Economics of Supplemental Feeding Public ... - All...

Economics of Supplemental Feedingof Malnourished Children:Leakages, Costs, and Benefits SWP451

World Bank Staff Working Paper No. 451

April 1981

Prepared by: Odi K. KnudsenAgriculture and Rural Development

Department andSouth Asia Programs Department

Copyright ® 1981The World Bank1818 H Street, N.W. f 7 k A Washington, D.C. 20433, U.S.A. D O iNOTThe views and interpretations in this document are those of the author R E M O V E

PUB and should not be attributed to the Vbrid Bank, to its affdiatedHG organizations, or to any individual acting in their behalf.3881.5.W57W67no.451

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The views and interpeetations in this document are those of the author andshould not be attributed to the World Bank, to its affiliated organizations,or to any individual acting in their behalf.

WORLD BANK

Staff Working Paper No. 451

April 1981

ECONOMICS OF SUPPLEMENTAL FEEDING OF MALNOURISHED CHILDREN:

LEAKAGES, COSTS, AND BENEFITS

This paper analyzes some of the economic issues involved in thesupplemental feeding of malnourished children. The paper is divided intofour major sections. The first section discusses the potential leakages toother family members and other households that are common to both on-siteand take-home feeding programs. The second section describes the proba-bility of errors involved in using entry and exit criteria in supplementalfeeding programs and describes a feasible criterion for entry based on achild's weight gain. The third presents a simulation model for estimatingthe number of beneficiaries and costs of supplemental feeding under differentprevelances of.malnutrition, durations of feeding, and probabilities ofrecovery and relapse. The fourth calculates the costs and beriefits of asupplemental feeding program by using efficiency, social and basic needapproaches.

Although alleviating poverty and increasing food production arethe only permanent solutions to malnutrition, the existing and continuingmalnutrition among children and the legacy it carries requires that tar-getted interim interventions, such as supplemental feeding, be adopted whichincrease the food intake of the population most in need, the malnourishedchildren of the poor. However, in supplemental feeding, significant levelsof substitution and sharing of supplemental food can be expected. There-fore, the ration should be fed on-site and be of a size near the full nutri-tion requirements of the child to assure effectiveness, and the duration offeeding should be short, two to three months to reduce leakages. Also,entry and exit criteria should be an integral part of a feeding programsince, without it, the program takes on the character of an income transferand substitution will be high and effectiveness low. The analysis of thispaper demonstrates for a project in India that supplemental feeding pro-grams are economically justified if minimum improvements in mortality ratesand more substantial increases in productivity (originating from the comple-mentarity of nutrition and education) take place. This becomes especiallythe case if social and basic needs benefits are included along with thestandard efficiency gains.

Prepared by: Copyright © 1981Odin K. Knudsen The World BankAgriculture and Rural Development 1818 H Street, N.W.

Department and Washington, D.C. 20433South Asia Projects Department U.S.A.

TABLE OF CONTENTS

Page No.PREFACE

SUMMARY AND CONCLUSIONS

I. INTRODUCTION ......................................................... 1

II. LEAKAGES FROM SUPPLEMENTAL FEEDING PROGRAM ..... ........ 5

Intra-Family Leakages . .............................. ....... 6Leakages to Unintended Beneficiaries ................... 12The Income Leakage . .. ................ ..... 19

III. ENTRY AND EXIT CRITERIA FOR A SUPPLEMENTALFEEDING PROGRAM .......................................... 22

The Entry Criteria ...... ............. ........... ....... .. . 22The Exit Criterion .. ............................... . 27

IV. THE COSTS OF SUPPLEMENTAL FEEDING AND THEQUANTITY OF FOOD REQUIRED ...... .......................... 29

The Mathematical Model ..... ..................... ... ....... . 29A Simulation Model of Supplemental Feeding ............. 33

V. THE BENEFITS OF SUPPLEMENTAL FEEDING OFCHILDREN AND PREGNANT AND LACTATING WOMEN .... ............ 39

The Project ........................................................ 40The Efficiency Benefits .... ............................ 42The Productivity Benefits .................... ......... 48

VI. A BENEFIT AND COST ANALYSIS OF A SUPPLEMENTALFEEDING PROGRAM .. .. . . .............. . .. .

Efficiency Benefits and Costs Attributing ZeroSocial Cost to Population Expansion .................. 54

The Social Benefit Analysis ............................ 58

LIST OF TABLES AND FIGURES

I. INTRODUCTION

Table 1 : Average Dairy Intakes of Children and PregnantLactating Women in Tamil Nadu .............. 3

Table 2 : Feeding Programs in Tamil Nadu - 1976-1977 ... 4

II. LEAKAGES FROM SUPPLEMENTAL FEEDING PROGRAM

Figure 1 : Probability Tree on Entry Into Feeding Program 15

Table of Contents (cont.)

Page No.

Table 3 : Probabilities of Committing Entry or ExclusionErrors ........................................ 16

Table 4 : Probability of Committing Entry Error UnderDifferent Correlations Between Periods ofWeight Gain ................................... 17

III. CRITERIA FOR ENTERING AND EXCLUDING CHILDREN FROM ASUPPLEMENTAL FEEDING PROGRAM

Table 5 : Mean and Standard Deviations of Weights andMaximum Intra-Daily and Inter-Daily WeightChanges ....................................... 24

Table 6 : Maximum Weight Variation Between the SameTime of Day ................................... 24

Table 7 : Probability of By-Passing Children from Ages6 to 11 Months with Weight Changes of 500to -100 Grams/Month ........................... 28

Table 8 : Probability of By-Passing Children from Ages12 to 35 Months with Weight Gains from 167to -33 grams per Month ........................ 28

IV. THE NUMBER OF DIRECT BENEFICIARIES OF SUPPLEMENTALFEEDING AND THE QUANTITY OF FOOD REQUIRED

Figure 2 : Model of Entry and Exit from SupplementalFeeding Program ............................... 34

Table 9 : Summary of Assumptions of a SupplementalFeeding Program ............................... 36

Table 10 : Average Beneficiaries Per Day as a Functionof Six-Month-Relapse-Rate - PartialFeeding ....................................... 38

Table 11 : Quantity of Food Required as a Function ofSix-Month-Relapse-Rates - Partial Feeding ........ 39

V. THE BENEFITS AND COSTS OF SUPPLEMENTAL FEEDING OFCHILDREN AND PREGNANT AND LACTATING WOMEN

Table 12 : Project Description ............................. 40

Figure 3 : Probability of Surviving With and WithoutProject ....................................... 43


Page No.

Table 13 : Assumptions on Mortality - Calculationsof Benefits ................................... 45

Figure 4 Earnings Streams With and Without CompensatingBirth Rate Declines ........................... 47

Table 14 : Incremental Increase in Earnings FromImprovement in Cognitive Developmentas Measured by Preschool Ability Scores ....... 50

Table 15 Assumptions on Earnings Streams of RuralRich and Poor ................................. 51

Figure 5 : The Project's Effect on Population .

Table 16 Increase in Population Due to ProjectAssuming No Change in Birth Rate:Narangwal Assumptions ......................... 54

Table 17 Project Benefits and Costs ...................... 56

Table 18 : Efficiency Cost and Benefits: SensitivityAnalysis for Present'Values ......... .......... 58

Table 19 : Sensitivity Analysis to Project Assumptions: 59Economic Rate of Return for EfficiencyGains Without Social Costs to PopulationIncrease or Birth Rate Reduction.

Table 20 Estimates of National Parameters for Project 61Analysis: India (Summary).

Table 21 : Percentage of Individual Calorie Need 63Fulfilled by Age.

Table 22 : Consumption Data for Rural Tamil Nadu Based 68On NSS Survey Estimates (1974).

Table 23 : Distributional Weights for Children, Pregnant 69and Lactating Women and Households as aFuncton of Expenditure Group.

Table 24 : Expected Disbursement of Food by Expenditure 70and Basic Needs Distributional Weights.

Table 25 : Assumptions of Benefit Analysis .... ............. 71

Table 26 : Net Present Value, Social Rate of Return,and Sensitivity at Appraisal Values .... ....... 74

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Page No.

Table 27 : Economic and Social Rate of Return andNet Present Value Under DifferentAssumptions on Birth Rate Change .... .......... 75

Table 28 : Annual Social Costs Per Death AvertedNecessary to Have a Rate of ReturnEqual to 10% .................................. 76

Preface

This paper is part of the research sponsored under RPO 67180.

Most of the work was conducted when I was in the Agriculture and Rural

Development Department. I completed the research after my transfer to South

Asia Projects. I am indebted to many people for their continuing contribu-

tions and support of this work on food and nutrition. In particular,

Pasquale Scandizzo contributed significantly to this paper, especially to

the section on the cost and benefit analysis. We continue to be partners in

food and nutrition research and, as such, much of this work derives from our

discussions and search for some insights into this important policy area.

In addition, Montague Yudelman and Graham Donaldson and their interest in

food and nutrition policy provided the impetus for this paper and the series

of earlier papers. I am also indebted to the others who have supported and

contributed to this research: Samir Basta, Alan Berg, Rolf Carrier, James

Greene, Dr. Colin McCord, Shlomo Reutlinger, Emmerich Schebeck, Marcelo

Selowsky, Gurushri Swamy and Ewen Thomson. Also, Lloyd Harbert assisted me

in the computer work and the design of the food supplement program. Beverly

Bolden typed the draft manuscript and continued to support me in many admin-

istrative matters. But, at last, despite these contributions, I remain the

sole source of any errors.

SUMMARY AND CONCLUSIONS

1. The purpose of this paper is to present some of the economic con-siderations in the design of supplemental feeding programs for children.The paper is organized as follows: The first section describes the need forsupplemental feeding, the varieties of programs, and their general failings.The second section presents some of the leakages that occur. The third dis-cusses entry and exit criteria, the fourth, the costs of feeding, the fifth,the benefits, and the sixth presents a benefit and cost analysis. The paperis based upon a project designed for the State of Tamil Nadu, located in thesouth of India. With a population of abour 48 million, Tamil Nadu rankseighth in GNP per capita among Indian states, its population primarily growingand consuming rice. As in the rest of India, under-consumption and malnutri-tion are widespread.

2. Although income growth and expansion of food production at ratesabove those experienced in the past would alleviate some malnutrition, theprospects are for continuing widespread suffering into the 1990s. Even thoughpoor families will spend a large part of their income on food, malnutritionwill persist especially among children because of increasing food prices andthe uneven distribution of food within the household. 1/ Although alleviatingpoverty and increasing food production are the only permanent solutions tomalnutrition, the existing and continuing malnutrition among children and thelegacy it carries for the future adult population requires that something bedone now. The most specific and targetted solution is to increase thefood intake of the population most in need, the malnourished children ofthe poor. This is the objective of supplemental feeding programs for chil-dren.

Leakage from Supplemental Feeding Program

3. However, supplemental feeding programs invariably induce leakages tounintended beneficiaries. Leakages (other than pilfering) in a supplementaryfeeding program are of three types: (a) intra-family leakages from the foodeither directly or indirectly being shared by other members of the family; (b)income group leakages occurring when children in the feeding program are notmalnourished and are from families with sufficient income to feed their chil-dren; and (c) income leakages where the family's opportunity cost of partici-pating in the program reduces the net value of the food transfer.

4. From this paper's analysis of leakages, it appears certain thatleakages from a feeding program distributing a partial ration will be sub-stantial, whether the food is taken home or fed at the center. Also, unlessthe education component is considered to have sufficient value to compensatefor the loss of income, the mothers of malnourished children will not parti-cipate in the program and the effort to reorient the family's distributionof food toward the malnourished child will be ineffective. In on-site, fullfeeding programs, losses through these leakages are less than in partialfeeding programs, however, the costs of food are higher as the ration sizeis larger.

I/ See 0. Knudsen and P. Scandizzo, Nutrition and Food Needs in DevelopingCountries, World Bank Staff Working Paper No. 328.

5. The lessons from this analysis on leakages are as follows:

(a) Significant levels of substitution and sharing (the latterin a take-home program) of supplemental food can be expected.To assure effectiveness, ration sizes should be near thefull nutrition requirements of the child, should be fed on-site and the duration of feeding should be short, two tothree months.

(b) Entry and exit criteria should be an integral part ofany feeding program. Without it, the program takes onthe character of an income transfer and substitution willbe high and effectiveness low. Two types of entrycriteria are feasible: one based on the stock conditionof the child; the second on the trend in weight of thechild. The second criterion is the most difficult toimplement and has the greatest probability of committingType I entry error, where a child who does not requirefeeding is entered. However, it has the advantage ofidentifying trends toward malnutrition and thereby avoid-ing the damage to a child's body and intelligence result-ing from malnutrition.

(c) An income leakage occurs when income is foregone (throughthe opportunity cost of labor) in taking a child to a feedingcenter; therefore to enhance enrollment and attendance, theration size must be of sufficient value to compensate for thethe loss in income. As a consequence, the ration size shouldapproach quantities suffidient to meet the child's entireneeds and the center should allow for the child staying atthe site throughout the day. The first provides an appropriateeconomic incentive to bring the child in for feeding; thesecond reduces thelopportunity cost of interrupting a workday to bring the child in for feeding. 1/ Also, the seasonalnature of work opportunities for the mother needs to beaccounted for, with additional staff required during theharvest and sowing season, to assure that children requiringfeeding are brought to the center.

Criteria for Entering and Excluding Children from a SupplementalFeeding Program

6. Weight trend criteria can be used for entering and exiting chil-dren from a feeding program. The principal hypothesis of a feeding pro-gram using weight gain entry criteria is that a child that is not gainingweight adequately or is losing weight can be identified through a program ofmonthly weighings and that timely on-site feeding of a supplemental food tothis child will (in the majority of cases) result in the child's return toadequate weight gain. As a consequence, much of the detrimental effects ofmalnutrition can be avoided. To implement this program entry criteria are

1/ If older siblings bring the child in, much of the- educat-iQnal benetitsto the mother are lost and the child's attendance at thie feeding centeris often less frequent.

established which identify inadequately growing children with only a smallprobability of error, yet exclude, with a high probability, children thatare gaining weight adequately and hence do not require supplemental feeding.Likewise, exit criteria are established that assure that the children enteredinto the feeding program have returned to adequate weight gain before beingpermitted to leave the program.

The Number of Direct Beneficiaries and Costs of Supplemental Feeding and theQuantity of Food Required

7. In a supplemental feeding program, the number of children that willactually be fed a supplement and the costs of feeding will depend on severalfactors outside the influence of the program. The external factors includethe price of food and its general availability, income levels and its distri-bution, the quality of the water supply, the birth rate and the season of theyear. These determine to a large extent the degree of malnutrition that canbe expected in any village or region and hence the number of children eli-gible for the feeding program. The number of children actually fed out ofthe total number eligible depends on the incentives of potential beneficiariesto participate due to factors such as the size of the food supplement and itsperceived value, the opportunity cost to the mother of bringing the child infor feeding, the effectiveness of the nutrition worker, and the perceivedbenefits to be obtained from the education and nutritional services. Thenumber of chlldren that remain in the program after the intended days offeeding depends on the effectiveness of the education in inducing the familyto feed the child more at home (in partial feeding programs) and the caloriecontent of the ration given at the feeding center. Since some of the childrenbeing fed will have been in the program before but have relapsed afterleaving the feeding program, the number in the program during any given monthwill also depend on the relapse rate, which in turn is determined by the ex-ternal factors described above. As a consequence of these influences on thenumber of children being fed, the costs of feeding and the estimates of aprogram's beneficiaries are complicated and largely dependent on the environ-mental factors.

8. A simulation model has been constructed to estimate beneficiaryflows and the quantity of food required. The model is designed to estimatebeneficiary flows by age group for two categories of children: those thatare not third degree malnourished and entered by weight gain criteria andthose that are third degree malnourished. Each of these groups has a differ-ent probability of becoming malnourished and recovering from malnutrition dueto the feeding. The simulation model estimates beneficiary flows and costsas a function of the rate of malnutrition, rate of relapse, and a feedingprogram's efficiency in returning children to adequate weight gain or adequatenutritional status. The model consists of three principal components: onethat stimulates entry into the feeding program, one that describes the feedingand the monthly probabilities of returning to adequate weight gain, and onethat consists of the monthly probabilities of relapse through the first sixmonths after leaving the program.

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The Benefits and Costs of Supplemental Feeding of Children andPregnant and Lactating Women

9. The section on benefits quantifies both the efficiency andsocial benefits of supplemental feeding of children and pregnant and lactatingwomen in Tamil Nadu. The efficiency benefits are due to the increased produc-tion originating from extended working years and productivity gains of bene-ficiaries when they become adults. These benefits originate from reducedchildhood malnutrition and mortality. The social benefits result from incomein the form of food being distributed to the poor and from a basic needscommodity being supplied to those in need. The analysis of these socialbenefits is based on the Squire and van der Tak methodology of social benefitanalysis and the 9candizzo-Knudsen approach to the.evaluation of the benefitsof basic needs programs.

10. The project produces an anticipated economic rate of return from the,efficiency benefits of reduced mortality and increased productivity of about14% if no social costs are attached to a larger population or if there is nota compensatory birth rate reduction. If the annual social cost is US$100 percapita, or about equal to the consumption of an individual at the poverty line,then the rate of return equals the opportunity cost of capital of about 10%.If there is a compensatory birth rate reduction after a five year lag, thenthe rate of return is about 12%. Including social benefits raises the rate ofreturn to about 22% and adding a basic needs premium contributes an additionaltwo percentage points.

11. From the cost benefit analysis of a Tamil Nadu project, theseconclusions are evident:

(a) Supplemental feeding, if it results in at least a 10% improve-ment in mortality rates and a relatively modest 10% increase inproductivity, is economically justifiable, especially if accountis taken of social and basic needs benefits.

(b) Furthermore, the economic and social rate of return is re-markably invariant to changes in any individual performanceparameter and to many parameters if varied in tandem.

(c) The addition of social benefit analysis contributes about7 percentage points to the rate of return under the assumedperformance. Under the worst case assumptions, the addi-tion of social benefits raises the rate of return from belowto above the opportunity cost of capital.

(d) However, if social costs are attached to population increases,than these results become less favorable. In particular, ifthe social cost of a population increase is at nearly theannual consumption of an individual,then, at assumed parametervalues, the rate of return remains above the opportunity costof capital only if social benefits are taken into account.With social benefits included, then the annual social costof an additional person can be as high as Rs 1,200 before therate of return falls below the opportunity cost of capital.

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(e) If account is taken of compensatory birth rate reductions,then the results change slightly with the rates of returnfalling about 2 percentage points. Hence, if indeed familiestarget for a desired number of children and no social costsare taken into account for interim population increases, thenthe project remains viable over a broad range of performance.

(f) Finally, the issue remains if successful performance can beexpected when the ration is as small (from 240 to 480 calories)as in this project. A small ration increases project risksconsiderably because of high risk of low and irregularattendance, slow response to feeding, and substitution atother meals, while a larger, more costly ration could betolerated without the rate of return declining to below theopportunity cost of capital. In other words, there is con-siderable room for feeding amounts and cost increases beforethe project becomes inviable. The project benefits and costsanalysis points to increasing the ration to reduce the risk:of poor project performance.

I. INTRODUCTION

1.01 The purpose of this paper is to present some of the economic con-siderations in the design of supplemental feeding programs for children.The paper is organized as follows: the first section describes the needfor supplemental feeding, the varieties of programs, and their general fail-ings. The second section presents some of the leakages that occur. Thethird discusses entry criteria, the fourth, the costs of feeding, the fifth,the benefits.

1.02 The paper is based upon a project designed for the State of TamilNadu located in the south of India. With a population of about 48 million,Tamil Nadu ranks eighth in GNP per capita among Indian states with its popula-tion growing and consuming primarily rice. As in the rest of India, under-consumption and malnutrition are widespread. Although precise data areunavailable, estimates indicate the severity of these conditions.

1.03 The latest study from the National Nutrition Monitoring Bureau (NNMB)reports that the average calorie intake in Tamil Nadu was 2,477 calories perconsumer unit 1/ in 1977, which is slightly higher than the Indian Council ofMedical Research's (ICMR) requirement of 2,400. But it also found that 35% ofthe households and 44% of the individuals had inadequate calorie intakes. 2/The cumulative, results of their surveys from 1972-1976 show that about 42%.of rural households have calorie consumption rates below 80% of the ICMRrequirement and 31% of them are below 70%.

1.04 The other major survey of consumption in Tamil Nadu, the 26th roundof the National Sample Survey (NSS) (July 1971-June 1972) records an averageintake of 2,394 calories per consumer unit in rural Tamil Nadu. It also findsthat 26% of the households consume less than 80% of the ICMR requirements and18% consume under 70% of the requirement.

1.05 A survey sponsored by the USAID, the Tamil Nadu Food Habits Survey(FHS), found that 50% of over 12,000 individuals surveyed had calorie intakesbelow 80% of calorie needs, defined as 2,830 for a male of 20-24 years, 2,660for a male 25-29 years old, and 2,500 for a male of 30-34 years. These adult

\calorie needs are considerably higher than the ICMR standard of 2,400 calories.The standard used by the FHS for children is considerably lower than the ICMRrequirement, thus producing a statistic that is incompatible with the estimatesof the NNMB and the NSS. The FHS household data indicates that about 30 to35% of the households consume less than 70% of their calorie needs.

1/ A consumer unit is an individual converted to an adult equivalent by aset of weights related to age and sex.

2/ Calorie inadequacy is defined by the NNMB as consumption 30% below theICMR (1968) requirement.

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1.06 By any standard, these statistics indicate considerable caloriedeficiencies in Tamil Nadu. The cumulative results indicate that the percent-age of households with inadequate calorie intake (below 70% of the ICMRstandard) is probably between 20% and 35%. The percentage of individualsconsuming below 70% of the calorie requirement is about 35 to 40% accordingto the FHS and about 45% according to the NNMB.

1.07 These levels of under-consumption are intensified for the childrendue to the uneven distribution of food within the household. As shown inTable 1, average calorie intake of children in Tamil Nadu ranges from 47 to 85percent of requirements depending on age. The Tamil Nadu Food Habits Surveyfinds that the severest deficit occurs between 6 and 30 months of age and thatthis deficit exists even when the food availability in the household, ifproperly distributed, is sufficient to meet the calorie needs of each of itsmembers.

1.08 These calorie deficits combined with the high incidence of diseaseresult in many children being malnourished in Tamil Nadu. A 1974 survey bythe National Nutrition Monitoring Bureau found that 46% of male preschoolchildren were between 75 and 90% of normal weight for age (first degree mal-nutritin), 30% were between 60 and 75% (second degree malnutrition) and 9%were below 60% (third degree malnutrition). For female preschool childrenthe pattern is similar, with slightly less severe third degree malnutrition,but high incidence of the moderate second degree malnutrition. Some of thesechildren are actively malnourished (wasted) while about 30 to 33% are consideredto have experienced malnutrition sometime in the past but now have achievednormal weight for height (stunted). In other words, the NNMB survey estimatesthat nearly 50% of the children in Tamil Nadu are actively malnourished.

1.09 The prospects for normal income growth and increased food productionto alleviate malnutrition appear dismal. Even though poor families will spendlarge portions of their income on food, malnutrition will persist amongchildren into the 1990s because of increasing food prices and the unevendistribution of food within the households. 1/ Although alleviating povertyand increasing food production are the only permanent solutions to malnutri-tion, the existing and continuing malnutrition among children and the legacyit carries for the future adult population requires that something be donenow. The most specific and targetted intervention is to increase the foodintake of the population most in need, the malnourished children of the poor.This is the objective of supplemental feeding programs for children.

1.10 To attempt to supplement food intakes, the Tamil Nadu governmenthas adopted several types of programs, some of which are solely sponsored bythe State while others receive partial funding. Table 2 summarizes somepertinent statistics on the programs currently operating in Tamil Nadu.In addition to state programs, there are numerous smaller private programs,most notably the Erskine Hospital feeding program which receives assistance

1/ See 0. Knudsen and P. Scandizzo, Nutrition and Food Needs in DevelopingCountries, World Bank Staff Working Paper No. 328.

from the Royal Commonwealth Society for the Blind. 1/ The private programsgenerally have limited scope and funds.

Table 1: AVERAGE DAILY INTAKES OF CHILDREN AND PREGNANTAND LACTATING WOMEN IN TAMIL NADU

Age Group Calories % of ICMR Standard

12-23 months Boys 611 51Girls 567 47.3

24-35 months Boys 791 66.0Girls 798 66.5

36-47 months Boys 990 82.5Girls 940 78.3

48-59 months Boys 1,083 72.0Girls 1,037 69.0

60-71 months Boys 1,230 82.0Girls 1,222 81.0

Pregnant Women 1,856 56.3Lactating Women 1,959 52.9

1.11 The two most significant feeding schemes in the State are the MiddayMeals and the Balwadies programs. Of these two, the Midday Meals program isthe largest directing about 23,000 m tons of food to school age children.The Balwadie program, minor in comparison, feeds preschool children for 300days. It uses an entry criteria based upon a child's age for weight and feedsa ration of locally procured foods. The privately sponsored Erskine programfeeds children a high calorie ration for a period of 90 days or until thechild improves one category in nutritional status. Also, more intensive rehab-ilitation of severely malnourished children is conducted by Erskine Hospital.

1.12 In general, feeding programs for children fall into three categories:(1) General welfare feeding such as the Midday meals program where the princi-pal entry criteria is being a student in school; (2) partial or supplementalfeeding programs that depend on small increments in food intake given atfeeding centers (the Balwadies scheme); and (3) rehabilitative feeding wherelarge calorie rations are given several times during the day (Erskine Hospitaltype schemes). Such programs are usually directed toward severely malnou-rished children. The first type of feeding is directed at children regardlessof nutritional status; the second in most cases has an entry criteria but inmany cases generally not an exit criteria; the third is the most targetted,

1/ This program, although once operating in 46 villages, has been cut backto only a few demonstration sites.

Table 1: FEEDING PROGRAMS IN TAMIL NADU - 1976-1977

Costs PerBeneficiaryPer Feeding

Administering Days Day (RS) Costs of Estimated StateDepartment Fed Ration 0.43 Quantity Food Expenditure 5/ Total Costs 2/

Calories Protein Foodgrain Other (Rs '00D) (Rs '000) (Rs '000)(Kcal) (gma) (mt) (mt)

1. Midday meals Program Education 200 418 24 0.43 13,998 3/ 1,482 74.844 46,300 99,610days 9,297

II. Modified Special Program Social 300 347 23 0.28 5,110 14,512 4/ 15,284Welfare days

III. Special Nutrition Program Social - 281 15 0.30 2,610 230 11,700 1,800 12,310Welfare

IV. Mother and Child Welfare Social 300 282 15 0.31 2,110 190 8,997 4/ 10,369(Balwadies) Welfare days

V. Maternity to Child Health Health - 280 15 0.26 2,490 220 9,612 3,000 10,206

VI, Midday meals Corp. of - 418 23 0.85 363 3/ 345 8,015 - 8,455Madras 280 -

VII. Balvadies (Non - ANP) Rural - 280 15 0.28 1,915 169 7,217 7,900 7,924Development

VIII. Balwadies (ANP) Rural - 296 17 0.52 575 126 4,389 2,714 4,667Development

IX. ICDS Social - 397 22 0.45 805 60 3,144 4/ 3,939Welfare

X. Industrial Nutrition Program Labor - 280 15 0.24 575 50 2,035 100 2,126

1/ Data is preliminary and needs to be verified in appraisal.

2/ Includes cost of supplemental food at market value.

3/ Donated food.

4/ Total expenditure of social welfare is Rs 8.7 million.

5/ These expenditures are approximate; Total State expenditures on nutrition programs were Rs 73.7 million in 1976-1977.

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directing its foods at those children most likely to die and those who havealready suffered the most damage from malnutrition. All of these programs useon-site feeding. Previously in the State, take-home programs were attemptedbut later dropped.

1.13 In-depth evaluations of these feeding programs are scarce or, asin some cases, unavailable. One exception is an evaluation conducted by CAREof its feeding programs which found substantial substitution even in its on-site feeding programs and that nutrition status did not generally improvewith the duration of feeding. Likewise, a study of the Tamil Nadu take-homeprogram found high levels of substitution and sharing of the supplementalfoods. An evaluation of the Erskine program found substantive improvementduring feeding but some evidence suggests that once the feeding was termi-nated many of the children in the scheme's villages returned to their previousmalnourished state.

1.14 Three major problems are evident in feeding programs. 1/ The firstis that, under food scarcity situations, the family allocates food for thewell-being of the family, not necessarily for the well-being of the child. Asa consequence, food intended for the malnourished child is shared eitherdirectly or indirectly through cutting back on the child's other meals. Also,the programs use long duration feeding during vhich the entire family's con-sumption pattern adapts to the implicit income transfer to the family. Theprogram is viewed as another income source that happens to be directed at thechildren. The feeding scheme, subsidized or free food, might as well be afertilizer or housing subsidy, or for that matter, a direct income transfer asthe effect is the same--increased and shared overall family consumption, asmall portion of which is for the child. The second is that the programs arenot selective-children in the programs are often not actively malnourishedbut stunted, that is, at proper weight for height or even relatively well-nourished in the case where no entry criteria is used to screen children. Thethird is that the ration size and value is insufficient to compensate for theopportunity cost of bringing the child to the center. As a consequence, netbenefits are reduced and attendence is low and often irregular. In the nextsection these 'leakages' are discussed more formally and in more detail.

II. LEAKAGES FROM SUPPLEMENTAL FEEDING PROGRAM

2.01 Supplemental feeding programs invariably induce leakages to unin-tended beneficiaries. Leakages (other than pilfering) in a supplementaryfeeding program are of three types: (a) intra-family leakages where the foodeither directly or indirectly is shared by other members of the family; (b)income group leakages where children in the feeding program are not mal-nourished and are from families with sufficent income to feed their children;and (c) income leakages where the family's opportunity cost of participatingin the program reduces the net benefit of the food transfer because thi -

family's inmo-e from other sources in reduced.

1/ For a general survey of the state-of-the-art on supplemental feeding seeG.H. Beaton and H. Ghassemi, Supplementary Feeding Programmes for YoungChildren in Developing Countries, Report prepared for UNICEF and the ACsubcommittee on Nutrition of the United Nations, October 1979.

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Intra-Family Leakages

2.02 Intra-family leakages occur when, in response to the child havingbeen fed at the center, the family reduces the child's meals at home. Thisleakage is induced by the family implicitly treating the additional food asan income transfer which permits increased household expenditure and henceincreased food consumption by each member of the household. The child's netgain from the feeding at the center depends on the marginal propensity ofthe family to purchase food out of additional income and the allocation ofthis food between members of the family. The principle behind this substi-tution is described by Selowsky:

"Consumer's first reaction to a food program will be toconvert the concessionary element of the program into anequivalent income transfer. The "force of consumers'sovereignty" or the effort of consumers of having fullcontrol on the composition of his expenditure will alwaysbe present." 1/

He goes on to say:

"Site feeding programs delivering foods in similar propor-tions to the ones eaten at home must be able to fullyreplace previous consumption so as to be more effectivethan an equivalent income transfer. If they are distri-buted in a lesser amount, the percentage increase in eachchild's food and calorie consumption will be equal to theproduct of (a) the food distributed to each child as afraction of the food previously consumed at home and (b)the marginal propensity to spend in children's food,. .... ." 2/

2.03 He concludes that "only full feeding programs will be able toincrease consumption by amounts substantially above that (from a programthat feeds children half their previous consumption)". 3/ According toSelowsky, then, only on-site, full feeding programs will substantially resultin increased calorie intake by the child.

2.04 A partial feeding program would have an effect on the child'sintake but only equal to the child's marginal propensity to consume out offamily per capita income. If we call 0 the marginal propensity for the familyto increase per capita calories consumption out of per capita income andy the child's marginal share of these additional calories then the gain incalorie consumption of a child ACi from a food transfer of value T to a familywith F members will be:

1/ Marcelo Selowsky, The Economic Dimensions of Malnutrition in YoungChildren, World Bank Staff Working Paper No. 294, October 1978, p. 56.

2/ Ibid, p. 56-57.

3/ Ibid, p. 57.

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IC F(T/F) (1)

2.05 Assuming that the family shares these additional calories such thateach member gets a percentage equal to its previous share we have:

y = Ci/C (2)

And after substituting (1) becomes,

ACi = 8(ci/c) T/F (3)

where C is the average family per capita consumption.

2.06 Assuming that average per capita calorie consumption follows asemi-log function with respect to per capita income, or

C = a + b log Y (4)

then the marginal propensity to consumer calories will be

6 = SC/DY = b/Y (5)

Substituting (5) into (3) we get

ACi = b(Ci/C) (T/F)/Y (6)

Using e to be the per capita income elasticity to consume calories, we rewrite(6) so Ehat the proportional increase in calories will be

ACi/Ci = e . (T/F)/Y (7)

For rural Tamil Nadu, we have fit (4) to 1974 National Sample Survey data usingweighted regression techniques. The resulting estimated equation is:

2C = 2,581 + 1,221 log Y R = 0.94 (8)

(24.4)

2.07 The income elasticity for this relationship is,

e_ = 1,221/C (9)

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ACi/Ci = (1,221/C) (T/F)/Y (10)

2.08 Under the assumption of this model, if the value of the transferredfood is 10% of family income then the effective increase in calorie intakeof family member, i, will be about 7% for a family consuming at an average of80% of the FAQ calorie requirement of 2,110. 1/ With per capita expenditures(a proxy for disposable income) at this level of calorie intakes being about30 to 35 rupees per month (1974 prices), a child receiving a supplement ofvalue 0.30 rupees (290 calories) for 30 days will induce an increase inmonthly family incomes of 9 rupees or about 5 percent of per capita familyincome for a family of five. The resulting increase in average family percapita calorie intake will be about 4% (0.70 x 5%).

2.09 Since the average daily intake of a 24-35 month old boy in TamilNadu is 791, the induced effective increase in calories from a ration of290 calories will be about 40 calories, resulting in a leakage of about 250calories to other family members. For the average Tamil Nadu child from 12months to 23 months consuming at 600 calories and receiving a half ration of190 calories, the induced effect of a ration will be about 15 calories per dayor a leakage of about 175 calories to other family members. Consequently, ifthe food supplement is treated as an income transfer, considerable substitu-tion would result. 2/

2.10 Since these calculations have assumed that the cost of producing theration is its income-equivalent value to the family, they illustrate theeffects of the food supplement if the family is able to resell the supplement,retrieve the full cost of the food, and use the income to buy food that it iscurrently consuming. However, in most circumstances, the child would be fedon-site, a more expensive supplement than the child's diet at home (oftenunder the mistaken belief that much of the at-home substitution can thereby beavoided) and the value of the supplement in terms of family income would bethe calories valued in local foods, generally a much lower value than the costof a more protein rich supplement. In this case, on-site feeding wouldresult in lower calorie intake than those just calculated as the family isunable to retrieve the full cost of the food. Selowsky again identifies thedilemma:

1/ The calorie requirement assumes a male body weight of 50 kg, a femalebody weight of 40 kg, and moderal levels of activity. Note that theelasticity on the child's consumption is 0.7. James Lewinson foundelasticities for young children in rural India of less than 0.1. Ifthis estimate is correct then the substitution effect will be even greaterthan postulated in these calculations above. See James Levinson, Morinda:An Economic Analysis of Malnutrition Among Young Children in Rural India,Cornell-MIT Nutrition Policy Series, 1974.

2/ This assumes marginal propensities to consume equal to average propen-sities. If the supplement is divided equally then the effective increasein calories would be 90 and 45 calories in each case.

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"When a program distributes an inframarginal amount of afood previously being consumed, the released purchasingpower is used to expand the consumption of all food com-modities, by both adults and children. If the new foodbeing introduced by the program can only be consumed bychildren (specific baby foods), or is fed directly tochildren (milk programs in schools when the child wasnot previously consuming milk), the only mechanism bywhich the rest of the family can also benefit from thetransfer is by withdrawing some other food from thechild in question. Substitution takes place automatic-ally." 1/

And,

"As long as the rate of substitution between foods, asseen by the household, does not fully internalize thedifferent calorie intensity of foods, the resultingsubstitution could adversely affect the calorie consump-tion of children." 2/

2.11 For example, if the food withdrawn at home has a greater caloriedensity per expenditure (calorie-wise is cheaper) than the food being fed atthe center, the child's calorie intake would be adversely affected by the on-site feeding program. For example, a family with a monthly per capita incomeof 30 rupees would spend 25 rupees monthly on food, and purchase on theaverage food yielding 1,600 calories per capita per day. The average valueof 1,000 calories of this food to the family would be about 0.5 rupees. Ifthe supplemental food, because of its content of protein or other nutrientssupplies 1,000 calories at a cost of 1.0 rupees then the family would viewthe income transfer from the on-site feeding program as being equal to halfof the market value of the commodities, or equal to the value of the caloriesit can substitute at home. In this case, the induced increase in calorieintake of the child from the food supplement will only be 15 to 6 caloriesyielding thereby leakages of about 275 and 190 calories or over 95 percentof the calories delivered to the child by the on-site feeding. Clearly, ifthis type of substitution took place, on-site feeding would induce lowercalorie intakes than a take-home program where reselling of higher value foodis possible. 3/

2.12 This analysis has assumed that the education component of thefeeding program has not influenced the intra-family distribution of food.We now ask what would have to be the impact of the education component onintra-family distribution to allow the supplement to be transferred with

1/ Selowsky, Malnutrition in Young Children, p. 54.

2/ Ibid, p. 55.

3/ For example, if powdered milk is distributed, it would benefit thefamily and the child more if reselling of this high valued commoditywas even encouraged. On-site feeding of powdered milk would preventthis reselling and the net effect could be lower calorie intakes.

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only 50% leakage to the other family members. With this level of leakagefor a 290 calorie ration the child would gain an additional 145 caloriesof intake. To accomplish this gain in a family of five, the child's marginalshare of calories induced by the value of the food supplement would need toincrease by nearly a factor of five above the share in current allocation.If we are able to induce this kind of change in the child's marginal propen-sity to consume out of a food supplement, we would also be able to induce achange in how current calories are allotted, that is, change the currentshare of the child's intake in the family's per capita calorie consumption.If by education we are able to change this share from 0.5 to 0.7, then achild's calorie intake would increase by 340 for a family consuming at anaverage of 1,680 calories per capita. However, the average per capita decline(in a family of five) of the rest of the family's intake would be about 80calories per day.

2.13 We do not understand either the mechanics or logic of the family'sallocation of calories among its members or therefore the potential effectsthat education might have on this allocation. We even do not know if educa-tion that results in redistributing food within the family will increase thefamily's well-being and ensure its survival. Perhaps the logic of the cur-rent distribution is based on maximizing the family's income and overallwell-being. The existing intra-family distribution of food in poor families,even though increasing the risk of malnutrition in the least productivemembers of the family, the preschool children, could assure that the adultsand older children will have the energy to work and earn income for thefamily. Any other distribution could increase the entire family's vulner-ability to malnutrition. This, then is the risk of education that attemptsto induce a reallocation of food within the family. But, if we accept thecurrent family distribution, leakages due to this substitution within thefamily will be substantial in feeding programs that supply only a part ofthe child's calorie needs.

2.14 These leakages also indirectly beset an on-site program that feedsthe child its entire calorie needs. For example, if a malnourished child, con-suming 500 calories at home, is accepted into a feeding program and if thechild is fed its entire calorie needs, the 500 calories previously consumed athome would now be released to the rest of the family. In order to induce a'700 calorie increase in the child's consumption to its calorie requirementof 1,200 calories, a ration of 1,200 calories needs to be delivered. Thepercentage effectiveness of the food delivered is therefore about 60%. But toinduce an equivalent increase in the child's calorie intake, an on-site ortake-home program operating with partial feeding would have to induce anincome transfer to the family of 200% of current per capita income (140%/e )or supply the family with over 50 rupees per capita per month of additionaiincome through the food transfer. Clearly such an income transfer is an in-efficient way of feeding a malnourished child.

2.15 In summary, a partial feeding program, unless it can change througheducation or other means the pattern of food consumption within the family,will have high leakages to other family members. Also, unless the food thatis provided in a partial feeding program has higher calorie density per unitof expenditure than is being fed at home, the take-home program will be more

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effective than on-site partial feeding since it offers the possibility toresell the higher value food and substitute lower value food at home. Exceptfor the added inducement of educating the mother or innoculating the child,it appears that the take-home programs are at least and possibly more effec-tive than on-site partial feeding programs. However, full-ration programsto be effective must be fed on-site, otherwise, they will be beset with thesame levels of substitution that occurs in partial feeding programs. Althoughleakages occur in both programs, the more effective program appears to be thefull-ration, on-site feeding program, in which the child's full calorie intakecan be assured.

2.16 An assumption of the previous analysis has been that the food supple-ment is viewed by the family as any other income or asset transfer. As a con-sequence, the family consumes out of this income from this source as it wouldout of income from any other source. However, incomes from all sources arenot treated equally as has been demonstrated in studies of consumption behaviorin both developing and developed countries. 1/ For consumption decisions,income is regarded as having a permanent and a transitory component. 2/ Asoriginally hypothesized by Friedman, the permanent component reflects incomethat is regarded as continuing and hence can be considered a part of a per-manent stock of wealth. The transitory component of income reflects "accidental"or "chance" occurrences, or transfers that are considered as temporary eventhough they could have been fully foreseen. The propensities to consume outof these two sources of income are different, with the higher propensityoccurring for consumption of permanent income. Transitory income, beingtemporary in nature or of a "windfall" character, is associated with a lowpropensity to consume. Consumption is not significantly adjusted upward withincreases in transitory income since the income is considered to be only short-term.

2.17 An issue in regards to supplemental feeding programs is whether theimplicit income derived from the supplemental food has a higher transitorycomponent than that in current income derived from other sources. If it does,then the propensity to consume out of this food transfer will be lower thanthat out of the family's other sources of income and the effect on consumptionof the food supplement will be less than that estimated above. Of course, ifthe opposite situation holds, that is, that a food supplement is considered tobe a more permanent source than outside income, then the propensity to consumeout of the food transfer will be greater than out of other sources. To resolvewhich case holds in Tamil Nadu would require investigating the instabilitiesinvolved in different sources of the participants' household income anddetermining the components of transitory and permanent income involved in eachincome flow.

I/ For a review of these studies see Odin K. Knudsen and Andrew Parnes,Trade Instability and Economic Development, D.C. Health and Company,Cambridge, Massachusetts, 1975.

2/ Milton Friedman, A Theory of the Consumption Function, Princeton: Prince-ton University Press, 1957.

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2.18 Since such studies or data are unavailable, we can only hypothesize

on how the duration of the feeding would affect household consumption. How-

ever, it appears that the more the food transfer is regarded as transitory,the least effect it would have on the family's propensity to consume and themore likely it would be retained by the child.

2.19 If the feeding program is of long duration, the food transfer is

viewed as a permanent income flow, with the family's overall propensity to con-

sume increasing, including marginally the child's food intake but not to the

extent intended by the program. If, however, the feeding is short duration,three months or less, the income transfer would most likely be transitory,household consumption would not be adjusted upward as much, and the childwould receive a greater benefit from the food supplement.

2.20 Another assumption of the previous analysis is that the family does

not experience a money illusion, whereby the food transfer is regarded as morevaluable than its actual market value. To induce higher food intake in the

child, this money illusion needs to be consistently,biased upward so that thefood consumption is higher than dictated by the actual income transfers. In

reality, it can be expected that the bias in some households would be upward,

and in other households, downward, but on average, over all participatinghouseholds, the bias would be zero.

2.21 Until we know more about intra-family distribution of food, it is

difficult to calculate the degree of substitution that would occur fromdifferent food supplementary feeding programs. We do know, however, that a

full feeding program diffuses this issue as the program takes responsibility

for meeting the entire calorie needs of the child.

Leakages to Unintended Beneficiaries

2.22 The second type of leakage in supplemental feeding programs occurs

if children that are not malnourished are admitted to the program because of

lax or faulty entry criteria. If however entry criteria for the feeding pro-

gram are too rigid than an error of the opposite nature occurs, with childrenwho are malnourished being excluded. In the first instance, a leakage to

unintended beneficiaries occurs; in the second instance, the program's effec-

tiveness in lowering mortality and morbidity is reduced.

2.23 There are two basic approaches to entry criteria in feeding pro-

grams: the first is based on the change or trend in a child's status; the

second is based on the state of the child at any one point in time. Theformer is concerned with the trends in a child's nutritional status, whether

it is deteriorating or improving, and the latter is focussed on the "stock"

situation of a child, whether the child is malnourished or well nourished.The first entry criteria belongs primarily to preventative programs; the

second to rehabilitative programs. Both are capable of committing errors in

enrolling or excluding children from the feeding program. We will discussboth approaches in the context of these potential errors.l/

1/ It should be noted that the extent of targetting or entry selection is

really an issue to be resolved in a cost-benefit sense as generally the

benefits and the costs per unit of food distributed are higher the more is

the targetting.

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2.24 For any criteria on entry into the feeding program, two probabili-ties of error are associated:

Probability of Type I error (Pr(I)): The probability of entering achild that does not require thefeeding program.

Probability of Type II error (Pr(II)): The probability of excluding achild that requires the feedingprogram.

2.25 Associated with each of these errors is an expected loss that isequal to the value of the loss times the probability of the error beingcommitted. If we designated the loss associated with each error as L and

and L from a entry rule, d, the expected loss, L, is:

L(d) = L Pr(I/d) + L Pr(II/d) (11)1 2

2.26 In the case of a program that bases entry on a stock condition,whether the child is nourished or well nourished, the probability of errordepends on the reliability of the measurement criteria, that is, whether agefor weight or anthropometric measurements accurately detect malnourishment.In the case of a preventative program, where entry depends on trends in thechild's status, an additional probability needs to be accounted for: theprobability that the observed trend results in a condition of malnourishment.In other words, with the trend criteria, we have a series of probabilitiesthat contribute to the probability of an entry error. These consist of theprobability that the trend is measured correctly and the probability that thetrend will result in malnourishment. Referring to Figure 1 will illustrate.A child in a period of time can experience a positive or normal gain in weight,TP, or a negative or inadequate gain in weight, TN. The child is weighed ona scale of some assumed accuracy and the trend in weight is correctly or in-correctly identified. From this weighing, a child enters Y, or is excluded N,from the feeding program. However, a child that experiences a weight declineover one period might regain normal weight growth in the second period evenwithout the intervention of the feeding. On the other hand, the child mightnever recover from the initial downward trend in weight and continue to becomemalnourished. In Figure 1, the various paths are illustrated for two weigh-ing periods in which, for simplicity, it is assumed that a child with twoconsecutive periods of inadequate weight gain will become malnourished. 1/If this negative or inadequate weight trend is caught in the first period,then the program has accomplished its objective of preventative interventionbefore malnutrition has set in (the cases illustrated by an asterisk inFigure 1). By tracing the various paths in the probability tree of Figure 1,we find the conditional probability of feeding a properly nourished child,P(I/W), is:

1/ These weight periods could be three months each, for example, in theTamil Nadu Nutrition Project.

Figure 1: PROBABILITY TREE ON ENTRY INTO FEEDING PROGRAM

I/v I/w I/u I/u I/w O/w I/u O/u I/w I/w I/m* I/m* I/w O/w I/m 0/m

Y N Y' N' Y Y N' Y N Y' N' V N Y' N"f

TP Tp TP TN TP' TN'

TN

Begin

Key:TP - Trend in weight positive given that it was positive the month before.TN - Trend in weight negative given that it was positive the month before,TP' - Trend in weight pos.dve given that it was negative the month before.TN' = Trend in weight negative given that it was positive the month before.Y - Child entered into program on weighing given that the weight gain was positive.N Child excluded from program on weighing given that the weight gain was positive.Y = Child entered into program on weighing given that the weight gain was negative,N' - Child excluded from program on weighing given that the weight gain was negative,I - Entered in program.0 - Excluded from program.W - Not malnourished.M - Malnourished.U - Unclear, dependa on next three months.I/W - Entered irto program but not maltourished.* Indicates child In the program at proper time.

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2P(I/W) = P(TP) P(y)(l + P(N)) + P(TP') P(TN) [P(y') + P(N') P(y)] + P(TP) P(TP')

P(TN) [P(y) + P(N) P(y')] (12)

and that of excluding a malnourished child is:

2P(o/M) = P(TN) P(TN') P(N') [1 + P(TP) P(N)] (13)

where the P(_) represents the probability of the events in the argument. Forexample, P(TN) is the probability of a negative trend in weight gain giventhat the trend was positive the month before and P(TN') is that the trend isnegative given that it was negative the month before (the other variables aredefined in Figure 1).

2.27 Both of these probabilities P(I/W) and P(0/M) represent errors inthe criteria of entry or exclusion. The first, P(I/W) is Type I error; thesecond, P(0/M), Type II error. For example, assume the following probabil-ities:

P(TN) = 0.20P(TN') = 0.20P(TP) = 0.80P(TP') = 0.80P(y) = 0.10P(N) = 0.90P(y') = 0.90P(N') = 0.10

These probabilities indicate that the child's chances of having a negativeweight trend over any one weighing period is 20% and that the chance of ameasurement in error is 10%. It also assumes that the probability of havinga negative weight trend in one month is independent of the weight trend theprevious month; thus, P(TN) equals P(TN') and P(TP) equals P(TP') (later wewill modify this assumption). Using (12) and (13), we calculate for the prob-abilities of committing Type I error, 0.38, and Type II error, 0.0007. Thatis, under these assumptions, the probability of entering non-malnourishedchildren would be relatively high but the probability of excluding malnourishedchildren would be nearly zero. If our measurement criteria is more inaccuratesuch that the probability of making an error is 30% then the probabilitiesof commiting Type I error is 0.55 and Type II error, 0.006. If the accuracyof the measurement is high with only 5% chance of error, then the probabilityof Type I error is 0.34 and Type II error is 0.0002.

2.28 In Table 3, the probabilities of Type I and Type II error are calcu-lated for a variety of malnourishment rates and measurement errors. As canbe seen from these probabilities, the trend weight measurement as an entrycriteria has a high probability of entering into the program children who donot need the supplement and a low probability of passing up a malnourishedchild, which assumes of course that the malnourished child is brought in forweighing. Returning to our loss function, we would find that the ratio of

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L and L that sets the expected losses from each of the Type I and Type II

errors equal would range from nearly 10 to 2,000 depending on the probability

of a weight decline and the accuracy of its measurement. In other words,the costs of excluding a child on a trend to malnourishment needs to be 10

to 2,000 times as great as the costs of feeding the child for a given period

with the exact ratio depending on the measurement error and the probability of

inadequate weight gain.

Table 3: PROBABILITIES OF COMMITTING ENTRY OR EXCLUSION ERRORS

Probability of Inadequate Weight Gain in Any Period

10% 20% 30% 40% 50% 60%

Probability ofMeasurement Error 10%

(a) Probability ofType I Error 0.31 0.38 0.42 0.42 0.39 0.34

(b) Probability ofType II Error 0.0002 0.0007 0.0025 0.0025 0.0036 0.0049

(c) Ratio of ExpectedLosses 1,710 558 285 170 107 67



(b) Probability ofType II Error 0.0007 0.0026 0.0056 0.0095 0.0140 0.0190

(c) Ratio of ExpectedLosses 536 180 85 48 29 20



(b) Probability ofType II Error .0015 0.0056 0.0121 0.0204 0.0304 0.041

(c) Ratio of ExpectedLosses 374 99 44 24 14 8

Proportion BecomingMalnourished 3% 10% 20% 31% 44% 56%

2.29 The previous calculations have assumed for simplicity that the prob-

ability of weight gain or loss in any period is independent of the weight

change in the previous period. This assumption is inaccurate. A child experi-

encing a weight loss in the previous period would be expected to have a higher

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probability of continuing on a downward trend in weight in the followingperiod than a child who has previously had adequate weight gain. In Table 4,we present the implications on the probabilities of entry errors of thisinteraction of weight gains between consecutive periods. We assume in thesecalculations that, if a child experienced an inadequate weight gain in oneperiod, the probability of having a normal weight gain in the next periodis half that of a child on an adequate weight gain trend. Under this assump-tion, we find that the probability of committing an entry error declinessubstantially from a range of 31-42% to 22-26% for accurate measurement tech-niques (10% chance of measurement error). The probabilities of malnourish-ment (defined as two consecutive periods of inadequate weight gain) increasedsubstantially with this correlation between the weight gains from period toperiod, going from 3 to 44% to 15 to 66%, over a range of probabilities ofinadequate weight gains from 10 to 50%.

Table 4: PROBABILITY OF COMMITTING ENTRY ERROR UNDER DIFFERENTCORRELATIONS BETWEEN PERIODS OF WEIGHT GAIN

Probability of Inadequate Weight Gain

10% 20% 30% 40% 50%(a) Measurement Error 10%

Correlation Factor

(i) 0 0.31 0.38 0.42 0.42 0.39(ii) 0.5 0.23 0.25 0.26 0.24 0.22

(b) Measurement Error 20%Correlation Factor

(i) 0 0.35 0.47 0.48 0.45 0.41(ii) 0.5 0.32 0.35 0.32 0.29 0.25

(c) Measurement Error 30%Correlation Factor

(i) 0 0.55 0.55 0.53 0.49 0.42(ii) 0.5 0.48 0.43 0.39 0.34 0.27

(d) Probability of MalnourishmentCorrelation Factor

(i) 0 3% 10% 20% 31% 44%(ii) 0.5 15% 29% 43% 55% 66%

2.30 These calculations on entry errors have taken into account theprobabilities both of measurement error and the probabilities that a downwardtrend in weight would continue and the child would eventually become mal-nourished. In what follows we explore the factors involved with a measure-ment error.

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2.31 Measurement errors occur due to the inaccuracy of the scale, theoperator's reading of the scale, and the inter-daily and intra-daily fluctua-tions in the weight of a child that results from variations in body fluidsand the quantity of food matter in the stomach and intestines. For example,assume that the fluctuation in daily weight are normally distributed withmean 0 and standard deviation a = Va 2+ a 2. For example, if the standarddeviation in the child's weight due to Waily variation is 100 grams and thestandard deviation of the measurement is 50 gis, then ac = 112 grams. Forthis case, we would be able to discern the child's average weight within + 224grams with 68% accuracy (one standard deviation). This measurement accuracywould be sufficient to determine whether a child is third or second degreemalnourished, but, in a weight gain criteria measurement, it would be insuffi-cient to discern in marginal measurements whether adequate or inadequate weightgain has occurred over a period of say, five months.

2.32 Consider the following example of weighing in which actual weightincreases from P1 to P2 but that the measurement has an error that is norm-

ally distributed with a mean equal to 0 and a standard deviation of a .

2.33 We measure, in Period 1, a weight of W1 and, in Period 2, a weightof W2. The question is for a weight gain criteria rule (for example growthless than L would require entry into the program), what would the actualdifference in p and P need to be to commit a measurement error of prob-ability, P.

2.34 The difference, W2 - W1 has a mean equal to p2 - Pi and standarddeviation equal to r2a , or using the values from above, 158 grams( /Tx 112)(291) (we assume the measurements are independent). For a 10%probability error, L would need to be about 300 grams for a weight gaincriteria of 500 grams . 1/ This means that if a weight gain at least of 500gms is required over the period of measurement for adequate growth then wewould need to exclude children from the program who have a measured gain ofover 300 gms to commit only an 10% entry due to measurement. Associated withthis 300 gm weight gain criteria is the probability of excluding a child whoactually needs the program. An example will illustrate. Using the sameprocedures as above, we calculate the probability that a measured weight gainwith a normal distribution of mean 250 gms (the actual weight gain if thescale is unbiased) and standard deviation of 158 grams would be measured asa weight gain of greater than 300 grams. (This mean weight gain of 250 gramswould be half of the required weight gain for adequate growth). This cal-culation reveals that the probability of excluding this child is 0.38 on thisweighing. Similarly calculated, the probability of excluding a child with

1/ This example is appropriate for a normal child who grows at 167 gramsper month, and is weighted to determine weight gain for a three monthperiod.

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no weight gain is only 3%. Clearly in these cases the accuracy of themeasurement device and the demarcation rule on entry are critical parametersin determining the effectiveness of the program, in including children whoneed supplementary feeding, and in excluding children who do not need theprogram. 1/

2.35 In an actual feeding program, weighings would be taken on a monthlybasis and comparisons in weight gain would be made over various periods todetermine the trend in weight. If a child is measured over a three monthperiod and is excluded from the program because weight gain is measured asadequate but in fact is inadequate, the chances are that the child will bediscovered as needing the program in later months. This repetitive measure-ment assures that children on a trend toward malnourishment will be identi-fied; but, it also increases the risk of admitting children who do notrequire supplemental feeding as the probability of committing an entry errorcompounds with the number of weighings. For example if a population has apotential malnutrition rate of 30% (a 0.5 correlation between weight losses)and a measurement technique with 90% accuracy, reference to Table 4 showsthat about 25% of the adequately nourished children will enter the programalong with nearly all the malnourished children who are weighed, that is,for a 30% malnourishment rate about a third of the children being fed willnot require the program. A greater level of measurement error will induceeven a higher error of entry and hence higher leakages to unintended bene-ficiaries.

2.36 An entry criteria based on either longer trends in weight or on a"stock" measurement, such as age-for-weight or height-for-weight, will haveless chance of measurement error. On the other hand, the possibility of "im-munizing" the population to malnourishment will largely be foregone. Instead,moderate malnourishment will need to set in before the program permits entry.The trade-off then is between an entry criteria that errs heavily in the direc-tion of admitting adequately nourished children but captures (if they can befound to be weighed) almost infallibly, children on the course to malnutri-tion, and an entry criteria that requires moderate levels of malnutrition toset in before entry is permitted.

The Income Leakage

2.37 The income leakage occurs through two means: first, through well-nourished children from upper income families entering the program becauseof pressure from influential people in the community and second, through lossof income originating from a mother or older child foregoing work for at leastpart of the day to bring in the child.

1/ Note that previously, in measuring the program's probabilities of comit-ting Type I and Type II errors, we used equal values for both of theseerrors. These were simple estimates for illustrative purposes; clearlythe probability of each type of measurement error depends on the other,and in turn, both depend on the criteria used.

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2.38 The first form of leakage results from a child being entered intothe program because community leaders or wealthy individuals demand entryof the child and not because of a measurement error of the previously dis-cussed type. Since the food supplement and other activities at the feedingcenter (such as perhaps preschool education) have economic value, the feed-ing center supervisor could be pressured into entering children from influen-tial or privileged families. Although this type of pressure will always exist,the feeding program can be monitored to reduce the number of these unintendedbeneficiaries. This monitoring must be able to measure objectively, at thetime of inspection, whether the child indeed should be in the program. If aweight gain criteria for entry is used, on-site inspection will not work asthe child can now be gaining weight, although it can be claimed that a down-ward trend in weight was observed when the child was admitted to the program.However, if the entrance criteria involves a "stock" measurement, age-for-weightor anthroprometric measures, it can fairly well be determined that the childin the program is in need of feeding. Through this monitoring of the children'sstatus, for instance by personnel from the state or district headquarters, ade-quately nourished children can be removed from the program and this form ofleakage to unintended beneficiaries can be minimized. 1/

2.39 The second form of leakage results from the opportunity costs orthe loss in earnings from production activities that an adult or elder childforegoes to bring in for feeding a malnourished child. If the benefits fromthe feeding program do not exceed these opportunity costs, families will findit to their overall detriment to participate. This benefits versus opportun-ity cost comparison is particularly important to partial feeding programs thatrequire for success inducing the mother through nutrition education to feedmore to the malnourished child at home. If the mother finds that the incomelost from bringing in the child is greater than the value of the food supple-ment, she will probably not go to the center herself but will have the childbrought in by its younger brothers and sisters. As a consequence, this nutri-tion education of the mother will not take place or will only occur when themother's opportunity costs are low, i.e., when she is unproductive or unableto find employment. As a consequence, the mother and the child's participa-tion in the program will primarily be determined by the season and the workopportunities and secondarily by the incidence of malnutrition in her family.

2.40 To illustrate further this point consider the case of a mother whois employed 10 hours a day at a daily wage of 4 rupees. If it takes an hourto bring the child in for feeding, the value of the food supplement must beat least 0.4 rupees to have the family as well off as it was before the feed-ing. For a ration of lesser value, say 0.3 rupees, the family's net incomeand therefore consumption will decline by participating in the feeding program.If the mother is expected to go to the feeding site the other benefits tothe family of participating in the program, such as education or expected

1/ Alternatively, the feeding program could be regarded to have, either bydesign or unintentionally, a social stigma that assists in keeping outchildren from upper income families; however, this same stigma mightprevent entry of even children from poor families who are also sensitiveto this detriment.

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discounted earning of the child if it survives, will need to exceed this dif-ference. If the benefits are insufficient, the feeding center will primarilybe occupied by the malnourished children, accompanied by brother and sisterseither too young to work or with opportunity costs less than the value ofthe ration.

2.41 From this analysis of leakages, it appears certain that leakagesfrom a feeding program distributing a partial ration will be substantial,whether the food is taken home or fed at the center. 1/ Also, unless the educa-tion component is considered to have sufficient value to compensate for theloss of income, the mothers of malnourished children will not participate inthe program and the effort to reorient the family's distribution of foodtoward the malnourished child will be ineffective. In on-site, full feedingprograms, losses through these leakages are less than in partial feeding pro-grams; however, the costs of food are higher as the ration size is larger.

2.42 The lessons from these sections on leakages are summarized asfollows:

(a) Significant levels of substitution and sharing (the latter ina take-home program) of supplemental food can be expected.To assure effectiveness, ration sizes should be near thefull nutrition requirements of the child and the durationof feeding should be short, two to three months.

(b) Entry criteria should be an integral part of any feedingprogram. Without it, the program takes on the characterof an income transfer and substitution will be high andeffectiveness low. Two types of entry criteria are feasi-ble: one based on the stock condition of the child; thesecond on the trend in weight of the child. The secondcriteria is the most difficult to implement and has thegreatest probability of committing Type I entry error,where a child who does not require feeding is entered.However, it has the advantage of identifying trendstoward malnutrition with almost certainty and therebyavoiding the damage to a child's body and intelligenceresulting from malnutrition.

(c) The income leakage results from loss of income resultingfrom foregoing work to take a child to a feeding center.To enhance enrollment and attendance the ration size mustbe of sufficient value to compensate for the loss inincome. As a consequence, the ration size should approachquantities sufficient to meet the entire child's needsand the center should allow for the child staying at thesite throughout the day. The first provides an appropriateeconomic incentive to bring the child in for feeding; thesecond reduces the opportunity cost of interrupting a work

1/ As shown in Section 5, this does not mean that leakages are without benefits.Intra-family food leakages receive a benefit in the cost-Benefit analysisif the household i8 below the puverty line. However, tefi overall benefitswould generally be less the greater are the leakages.

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day to bring the child in for feeding. 1/ Also, the sea-sonal nature-of work opportunities for the mother needs tobe accounted for with additional staff required during theharvest and sowing season to assure that children requiringfeeding are brought to the center.

2.43 In the next section, we describe an entry criteria based on weighttrend that is feasible fo: field operation.

III. ENTRY AND EXIT CRITERIA FOR ASUPPLEMENTAL FEEDING PROGRAM

3.01 The purpose of this section is to describe a feasible weight trendcriteria that can be used for entering and exiting children from a feedingprogram. The principal hypothesis of a feeding program using weight gainentry criteria is that a child that is not gaining weight adequately or islosing weight can be identified through a program of monthly weighings andthat timely on-site feeding of a supplemental food to this child will (in themajority of cases) result in the child's return to adequate weight gain. Asa consequence, much of the detrimental effects of malnutrition can be avoided.To implement this program entry criteria are established which identify in-adequately growing children with only a small probability of error, yetexclude, with a high probability, children that are gaining weight adequatelyand hence do not require supplemental feeding. Likewise, exit criteria areestablished that assure that the children entered into the feeding programhave returned to adequate weight gain before being permitted to leave theprogram. Since such a program will be implemented in rural areas these cri-teria must be simple enough that a community nutrition worker can determinethat a child is eligible for entry and that a nutrition supervisor, after re-weighing of the child, can confirm the validity of the initial weighing of thenutrition worker (to reduce village pressure on the nutrition worker, only thesupervisor is permitted to enter a child into the feeding program). As dis-cussed in the previous section, even though these entry and exit criteriawill be implemented by trained and supervised personnel, certain measurementerrors are inevitable because of the inaccuracy or misreading of the weighingdevice and the daily body weight fluctuations that occur unrelated to nutri-tional trends.

The Entry Criteria

3.02 To set the entry criteria, the rates of weight change that consti-tute adequate weight gain must be established. According to the Harvardstandards, a 'normal' child between 6 and 11 months old gains weight at 500gms per month, between 12 and 14 months old, at 200 gms per month, and between15 and 35 months old, at 167 gms per month. A child that is malnourished (lst

1/ Although older siblings can bring the child in, much of the educationalbenefits to the mother are loss and attendance can be unreliable.

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through 3rd degree by a weight-for-age criterion) and gaining weight at 300gms per month during the 6 to 12 month age period and at 100 gms per monthafter this period will maintain nutritional status quo. Weight gain lessthan these magnitudes sustained over many months will eventually result ina deterioration in nutritional status, possibly resulting in 3rd degreemalnutrition and a rapidly increasing risk of death. The entry criteriamust therefore be designed for the timely identification of children whoseweight gain is substandard as well as for those children who maintain anddo not improve their nutritional status. These entry criteria must howeverbe balanced against the risk of entering children with adequate weight gaininto the program.

3.03 As discussed previously, in implementing entry criteria based onmeasuring weight gain, three forms of error are possible. The first resultsfrom the scale's inaccuracy or miscalibration, or the operator's misreading ofthe indicated weight. On a balance type scale, this measurement error wouldhave a standard deviation of 50 gms. The second form of error results fromthe daily and intra-daily fluctuations in the child's weight that results fromchanges in the body's fluid content or in the quantity of food matter in thestomach and intestines. At the Institute of Child Health in Madras, 17 chil-dren were weighed over 5 days every two hours during the day to determine themagnitude of this fluctuation in weight. Summary statistics of the results ofthese weighings are given in Tables 5 and 6. As can be seen from the data inthese tables, daily and intra-daily weight changes are substantial. However,the weight change is less between similar times of the day, in particular, inthe morning. To minimize the effect of intra-daily fluctuation, a nutritionworker will weigh the children in the mornings before supplemental feeding.With the weighings conducted in the morning, the daily fluctuation in totalweight is estimated to have a standard deviation of 100 gms. The third formof error results from weight changes due to interim illnesses or episodes ofdiarrhea. Diarrhea that results in a semi-solid discharge 4 or 5 times a daycan change daily body weight by 5 percent. Diarrhea consisting mostly ofliquid and occuring 6 or 7 times a day can result in body weight losses of 7percent. A child weighing about 10 kg can therefore lose 500 to 700 gns ofweight in a single day due to diarrhea. Since this does not necessarilyindicate a long term nutritional problem, the entry criteria are designed toexclude a child unless the weight loss persists and adequate weight gain isnot reestablished. To do this, a child that has experienced diarrhea withinthe previous week of the weighing will be reweighed one week after the diar-rhea episode.

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Table 5: MEAN AND STANDARD DEVIATIONS OF WEIGHTS AND MAXIMUMINTRA-DAILY AND INTER-DAILY WEIGHT CHANGES

Mean Standard Maximum Intra-Daily (Inter-daily) ChangeWeight Deviation #1 #2 #3 #4 #5

#1 10.64 49 100 (100) 100 (100) 100 (100) 100 (100) 100#2 11.27 46 100 (100) 100 (100) 100 (100) 100 (100) 100#3 12.34 51 100 (100) 100 (100) 100 (100) 100 (100) 100#4 14.35 51 100 (100) 100 (100) 100 (100) 100 (100) 100#5 15.45 51 100 (100) 100 (100) 100 (100) 100 (100) 100#6 8.71 89 100 (100) 100 (100) 200 (400) 200 (400) 100#7 8.83 85 225 (300) 100 (200) 125 (225) 150 (200) 100#8 9.47 223 500 (500) 500 (700) 700 (700) 700 (700) 700#9 10.20 84 300 (300) 200 (200) 100 (200) 200 (200) 100#10 10.58 148 300 (500) 500 (300) 300 (300) 300 (300) 300#11 8.82 108 600 (500) 0 (0) 0 (0) 100 (100) 100#12 9.16 168 500 (500) 500 (600) 300 (500) 200 (200) 200#13 9.62 101 200 (200) 100 (300) 200 (200) 200 (200) 200#14 9.22 119 300 (300) 300 (300) 300 (300) 100 (100) 100#15 11.34 155 500 (600) 300 (300) 300 (300) 300 (300) 300#16 11.88 114 300 (400) 200 (300) 200 (100) 100 (400) 400#17 10.30 68 100 (200) 200 (300) 200 (200) 100 (200) 100

Table 6: MAXIMUM WEIGHT VARIATION BETWEEN THE SAME TIME OF DAY

Maximum Variations Maximum VariationsChild Day 1 Day 2 Day 3 Day 4 in Morning Weights Over Five Days

1 100 100 100 100 100 1002 0 0 100 100 100 1003 100 100 100 100 100 1004 100 100 100 100 100 1005 100 100 100 0 100 1006 175 175 200 300 200 4007 300 200 150 150 200 3008 200 200 0 0 200 7009 200 100 200 200 200 30010 200 200 0 100 100 50011 500 0 100 0 100 50012 200 500 400 0 300 60013 100 300 100 100 200 30014 200 200 200 0 200 30015 600 0 0 0 600 60016 400 200 100 300 400 50017 100 100 100 100 100 200

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3.04 Because of these measurement errors and fluctuations in body weights,the criteria will result in two types of entry error with different probabil-ities. The first is the probability that a child with inadequate weight gainwill be incorrectly assessed and be excluded from the program. The second isthe probability that an adequately growing child will enter the program. Asthe entry criteria reduce the probability of one form of entry error, it canincrease the probability of the other form. To balance the probability ofeach form of error, the potential costs associated with each error need to bedetermined and expected losses compared at least qualitatively.

3.05 If the first form of entry error is committed, that is, a poten-tially malnourished child is bypassed, the resulting loss is ineffectivenessof the program, physical and possibly mental damage, and increased risk ofearly death. If the second form of error is committed, that is, a childentered into a program who does not need it, then the credibility of theprogram is reduced and the program's feeding costs are increased. Clearly,in comparing the relative losses, we must consider that the more seriousis the loss associated with excluding a malnourished child. As a consequence,the entry criteria are designed to reduce the probability of bypassing amalnourished child but doing so at the cost of an increased probability ofentering a child with adequate weight gain.

3.06 Since a child is weighed monthly and therefore up to 30 times betweenthe ages of 6 and 35 months, the probability of bypassing a malnourished childbetween these ages is nearly zero since the chances are that the malnourishedchild will be identified at least once in so many weighings. On the otherhand, the probability of entering a child gaining adequate weight will berelatively high with repetitive weighing compared to the probability of enter-ing a child in any single weighing. Even though the probability of commit-ting the entry error in any single weighing is low, the repetition of theweighing contributes to an increasing probability of error over the 30 montheligible age period of the child. (It is analogous to rolling a die where theprobability of coming up with one dot is small in any one roll but, with manyrolls, the probability is much higher than one dot will appear at least once.)As a consequence, the probability of bypassing a malnourished child is mini-mized but the probability of entering an adequately growing child is rela-tively substantial over its eligible life.

3.07 Because normally growing children gain weight more rapidly from theages of 6 to 11 months than from 12 to 35 months, two sets of entry criteriaare needed. The entry criteria established are:

(a) For children 6 to 11 months old:

(When adequate weight gain is 500 grams per month.)

(i) Enter a child if it did not gain weight over theprevious month; or

(ii) Enter a child if its weight gain in two consecutivemonths has been less than 300 grams in each month.

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This is provided, however, that the child has nothad diarrhea in the previous week. If diarrhea hasoccurred, reweigh the child one week later and re-apply criteria l(a) and (b).

(b) For children 12 to 35 months:

(When adequate weight gain is 500 to 600 grams every threemonths.)

(i) Enter a child if its current weight is less than itwas three months previously, or

(ii) If the average weight change over the previous threemonths has been less than 300 grams, identify thechild as being at risk but do not enter it into theprogram at that weighing. If, however, on the nextmonthly weighing the child has still gained lessthan 300 gms in the previous three month period,enter it into the program provided, that is, anepisode of diarrhea has not occurred during theprevious week. If diarrhea has occurred conducta follow-up weighing and apply criteria 2 (a) and(b).

3.08 The follow-up weighings one month later in l(b) and 2(b) makes itmore probable that the weight change actually indicates a trend of inadequateweight gain and is not just a temporary phenomenon or a measurement error.Since these inadequate weight gains do not place the child in immediate risk,the follow-up weighing prevents excessive entry of children with adequateweight gain without bypassing children with long term trends of inadequateweight gains.

(a) In Table 7 the probability of bypassing a child aged 6 to11 months having weight changes from 100 to 500 gms permonth are given for the entry criteria l(a) and l(b). Ascan be seen from the table, the probability of enteringinto the program a child with adequate weight gain (500gms/month) is only 0.01 in any one weighing and 0.06 overthe five weighings of the child as it ages from 6 to 11months old. A child gaining weight at 300 gms per month,that is, gaining weight at an inadequate but not critic-ally low rate will enter the program with 0.78 probabilityover the five weighings. A child that is not gainingweight at all will be entered with probability 0.33 afterthe first month of no weight gain and with near certainty,0.97 probability, after the second month of no weightgain. A child that loses weight enters the program withnear certainty the first month that the weight loss occurs.

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3.09 These weighings occur at a particularly critical stage in theinfant's growth when the quantity of breast milk from the mother is decliningand the child's calorie needs are increasing. These entry criteria assurethat any child with inadequate weight gain in these critical months will beidentified and entered into the supplemental feeding program.

3.10 For entry criteria 2(a) and 2(b), Table 8 shows the probability ofbypassing a child aged 12 to 35 months having weight changes from 100 to 500grams over a three month period. As can be seen from this table, a childgaining adequate weight will have only .01 probability of entering the feed-ing program in any one weighing. Within 20.weighings the probability is 0.20that the child will enter the feeding program at least once. A child gainingweight at an inadequate rate (300 grams over a three month period) but suffi-cient to maintain its nutritional state will enter into the feeding programat least once with near certainty and with 0.76 probability within 8 months.A child gaining 200 grams over a 3-month period will be identified with 0.3probability within 5 months. A child gaining 100 grams over 3 months will beidentified with 0.83 probability within 3 months. A child that is not gain-ing any weight will be identified with near certainty within the first 3months. In summary, children that are gaining weight at an inadequate ratewill enter the feeding program with near certainty at least once over their30 months of eligibility; how quickly they are identified depends on thedegree to which weight gain is inadequate. The probabilities of entry indi-cate that those children with marginally inadequate weight gain will not enterfor many months while children with very inadequate weight gain or with weightloss will be identified nearly immediately. The system of entry identifieschildren for the feeding program under an implicit priority ranking with thechildren with the most likelihood of becoming malnourished, that is, thosewith the most inadequate weight changes being rapidly identified with thehighest probability, while those with marginally inadequate weight changeshave a lower probability of being identified early but eventually areidentified.

The Exit Criterion

3.11 The exit criterion for children who have been in the feeding programfor at least three months assures with high probability that a child is gain-ing adequate weight before leaving the program. This criterion is to considera child recovered and to remove it from the program if it has gained 500 gmsover the three months of supplemental feeding. To determine whether a childhas actually gained 500 gns, two sets of three weighings are conducted andaveraged at entry and exit. Upon entry, the supervisor will average the ini-tial weighing of the nutrition worker, her follow-up weighing, and a weighingon the day of entry to establish the child's initial entry weight. For theexit weight, the child is weighed at least three different days just beforethe three months of feeding have elapsed. These weighings, conducted in themornings before feeding, are averaged to establish the final weight of thechild. The difference in the everage weights at entry and after three monthsof feeding must be at least 500 gms for the child to leave the program. Ifweight gain is less than 500 gms, the child is checked by the health workerfor signs of diseases or parasites that might have hindered weight gain. Therecommendation of the health worker is used to determine if the child shouldbe retained for continued feeding.

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3.12 The statistical reason for this procedure is that the multipleweighings at entry and exit reduce the standard deviation of the measurementerror by the inverse of the square root of the number of weighings. Hencewith three weighings the standard deviation goes down by a factor of 0.6 toabout 65 gms. A child in the feeding program who has gained 400 grams overthe three months will, by random error, be exited from the feeding programwith probability 0.06. The probability of allowing the exit of a childwith less than 400 grams weight gain is therefore very slight. The healthcheck-up and the multiple weighings combine to ensure that the children whoremain in the feeding program beyond three months are in need of additionalfeeding and that those children that leave the program are gaining weightadequately.

Table 7: PROBABILITY OF BY-PASSING CHILDREN FROM THE AGES 6 to 11MONTHS WITH WEIGHT CHANGES OF 500 to -100 GRAMS/MONTH

Actual Months of WeighingMonthly Growth 1 2 3 4 5(grams/month)

500 .99 .98 .97 .96 .94400 .93 .86 .80 .74 .68300 .74 .54 .40 .24 .22200 .43 .19 .08 .03 .01100 .17 .03 .00 .00 .000 .04 .00 .00 .00 .00

-100 .01 .00 .00 .00 .00

Table 8: PROBABILITY OF BY-PASSING CHILDREN FROM THEAGES OF 12 to 35 MONTHS WITH WEIGHT

GAINS FROM 167 to -33 GRAMS PER MONTH

Actual Average Months of Monthly WeighingsThree Month Weight Gain 3 4 5 6 7 13 23(monthly weight gain)

500 (167/mo.) .99 .98 .97 .96 .94 .89 .80400 (133/mo.) .93 .86 .80 .74 .68 .47 .22300 (100/mo.) .74 .54 .40 .24 .22 .05 .00200 (67/mo.) .43 .19 .08 .03 .01 .00 .00100 (33/mo.) .17 .03 .00 .00 .00 .00 .000 (0/mo.) .04 .00 .00 .00 .00 .00 .00

-100 (-33/mo.) .01 .00 .00 .00 .00 .00 .00

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IV. THE COSTS OF SUPPLEMENTAL FEEDINGAND THE QUANTITY OF FOOD REQUIRED

4.01 In a supplemental feeding program, the number of children thatwill actually be fed a supplement will depend to a large extent on externalfactors, including the price of food and its general availability, incomelevels and its distribution, the quality of the water supply, the birth rateand the season of the year, which determine to a large extent the degree ofmalnutrition that can be expected in any village or region. The number ofchildren actually fed out of the total number malnourished and eligibledepends on the incentives to potential beneficiaries to participate, which arerelated to factors such as the size of the food supplement and its perceivedvalue, the opportunity cost to the mother or older sibling of bringing thechild in for feeding, the effectiveness of the nutrition worker in reachingchildren to weigh them, and the perceived benefits to be obtained from theeducation and nutritional services. The number of children that remain in theprogram after the intended days of feeding depends on the effectiveness of thenutrition worker in inducing the family to feed the child more at home and thecalorie content of the ration given at the feeding center (the larger theration, the more independent to the amount fed at home is the program'ssuccess in rehabilitating malnourished children). Since some of the childrenbeing fed will have been in the program before but have relapsed after leav-ing the feeding program, the number in the program during any given monthwill also depend on the relapse rate, which in turn is determined by theexternal factors described above. As a consequence of these influences on thenumber of children being fed, the estimates of a program's beneficiaries arecomplicated and largely dependent on these environmental factors.

4.02 To begin, we will construct a mathematical model, which illustratesthe parameters that influence a feeding program. We will then present asimulation model to do estimates of the number of beneficiaries and food costsunder various parameter values.

The Mathematical Model _/

4.03 In this model, a child enters a feeding program for a fixed period.During this period, the child has a probability of recovering in any onemonth and leaving the program. Once having recovered, the child enters a highrelapse group and is closely monitored for a reoccurrence of malnutrition.If successful in passing through this high relapse group, the child has thesame or perhaps a somewhat lesser risk of becoming malnourished and reenteringthe program then children who have never been malnourished. 2/

1/ For those non-mathematically inclined this section can be skipped infavor of the section on the simulation model.

2/ This of course assumes that the education component has alleviated some-what the risk of malnutrition. If environment dominates the risk, thenthe selection process of having been malnourished once before would meanthat the probability would be greater than for other children.

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4.04 To calculate the influences on costs of parameters of the feedingprogram, we construct the model using the following variables:

Fi = number being fed in any month i

X. = number in the jth month of feeding

Y k = number in the kth month in the high relapse group

Pj = the probability of leaving the program after j months of feeding

PR = the probability of relapsing after k months in the highk relapse group

= proportion of target population N entering the program1 in the ith month

R. = number relapsing in the ith month

RGi = number in potential relapse group

T = total possible months of feeding

TR = total possible months in potential relapse group

The total number of children being fed in any month is:

TF. Z X (14)

L J.1-1

The number of children entering the program consists of new entries, e Naand children that have relapsed, R. or

X Ni + R (15)1 2

where Ni = (N - RG. - Fi)

The number of children passing from the j to j + 1 feeding period is

Xj+l = (1 - P.)X., j - 1, T (16)

and the number entering the potential relapse group is

Ty. pi'x (17)

J-1

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The number of children moving from relapse period K to K + 1 without relaps-ing is

Yk+l =( -PRk)Yk k = 1, TR (18)

and the number who relapse in month i is

TR

R. = E PRk+l Yk+l (19)1 k-1


TR-1R E PR k+l ( PRk)Y k (20)

k-0

or

R. k0TR-1 P=l k (21)R =E PR k+l ii (1-PRk)'21)

Likewise using (16) and (14) we get for the number being fed

F. I 1 k (1 -P.j_) X1 (22)

or TF. = ~ k,rjlP )J(cN + R.) (23)

1= Ti =1 ~j-l i 1 23

From (23), (17) and (21) we can derive a complex and not easily manageableexpression for the number being fed (using this expression, a simple computersimulation has been constructed which allows one to determine actual numbersbeing fed over time).

4.05 To get a simpler expression for (23), we will now make some approxi-mations. Assume that the feeding period is T months and that all childrenbeing fed recover. That is, assume that

p 1

whileP. = 0 for all i 0 T

Also assume that the probability of relapsing is equal in any month and thatthe target population is large in comparison to the number being fed in therelapse group. That is, assume that

PR. = PR. - PR for all i and jJ 1.

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and that

Ny>F i + RG

Under these assumptions, since Xi = X = ...XT (24)

or F. = T Xl (25)

F. = T(eN + R.)1 1.

The number of children relapsing from (21) is

TR-lR. PR(1-PR) (26)

1 kik-0

The probability of relapsing in TR monthsTR-1 k

v = I PR(l-PR) (27)

k=0

then R = v(eN + R ) (28)

or

Ri = EN (29)

1-v

and the number fed from (25) is

Fi = T (CN)(l/(l-v)) (30)

In other words, for this simple case, the number fed is directly proportional

to the length of feeding T, entry criteria, c, and inversely proportional to

the relapse rate, V. The feeding costs are F times the cost of the daily

ration, C. or

CF = Ci TeN(l/(l-v))

As a first approximation if we consider that a full ration feeding program

would require about four times the ration quantity, about half the duration

of feeding, and have a relapse rate of about half that of a partial ration

program, the food costs of full feeding to be equal to that of partial feed-

ing would need to have an entry criteria that excluded about 44% of the

children that would be fed in a partial feeding program (assumes a 20% relapse

rate in partial feeding programs). If the relapse rates were equal then the

exclusion would need to be 50% of those in a partial feeding program for food

costs to be equal.

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A Simulation Model of Supplemental Feeding

4.06 A simulation model has been constructed to estimate beneficiaryflows and the quantity of food required. 1/ The model is applied to theconditions in Tamil Nadu and a supplemental feeding program of the followingcharacteristics:

Entry Criteria : Any third degree malnourished child by age-for-weight and children with inadequate weight gain.

Age of Participation: Preschool children from the ages of 6 to 35months.

Ration Size : Children from 6-23 months old, 145 calories perday (40 gis/day). Children from 24-35 months old290 calories per day (80 gms/day). Third degreemalnourished children receive double the aboverations.

Minimum Durationof Feeding Three months.

4.07 The model is designed to estimate beneficiary flows by age groupfor two categories of children: those that are not third degree malnourishedand entered by weight gain criteria and those that are third degree mal-nourished. Each of these groups has a different probability of becoming mal-nourished and recovering from malnutrition due to the feeding. The specificassumptions are described in the following paragraphs.

A Simulation Model

4.08 The simulation model estimates beneficiary flows and costs as afunction of the rate of malnutrition, rate of relapse, and a feeding program'sefficiency in returning children to adequate weight gain or adequate nutri-tional status. As shown in Figure 2, the model consists of three principalcomponents: one that simulates entry into the feeding program, one thatdescribes the feeding and the monthly probabilities of returning to adequateweight gain, and one that consists of the monthly probabilities of relapsethrough the first six months after leaving the program.

4.09 The first component simulates entry into the program by age group:under 1 year old, 1 to 2 years old, and 2 to 3 years old. 2/ Associated witheach age group is a monthly probability of becoming eligible for the programthat depends on whether the child has been malnourished previously, whether

the child is third degree malnourished and whether the child has been in thefeeding program within the previous six months and is therefore considered to

1/ This is based on a model originally developed by Dr. Kalyani Krishna,Indian Institute of Technology, Madras, India and Dr. Nirmal Murthy,Management Sciences of Health, Boston, Massachusetts.

2/ For illustration, we simulate a feeding program for children between theages of 6 months and 3 years only. The model is of course expandable toother age groups.

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Figure 2: Model of Entry and Exit from Supplemental Feeding Program 1/

Children ChildrenWho Have Who HaveNever Been Been in theMalnourished Program and

By R ereedAgeGroup

/ Monthly \ / MonthlyProbability - Probabilityof Becoming of Becoming

Ianourished Malnourished

FeedingProgram

Initial NPrntiln 7 Months/PProportionroail_RelapsinglWithin. First SxMnths After \\ Rcovery/\

\ / ~~~~~~Probability \of

RecoveryAfter N + i

High Risk. _ ~~~~Relapse

Group

(6Months)

Pobability of Passing

Through HighRisk

I/ The model is repeated for each age group: 6 to 11 months, 12 to 23 monthsand 24 to 35 months and for three groups of children; those coming fromhouseholds with inadequate caloric availability, those from householdswith adequate caloric availability, and third degree malnourished children.

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have a high risk of relapse. These three categories for each age group cons-titute the population that can enter the feeding program. The probabilitiesassociated with each category and age group can diminish or increase overtime thereby simulating the trends in malnutrition rates or the effects ofa communication component in improving feeding or community hygiene.

4.10 The second component of the model simulates feeding in which chil-dren enter the feeding program each month, are fed for a minimum of 3 months,and have a probability of recovering each month after the initial 3 months offeeding. The ratio of the number of children who recover (who return to anadequate growth path within 3 months) to the total number of children beingfed is called the recovery rate. This rate is estimated to vary between 10and 40% of the children being fed.

4.11 The third component of the simulation takes into account the higherprobabilities of relapse that exist in the months just after feeding andrecovery. In the model, after recovery the child enters a high risk relapsegroup for 6 months. While in this group the child initially has a low proba-bility of relapse, then after about 4 months a higher probability and atnearly 6 months a return to a lower probability. This high risk relapse groupis assumed to have a relapse rate of between 10 and 40%. Once leaving thefeeding program and the high risk relapse group, the child is assumed to ex-perience a risk of malnutrition below that of other children that have neverbeen in the program. The specific assumptions for each age group and classi-fication by calorie availability are summarized in Table 9.

4.12 Mortality rates along with birth rates determines the demographicsof the model and the impact of feeding on life span of the population. Themortality rates are based upon the Narangwal intervention in the Punjab, anexperiment conducted from 1968 to 1973 by the Indian Council of MedicalResearch and the John Hopkins Department of International Health. It was areasonably large study in which control villages were used to differentiatethe impact of medical and nutrition interventions. Although this experimentwas conducted in the Punjab, the measurements correspond to infant morbidityand mortality rates of Tamil Nadu.

4.13 The mortality rates associated with the third degree malnourishedchildren are based on a Bangladesh study of mortality among children of dif-ferent degrees of malnutrition. This study found that third degree childrenhave a 3 to 5 times greater mortality rate than adequately or even moderatelymalnourished children. For the purposes of the simulation a mortality rate of3 times that of other children is used for the third degree malnourishedchildren. Although reduced mortality rates from feeding tend to increase thenumber of children in each age group, other factors operate to decrease birthrates. Since the existence of a feeding program increases the probability ofa child surviving to adulthood, a family can be more assured of achieving a"target" level of family size and a desired number of surviving children.Since the losses associated with a family size that is less than desired arehigh in terms of social prestige, labor and income losses, and potentialsupport to the parents in their old age while the losses of a larger familysize are relatively less in terms of increased food expenditures and othercosts, the tendency will be for parents to have a greater than desired numberof children. This bias towards a larger family size will increase with the

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Table 9: 8UMHARY OF ASSUMPTIONS OF SUPPLEMENTAL FEEDING MODEL

6-11 MoB 12-23 Mos 24-35 Moe

I. Proportion of participants becomingeligible by weight gain

a. No previous Malnourishment 0.50 0.20 0.15group

b. Previously malnourished group 0.65 0.28 0.22

II. Probability 1/ of recovery after 0.8 0.8 0.8feeding

III. Probability of relapse / after 0.1-0.4 0.1-0.4 0.1-0.46 months

IV. Ration 3/ size (grams/day) 40 40 40

V. Minimum days of feeding 90 90 90

VI. Initial population size 4/ 1,327 2,602 2,579

VII. Initial 5/ mortality rates 6 Moe - 11 MoeLee than 6 moo Over 6 Mos

104 26 12 61,000 1,000 1,000 1,000

Infant Mortality 1301,000

VIII. Fifth year mortality rates 64 16 8 51,000 1,000 1,000 1,000

301,000

IX. Initial participation rates 602 70X 702

Increment per year 05X 052 05S

Maximum participation rater; 902 902 902

X. Initial third degree 10 152 152malnutrition r2te

XI. Third degree participation rate 602 602 70%

XII. Proportion of children becoming 102 10% 102third degree after program

XIII. Proportion of recovered third degree 15X 152 152children relapsing into third degreeafter feeding and full recovery 6/

XIV. Ration size (grams/day) 7/ 80 80 160

1/ Probability of recovery ls:End of month 1 2 3 4 5 6 7

0 0 .8 .85 .90 .95 .992/ Probability of relap e in the eix months after reevrery for 20X ralapae rate Ls:

Month 1 2 3 4 5 6.020 .051 .065 .034 .036 .012

3 Under 2 year old are given a 1/2 ration.4/ Birth rate initially Is 30/1,000 going to 28/1,000 by year 5.5/ Mortality rates decline to 5th year levels in fixed increments per year. Based on

Narangwal data.6/ Third c!agree children are assumed to recover at an 802 rate after 90 days of feeding

and to relapse at a 302 rate within the first 6 months of leaving the progrin. Therelapse probabilities during those 6 months areiMonth 1 2 3 4 5 6

.015 .0S', .062 .099 .091 .060y Third degree malnourished children are fed for minimum 90 days a full ration if they

are under 2 years old and a double ration if they are between 2 and 3 years old.

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risk of not having the desired number of children. As the risk of mortalityis lowered for children, the bias will decrease and as a consequence fewerbirths will be required and family sizes will decline. With the projectreducing the risk of early mortality, it can be expected that birth rates willalso fall. It is conservatively assumed here that birth rates will declinefrom 30/1000 to 28/1000 over 5 years.

4.14 The final factor that needs to be accounted for is the participationrates that can be expected. During the first year of the feeding program(project year 2) it is anticipated that about 60% of the under 2 year olds and70% of the children between 2 and 3 years will be weighed and hence be eligi-ble for supplemental feeding. 1/ As the program continues in operation, it isalso anticipated that these participation rates will increase at about 5 per-centage points per year until 90% participation is achieved. This participa-tion rate along with the population growth determines the number of childreneligible for feeding. The malnutrition rates of the children that are weighedestablishes the number actually entering the feeding program.

4.15 In Tables 10 and 11, the beneficiary flows and quantity of foodrequired to feed malnourished children from a 100,000 population are presentedfor relapse rates of 10 to 40%. The non-third degree malnourished are enteredby weight-for-age.

4.16 Before entry is permitted for those entering by weight gain, severalmonths of weighing must pass, while, for third degree malnourished, entryoccurs immediately upon discovery of sufficiently low weight-for-age. Ini-tially then the feeding of weight gain children begins slowly, increasing asoccurrences of insufficient weight gain are found, and as participation in theweighing becomes more widespread. In the case of the third degree malnourished,an initial survey of the eligible population finds many malnourished children,enters them into feeding, and results in their recovery. Once this initialsweep is completed then only new occurrences of malnutrition are treated alongwith the third degree malnourished children from newly participating popula-tions. As a result, the number of children being fed who are not third degreemalnourished increases in a gradual trend while the number of third degree hasthis initial increase, a falling off as the historical stock of malnourishedare fed, and then a gradual increase as participation expands. Except ini-tially (due to this sweep), the number of children being fed who are thirddegree malnourished will be about 25 percent of all children being fed. For a20% relapse rate on both third degree and non-third degree malnourished, thecenters will be feeding approximately 1,400 children daily out of a totalpopulation of 100,000 with about 6,500 eligible children. Therefore, about20% of all eligible children will be fed at any one time, given the conditionsexisting in Tamil Nadu.

4.17 This feeding will require about 35 tons of food a year or approxi-mately 105 million calories. If divided amongst the total children eligiblefor feeding, this quantity of food would provide 1,200 calories for about 13

1/ The first year consists of establishing the feeding centers and providingthe initial investments; feeding begins in the second year. This makesthe timing of feeding costs consistent with the cost-benefit analysisof Section V.

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Table 10: AVERAGE BENEFICIARIES PER DAY AS A FUNCTION OFSIX-MONTH-RELAPSE-RATE - PARTIAL FEEDING 1/ 2/

I. Average Beneficiariesper day per 100,000population

A. Non-3rd malnourished Year 1 Year 2 Year 3 Year 4 Year 5

1. Relapse rate - 10%

(a) 6-11 months - 197 283 297 307(b) 11-23 months - 208 346 386 402(c) 24-35 months - 152 265 310 329

Total - 557 894 993 1,038



Total - 569 954 1,057 1,108


(a) 6-11 months - 200 296 310 321(b) 11-23 months - 219 404 449 469(c) 24-35 months _ 161 317 371 396

Total - 580 1,017 1,130 1,086

4. Relapse rate * 40%

(a) 6-11 months - 202 304 317 329(b) 11-23 months - 225 437 487 510(c) 24-35 months _ 165 348 410 438

Total - 592 1,089 1,214 1,277

B. 3rd malnourished



Total - 324 282 304 322

2. Relapse rate * 201

(a) 6-11 montha - 60 59 63 66(b) 11-23 months - 133 117 127 134(c) 24-35 montha - 146 126 137 145

Total - 339 302 327 345


(a) 6-11 months - 61 60 64 68(b) 11-23 months - 139 127 137 145(e) 24-35 months - 155 138 150 159

Total - 355 325 351 372


(a) 6-11 months - 62 62 66 70(b) 11-23 months - 145 137 148 157(e) 24-35 months 163 152 165 175

Total - 370 351 379 402

1 Sae Table 4-1 for aes ptions.S lix month relapse rates are the pereentage of program graduates vho relapse

within 6 months.

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days. If full feeding is used instead of partial feeding and the duration offeeding is reduced from 90 to 60 days then the total quantity of food requiredwould be approximately 100 tons of food per year - a tripling of food costs.Whether such an increase in food costs would result in a project that iseconomically viable will be examined in the next section on benefits and costs.

Table 11: QUANTITY OF FOOD REQUIRED AS A FUNCTION OFSIX-MONTH-RELAPSE RATES - PARTIAL FEEDING

Year 1 Year 2 Year 3 Year 4 Year 5

I. Total Quantity of FoodRequired per 100,000Population (tons/year)

A. Non-3rd DegreeMalnourished1. Rate of Relapse = 10% - 10.22 16.71 18.74 19.692. Rate of Relapse = 20% - 10.44 17.90 20.90 21.133. Rate of Relapse = 30% - 10.67 19.23 21.63 22.784. Rate of Relapse = 40% - 10.90 20.69 23.41 24.69

B. 3rd DegreeMalnourished1. Rate of Relapse = 10% - 13.27 11.46 12.36 13.092. Rate of Relapse = 20% - 13.96 12.33 13.31 14.103. Rate of Relapse = 30% - 14.66 13.34 14.41 15.274. Rate of Relapse = 40% - 15.36 14.50 15.69 16.64

V. THE BENEFITS AND COSTS OF SUPPLEMENTAL FEEDINGOF CHILDREN AND PREGNANT AND LACTATING WOMEN

5.01 The purpose of this section is to quantify both the efficiency andsocial benefits of supplemental feeding of children and pregnant and lactatingwomen. The efficiency benefits are due to the increased production origina-ting from extended expected working years and productivity gains of benefi-ciaries when they become adults. These benefits are the result of reducedchildhood malnutrition and mortality. The social benefits result from incomein the form of food being distributed to the poor and from a basic needscommodity being supplied to those in need. The analysis of these socialbenefits is based on the Squire and van der Tak methodology of social benefitanalysis 1/ and the Scandizzo-Knudsen approach to the evaluation of thebenefits of basic needs program. 2/

1/ Lyn Squire and Herman G. van der Tak, Economic Analysis of Projects, AWorld Bank Research Publication, the John Hopkins University Press,Baltimore, 1975.

2/ Pasquale L. Scandizzo and Odin K. Knudsen, "The Evaluation of the Bene-fits of Basic Needs Policies", American Journal of Agricultural Economics,February 1980.

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The Project

5.02 To illustrate how these methodologies apply to the evaluating ofnutrition projects, we determine the benefits and costs of a proposed feedingand nutrition education project in six districts of Tamil Nadu, covering apopulation of about 14 million. These districts are to be phased in over afive year period with a supplemental ration being fed to eligible children, 6to 35 months of age, and to pregnant and lactating women at about 8,000 commu-nity nutrition centers. Children would be entered according to weight gaincriteria while pregnant women would be selected by rural health workers. Thechildren's ration would be relatively small, from 80 grams (240 calories) to160 grams (480 calories) depending on the child's condition, and would be fedfor a minimum of ninety days. The pregnant women would receive a singleration of 240 calories for the last trimester of pregnancy and for four monthsduring lactation. Mothers would be educated to improved child feeding prac-tices at community nutrition centers and through a communication campaignwhich provides wall posters, radio advertisements, short films, etc. A moni-toring and evaluation component would monitor the progress of the project anda sixth year evaluation would be conducted to measure its effects on malnutri-tion and mortality. The details of the project are summarized in Table 12.

TABLE 12: PROJECT DESCRIPTION

Description : A nutrition project primarily consisting ofthe supplemental feeding of preschool chil-dren and pregnant lactating women. The pro-ject includes an education-communicationcomponent, along with widescale dewormingand diarrhea management education. About8,000 community nutrition centers would de-liver nutrition services and food.

Location : Six districts in Tamil Nadu with a ruralpopulation of about 14 million includingabout 1.5 million children in the eligibleage groups.

Feeding A ration consisting of a 240 calorie biscuitgiven to children entered in the program byweight gain criteria and a double ration of480 calories given to third degree malnou-rished children. A single ration of 240calories would be provided to pregnant andlactating women.

Duration ofFeeding Feeding at the centers would be for a mini-

mum of 90 days for children and for 7 monthsfor women, 3 months while pregnant followedby 4 months when lactating.

- 41 -

Entry Criteria For children: based upon weight gain criteriafor most children (see section III for details)and by weight-for-age criteria to determinethird degree malnourishment. For women: se-lection by health worker according to need.

Exit Criteria : 90 days of feeding or until adequate weightgain is achieved.

5.03 The project proposes a substantial supervisory infrastructure, fromstate headquarters down through block, taluk, and village levels. At thevillage each 10 nutrition workers would be supervised by one nutrition super-visor. One step up the hierarchy, each 5 nutrition supervisors would have aninstructress overseeing their duties and conducting training. In addition,support staff in each taluk (averaging 12 taluks per district) would be neces-sary along with vehicle s and office equipment. This heavy supervisory infra-structure contributes to a high "overhead" cost in the delivery of thesupplemental food. 1/ Over the five years of project implementation, nutri-tion delivery cost including salaries and equipment will be US$21 millionwhile the cost of the food delivered is US$6 million, a ratio of 3.5 to 1.The question is what level of benefits would be necessary to justify thesecosts?

5.04 Clearly, the food delivery costs do not simply justify the amountof food that is being delivered. Even India's public food distribution sys-tem with its inefficiencies and its ration shop structure is able to deliverfood to the target group with an overhead of 20 percent, 2/ including leak-ages to unintended beneficiaries. Nor could the project be justified solelyon its income redistributive effects. Subsidizing consumption of the pooror taxing the rich could deliver or take away income much more efficientlythan such an elaborate structure of delivery. Instead, the benefits of theproject must occur because of some multiplier effect, whereby the smallamount of food acts as a catalyst for improved nutrition, through inducingmore equitable distribution of food within the family or improved food pre-paration and utilization. We therefore must begin with the assumption thatthe "educating" aspects of the project bring about this multiplier effect.Otherwise, we can end the analysis at this point, since alternative forms offood delivery to the household are more efficient and net benefits can onlybe claimed to the extent that they are greater than that of the next bestalternative.

5.05 The next major question is how well will the system function. Willit achieve lower mortality of preschool children? Will it be able to avoid

1/ A less costly organization would be to combine the health and nutritioninfrastructure into one unit in which the village worker deliver bothnutrition and health services. As such, the project should not be con-sidered an ideal model of a nutrition delivery system. Likewise, theadministrative costs should not be regarded as typical.

2/ See P. Scandizzo and J. Graves, "Alleviation of Malnutrition; Impact andCost Effectiveness of Official Programs." AGREP Working Paper No. 9, 1979.

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large amounts of intra-family substitution? Will a large portion of the mal-nourished children participate in the feeding? Clearly, the benefits thatthe project will realize depend on these outcomes, which are at the presentunknown without a pilot project. The performance of the project thereforeis a parameter of the analysis to which the sensitivity of the benefits willbe tested. The procedure then for the benefit analysis is to assume somereasonable performance parameters, calculate the costs and benefits underthese values, and test their sensitivities.

5.06 We begin by estimating the efficiency benefits, that is, thosebenefits that are manifested in high earnings from extended working yearsand more productivity. We then determine the social or redistributive bene-fits, or those benefits accruing because society values income to the poorgreater than that to the rich. We complete the analysis by adding on thebenefits from a basic needs commodity being supplied to those in need.

The Efficiency Benefits

5.07 We now examine the benefits that result from reduced preschoolmortality and extended working years and the productivity gains as an adult,resulting from avoiding malnourishment as an infant or preschool child. Webegin with the mortality reduction and extended working years. 1/

5.08 Because the project is directed primarily to the poor and the riskof early death is different for the rich and poor, we divide the populationinto those households with adequate calorie availability (the "rich") andthose without adequate calories (the "poor") and calculate the probabilityof death for children from each group. In Figure 3, we give a diagram forthe probability of surviving past the age of three with and without the pro-ject (the probabilities in the diagram are based on the Narangwal study). 2/Beginning on the left side of the diagram, we can trace from the probabilityof being rich or poor through to the probability of surviving through thefirst year of life. 3/ During the second and third years of life, a survivingchild can become malnourished with a probability that depends on whether itcomes from a rich or poor household. Being malnourished, a child has a pro-bability of surviving or dying. By tracing the various paths, we get theprobability of surviving for children of the rich and poor through the firstthree years of life.

1/ Studies in Bangladesh indicate that mortality rates between adequatelynourished children and 1st and 2nd degree malnourished children do notdiffer significantly. However, the mortality rate for 3rd degree mal-nourished children is 3 to 5 times that of the above group. Hence, inthese mortality calculations, we have the project only influencing themortality rates of those who are or would have become 3rd degree mal-nourished.

2/ In the tables that follow these particular probabilities are called the"Narangwal assumptions".

3/ The rich or poor differentiation on mortality are based on mortalityrate differences between castes (artisans, merchants versus agriculturallaborers) from the Narangwal study.

Figure 1: Ptobability of Surviving With and Without Project 2

Life YearsAfter 3 Years

( 981) S W/O (.810) x (.610) x (.980) = .480 of AgeS .98 \Poor/Not M)jnourished

(.610 19) With(.858) x (.870) x (.981) = .732 50W .6~~~~~~~~~~~~~~~~~~~6

(.85 3 9 0 (.910) W /O (.810) x (.390) x (.900) - .280 .832

0.38 -1/ G ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~/40poor38 .190 (.090) With(.858) x (.130) x (.910) - .102

0.62 1/ Life Yearsvrich (995) After 3 Years

S (-995W/0 (.910) x (.920) x (.995) = .833 of Age\W 950) ° AS DRich/Not Malnourished

(.919 .05) With(.919) x (.950) x (.995) = .869 600 005) ~~~~~~~~~~~~~.904

\ \ (.982) S g .914

\ (.081) \ S .980 W/O (.910) x (.080) x (.980) = .071D \ .090 D.018 Rich/Malnourished

With(.919) x (.050) x (.982) = .045 50S - SurviveD = DeathW = Adequately nourishedM = Malnourished (Third Degree)

W/0 = Without projectW - With projectpoor = Children from households below the FAO/WHO calorie requirementrich = Children from households above the FAO/WHO calorie requirement( ) = Probabilities with project

(y e a r s o f 1 i f e )0 1 3 6

1/ Probability varies with increasing calorie availability; 0.38 and 0.62 are the initial assumptions for 1980.2/ With project situation in parenthesis.

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5.09 After the first three years of life, we assume for simplicity thatthe life span is a fixed number of years, the specific number being dependenton whether the household has adequate calories available and whether thechild was ever third degree malnourished. 1/ Depending on which category anindividual falls, an expected earnings stream is accrued, with the higherearnings going to the rich and never malnourished and the lower earnings tothe poor and malnourished. The specific earnings are summarized in Table 13.They assume that the difference in earnings of those who have been thirddegree malnourished and those who have not is 25% (centered about the averageunskilled laborer's wage). We also assume a 50% unemployment rate and a de-clining percentage of households with calorie availability below the FAO/WHOrequirement. 2/

5.10 As illustrated in Table 13 and Figure 1, the project is expectedto (a) redVce the probability of death during the first year of life, (b)reduce the probability of becoming third degree malnourished, and (c)reduce the probability of death of those who become third degree malnourished.At birth then, life expectancy increases as a consequence of the project andif a reduction in birth rates does not occur, the population in each agegroup expands. As a consequence of this population expansion, eventuallymore people will be working, and GNP will increase. If we measure benefitsof the project in part by its contributions to GNP, we are incorporating theeffect of this increased population. Should a larger population in thecountry already over-populated be considered a benefit? Although we haveother productivity benefits from the project, people working for longerperiods at higher levels of productivity, we also have an expanded popula-tion in a crowded, labor surplus country accruing therefore a cost to society.

1/ In doing this calculation, we are assuming, for simplicity, no movementfrom rich to poor or vice versa. We do provide, however, for the numberof poor to decline over time; essentially then we assume that the child'sbirth status, rich or poor, determines the probability of surviving thefirst three years of life and the life span thereafter.

2/ The projection is based upon calculations in Odin Knudsen and PasqualeScandizzo, Nutrition and Food Needs in Developing Countries, World BankStaff Working Paper No. 328, May 1979.

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Table 13: ASSUMPTIONS ON MORTALITY - CALCULATIONS OF BENEFITS

Overall Poor /b Rich /b

A. Without Project

1. Infant mortality rate: 130/1000 /a 190/1000 90/1000

2. One to three year oldmortality rates:

a. Third degree malnourished: - 100/1000 20/1000b. Non-third degree mal-

nourished: - 20/1000 5/1000

3. Probability of becomingthird degree malnourished: 0.15 /a 0.39 0.08

4. Lifetime after survivingfirst three years of life:

a. Third degree malnourished: - 40 50b. Non-third degree mal-

nourished: - 50 60

B. With Project for Participants(% change from without project rates)

1. Infant mortality: 105/1000 /a 142/1000 81/1000(-25%) (-1O%)

2. One to three year oldmortality rates:

a. Third degree malnourished: - 90/1000 18/1000(-10%) (-10%)

b. Non-third degree mal- - 19/1000 5/1000nourished: (-5%) (0%)

3. Probability of becoming thirddegree malnourished: 0.15 /a 0.13 0.05

(-67%) (-40%)4. Lifetime after surviving first

three years of life:

a. Third degree malnourished: - 40 50b. Non-third degree mal-

nourished: 50 60

/a Changes with ratio of "rich" to "poor

/b Defined as households with calorie availability below (poor) or above FAO/WHO calorie requirement (rich).

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5.11 There are several ways of handling the expansion in population inthe analysis. First, we could assume that the increased production, despitethe larger population, is a net benefit, that is, not deduct the social costsof the population increase. 1/ Second, we could assume that the increasedpopulation carries a social cost equal to the additional expenditures onsocial services induced by the larger population. Third, we could do thecalculations assuming a constant population, that is, count only those bene-fits that do not originate from an expanded population. A fourth, more eso-teric method, would be to measure the loss in consumer surplus resulting frompopulation pressure on prices of scarce commodities and count this loss asthe costs of expanded population. A fifth procedure would be to deduct fromtheir earnings the consumption of the increased population, essentiallycounting only their savings as a benefit. A sixth procedure would be tovalue the benefits as the willingness-to-pay for reduced children's mortalityas demonstrated by families' expenditures on health, safer water supplies,etc.

5.12 For our analysis, we adapt several sequential procedures. First,we calculate the net benefits without attributing the costs of expanded popu-lation and then ask what would the social costs per life saved need to be toreduce the economic rate of return to the opportunity cost to capital. Thenwe repeat the calculation assuming a compensating reduction in birth rates sothat population remains constant. Reference to Figure 4 will illustrate.

5.13 In panel A of Figure 4, we depict a case where project costs areaccrued on a,one time basis in year 1 and lives are saved in the same year.As a result, starting in year 13, an incremental earnings stream begins asthe life saved reaches working age, and continues until death at age 53. Inpanel B, we assume that an exactly compensating birth rate reduction occursthe year after the lives are saved. Without the birth rate reduction, thesenew births would have reached working age in year 14 and continued on workinguntil year 54 of the project. Since this earnings stream is no longer avail-able, it is deducted from the earnings of the lives saved. As a consequence,a net earnings increase occurs in year 13 and a net earnings decline occursin year 54. In this simple case, the project's effect is to accelerate earn-ings in the earlier years at the cost of earning reductions later on. Indiagram C, we depict a more realistic case in which the birth rate reductionis more gradual.

5.14 Under what circumstances would we find such a gradual compensatingeffect? Consider a case where families target the number of children: afamily continues to have children until a targetted number of children havelived to an age when the probability of early death is low, after five yearsold. Under this circumstance, a child surviving to be five years old resultsin an additional birth being unnecessary. The project would, through increa-sing the probability of surviving to five years old, accelerate the achieving

1/ Note that implicitly we are assuming that the percentage of unemployedwill not increase because of the larger population. For the populationincrease that we are discussing here - around 300,000 - this is a rea-sonable approximation.

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Figure 4: Earnings Streams With and Without Compensating Birth Rate Declines

A. Earnings From Lives Saved Without Birth Rate Reduction.

Earnints from lives saved

_ ~~~~13 53 yearsProject

_+ 1 r Costs

B. Earnings From Lives Saved With Exactly Compensating Birth Rate ReductionOne Year Later.

+Ne

53 54

_ 13 14 x years

_ ProJect . X

C. Earnings From Lives Saved With Lagged Birth Rate Reduction.

+ NetBenefitt

13 7/yearsProject A

_ Coats ,/\ / t:/Nets

- 48 -

of this target family size. As a result, the age composition of the popula-tion would change, with people beginning to work earlier than would have beenthe case with lower survival rates for children. This additional benefit ofaccelerated earnings is depicted in panel C of Figure 4.

5.15 In summary, the mortality rate reduction occurs because the projectchanges the age composition and size of the population. These changes resultin an accelerated and larger earnings stream that, in calculating the netbenefits of a mortality rate reduction, is reduced by a social cost streamresulting from a larger population. We now explore the third element in theefficiency benefits: the effects on productivity.

The Productivity Benefits

5.16 Reduced malnutrition in preschool ages yields an additional bene-fit through increased productivity as an adult. In a recent paper, Selowskyreviews the empirical evidence on the relation between malnutrition duringthe preschool years and productivity as an adult. 1/ He observes that anincreasing number of studies have shown that preschool children of the poorhave substantially lower scores on tests of cognitive development than higher-income groups. Furthermore, studies on earnings functions show an independenteffect on early ability of future earnings. Also, the evidence indicates acomplementarity between schooling and ability, with the marginal productivityof additional schooling depending on preschool ability. Malnutrition there-fore seems to reduce productivity of adults by reducing ability and the num-ber of years and effectiveness of education.

5.17 To quantify these relationships, Selowsky begins with an earningsfunction where wages, W, are related to years of schooling, S, preschoolability, A, and age, T, in a semi-log format:

Log W = a + bS + cA + dT (32)

Differentiating (1) with respect to A, we get

dW/W = (b aS/a A + c) dA (33)

5.18 As shown by this equation, the effect on wages, W, of increased pre-school ability, A, originates from a direct effect through the coefficient c,and an indirect effect, through the complementarity on schooling representedby aS/aA. That is, additional increments of preschool ability are assumedto result in additional years of schooling.

5.19 By assuming a diminishing rate of return to additional years ofschooling and behavior where households equate the opportunity cost of capi-tal to the marginal rate or return to schooling, Selowsky derives the fol-lowing relation:

1/ Marcelo Selowsky, "Nutrition, Health and Education: The EconomicSignificance of Complementarities at Early Ages". Present at the SixthWorld Congress of International Economics Association, Mexico City,August 1980.

- 49 -

aS/DA = c/(0 - b - d) (34)

Where c, b, and d are defined from (32) and 0 is the precentage increasein schooling costs for each additional year of schooling.

5.20 From a series of empirical studies of developing countries, Selowskyderives ranges for the coefficients in (32) and (34). From these studies, heselects values for c, b, d and 0, such that, c = 0.05, b = 0.18, d = 0.06 and0 = 0.28.

Therefore, substituting these values in (32) and then (34) we get:

dS = 1.25 dA (35)

and

dW = [(.18)(1.25) + .05)] W dA= (.275) W dA (36)

5.21 According to these parameters for an increase of one standard devia-tion in dA, wages would increase by 27.5%, with 5% of the wage increase comingdirectly from ability increases (operating through c with dS/dA = 0) and theremaining 22.5% coming from induced additional years of schooling.

5.22 What magnitude of improvement in ability, dA, can be expected fromreducing malnutrition in early ages? Selowsky sites two studies: one fromColumbia, the other from Chile. The Columbia study found that children withmild to moderate malnutrition (90 to 79 percent of weight and height for agenorms) could increase their ability scores at 43 months of age by one stan-dard deviation if nutrition is improved. The Chile study found that severelymalnourished children, less than 70 percent of the norm, could have improvedpreschool ability scores by two standard deviations if early malnutritionhad been avoided (from multiple regression results).

5.23 Although these studies are not necessarily representative of resultsachievable in other parts of the developing world, they indicate the magni-tude of results that are conceivable. The results are summarized in the tablebelow:

- 50 -

Table 14: INCREMENTAL INCREASE IN EARNINGS FROM IMPROVEMENT IN COGNI-TIVE DEVELOPMENT AS MEASURED BY PRESCHOOL ABILITY SCORES

Due to DirectEffect of Increased Due to Increase

Cognitive Development in Schooling Overall /a

Severely Malnourished 10% 45% 55%Children

Moderately to MildlyMalnourished Chil- 5% 22.5% 27.5%dren

/a Note that the major part of the productivity increase comes fromincreased schooling. If schooling is unavailable, then the productivityincrease will be substantially less.

5.24 Using an average daily wage in rural areas for an unskilled workerof Rs 5 and an employment rate of 50% for 300 working days, we derive anannual wage of Rs 750 for an average worker. Since those who have not exper-ienced severe malnutrition as a child would be more productive, we assumea 15% premium above average wages, while for those who have experienced mal-nutrition, we assume a 15% deduction from the average. Furthermore, weassume that a child that has become malnourished and recovered will exper-ience as an adult a 25% productivity increase above that of someone who wasmalnourished. For those children from households with adequate calorie avail-ability, we-assume that average adult earnings would be about three timesthat of an unskilled worker. We also assume similar proportional deficitsin earnings if the person was malnourished as a child. Differences in thelength of working life are also assumed between the categories of rich, poor,malnourished, etc., however, when translated to earnings these differencesif discounted become minor as they occur 55 to 75 years after project imple-mentation.

- 51 -

Table 15: ASSUMPTIONS ON EARNINGS STREAMS OF RURAL RICH AND POOR

A. Households with inadequate calorie availability (poor):

(a) Earnings/never malnourished (years 13 to 53): Rs 862.5/year /a(b) Earnings/malnourished (years 13 to 43): Rs 644/year /b(c) Earnings/malnourished, recovered (years 13 to 53): Rs 805/year /c

B. Households with adequate calorie availability (rich):

(a) Earnings/never malnourished (years 13 to 63): Rs 2,400/year(b) Earnings/malnourished (years 13 to 53): Rs 1,800/year /d(c) Earnings/malnourished, recovered (years 13 to 53): Rs 2,250/year /e

/a Based on Rs 5/day x 300 day x .5 unemployed x 1.15 productivity factorabove that of average worker due to having never been malnourished.

/b 75% of an adequately nourished worker's earnings.

/c 25% productivity increase over that of malnourished workers to 93%earnings of a worker who has never been malnourished.

/d 75% of adequately nourished worker's earnings.

/e 25% productivity increase over that of malnourished workers to 90% ofearnings of never malnourished worker.

5.25 To summarize, we have several efficiency effects of a nutrition proj-ect which saves childrens' lives through reducing malnutrition and improvingfeeding practices:

1. Increased productivity from avoiding the detrimental effectsof malnutrition in the preschool years.

2. Increased populations in certain participant age groups com-pensated for by reduced populations in younger age group asbirth rates decline.

3. And as a consequence, accelerated earnings in the early yearswith declines later as the demographic cycle of lives-being-saved and births-being-avoided takes effect.

5.26 For the purpose of calculating the benefits of the project, wehave divided the beneficiaries into two groups - the third degree malnourished

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children and those children entered by the weight gain criteria. Four typesof benefits accrue to those in the third degree malnourished category -reduced mortality, increased productivity, accelerated earnings, and extendedworking years. For those in the weight gain category, we attribute as bene-fits only productivity increases as studies have shown only minor differencesin mortality rates between mildly to moderatily malnourished and adequatelynourished children.

VI. A BENEFIT AND COST ANALYSIS OF ASUPPLEMENTAL FEEDING PROGRAM

6.01 In this gection, we combined the benefits and costs of this supple-mental feeding program. We have already assumed a level of performance ofthe feeding program in regards to participation, recovery and relapse inSection IV. (Those assumptions are summarized in Section IV, Table 9.) Tosummarize briefly, we have assumed increasing participation rates during theyears of the project from 60% to 90% of the eligible chidren, recovery ratesfrom 70 to 80%, and relapse rates of 30 and 20%, varied by the age of thechild and the degree of malnourishment. In addition, we assume that thefeeding program will operate in any one location for 15 years. Since theproject phases in over five years, the project will be complete by year 20,with feeding having ended in all districts. 1/

6.02 The simulation model of supplemental feeding along with the districtphasing have been used to calculate the costs and quantity of supplementalfood and the beneficiaries flows of the project. To calculate benefits, wehave assumed that 90 percent of the children that enter the feeding programwould have become malnourished to an extent that would have resulted inproductivity declines. We further assume that the program is 80% successfulin avoiding these productivity declines in those who participate in theprogram. Later, we will test the sensitivity of the benefits and costs tothese performance parameters. In the meantime, we will evaluate the efficiencybenefits and costs at the assumed values.

6.03 The effect of the project is to save children's lives and extendtheir life as adults. As a consequence, during the project years, populationincreases as more children are alive, and again much later, when death wouldhave occurred, adults continue to live on due to their improved childhoodnutrition (here we assume no effect on birth rates). This additional popu-lation reaches a steady state in year 20 when the project ends, maintains thislevel for a period, and then again increases (relative to the size it wouldhave been without the project) when death would have normally occurred.Figure 5 illustrates by tracing the population in an age group affected bythe project. Without the project, a population age group A would have sur-vived the first three years of life and then would have died at ages 40onward. But because of the project, a larger population age group B survivesand lives longer. The difference between these populations A and B is theincreased population alive in any year in that age group. The summation ofthese incremental populations in each age group is the increase in population

1/ Implicitly we are assuming that the reduced levels of malnutrition by1995 to 2000 will not justify the cost of the feeding centers.

- 53 -

Figure 5: The Project's Effect on the Population

PopulationCohort

/ ~~~~Population B\

Population A

10 20 30 40 50 years

IncrementalPopulation(B-A)

10 20 30 40 50 yearl'

- 54 -

induced by the project, if no reduction in birth rate occurs. This increaseis given in Table 16.

6.04 Without a birth rate effect, the project results in an increasedpopulation in year 20 of about 140,000 and reaches a maximum of around 310,000in year 48. This projection assumes no effects on birth rates and disregardsthe additional population resulting from those surviving having children.We have then in Table 16, the minimum population increase given no birth ratereduction. If we account for the additional children of survivors, we canconservatively double these population projections in the later years.

Efficiency Benefits and Costs Attributing Zero Social Cost toPopulation Expansion

6.05 In the analysis that follows, we calculate the efficiency benefitsand costs of the project under the assumption that the expansion in popula-tion is without social cost and that it achieves mortality rate reductionscomparable to those of the Narangwal experiment. This will produce the upperlimits on the benefits of the project assuming that birth rates are unaffec-ted by reduced infant and preschool mortality. 1/ We will then test thesensitivity of the economic rate of return to the performance parameters ofthe project.

6.06 Project costs have been converted to economic costs using the stan-dard conversion factor for India of 0.83 except for increased food consumptionwhcih is converted at the factor for foodgrains of 1.1. 2/ The food transferhas been treated as an income transfer where food consumption for the householdincreases by the amount of the income transfer multiplied times the propen-sity to consume. This increased food consumption receives the foodgrain con-version factor weight while the increased non-food consumption receives thestandard conversion factor weight. Otherwise costs and benefits are handledwithout regard to which income class or public account accures them

6.07 In Table 17, the economic cost and benefits for the project are pre-sented (note that in year 1 some start-up costs occur; in year 2, a test blockis initiated and operation begins in year 3). The benefits do not begin untilyear 14 when the beneficiaries reach working age. 3/

1/ In the Narangwal experiment, a twice daily ration was fed any child inthe village throughout the year. If both feedings were taken, the supple-ment provided 400 calories. Since the project in Tamil Nadu provides 240calories to most children for a minimum of ninety days, the Narangwalresults are only indicative and probably represent an upper "bound" onthis project's performance.

2/ The conversion factor is the ratio of the shadow price to the domesticprice. See Squire and van der Tak, Economic Analysis of Projects fora detailed discussion.

3/ In reality, children work before age 13. However, this is probably ofminor economic significance; for simplicity, we assume it to be zero.

- 55 -

Table 16: INCREASE IN POPULATION DUE TO PROJECT ASSUMINGNO CHANGE IN BIRTH RATE: NARANGWAL ASSUMPTIONS

Additional AdditionalPopulation Population Totalfrom 'Poor' from 'Rich' Additional

Perlods Households Households Population

I 0.00 0.00 0,002 75.62 32.18 107.803 2408.12 1163.58 3571.704 5552.12 2736.58 8288.705 10330.20 5274.39 15604.596 16595.10 8795.65 25390.757 21510.37 11462.82 32973.198 26766.88 14316.53 41083.419 32362.04 17355.68 49717.7310 38217.76 20542.32 58760.0811 44262.94 23840.29 68103.2312 50405.10 27197.95 77603.0513 56547,26 30555.61 87102.8714 62689.42 33913.26 96602.6915 68831.58 37270.92 106102.5116 74973.74 40628.58 115602.3217 81069.66 43966.56 125036.2218 85759.59 46621.34 132380.9319 89169,82 48625.27 137795,0920-32 909i5.58 49699.68 140615.2633 91136.65 49699.68 140836.3334 97955.55 49699.68 147655.2235 107146,79 49699.68 156846.4736 121115.16 49699.68 170814.8437 139430.16 49699.68 189129.8438 153799.61 49699.68 203499.2939 169166.62 49699,68 218866.3040 185523.69 49699.68 235223.3741 202642.46 49699.68 252342.1442 220315,09 49699.68 270014.7743 237974.56 49745.91 287720.48

44 246779.34 51371.65 298150.9945 252400.27 53631.94 306032.2146 251609.99 57278.58 308888.5747 244986.25 62338.36 307324.6148 243522.50 66170.89 309693.3949 236609.65 70271.45 306881.1050 224626.98 74638.48 299265.4651 206756.10 79217,44 285973.5552 183038.29 83956.38 266994.67S3 158939.97 68702.67 247642.6354 134841.64 90770.23 225611.8655 110743.31 91761.64 202504.9556 86644.98 90401.89 177046.8657 62546.65 e6645.55 149192.2b58 38629.76 84942.28 123572,0459 20229,16 81802.72 102031.8860- 6849.37 77276.04 84125.4161 0.00 71054.28 71054.2862 0.00 63017.38 63017.3863 0.00 54835.02 54835.0264 0.00 46652.66 46652.6665 0.00 30470.30 38470.3066 o0oo 30287.94 30287.9467 0.00 22105.58 12105.58as 0.00 13971.17 13971,1769 0.00 7501.68 7501,6870 o0oO 2618.26 2618.2571-100 0.00 0.00 0.00

| | ̂ C° 00-4°00.d o.. ° ° O ° n0000 o o 00.0C.° 00 0°-4C.-,-400 0o 00 Cc0o03

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0000.040-4004040.0400 .0000000000 ..... 0 .... 00000000000.0.0....0000000000

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40 440 00.0000~~~~~~~~~~~~~<v °z 800000000000000004000~ o St a°R b-n 000 00 0 40 4 4 4 4 2 2 < _ _ >- 0000.0.g0.a a,4 C0 0 0 .0 0 0 C0 0 0 0 44.40

440.004.000. uv oSSSSos C00.0.CC4040..t0…OC0.00'000 C004CC000 0000 i i0i

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C -40 40-4 0C0. 0 0400 0 ^04 0 C C O C C C O C C. O C C C 0 0 0 0 0 4 4 00 4 0 0 0 0 .0 . 0 0 0 Z0 4 0 0

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- 57 -

6.08 Three benefit streams are recorded: one for the mortality reduc-tion of the poor, one for the mortality reduction of the rich, and one forproductivity gains. Because the earnings potential of the rich is muchgreater than that of the poor, even the slight reductions in the rich'smortality outweighs that of the poor's more substantial mortality reduction.The benefits of the increase in productivity about equals that of the mor-tality reduction, illustrating the widespread participation in the feedingprogram and the relatively substantial 25% productivity increase. At anopportunity cost of capital of 10%, the net present values are presented inTable 18 along with their individual sensitivities. The project produces ananticipated economic rate of return of 14.5%.

6.09 In Table 19, we analyze the sensitivity of the economic rate ofreturn to the performance parameters of the project. The rate of returnremains above the opportunity cost of capital except under some worst caseassumptions: if the impact on third degree malnutrition rates is only a 10%reduction, if the impact on infant mortality is 10% or less reduction, if thesuccess rate in avoiding malnutrition is 60%, and if productivity gains are10% for the non-third degree participants. A reduction in participation ratesto 67% of the eligible population in addition to the other reductions in per-formance reduces the rate of return to 7.7%. If productivity gains to thenon-third degree malnourished participants is zero but the other performanceparameters are maintained, then the rate of return approaches the opportunitycost of capital. However, in general, the rate of return is relatively insen-sitive to many of the individual performance assumptions.

6.10 The previous analysis has assumed that the social costs of addi-tions to the population are zero. We now ask what the annual social costper capita, beginning at birth, needs to be to reduce the rate of return toequal the opportunity cost of capital. Clearly, for the "worst case" assump-tions of rows 12 and 13 in Table 19, the social cost must be less than zerosince the rate of return is below 10%, the opportunity costs of capital. Forthe assumed parameters, the social cost is $100 per capita - or about equal tothe consumption of an individual at the poverty line. If the project has 75%less participation to 67% of eligible children at full implementation, but theother performance parameters remain as assumed, then the annual social costsmust be no more than $83 per capita. Recall that this disregards the costs ofsubsequent population increases, that is, the social costs of the beneficiaries'children.

6.11 But what if birth rates subsequently compensated for the increasedpopulation after a five year lag'- that is, population remains as it wouldhave without the project but with a five year adjustment lag. This wouldproduce five years of earlier earnings as shown in Figure 4 panels B and C.At assumed parameters values, we find that this assumption would produce arate of return of 12.5% and, at the "worst case" assumptions of row 12 inTable 19, a 6.3% rate of return. By disregarding social costs, we have themgiving the project an additional 2 percentage points of rate of return.

6.12 There remains one more issue in this regard. Is it actually indeedthe "worst case", or, in fact, is it the realistic case, especially consider-ing the small ration that is being administered? Can we expect 90% partici-pation when the ration does not meet the mother's opportunity costs of coming

- 58 -

Table 18: Efficiency Cost and Benefits: Sensitivity Analysis for Present Values 1/

Appraisal Values - Net Present Values

DISCOUNTRATE B.MORTP B.MORTR B,PRWGP C.FD C.NFD C-NUTRDELR C.COMMR C.CMERR

…__ _ _ _ _ - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - -- - - - - - - - - -- - _ _ _ _ _ _ -- - - - - - - - - _ _ _ _ _ _ _ _ _ _10.00 178.06J162.5 205,930$405.4 365442666.1 73059058.3 11801524.8 209637492.8 33022831.9 5564760.0

SWITCHING VALUES

DISCOUNTRATE B-MORTP B.MORTR B.PRWGP C.FD C.NFD C.NUTRDELR C.COMMR C.CMERR

…__ _ _ _ _ - - - - - - -- - - - - -- -- - - - - - - -- - - - - - - - - - - - - - -- - - - - - - - - - -- - - - - - - -- - - - - - - -- - - - - - -- - - - - - - -10.00 -.23829E+09 -.21042E+09 -50908900.2 489410624.6 428153091.1 625989059.1 449374398.2 421916326.3

PERCENTAGE CHANGE - Net Present Values=======5=========_ O _ = D D===

DISCOUNTRATE B.MORTP B.MORTR B.PRWGP C.FD C.NFD C.NUTRDELR C.CoMMR C.CMERR

10.00 -233.8 -202.2 -113.9 569.9 3527.9 198.6 1260.8 74,1.9

SUMMARY ECONOMIC CHARACTERISTICS

DISCOUNT PRESENT PRESENT NET PRESENT NPV AS X OF INTERNAL RATERATE BENEFITS COSTS VALUES PRESENT COSTS OF RETURN

…__ _ _ _ _ _ -- - - - - - - - - - - - -- - -- - - - - - - -- - - - - - - - -- -- - - - - - - -- - - - - - - --

10.0 749437234.0 333085667.7 416351566.3 125.0% 14.455X

B.MORTP - Social Benefits of Mortality Reduction and Productivity Gains - Poor

B.MORTR - Social Benefits of Mortality Reduction and Productivity Gains - RichB.PRWGP - Social Benefits of Productivity Gains - Children Entered by Weight Gain CriteriaC.FD - Economic Costs of Food TransferredC.NPD - Economic Costs of Non-Food Consumption

C.NUTRDELR - Economic Costs of Nutrition Delivery and Administration

C.C0MNR - Economic Costs of Cousmunication ComponentC.CMERR - Economic Costs of Monitoring end Evaluation

T1aM 19 51UIYIT A*L&TIS 20 12JCr AIRLWS: inB sC gM OF MTO 1m8 U1fl SiS WUIT SKZAL 0aM 1 FORMATIO INCKLASUS O uTm MPI 3cF0

PercentagePercentage Reduction in I to Percentaes Reduction Percentage Reduction Full Tmplementatiop Success Rate ResultingReduction in 2 Year Old Kartality in 1 to 2 Year Old in Third Degree Percentage In Avoiding Productivity Economic RateSensitivity Infant Mortalitv Not Malnourished Mortalitv - Malnourished Malnutrition Rates Participation Rate Malnutrition Gain of ReturnParameter(s) Poor Rich Poor Ric' Poor Rich Poor Rich

Nar&neval Assunptions 25 10 5 0 10 10 67 40 90 80 25 14.5%

Malnutrition Rates 25 10 5 0 10 10 (33) (15) 90 80 25 13.7%

Infant Mortality (10) (5) 5 0 10 10 67 40 90 80 25 13. 7%

Recovery Rate 25 10 5 0 10 10 67 40 90 (60) 25 13.7.AWslnutrition Rates

and Infant Mortality (10) 10 5 0 10 10 (33) (15) 90 80 25 13.4%

.Ialnutrition Rates 25 10 5 0 10 10 (10) (10) 90 80 25 13.2X

?articipation Rates 25 10 5 0 10 10 67 40 (67) 80 25 13s2o

Productivity 25 10 5 0 10 10 67 40 90 80 (10) 12.4%

Infant Mortelity andMalnutrition Rates (10) (5) 5 0 10 10 (10) (10) 90 80 25 12.3% o

Malnutrition KaCesand Infant Mortalityand Productivity (10) 10 5 0 10 10 (33) (15) 90 80 (10) 10.9.

Io Productivity Gains 25 10 5 0 10 10 67 40 90 80 (0) 10.7%

Infant Mortality andMalnutrition Rate plussuccess Rate plusRecovery Rate (10) (5) 5 0 10 10 (10) (10) 90 (60) (10) 8.8%

Mormality Rat" andParttcipation Rate,Productivoty (10) (5) 5 a 10 10 (lo) (10) (67) (60) (10) 7.7%

1/ Parentheses indicate parmeters changed from Narangval values.'/ Productivity gain refers only to children entered by weight gain; third degree productivity gain still applicable.

- 60 -

to the center? Can we expect 240 calories to be sufficient consideringpotential levels of substitution? Consider if we triple food costs - that ishave a full feeding where moderately malnourished children receive nearly a1,000 calorie ration, if third degree malnourished, nearly 1,500 calories oras much as they could eat, and where pregnant and lactating women receivedan intake nearly equal to 50% of their daily requirements. Other secondaryeffects would possibly result: more rapid recovery, shorter duration offeeding, more consistent attendance at the center, and perhaps some addi-tional administration costs. Could, at assumed performance, the project bejustified? Reference to Table 18 gives an indication. If food costs in-creased by nearly 600%, the rate or return would decline to the opportunitycost of capital. A rough estimate indicates that at triple the appraisedfood costs, the economic rate of return would fall to about 12 to 13%, aninsignificant decline, especially considering the additional guarantees thatthis would ensure in project performance.

The Social Benefit Analysis

6.13 We now examine the benefits and costs when both the efficiency andsocial gains are taken into account. The social benefit analysis places anadditional benefit to income that accrues to the poor. Even if supplementalfeeding did not result in increases in production and therefore incomes,redistributive benefits would nevertheless occur because of the income speci-fic nature of the nutritional services. Since the nutrition services haveeconomic value, households and individuals that participate in the projectreceive a real increase in income. In the social benefit analysis, thetransfer of these services to the poor results in a benefit that is greaterthan the market value of the food and services. To calculate this benefit,social parameters that yield income specific weights are used along withestimate of the disbursement among income groups of the project's commoditiesand services. The social parameters used to weight these disbursements arefrom a working paper by A. Pinell-Siles and are given in Table 20. They indi-cate that the value of public income is 1.54 and that the distributionalweights are disbursed among income classes in a manner given by the parametern = 1. 1/ This particular value for n means that the distributional weightfor an income group is equal to the average level of consumption for all in-come groups divided by its level of consumption. Thus, a ratio of these con-sumption levels of 2 assumes that additional income for these relatively poorproduces twice the benefits than if it had gone to those at the average con-.sumption level.

1/ See Squire and van der Tak, Economic Analysis of Projects for moredetail on this social analysis. Essentially, weights are assigned toincome classes with the larger weights going to the poorer groups bymeans of a specific utility function. These weights increase the valueof income or other transfers going to the poor and decrease them to therich in calculating benefits.

- 61 -

Table 20: ESTIMATES OF NATIONAL PARAMETERS FOR PROJECT ANALYSIS: INDIA(Summary)

Conversion Factors:

Standard Conversion Factor 0.80Consumption Conversion Factor 0.82- for incomes below poverty line 0.84- for incomes above average 0.80(a) Rural 0.82(b) Urban 0.74

- for cereals 1.10Opportunity Cost of Capital

in Border Prices 10%Shadow Wage Rate (as a percent of Mar-ket Wage Rate; unskilled labor) 50%

Social Parameters

Value of public income relative toaverage consumption (v) 1.54

Consumption Distribution Parameter (n) 1.00Critical Consumption Level (as a

percent of national per capitaincome) 60%

Accounting Rate of Interest 9%-10%

6.14 The other social parameter in the Social Benefit Analysis is theconversion factor B. Because of taxes and subsidies in the Indian economy,the value of domestic consumption in terms of foreign exchange is not one-to-one. This coefficient reflects that if consumption is subsidized (taxes)more (less) foreign exchange is used than indicated by domestic values. Be-cause consumption varies between income levels, B also varies due to differ-ences in tariffs and subsidies on individual commodities. For India, thisconversion factor varies slightly from 0.84 for low incomes to 0.80 for in-comes above the poverty line. For cereals, a commodity being distributed inthe feeding program, the conversion factor is 1.10.

6.15 Using these social parameters, benefits are calculated from theincome weights and the estimated disbursement of food and services. Sincethe nutrition component attempts to reach the malnourished preschool child(an individual who is particularly poor even in comparison to the others inits household), individual specific weights are appropriate. To converthousehold weights on income to those for individuals, we need to derive indi-vidual real income levels. Since real income data by individuals are nearlyimpossible to come by, an approximate procedure has been used. This proce-dure assumes, except for food, household income is equitably distributedaccording to need. In the Tamil Nadu Nutrition project communication andeducational components have been included that attempt to improve the intra-family distribution in favor of these preschool children. Hence, in thebenefit analysis, we take into account this group's income relative to that ofother household members as well as relative to those in other households.

- 62 -

6.16 To do this relative weighting, we assume that in the household, realconsumption of non-food items is shared equitably (as measured by need) butthat food is distributed inequitably (this inequitable distribution is veri-fied by individual calorie consumption data for Tamil Nadu). In particular,we assume that food consumption is distributed according to the relativecalorie intake of an individual c0 to his requirement, rO divided by therelative calorie intake of the household c°, to its aggregate requirement,r°. Letting cf represent average household per capital food expenditure andci average household per capital consumption expenditures, the relative con-sumption position of an individual j, cj, in household i can be written as thesummation of non-food consumption (ci - cf) and consumption of food or:

cj = (ci - cf) + a cf (37)

where a = (c° / r3) / (cl / r°)

is the relative fraction of calorie needs fulfillment of individual j to thatof the household i. If in this equation a equals 1, consumption of individualj is equal to that of the average per capital consumption of the household andan additional distributional weight above that given to the household is un-necessary. However, if a is less than 1 (indicating that in terms of foodconsumption) the individual is relatively worse off than others in the house-hold, then the distributional weight for this individual will be greater thanthat for the other household members. If a is greater than 1, then the oppo-site holds, with the weight being less for this individual.

6.17 By using these individual specific distributional weights, we areable to account for the particularly acute nutritional situation of childrenand pregnant and lactating women by placing a greater benefit to food thatgoes to them versus food that goes to other relatively better off members ofthe household. We additionally estimate distributional weights specific bythe age of the child and hence account for the social benefits of feedingparticularly malnourished younger children within the family. We thereforeset distributional weights by households according to average income levelsand by individuals in the household according to age, consumption level, andreproductive status.

6.18 Table 21 gives the distribution weights calculated by household,by age of the child. As shown by the first columns in the table, calories(according to need) are distributed inequitably especially in households ofthe Rs 24 to 75 per month expenditure groups and in particular to the 1 yearold.. At very low expenditure levels, calories are distributed relativelyequitably. As expenditure levels rise, the distribution to children becomesmore inequitable with the 1 year olds' conaumption remaining nearly constantuntil an expenditure of about Rs 55 per month is reached whereupon consump-tion begins to rise again but remaining inequitable. As a consequence ofthis distributional pattern the benefit weights for food going to thechildren, in particular the 1 year olds, are higher than for the householdin general.

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Table 21: PERCENTAGE OF INDIVIDUAL CALORIE NEED FULFILLED BY AGE /a

Percentage ofCaloric NeedsMet:Household Percentage Calorie Needs Met:Individuals

1 Year Old 2 Year Old 3 Year Old

60% 57 56 5870% 65 65 6680% 65 72 7490% 68 84 86100% 71 93 98110% 78 98 104

/a Source: Tamil Nadu Nutrition Study.

6.19 A similar procedure is used to set the distributional weights forpregnant and lactating women. The Tamil Nadu Nutrition Study found thatthese women are relatively more deprived in respect to calorie needs thanother women. Of women from ages 20 to 24, the study found that on the aver-age 80% of their calorie needs are met. Yet, for pregnant women, it foundthat only 73% of needs are met and for lactating women, only 64%. Therefore,commodities and services for these women receive a greater distributionalweight than for other household members.

6.20 Besides these distributional weights, food transferred to those inbasic needs deficit received a basic needs weight that shadow prices foodabove its private value. This basis needs weight originates because Indiaplaces priority on the fulfillment of basic needs. 1/ An increase in theconsumption of the malnourished is considered a social externality originatingbecause society attaches value to the fulfillment of basic needs. As appliedto food, this externality results in a shadow price for food which is greaterthe more widespread is malnutrition. Taking the FAO calorie requirementsadjusted for individual variability and accounting for losses within thefamily, we have estimated this basic needs weight at 1.25 for India. 2/Therefore, the distributed weights on food transfers are increased by 1.25 ifan increase in food consumption results.

6.21 The direct benefits from the supplemental feeding originate withthe increased calorie intakes of the child and of the household (the latter

1/ The concept behind these basic needs weights is given in P. Scandizzoand 0. Knudsen "The Evaluation of the Benefits of Basic Needs Policies",American Journal of Agricultural Economics, February 1980.

2/ The FAO calorie requirement for India is about 2,100 calories if accountis taken of weight and age and sex distribution of the population. Forthis calculation see 0. Knudsen and P. Scandizzo, Nutrition and FoodNeeds in Developing Countries, World Bank Staff Working Paper No. 328,May 1979, Appendix 4.

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from leakages) and the increased consumption of other commodities that resultsfrom the income implicit in the value of the food supplement. The foodsupplement acts as an income transfer to the household even when it is fedon-site, directly to the child. Since the household can refrain from buying asmuch food as it normally would and use the additional income on other consumergoods, the value of the food supplement to the household is measured by thevalue of the consumption that the household can now direct according to itspreferences. The value of the food operating through the propensity toconsume thus determines the increase in the household's food consumption.The part that goes to the child depends, in part, on the effectiveness ofthe education and communication components of the project in convincing thehousehold of the child's nutritional needs. If these components are effectivethen the leakage to others in the household will be minimal and the child willreceive most of the benefits of the supplement. If these components areineffective, then the child will be fed the supplement on-site but at homewill receive less food, in effect a substitution for supplemental food.Although this substitution results in the program being less effective inreducing malnutrition of children, it is not without benefit to other house-hold members who are poor. But since the distributional weight for additionalconsumption of the child is greater than that of the general household, aportion of the total benefits of the food supplement is lost, the amount beingequal to the difference in the distributional weights multiplied by the valueof the food that goes to other household members. If the leakages to otherhousehold members increase, the benefits of the project are reduced but arenot entirely lost since others in the household are also below the criticallevels of consumption and hence have distributional weights greater than 1.Also, since the food that goes to the other household members results inincreased food consumption, transfers to the child and leakages to otherhousehold members receive a basic needs weight.

6.22 The proportion of the value of the food transferred to the house-hold that is not consumed as food also receives a distributional weight butnot a basic needs weight. The social benefits given to the value of the foodtransferred to the household, therefore, depends on how much of the addi-tional food is consumed by the intended beneficiary, how much is consumed byothers in the household, and how much is directed to purchase non-food items.Note that all these leakages away from the intended beneficiaries can occurwithout reselling the food; what is required is merely that food formerlypurchased not be purchased.

6.23 Another benefit of the project results from the reallocation offood within the family, which is induced by the education and communicationcomponents. In many households, the mother and other adults in the householddo not recognize the full nutritional needs of the preschool child and infant.Through education and communication on the child's needs, the household willdirect small quantities of food away from other household members to thechildren most in need. Since the distributional weight of these children'sconsumption is greater than that of the household, a benefit results that isequal to the value of the increased consumption multiplied times the diffe-rence in the distributional weights between that of the children and thatof the household. However, this benefit can only be achieved in householdswhere there exists the potential to redistribute food away from members inrelative surplus and in households where the caloric needs of the child are

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not being met. As a consequence, this redistribution primarily occurs inthe moderately low to moderately high expenditure groups.

6.24 Another benefit of the project results from the more efficientutilization of food by the child's body which results from diarrhea manage-ment and deworming. Even though a child consumes a certain quantity of food,a proportion of this food is not converted to energy due to diarrhea andparasites. By shortening the duration and reducing the frequency of diarrheathrough health care, education and oral rehydration, the effective calorieintake of the child will be increased. Likewise by reducing worm infestationthe child's body will utilize available food more effectively. As a resultof these measures, we estimated that effective calorie intake will increaseby 15% for the children under 3 years old. 1/ This increase in calorie intakewill occur primarily for children in households that have average per capitaexpenditures from Rs 24 to 75 each month as those below the lower level willbe difficult to reach and those above the upper level will be less in need ofthese services. Since, on average, the households are below the poverty line,a distributional weight of 1.36 is given to the value of the increased effec-tive consumption resulting from diarrhea control and deworming. 2/

6.25 In Tables 22 through 25, the basic data for calculating the socialand basic needs benefit are given. In Table 22, the calorie consumption andfood expenditures by expenditure group are present as calculated from the1974 National Sample Survey for rural Tamil Nadu. As shown in the table, thepoorest 33% of the population consume 25% of the calories while the richest33% consume about 38% of the calories. About 50% of the households have anaverage per capita calorie availability of less than 1,830 calories indica-ting that calorie deficits are widespread in rural Tamil Nadu.

6.26 In Table 23, the consumption per capita and the distributionalweights, di, are shown by expenditure group for children, women by repro-ductive status, and the households. As demonstrated in the table by theconsumption per capita and the distributional weights, the children and preg-nant and lactating women are relatively poorer than the general household.This relative poverty position results in children and these women receivingdistributional weights greater than that for household.

6.27 In Table 24, the disbursement of the food supplement is given byexpenditure group. In this disbursement, it is assumed that the third degreemalnourished children are distributed among households proportional to thehousehold's average per capita calorie deficit from 1,800 calories. Thisresults in about 37% of the third degrees being in the poorest 6% of thehouseholds. The children that enter the supplemental feeding program by the

1/ Depending on the severity of the infestation, nutrient utilization can beincreased from 3 to 25Z. See for more detail, L. Latham, M. Latham andS. Basta, "The Nutritional and Economic Implications of Ascaris Infectionin Kenya", World Bank Staff Working Paper No. 271, September 1977.

2/ The distributional weights are weighted by the population proportions ineach expenditure group.

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weight gain criteria will most probably come from households that are slightlybetter off than those with third degree malnourished children. Also, sinceweight changes that qualify children for entry in the program occur evenin households with only minor calorie deficits, it is assumed that the dis-tribution of these children will be proportional to the household's caloriegap from the FAO/WHO calorie requirement of 2,100 calories. In regards topregnant and lactating women participating in the supplemental feeding, itis assumed that they will come from the poorest households, those that tendto produce third degree malnourished children (the entry criteria allowsentry of only 30% of the pregnant and lactating women).

6.28 In Table 25 a summary of other specific parameters used in thebenefit calculations are given. The assumptions of participation in the pro-gram are based on Section IV, Table 9. The calculations of the distribu-tional weights gives an average weight of 2.5 for under 1 year olds, 2.1 for1 to 2 year olds, 2.6 for 2 to 3 year olds, 2.3 for pregnant women and 2.7for lactating women. The propensity to consume food is 0.83; the value ofthe food supplement is 3,800 Rs/ton; the value of at-home consumption is2,500 Rs/ton. It is also assumed that 30% of the households will react tothe educational and communication component by increasing the calorie intakeof the under 3 year olds by 20%. The participation rate in diarrhea controland deworming is assumed at 50% and the resulting efficiency gain is 15% ofcurrent calorie intake levels.

6.29 The results of the social cost-benefit analysis without basic needsweight but using the assumed performance from Narangwal are given in Table 26.They show that the overall project achieves a net present value of Rs 694 Mand a social rate or return of 21.5%. This compares to a net present value ofRs 416 M and an economic rate of return of 14.5% if only the efficiencybenefits and costs are taken into account.

6.30 In Table 27, the rates of return for the efficiency and socialbenefit-cost analysis are compared for the case of the assumed parametersand for some of the worst case assumptions and under the case where socialcosts of increase population size are considered to be zero. As shown, ifthe worst case assumptions become reality, then the accounting for socialbenefits raises the rate of return from below (7.7%) to slightly above(11.5%) the opportunity cost of capital. If, in addition, the basic needsbenefits are included then the rate of return slightly improves to 12.2%.

6.31 If account is taken of an initial population increase followed bya reduction in birth rates five years later then the rates of returns declineby about 2% points, such that, under the worst case assumptions the rate ofreturn fails slightly below the opportunity cost of capital.

6.32 In Table 28, the minimum social costs per additional populationthat would drive the economic and social rate of returns to the opportunitycost of capital are given. The inclusion of social benefits raises the per-missible per capita social costs to Rs 1,247 from Rs 802 under the assumedparameters. At the worst case values the permissible social costs are nega-tive, indicating that essentially any social cost to increased populationwill result in a rate of return below the opportunity cost of capital.

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6.33 Finally, the rate of return is relatively insensitive to anincrease in the amount or costs of food. In the social benefit analysis, anincrease in food costs of 900% is possible before the rate of return fallsbelow the opportunity costs of capital. Indeed, if the ration size or valuein increased, and the food remains targetted to the poor, the social benefitswould increase with the amount of food delivered, the result being that therate of return would be higher than that calculated, given that administra-tive costs remain about the same. This phenomena occurs because of the re-distributive benefits attributable to the.fe6d traa6fe,s.

6.34 From this analysis, these conclusions are evident:

(a) Supplemental feeding, if it results in minimum improvementsin mortality rates and a relatively substantial increase inproductivity, is economically justifiable, especially ifaccount is taken of social and basic needs benefits.

(b) Furthermore, the economic and social rate of return is remark-ably invariant to changes in any individual performanceparameter and to many parameters if varied in tantum.

(c) The addition of social benefit analysis contributes about7 percentage points to the rate of return under the assumedperformance. Under the worst case assumptions, the addi-tion of social benefits raises the rate of return from belowto above the opportunity cost of capital.

(d) However, if social costs are attached to population increasesthan these results become less favorable. In particular ifthe social cost of a population increase is at nearly theannual consumption of an individual then at assumed para-meter values the rate of return remains above the opportun-ity costs of capital only if social benefits are taken intoaccount. With social benefits included, then the annualsocial cost of an additional person can be as high asRs 1,200 before the rate of return falls below the opportun-ity cost of capital.

(e) If account is taken of compensatory birth rate reductions,then the results change slightly with the rates of returnfalling about 2 percentage points. Hence, if indeed familiestarget for a desired number of children and no social costsare taken into account for interim population increases thenthe project remains viable over a broad range of performance.

(f) Finally, the issue remains if successful performance can beexpected when the ration is as small as in this project.Clearly a small ration increases project risks considerablywhile a larger, more costly ration could easily be toleratedwithout the rate of return declining to below the opportunitycost of capital. In other words, there is considerable roomfor increases in feeding cost before the project becomes in-viable. The project benefits and costs analysis points toincreasing the ration to reduce the risk of poor projectperformance.

Table 22: CONSUMPTION DATA FOR RURAL TAMIL NADU BASED ON NSS SURVEY ESTIMATES: 1974

Rural Tamil Nadu

% share HouseholdExpenditure Average Food % Cumulative tdtal Caloric Distributional

Class Group Expenditure Expenditure Caloric Intake Population % Population intake Weight(R/mo) (R/Mo) (R/mo) (Cal/capita/day)

1 0-21 18 15 1,096 5.8 5.8 3.2 3.05

2 21-24 22 19 1,329 6.1 11.9 4.1 2.50

3 24-28 26 21 1,457 7.2 19.1 5.3 2.12

4 28-34 31 25 1,567 14.3 33.4 11.2 1.77

5 34-43 39 31 1,834 20.8 54.2 19.1 1.41 1

6 43-55 48 38 2,155 19.1 73.3 20.6 1.15 X

7 55-75 63 46 2,403 15.5 88.8 18.7 .87

8 75-100 85 60 2,919 6.6 95.4 9.7 .65

9 100-150 117 72 3,374 3.3 98.7 5.6 .47

10 150-above 190 96 3,929 1.3 100.00 2.6 .29

E = 1,994.2

Table 23: DISTIIBMIAL VEIGifS FOR C'ILDRIIN, PREIANT AND IACTATII I AND HOUSEOLDS AS A UNCTIC oF ERXPENDITURE CGOUP

llousehold Caloric Intaker';penditure as a Percentage of Rea' Cons vtior./Cap,tta Di_tributional Weight

Group Caloric ae uireent (R/mo) Pregnant Lactating Pregnant Lactating(per canita) Tousehold I Year 2 Year 3 Year Household I Year 2 Year 3 fear Women _Women Household I Year 2 Year 3 Year Women 3/ Woman 3/

Old Old Old Oid Old Old - -Old Old Old

0-21 52% 522 482 522 18 18 17 18 18 17 3.05 3.05 3.24 3.05 3.05 3.24

21-24 63 61 58 61 22 22 20 22 22 20 2.50 2.50 2.75 2.50 2.50 2.75

24-28 69 64 63 64 26 24 24 24 24 24 2.12 2.29 2.29 2.29 2.29 2.29

28-34 74 66 65 66 31 28 28 28 28 28 1.77 1.96 1.96 1.96 1.96 1.96

34-43 87 66 68 69 39 31 32 32 31 32 1.41 1.77 1.72 1.72 1.72 1.72

43-55 102 71 93 98 48 37 45 46 37 45 1.15 1.45 1.22 1.19 1.19 1.19

55-75 113 83 110 113 63 52 62 63 52 62 0.87 1.06 0.89 .87 .87 .87

75-100 138 105 138 133 85 71 85 35 71 85 0.65 0.77 0.65 0.65 .65 .65

100-150 160 127 160 160 117 103 117 117 103 117 0.47 0.53 0.47 0.47 .47 .47

150-above 185 152 185 185 190 173 190 149 173 190 0.29 0.32 0.29 0.29 .29 .29

1/ Derived from daca from the Tail NIadu Nutrition Study.21 Real Consumption - C + (a - 1) CF

where C . per capita consumption expenditure of the household

CFp per capita food consumption expenditure of the household

a - ratio of caloric fulfillment of child to caloric fulfillment of household.3/ On the average pregnant woen achieve 802 of their caloric reeds and lactating women 702 compared to women in general achieving 902 of their needs.

Table 24: EXPECTED DISBURSEMENT ON FOOD BY EXPENDITURE AND BASIC NEEDS DISTRIBUTIONAL WEIGHTS

Expenditure Percentage of Food dGroup Distributed By Expenditure Class Basic Needs Distributional Weights 4/ (a i/ - B,)

Entered By Pregnant Lactating3rd Degree 1/ Weight Gain 2/ Women 3/ Household 1 Year Old 2 Year Old 3 Year Old Women WomenChildren

1 0-21 37 20 37 1.66 1.66 1.81 1.66 1.66 1.81

2 21-24 24 17 24 1.21 1.21 1.41 1.21 1.21 1.41

3 24-28 19 16 19 0.90 1.04 1.04 1.04 1.04 1.04

4 29-34 20 28 20 0.62 0.77 0.77 0.77 0.77 0.77

5 34-43 - 19 - 0.32 0.62 0.58 0.58 0.58 0.58

6 43-55 - - - 0.11 0.36 0.17 0.15 0.17 0.15

7 55-75 - - - -0.11 0.04 -0.10 -0.11 -0.10 -0.11

8 75-100 - - - -0.29 -0.39 -0.29 -0.29 -0.29 -0.29

9 100-150 - - - -0.44 -0.39 -0.44 -0.44 -0.44 -0.44

10 150-above - - - -0.58 -0.56 -0.58 -0.58 -0.58 -0.58

1/ Assumes 3rd degree malnourished children are distributed in household proportional to the coloric gap of the household from 1800calories per capita (300 calories below the requirement)

2/ Assumes children that enter feeding program by weight gain are proportional to the household's caloric gap from the FAQ/WHOcaloric requirement of 2100 calories.

3/ Since only 30% of the pregnant and lactating women are to be fed the participation is assumed to be proportional to the house-hold's caloric gap from 1800 calories.

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Table 25: ASSUMPTIONS OF BENEFIT ANALYSIS

Household

Propensity to Consume 0.83Average Distributional Weight

Very poor : 2.48Less poor : 2.14Others : 1.37Basic Need Weight : 1.25

6-11 Months Old Children

3rd Degree Malnourished

Average Distributional Weight = 2.56Substitution Rate = 25%

Non-3rd Degree


Others

Average Consumption per 6 mos = 0.032 tons grain equivalentsAverage Distributional Weight = 1.63Average Increase in Consumption = 10%Efficiency Gain = 10%



Average Distributional Weight 2.69Substitution Rate = 50%

Non-3rd Degree


Others

Average Consumption per Year - 0.081 tons grain equivalentsAverage Distributional Weights = 1.53Average Increase in Consumption = 10%Efficiency Gain = 10%

- 72 -

Table 25 (cont.)



Average Distributional Weight 2.56Substitution Rate = 50%

Non-3rd Degree

Average Distributional Weight 3 2.28Substitution Rate 50%

Others

Average Consumption per Year - 0.97 tons/yearAverage Distributional Weight = 1.52Average Increse in Consumption 10%Efficiency Gain 3 10%

Lactating Women

Participants

Average Distributional Weight G 2.69Substitution Rate 50%

Others

Average Consumption per Year - 0.213 tons/yearAverage Distributional Weight 1.52Average Increase in Consumption 6%

Pregnant Women

Participants

Average Distributional Weight - 2.56Substitution Rate - 80X

Others

Average Consumption per Year - 0.201 tons/yearAverage Disributional Weight - 1.53Average Increase in Consumption - 6X

General

Basic Needs Weight - 1.25Value of Food Transferred - 3,800 Rs/yearValue of Increased Consumption - 2,200 Rs/year

- 73 -

Table 25 (cont.)

Average Distributional Weight forEarnings of Poor = 1.96

Average Distributional Weight for

Earnings of Rich - 0.91

Block Phasing* Year 1 Year 2 Year 3 Year 4 Year 5

0.8 27.9 26.2 36.3 40.8

* In 100,000 population units.

Table 126: Wf MUCK VPM SeCU L #ATh7 Oy Zflt. - m1 ny At APfAISAL VAIS

APPRATIA!. VALUEt - FFT PRESE`T VAlItIES

DISCOlINTRAIT B. 3nARTP P.SMORTR P.SPfhi,P B. iIRECI _.tu_ __Er l f1.'1LNY P.EDCM P. EFCAL C.FD C. NFD

10.00 226853743.1 121807834.8 469573V56.6 47443064.9 570O0709.9 21152668.4 16742180.5 686697110.9 73057058.3 11801524.8

DISCOUNTRATE C.NUTRTkELR C.COhtMR C.CMERR

10.00 209637492.8 33022C31.9 5564760.0

SWITCHING VALUES - WeT P' t "^^ '-'

DISCOUNTRATE B.SMORTP B.SMORTR 1.SFRUGP B.DIRECI D.DIRC:H B.t'1RFCNY B -.EDCM I.EFCAL C.FD C.NFD

10.00 -. 46758E409 -.S7263E+09 -.22886Et,09 -. 64679Et09 -. 63736EtO9 -.67329VEt09 -. 67570OE09 -. 62577C 109 767496964.6 706239431.1

DISCOUNTRATE C.NUTRI'ELR C.COMMR C.ChERR_ _ _ _ _ _- _ -_ _ _ _ -- -----_ --- - --- -_ _ _ __-- -

10.00 904075399.1 727460738.2 700002666.3

PERCENTAGE CHANGE

DISCOUNTRATE P.SIORTP B.SMORTR D.SPR.uP P.riRECI D.DIRCECH D.DIRECNY B.EDCM D.EFCAL C.FD C.liFD

10.00 -306.1 -570.1 -149.2 -1457.6 -1216.6 -3283.0 -3705.2 -1011.3 950.5 5884.3

DISCOUNTRATE C.NUTRUELR C.CO'9HR C.CMERR

10.00 331.3 2102.9 12479.2

SUMMARY ECONOMIC CHARACTERISTICS

DISCOUNT FRESENT PRESENT NET FRESENT NPV AS X OF INTERNAL RATE

RATE BENEFITS colsS VALUFS fRiL.ENT COSTS OF fEfrUN

10.0 .102.fEtiO 3330056A/.7 694437YO6.3 208.S% 21.512Z

S. SMRTP . Social Benefits of Mortality RedulctIon and Productivity Cains - Poor

B.SSDRTR - Social Benefits of Mortality Redaction and Productivity Gains - Rich

B.SPRWGP . Social Benefits of Productivity Cains - Children Entered by Weight Cain Criteria

B.DIRECI - Social Benefits of Food Trarsfer to Children

B.DtRECH - Social Benefits of Food Transfer to Household frog. Leakages

B.DIRECNY - Social Benefits of Non-Food Consu.tcion Increases

S.EDCH - Social Benefits of Improved Intre-Femily Food Distribution

B.EFCAL - Social Benefits of De-orwingC.FD - Economic Costs of Food TransferredC.11FD - Economic Costs of Non Food ConsumptionC.HNLrRDEIJ . Economic Costs of Nutrition Delivery and Administration

C.COM?H - Econowic Costa of Cowmmnicstion ComponentC.CHERS. - Economic Costa of lIbtertu ad Uvslustio

- 75 -

Table 27: ECONOMIC AND SOCIAL RATE OF RETURN AND NET PRESENTVALUE UNDER DIFFERENT ASSUMPTIONS ON BIRTH RATE CHANGE

I. Condition A: No Birth Rate Change; No Social Costs of AdditionalPopulation

Economic Rate Social Rateof Return Of Return

a. Narangwal Assumptions 14.5 21.5

b. Worst case withappraisal participa-tion rates Ia 8.8 13.5

c. Appraisal values with75% less participationrates lb 13.2 18.3

d. Worst case with 75%less participation /c 7.7 11.5 /d

II. Condition B: Compensating Birth Rate Change with Five Year Lag

a. Narangwal Assumptions 12.5 19.5

b. Worst case withappraisal participa-tion rates /a 6.3 11.8

c. Narangwal Assumptionswith 75% lessparticipation /b 11.2 17.0

d. Worst case with 75%less participation /c 5.2 9.8

/a From row 12, Table 19.

/b From row 7, Table 19.

/c From row 13, Table 19.

/d If basic need benefits are added this rate of return increases to 12.3%.

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Table 28: ANNUAL SOCIAL COSTS PER DEATH AVERTED NECESSARYTO HAVE A RATE OF RETURN EQUAL TO 10%

Economic Rate Social Rateof Return Of Return

---- Rs/Year/Additional Life----

1. Narangwal Assumptions 802 1,247($100) ($156)

2. Worst case with highparticipation rates Negative /a 559

($70)

3. At Narangwal values 663 1,148with 75% less partici- ($83) ($144)pation

4. At worst case values Negative /a Negative /awith 75% less partici-pation

/a Rate of return below the opportunity cost of capital.

PUB HG3881.5 .W57 W67 no.451

Knudsen, Odin K.Economics of supplemental

feeding of malnourishedchildren : leakages, costs,

PJB HG3881.5.W57 W67 no.451Knudsen, Odin K.Economics of supplemental

feeding of malnourishedchildren :

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