) and P.4k(B,T')is the costin foregoneundernutrition-reduction whenno foodsharing is assumedin the calculationof upperage eligibility,even though food sharing does indeedtake place. Again, if B. is the solutionof the following equation:

Poc(B,T*)- aoc(Bej

thedifference between B. and B is a measureof the costof makingthe wrongassumption on foodsharing. Table 4 presentsequivalent gains forvarious values of B and a. As can be seen,this cost is virtually zerosince age is no longerclosely associated with the delivery of calories to those who need them most.

6. CONCLUSION The objectof thispaper has been,first to developa framework for upper-limitindicator targeting, and to illustrateit for age basedtargeting of nutritioninterventions using data from the Philippines.Second, we haveprovided quantitative estimates of the valueof individuallevel information and of knowledgeof the intra- householdallocation of calories.For our sample,age provedto be a goodindicator of undernutrition.However, this proved not to be the casewith household level calorie adequacy which rendered age a0argnt]x lessuseful as a targetinginstrument, at an often -16-

considerablecalorie cost. Foodsharing, on the otherhand, trulv renderedage impotentas a targetinginstrument because of within- householdleakage. This effect was strengthenedbecause each householdcontained at leastone preschooler.Therefore, getting the age 'wrong'here had fewconsequences in termsof calorieforegone. We concludethat the designof nutritioninterventions can be verysusceptible to the levelof aggregationof availableinformation. This is consistentwith our findingsin Haddadand Kanbur(1990a), thatwhile poverty or undernutritionrankings of groupsdefined on householdlevel characteristics were not sensitiveto the levelof aggregation,the rankingsof groupsdefined on individual characteristicswere very sensitive. Possibly the costsof collection of theseintra-household data outweigh the benefits,but the experimentsin thispaper begin to answerquestions about the costsof M collectingthem. igure 1: Man calorie adequacy within each age group and Ohat for 0 1.4 1.3- 1.2- roancalorie 1 adequac~~~~~~~~~j withinage ~~~~ ~nean X *-,. * *.* n''""'at

9.6 9.5

1 11 21 31 41 51 61 age group (irs) -18-

,4 -

Om~~~~~~~C

S.. U,~~~~~~~~~...... o .- ~12S¶4*.. . . La w S..~~~~~~~~~~......

P4 ~~ ~ ~ ~ ~ ~ .P

' 0r) ...... i.

00

4'~~~~~~~~~~~~~~~~~~~~~~~~~~~~- 1 '4p4~~~~~~~~~~~~~~~c

ZI.

I 2~~~~~~ V u Figure3: Undernutritionlevels, ac=l, for differentupper age cutoffsand calorieinterventions (B=nillions of calories)

8.2 8.18 -P1, B=O 8.16 811 [ \------'|---1,-= 25|N ft 8.1:2 ,.--.-P1a.=8.S 8.14lPl, B=O._5 &, ,M,,.,c.-a~~~~~ - -m P 1, EB8.715 8.886.16 .

8 .E;. ~~~~~~~~~~~P1, Bt=1

2 7 12 17 22 27 32 37 42 47 52 58 65 upper age eligibilitg(ygears) -20-

Figure4: Surfacesof undernutrition-minimizingupperage eligibilities for differentcalorie interventions at different sensitiviesto undernutrition

14.9 N

21.21\

:OotRm 14.9 / / I // I\ /\ Optimal upper age ellibility 84///\,

JIf 2.3 -~/t

0.7~ ~ ~ . 0.1 Sensitivity to depthof undernutrition Caorie intervention(B)() Cl (millions) Figure 5: Undernutrition, =1, individual (0) versus household (Ohat) level data

6.16______

0.14 -P1i, B=0.5

P8 .12 P1P, B=1 l

ftE. . -- - -- n e…ee…-… _-_ ---- P10hat, B=1

o.86 Plhat, B=8.5

2 7 12 17 22 27 32 37 42 47 52 58 65 upper age eligibilitg (years) Figure 6: Undernutrition, a=2: intra-household calorie shares naintained

0.813 …~~~~~~~~~~~~~~

0.8125-** , , l

0.012 - - P0c(m=2,b=1.00)

0.0115 \\ _.\ ~ . - - --- P0c(m=2,b=B.25)

- = ~-oo P0c(K=2,b=0.50) 0.811

0.E*185 I**I2* * * *t* , *t t ' ' 2 7 12 17 22 2 32 37 42 47 52 58 65 upper age eligibility (years) Figure 7: Undernutrition, 0K=1,for individual level (0) householdlevel (Ohat), both no leakage, and individual level and leakage (0c) 6.18

8.16 _ 8.14 IB 1

6.1 Pa - P0hat(M=1,b=1.00) 8.88

P0c(K=1,b=1 .88) 8.84- 8.6 food sharing 8. 2 7 1217 22 27323742 4752 5865 upperage eligibility(gears) -24-

Table 1--Optimal age cutoffs (T) for various values of a and calorie intervention

Intervention (millionsof calories) a values 0.1 0.5 1

0 2.30 6.00 11.60 1 5.00 13.30 17.50 2 5.40 14.30 21.20 -25-

Table2--The equivalent cost (in calories) of not havingindividual-level data withwhich to target

---- , ------. - , -- -- - a calorie T (X)T ( 4 ) P (T (T)) P (T( 4 )) differenceequivalent intervention(yrs) (yrs) V(1) (2) (2)-(1) gain(cals) 0 100000 2.3 3.5 0.66736 0.67500 0.00764 20200 0 200000 3.7 5.1 0.63090 0.64028 0.00938 18300 0 300000 4.8 6.2 0.59688 0.60972 0.01284 23500 0 400000 5.8 8.3 0.56285 0.58576 0.02291 55500 0 500000 6.0 9.1 0.53125 0.54757 0.01632 39800 0 600000 7.0 10.5 0.50104 0.51910 0.01806 51100 0 700000 8.8 11.4 0.46840 0.49236 0.02396 60700 0 800000- 9.4 13.4 0.43368 0.46944 0.03576 96900 0 900000 10.5 15.7 0.40799 0.44549 0.03750 100000 0 1000000 11.6 18.7 0.38194 0.42014 0.03820 109800 1 100000 5.0 9.1 0.16722 0.16865 0.00143 2500 1 200000 7.3 11.5 0.15112 0.15270 0.00158 3700 1 300000 8.5 14.2 0.13661 0.13809 0.00148 3200 1 400000 11.8 18.8 0.12289 0.12589 0.00300 14600 1 500000 13.3 55.0 0.11008 0.12735 0.01727 153500 1 600000 14.2 65.4 0.09803 0.11679 0.01876 176900 1 700000 14.2 65.4 0.08729 0.10655 0.01926 192800 1 800000 17.5 65.4 0.07745 0.09683 0.01938 205700 1 900000 17.5 65.4 0.06835 0.08764 0.01929 217500 1 1000000 17.5 65.4 0.06047 0.07893 0.01846 221700 2 100000 5.4 11.9 0.05681 0.05748 0.00067 0 2 200000 11.4 18.3 0.04882 0.05013 0.00131 4000 2 300000 11.9 54.9 0.04173 0.04878 0.00705 113400 2 400000 14.2 54.9 0.03560 0.04341 0.00781 140700 2 500000 14.3 65.4 0.03044 0.03860 0.00816 163800 2 600000 17.5 65.4 0.02617 0.03410 0.00793 175000 2 700000 17.5 65.4 0.02230 0.03000 0.00770 187800 2 800000 19.8 65.4 0.01904 0.02627 0.00723 194500 2 900000 21.2 65.4 0.01622 0.02291 0.00669 198300 2 1000000 21.2 65.4 0.01387 0.01988 0.00601 195600 Note:the tolerancefor (2)-(l)is 0.001,with incrementsof 1000calories. -26-

Table3-Targstins idividals: Dsribiltity ad feaibility

DOsirable Feasble

to"e (1) (2) (3 (4) t5) (6) Are _uia9Inee Doe TO a is themr is there Any of failuro masured DoesIt tkesnse to target lnterventfmw Scerlo to lowr utrient su*stnftil signif leant Intre- at an ndividlO scenarlolevel? ant sutrisnt adeACy? houhold food Intrahouseld houshold admcy afW ss*stitutimn ftrient IneqaslIty? eer for TO activity? inqality ay

I Ye yu no no no desirable, feasible 2 ye yes no no we desiroble.fesfble, wrengag 3 yes yes no ye no desirable,feasible, e 2 4 Yu Yes no yeu yae desirable,feasible I S Ys Ye Ys no n dfirable, feaible 6 VWa we we no Ye desirable, Mntlx lnfesiblet 7 s we VWe wes no desirable,inruntz fnfmaible. wru age a we we ws dsirabte. not Infeasble 3 Notes:

I ot wouldagree that the, wer to qetion (1) is ywe'. Na microdata sets find lowr calorie adeqacies Is also swe'. Thetatter result for prechoolerssugtin that the ser to (2) coutdbe true or false. Faisenesscould cme frommesurnt errors on the Intakeside (hae prescholersbeen fully weaed? do they exhibit sacking behavior?) or the reqflrnts sfde. On the other hwd, the results health presooler. could be a true reflectiln of a lak of a reference rorm for a

2. O(M)Is dilficult to aer, but a stron posibility exists for sherirg of a presdoler's food increment,or incrementIs dlltd-epecifIc. a reictlon In replar food to preschoolerIf the 3. 0(4): Researchwith this date set sugsts that inerality exists, slthough asomnt (4) could be 'no'. pblm men that althoug the nser to (S) Is "ye'. the answerto 4 0(6): Theuwr to this qustion depnds an a ohole host of logistic and ost varables that w he cenw iently abstrated from, but &lSeISmfLm. how doesthe anser to this qLmstiondepnd on the swes to qtlens 1-5? .27-

Table 4--The equivalent cost (incalories) of assumingno leakage whencomputing optimal upper age eligibilities

...... O.*...... O...... @...... a calorie T*e(O) T (0) P *O(T. (0)) P(T*(0)) difference equivalent interv (yrs) (yrs) (if (2) (2)-(l) gain (cals) ------. …--- - . ------. 0 100000 5.3 2.3 0.67535 0.68160 0.00625 1000 0 200000 11.0 3.7 0.65382 0.65903 0.00521 1000 0 300000 13.1 4.8 0.63194 0.63889 0.00695 1000 0 400000 3.8 5.8 0.61042 0.61979 0.00937 1000 0 500000 4.5 6.0 0.58611 0.59167 0.00556 1000 0 600000 4.8 7.0 0.56424 0.57257 0.00833 1000 0 700000 4.4 8.8 0.54410 0.55035 0.G0625 1000 0 800000 7.3 9.4 0.52431 0.52674 0.00243 1000 0 900000 8.0 10.5 0.50382 0.50868 0.00486 1000 0 1000000 9.0 11.6 0.48403 0.48993 0.00590 1000 1 100000 12.1 5.0 0.17562 0.17630 0.00068 0 1 200000 13.9 7.3 0.15535 0.16607 0.00072 0 1 300000 13.9 8.5 0.15550 0.15652 0.00102 1000 1 400000 13.9 11.8 0.14608 0.14662 0.00054 0 1 500000 18.4 13.3 0.13702 0.13734 0.00032 0 1 600000 18.4 14.2 0.12835 0.12860 0.00025 0 1 700000 20.4 14.2 0.12010 0.12045 0.00035 0 1 800000 20.4 17.5 0.11221 0.11252 0.00031 0 1 900000 20.4 17.5 0.10470 0.10504 0.00034 0 1 1000000 20.4 17.5 0.09758 0.09793 0.00035 0 2 100000 13.9 5.4 0.06236 0.06296 0.00060 0 2 200000 18.4 11.4 0.05750 0.05762 0.00012 0 2 300000 18.4 11.9 0.05297 0.05305 0.00008 0 2 400000 18.4 14.2 0.04876 0.04886 0.00010 0 2 500000 18.4 14.3 0.04485 0.04499 0.00014 0 2 600000 18.4 17.5 0.04123 0.04131 0.00008 0 2 700000 18.4 17.5 0.03787 0.03796 0.00009 0 2 800000 18.4 19.8 0.03477 0.03487 0.00010 0 2 900000 18.4 21.2 0.03190 0.03200 0.00010 0 2 1000000 18.4 21.2 0.02927 0.02935 0.00008 0 Note: the tolerance for (2)-(l) is 0.001, with increments of 1000calories. -28-

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