Economics of Supplemental Feeding of Malnourished Children: Leakages, Costs, and Benefits SWP451 World Bank Staff Working Paper No. 451 April 1981 Prepared by: Odi K. Knudsen Agriculture and Rural Development Department and South Asia Programs Department Copyright ® 1981 The World Bank 1818 H Street, N.W. f 7 k A Washington, D.C. 20433, U.S.A. D O iNOT The 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 affdiated HG organizations, or to any individual acting in their behalf. 3881.5 .W57 W67 no.451 The views and interpeetations in this document are those of the author and should 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 the supplemental feeding of malnourished children. The paper is divided into four major sections. The first section discusses the potential leakages to other family members and other households that are common to both on-site and take-home feeding programs. The second section describes the proba- bility of errors involved in using entry and exit criteria in supplemental feeding programs and describes a feasible criterion for entry based on a child's weight gain. The third presents a simulation model for estimating the number of beneficiaries and costs of supplemental feeding under different prevelances of.malnutrition, durations of feeding, and probabilities of recovery and relapse. The fourth calculates the costs and beriefits of a supplemental feeding program by using efficiency, social and basic need approaches. Although alleviating poverty and increasing food production are the only permanent solutions to malnutrition, the existing and continuing malnutrition among children and the legacy it carries requires that tar- getted interim interventions, such as supplemental feeding, be adopted which increase the food intake of the population most in need, the malnourished children of the poor. However, in supplemental feeding, significant levels of 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 of feeding should be short, two to three months to reduce leakages. Also, entry and exit criteria should be an integral part of a feeding program since, without it, the program takes on the character of an income transfer and substitution will be high and effectiveness low. The analysis of this paper demonstrates for a project in India that supplemental feeding pro- grams are economically justified if minimum improvements in mortality rates and more substantial increases in productivity (originating from the comple- mentarity of nutrition and education) take place. This becomes especially the case if social and basic needs benefits are included along with the standard efficiency gains. Prepared by: Copyright © 1981 Odin K. Knudsen The World Bank Agriculture and Rural Development 1818 H Street, N.W. Department and Washington, D.C. 20433 South 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 . .............................. ....... 6 Leakages to Unintended Beneficiaries ................... 12 The Income Leakage . .. ................ ..... 19 III. ENTRY AND EXIT CRITERIA FOR A SUPPLEMENTAL FEEDING PROGRAM .......................................... 22 The Entry Criteria ...... ............. . .......... ....... .. . 22 The Exit Criterion .. ............................... . 27 IV. THE COSTS OF SUPPLEMENTAL FEEDING AND THE QUANTITY OF FOOD REQUIRED ...... .......................... 29 The Mathematical Model ..... ..................... ... ....... . 29 A Simulation Model of Supplemental Feeding ............. 33 V. THE BENEFITS OF SUPPLEMENTAL FEEDING OF CHILDREN AND PREGNANT AND LACTATING WOMEN .... ............ 39 The Project ........................................................ 40 The Efficiency Benefits .... ............................ 42 The Productivity Benefits .................... ......... 48 VI. A BENEFIT AND COST ANALYSIS OF A SUPPLEMENTAL FEEDING PROGRAM .. .. . . .............. . .. . Efficiency Benefits and Costs Attributing Zero Social 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 Pregnant Lactating 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 Exclusion Errors ........................................ 16 Table 4 : Probability of Committing Entry Error Under Different Correlations Between Periods of Weight Gain ................................... 17 III. CRITERIA FOR ENTERING AND EXCLUDING CHILDREN FROM A SUPPLEMENTAL FEEDING PROGRAM Table 5 : Mean and Standard Deviations of Weights and Maximum Intra-Daily and Inter-Daily Weight Changes ....................................... 24 Table 6 : Maximum Weight Variation Between the Same Time of Day ................................... 24 Table 7 : Probability of By-Passing Children from Ages 6 to 11 Months with Weight Changes of 500 to -100 Grams/Month ........................... 28 Table 8 : Probability of By-Passing Children from Ages 12 to 35 Months with Weight Gains from 167 to -33 grams per Month ........................ 28 IV. THE NUMBER OF DIRECT BENEFICIARIES OF SUPPLEMENTAL FEEDING AND THE QUANTITY OF FOOD REQUIRED Figure 2 : Model of Entry and Exit from Supplemental Feeding Program ............................... 34 Table 9 : Summary of Assumptions of a Supplemental Feeding Program ............................... 36 Table 10 : Average Beneficiaries Per Day as a Function of Six-Month-Relapse-Rate - Partial Feeding ....................................... 38 Table 11 : Quantity of Food Required as a Function of Six-Month-Relapse-Rates - Partial Feeding ........ 39 V. THE BENEFITS AND COSTS OF SUPPLEMENTAL FEEDING OF CHILDREN AND PREGNANT AND LACTATING WOMEN Table 12 : Project Description ............................. 40 Figure 3 : Probability of Surviving With and Without Project ....................................... 43 Table of Contents (cont.) Page No. Table 13 : Assumptions on Mortality - Calculations of Benefits ................................... 45 Figure 4 Earnings Streams With and Without Compensating Birth Rate Declines ........................... 47 Table 14 : Incremental Increase in Earnings From Improvement in Cognitive Development as Measured by Preschool Ability Scores ....... 50 Table 15 Assumptions on Earnings Streams of Rural Rich and Poor ................................. 51 Figure 5 : The Project's Effect on Population . Table 16 Increase in Population Due to Project Assuming No Change in Birth Rate: Narangwal Assumptions ......................... 54 Table 17 Project Benefits and Costs ...................... 56 Table 18 : Efficiency Cost and Benefits: Sensitivity Analysis for Present'Values ......... .......... 58 Table 19 : Sensitivity Analysis to Project Assumptions: 59 Economic Rate of Return for Efficiency Gains Without Social Costs to Population Increase or Birth Rate Reduction. Table 20 Estimates of National Parameters for Project 61 Analysis: India (Summary). Table 21 : Percentage of Individual Calorie Need 63 Fulfilled by Age. Table 22 : Consumption Data for Rural Tamil Nadu Based 68 On NSS Survey Estimates (1974). Table 23 : Distributional Weights for Children, Pregnant 69 and Lactating Women and Households as a Functon of Expenditure Group. Table 24 : Expected Disbursement of Food by Expenditure 70 and 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 - iv - Table of Contents (cont.) Page No. Table 27 : Economic and Social Rate of Return and Net Present Value Under Different Assumptions on Birth Rate Change .... .......... 75 Table 28 : Annual Social Costs Per Death Averted Necessary to Have a Rate of Return Equal 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 for supplemental 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 paper is based upon a project designed for the State of Tamil Nadu, located in the south of India. With a population of abour 48 million, Tamil Nadu ranks eighth in GNP per capita among Indian states, its population primarily growing and 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 rates above those experienced in the past would alleviate some malnutrition, the prospects are for continuing widespread suffering into the 1990s. Even though poor families will spend a large part of their income on food, malnutrition will persist especially among children because of increasing food prices and the uneven distribution of food within the household. 1/ Although alleviating poverty and increasing food production are the only permanent solutions to malnutrition, the existing and continuing malnutrition among children and the legacy it carries for the future adult population requires that something be done now. The most specific and targetted solution is to increase the food intake of the population most in need, the malnourished children of the 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 to unintended beneficiaries. Leakages (other than pilfering) in a supplementary feeding program are of three types: (a) intra-family leakages from the food either directly or indirectly being shared by other members of the family; (b) income group leakages occurring when children in the feeding program are not malnourished 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 that leakages from a feeding program distributing a partial ration will be sub- stantial, whether the food is taken home or fed at the center. Also, unless the education component is considered to have sufficient value to compensate for the loss of income, the mothers of malnourished children will not parti- cipate in the program and the effort to reorient the family's distribution of food toward the malnourished child will be ineffective. In on-site, full feeding programs, losses through these leakages are less than in partial feeding programs, however, the costs of food are higher as the ration size is larger. I/ See 0. Knudsen and P. Scandizzo, Nutrition and Food Needs in Developing Countries, 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 latter in a take-home program) of supplemental food can be expected. To assure effectiveness, ration sizes should be near the full nutrition requirements of the child, should be fed on- site and the duration of feeding should be short, two to three months. (b) Entry and exit criteria should be an integral part of any feeding program. Without it, the program takes on the character of an income transfer and substitution will be high and effectiveness low. Two types of entry criteria are feasible: one based on the stock condition of the child; the second on the trend in weight of the child. The second criterion is the most difficult to implement and has the greatest probability of committing Type I entry error, where a child who does not require feeding is entered. However, it has the advantage of identifying 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 (through the opportunity cost of labor) in taking a child to a feeding center; therefore to enhance enrollment and attendance, the ration size must be of sufficient value to compensate for the the loss in income. As a consequence, the ration size should approach quantities suffidient to meet the child's entire needs and the center should allow for the child staying at the site throughout the day. The first provides an appropriate economic incentive to bring the child in for feeding; the second reduces thelopportunity cost of interrupting a work day to bring the child in for feeding. 1/ Also, the seasonal nature of work opportunities for the mother needs to be accounted for, with additional staff required during the harvest and sowing season, to assure that children requiring feeding are brought to the center. Criteria for Entering and Excluding Children from a Supplemental Feeding 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 gaining weight adequately or is losing weight can be identified through a program of monthly weighings and that timely on-site feeding of a supplemental food to this child will (in the majority of cases) result in the child's return to adequate weight gain. As a consequence, much of the detrimental effects of malnutrition can be avoided. To implement this program entry criteria are 1/ If older siblings bring the child in, much of the- educat-iQnal benetits to the mother are lost and the child's attendance at thie feeding center is often less frequent. established which identify inadequately growing children with only a small probability of error, yet exclude, with a high probability, children that are gaining weight adequately and hence do not require supplemental feeding. Likewise, exit criteria are established that assure that the children entered into the feeding program have returned to adequate weight gain before being permitted to leave the program. The Number of Direct Beneficiaries and Costs of Supplemental Feeding and the Quantity of Food Required 7. In a supplemental feeding program, the number of children that will actually be fed a supplement and the costs of feeding will depend on several factors outside the influence of the program. The external factors include the 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 the year. These determine to a large extent the degree of malnutrition that can be 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 of the total number eligible depends on the incentives of potential beneficiaries to participate due to factors such as the size of the food supplement and its perceived value, the opportunity cost to the mother of bringing the child in for feeding, the effectiveness of the nutrition worker, and the perceived benefits to be obtained from the education and nutritional services. The number of chlldren that remain in the program after the intended days of feeding depends on the effectiveness of the education in inducing the family to feed the child more at home (in partial feeding programs) and the calorie content of the ration given at the feeding center. Since some of the children being fed will have been in the program before but have relapsed after leaving the feeding program, the number in the program during any given month will 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 the number of children being fed, the costs of feeding and the estimates of a program's beneficiaries are complicated and largely dependent on the environ- mental factors. 8. A simulation model has been constructed to estimate beneficiary flows and the quantity of food required. The model is designed to estimate beneficiary flows by age group for two categories of children: those that are not third degree malnourished and entered by weight gain criteria and those that are third degree malnourished. Each of these groups has a differ- ent probability of becoming malnourished and recovering from malnutrition due to the feeding. The simulation model estimates beneficiary flows and costs as a function of the rate of malnutrition, rate of relapse, and a feeding program's efficiency in returning children to adequate weight gain or adequate nutritional status. The model consists of three principal components: one that stimulates entry into the feeding program, one that describes the feeding and the monthly probabilities of returning to adequate weight gain, and one that consists of the monthly probabilities of relapse through the first six months after leaving the program. - 4 - The Benefits and Costs of Supplemental Feeding of Children and Pregnant and Lactating Women 9. The section on benefits quantifies both the efficiency and social benefits of supplemental feeding of children and pregnant and lactating women 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 reduced childhood malnutrition and mortality. The social benefits result from income in the form of food being distributed to the poor and from a basic needs commodity being supplied to those in need. The analysis of these social benefits is based on the Squire and van der Tak methodology of social benefit analysis and the 9candizzo-Knudsen approach to the.evaluation of the benefits of basic needs programs. 10. The project produces an anticipated economic rate of return from the, efficiency benefits of reduced mortality and increased productivity of about 14% if no social costs are attached to a larger population or if there is not a compensatory birth rate reduction. If the annual social cost is US$100 per capita, 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, then the rate of return is about 12%. Including social benefits raises the rate of return to about 22% and adding a basic needs premium contributes an additional two percentage points. 11. From the cost benefit analysis of a Tamil Nadu project, these conclusions are evident: (a) Supplemental feeding, if it results in at least a 10% improve- ment in mortality rates and a relatively modest 10% increase in productivity, is economically justifiable, especially if account is 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 performance parameter and to many parameters if varied in tandem. (c) The addition of social benefit analysis contributes about 7 percentage points to the rate of return under the assumed performance. Under the worst case assumptions, the addi- tion of social benefits raises the rate of return from below to above the opportunity cost of capital. (d) However, if social costs are attached to population increases, than these results become less favorable. In particular, if the social cost of a population increase is at nearly the annual consumption of an individual,then, at assumed parameter values, the rate of return remains above the opportunity cost of capital only if social benefits are taken into account. With social benefits included, then the annual social cost of an additional person can be as high as Rs 1,200 before the rate of return falls below the opportunity cost of capital. - 5 - (e) If account is taken of compensatory birth rate reductions, then the results change slightly with the rates of return falling about 2 percentage points. Hence, if indeed families target for a desired number of children and no social costs are taken into account for interim population increases, then the project remains viable over a broad range of performance. (f) Finally, the issue remains if successful performance can be expected when the ration is as small (from 240 to 480 calories) as in this project. A small ration increases project risks considerably because of high risk of low and irregular attendance, slow response to feeding, and substitution at other meals, while a larger, more costly ration could be tolerated without the rate of return declining to below the opportunity cost of capital. In other words, there is con- siderable room for feeding amounts and cost increases before the project becomes inviable. The project benefits and costs analysis 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 need for supplemental feeding, the varieties of programs, and their general fail- ings. The second section presents some of the leakages that occur. The third 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 Tamil Nadu 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 are unavailable, 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 per consumer unit 1/ in 1977, which is slightly higher than the Indian Council of Medical Research's (ICMR) requirement of 2,400. But it also found that 35% of the 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 ICMR requirement and 31% of them are below 70%. 1.04 The other major survey of consumption in Tamil Nadu, the 26th round of the National Sample Survey (NSS) (July 1971-June 1972) records an average intake of 2,394 calories per consumer unit in rural Tamil Nadu. It also finds that 26% of the households consume less than 80% of the ICMR requirements and 18% 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 intakes below 80% of calorie needs, defined as 2,830 for a male of 20-24 years, 2,660 for 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 ICMR requirement, thus producing a statistic that is incompatible with the estimates of the NNMB and the NSS. The FHS household data indicates that about 30 to 35% of the households consume less than 70% of their calorie needs. 1/ A consumer unit is an individual converted to an adult equivalent by a set of weights related to age and sex. 2/ Calorie inadequacy is defined by the NNMB as consumption 30% below the ICMR (1968) requirement. -2 - 1.06 By any standard, these statistics indicate considerable calorie deficiencies in Tamil Nadu. The cumulative results indicate that the percent- age of households with inadequate calorie intake (below 70% of the ICMR standard) is probably between 20% and 35%. The percentage of individuals consuming below 70% of the calorie requirement is about 35 to 40% according to the FHS and about 45% according to the NNMB. 1.07 These levels of under-consumption are intensified for the children due to the uneven distribution of food within the household. As shown in Table 1, average calorie intake of children in Tamil Nadu ranges from 47 to 85 percent of requirements depending on age. The Tamil Nadu Food Habits Survey finds that the severest deficit occurs between 6 and 30 months of age and that this deficit exists even when the food availability in the household, if properly distributed, is sufficient to meet the calorie needs of each of its members. 1.08 These calorie deficits combined with the high incidence of disease result in many children being malnourished in Tamil Nadu. A 1974 survey by the National Nutrition Monitoring Bureau found that 46% of male preschool children 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 children the pattern is similar, with slightly less severe third degree malnutrition, but high incidence of the moderate second degree malnutrition. Some of these children are actively malnourished (wasted) while about 30 to 33% are considered to have experienced malnutrition sometime in the past but now have achieved normal weight for height (stunted). In other words, the NNMB survey estimates that nearly 50% of the children in Tamil Nadu are actively malnourished. 1.09 The prospects for normal income growth and increased food production to alleviate malnutrition appear dismal. Even though poor families will spend large portions of their income on food, malnutrition will persist among children into the 1990s because of increasing food prices and the uneven distribution of food within the households. 1/ Although alleviating poverty and increasing food production are the only permanent solutions to malnutri- tion, the existing and continuing malnutrition among children and the legacy it carries for the future adult population requires that something be done now. The most specific and targetted intervention is to increase the food intake 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 government has adopted several types of programs, some of which are solely sponsored by the State while others receive partial funding. Table 2 summarizes some pertinent 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 Developing Countries, World Bank Staff Working Paper No. 328. from the Royal Commonwealth Society for the Blind. 1/ The private programs generally have limited scope and funds. Table 1: AVERAGE DAILY INTAKES OF CHILDREN AND PREGNANT AND LACTATING WOMEN IN TAMIL NADU Age Group Calories % of ICMR Standard 12-23 months Boys 611 51 Girls 567 47.3 24-35 months Boys 791 66.0 Girls 798 66.5 36-47 months Boys 990 82.5 Girls 940 78.3 48-59 months Boys 1,083 72.0 Girls 1,037 69.0 60-71 months Boys 1,230 82.0 Girls 1,222 81.0 Pregnant Women 1,856 56.3 Lactating Women 1,959 52.9 1.11 The two most significant feeding schemes in the State are the Midday Meals and the Balwadies programs. Of these two, the Midday Meals program is the largest directing about 23,000 m tons of food to school age children. The Balwadie program, minor in comparison, feeds preschool children for 300 days. It uses an entry criteria based upon a child's age for weight and feeds a ration of locally procured foods. The privately sponsored Erskine program feeds children a high calorie ration for a period of 90 days or until the child 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 supplemental feeding programs that depend on small increments in food intake given at feeding centers (the Balwadies scheme); and (3) rehabilitative feeding where large calorie rations are given several times during the day (Erskine Hospital type schemes). Such programs are usually directed toward severely malnou- rished children. The first type of feeding is directed at children regardless of nutritional status; the second in most cases has an entry criteria but in many cases generally not an exit criteria; the third is the most targetted, 1/ This program, although once operating in 46 villages, has been cut back to only a few demonstration sites. Table 1: FEEDING PROGRAMS IN TAMIL NADU - 1976-1977 Costs Per Beneficiary Per Feeding Administering Days Day (RS) Costs of Estimated State Department 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 99,610 days 9,297 II. Modified Special Program Social 300 347 23 0.28 5,110 14,512 4/ 15,284 Welfare days III. Special Nutrition Program Social - 281 15 0.30 2,610 230 11,700 1,800 12,310 Welfare 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 - 8,455 Madras 280 - VII. Balvadies (Non - ANP) Rural - 280 15 0.28 1,915 169 7,217 7,900 7,924 Development VIII. Balwadies (ANP) Rural - 296 17 0.52 575 126 4,389 2,714 4,667 Development IX. ICDS Social - 397 22 0.45 805 60 3,144 4/ 3,939 Welfare 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. - 5 - directing its foods at those children most likely to die and those who have already suffered the most damage from malnutrition. All of these programs use on-site feeding. Previously in the State, take-home programs were attempted but later dropped. 1.13 In-depth evaluations of these feeding programs are scarce or, as in some cases, unavailable. One exception is an evaluation conducted by CARE of its feeding programs which found substantial substitution even in its on- site feeding programs and that nutrition status did not generally improve with the duration of feeding. Likewise, a study of the Tamil Nadu take-home program found high levels of substitution and sharing of the supplemental foods. An evaluation of the Erskine program found substantive improvement during feeding but some evidence suggests that once the feeding was termi- nated many of the children in the scheme's villages returned to their previous malnourished state. 1.14 Three major problems are evident in feeding programs. 1/ The first is that, under food scarcity situations, the family allocates food for the well-being of the family, not necessarily for the well-being of the child. As a consequence, food intended for the malnourished child is shared either directly 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. The program is viewed as another income source that happens to be directed at the children. The feeding scheme, subsidized or free food, might as well be a fertilizer or housing subsidy, or for that matter, a direct income transfer as the effect is the same--increased and shared overall family consumption, a small portion of which is for the child. The second is that the programs are not selective-children in the programs are often not actively malnourished but 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. The third is that the ration size and value is insufficient to compensate for the opportunity cost of bringing the child to the center. As a consequence, net benefits are reduced and attendence is low and often irregular. In the next section 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 supplementary feeding program are of three types: (a) intra-family leakages where the food either 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 participating in 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 see G.H. Beaton and H. Ghassemi, Supplementary Feeding Programmes for Young Children in Developing Countries, Report prepared for UNICEF and the AC subcommittee on Nutrition of the United Nations, October 1979. -6- Intra-Family Leakages 2.02 Intra-family leakages occur when, in response to the child having been fed at the center, the family reduces the child's meals at home. This leakage is induced by the family implicitly treating the additional food as an income transfer which permits increased household expenditure and hence increased food consumption by each member of the household. The child's net gain from the feeding at the center depends on the marginal propensity of the family to purchase food out of additional income and the allocation of this 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 to convert the concessionary element of the program into an equivalent income transfer. The "force of consumers' sovereignty" or the effort of consumers of having full control on the composition of his expenditure will always be 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 fully replace previous consumption so as to be more effective than an equivalent income transfer. If they are distri- buted in a lesser amount, the percentage increase in each child's food and calorie consumption will be equal to the product of (a) the food distributed to each child as a fraction 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 to increase consumption by amounts substantially above that (from a program that feeds children half their previous consumption)". 3/ According to Selowsky, then, only on-site, full feeding programs will substantially result in increased calorie intake by the child. 2.04 A partial feeding program would have an effect on the child's intake but only equal to the child's marginal propensity to consume out of family per capita income. If we call 0 the marginal propensity for the family to increase per capita calories consumption out of per capita income and y the child's marginal share of these additional calories then the gain in calorie consumption of a child ACi from a food transfer of value T to a family with F members will be: 1/ Marcelo Selowsky, The Economic Dimensions of Malnutrition in Young Children, World Bank Staff Working Paper No. 294, October 1978, p. 56. 2/ Ibid, p. 56-57. 3/ Ibid, p. 57. - 7- IC F(T/F) (1) 2.05 Assuming that the family shares these additional calories such that each 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 a semi-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 using weighted regression techniques. The resulting estimated equation is: 2 C = 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) - 8- Substituting (9) into (7) we get ACi/Ci = (1,221/C) (T/F)/Y (10) 2.08 Under the assumption of this model, if the value of the transferred food is 10% of family income then the effective increase in calorie intake of family member, i, will be about 7% for a family consuming at an average of 80% 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 about 30 to 35 rupees per month (1974 prices), a child receiving a supplement of value 0.30 rupees (290 calories) for 30 days will induce an increase in monthly family incomes of 9 rupees or about 5 percent of per capita family income for a family of five. The resulting increase in average family per capita 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 Tamil Nadu is 791, the induced effective increase in calories from a ration of 290 calories will be about 40 calories, resulting in a leakage of about 250 calories to other family members. For the average Tamil Nadu child from 12 months to 23 months consuming at 600 calories and receiving a half ration of 190 calories, the induced effect of a ration will be about 15 calories per day or a leakage of about 175 calories to other family members. Consequently, if the 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 the ration is its income-equivalent value to the family, they illustrate the effects 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 is currently consuming. However, in most circumstances, the child would be fed on-site, a more expensive supplement than the child's diet at home (often under the mistaken belief that much of the at-home substitution can thereby be avoided) and the value of the supplement in terms of family income would be the calories valued in local foods, generally a much lower value than the cost of a more protein rich supplement. In this case, on-site feeding would result in lower calorie intake than those just calculated as the family is unable to retrieve the full cost of the food. Selowsky again identifies the dilemma: 1/ The calorie requirement assumes a male body weight of 50 kg, a female body weight of 40 kg, and moderal levels of activity. Note that the elasticity on the child's consumption is 0.7. James Lewinson found elasticities for young children in rural India of less than 0.1. If this estimate is correct then the substitution effect will be even greater than 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 increase in calories would be 90 and 45 calories in each case. - 9 - "When a program distributes an inframarginal amount of a food previously being consumed, the released purchasing power is used to expand the consumption of all food com- modities, by both adults and children. If the new food being introduced by the program can only be consumed by children (specific baby foods), or is fed directly to children (milk programs in schools when the child was not previously consuming milk), the only mechanism by which the rest of the family can also benefit from the transfer is by withdrawing some other food from the child in question. Substitution takes place automatic- ally." 1/ And, "As long as the rate of substitution between foods, as seen by the household, does not fully internalize the different calorie intensity of foods, the resulting substitution could adversely affect the calorie consump- tion of children." 2/ 2.11 For example, if the food withdrawn at home has a greater calorie density per expenditure (calorie-wise is cheaper) than the food being fed at the 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 income of 30 rupees would spend 25 rupees monthly on food, and purchase on the average food yielding 1,600 calories per capita per day. The average value of 1,000 calories of this food to the family would be about 0.5 rupees. If the supplemental food, because of its content of protein or other nutrients supplies 1,000 calories at a cost of 1.0 rupees then the family would view the income transfer from the on-site feeding program as being equal to half of the market value of the commodities, or equal to the value of the calories it can substitute at home. In this case, the induced increase in calorie intake of the child from the food supplement will only be 15 to 6 calories yielding thereby leakages of about 275 and 190 calories or over 95 percent of the calories delivered to the child by the on-site feeding. Clearly, if this type of substitution took place, on-site feeding would induce lower calorie intakes than a take-home program where reselling of higher value food is possible. 3/ 2.12 This analysis has assumed that the education component of the feeding program has not influenced the intra-family distribution of food. We now ask what would have to be the impact of the education component on intra-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 the family and the child more if reselling of this high valued commodity was even encouraged. On-site feeding of powdered milk would prevent this reselling and the net effect could be lower calorie intakes. - 10 - only 50% leakage to the other family members. With this level of leakage for a 290 calorie ration the child would gain an additional 145 calories of intake. To accomplish this gain in a family of five, the child's marginal share of calories induced by the value of the food supplement would need to increase 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 a change in how current calories are allotted, that is, change the current share 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 a child's calorie intake would increase by 340 for a family consuming at an average 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 80 calories per day. 2.13 We do not understand either the mechanics or logic of the family's allocation of calories among its members or therefore the potential effects that education might have on this allocation. We even do not know if educa- tion that results in redistributing food within the family will increase the family's well-being and ensure its survival. Perhaps the logic of the cur- rent distribution is based on maximizing the family's income and overall well-being. The existing intra-family distribution of food in poor families, even though increasing the risk of malnutrition in the least productive members of the family, the preschool children, could assure that the adults and older children will have the energy to work and earn income for the family. Any other distribution could increase the entire family's vulner- ability to malnutrition. This, then is the risk of education that attempts to induce a reallocation of food within the family. But, if we accept the current family distribution, leakages due to this substitution within the family will be substantial in feeding programs that supply only a part of the child's calorie needs. 2.14 These leakages also indirectly beset an on-site program that feeds the 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 the child is fed its entire calorie needs, the 500 calories previously consumed at home 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 requirement of 1,200 calories, a ration of 1,200 calories needs to be delivered. The percentage effectiveness of the food delivered is therefore about 60%. But to induce an equivalent increase in the child's calorie intake, an on-site or take-home program operating with partial feeding would have to induce an income 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 additionai income 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 through education or other means the pattern of food consumption within the family, will have high leakages to other family members. Also, unless the food that is provided in a partial feeding program has higher calorie density per unit of expenditure than is being fed at home, the take-home program will be more - 11 - effective than on-site partial feeding since it offers the possibility to resell the higher value food and substitute lower value food at home. Except for 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 programs to be effective must be fed on-site, otherwise, they will be beset with the same levels of substitution that occurs in partial feeding programs. Although leakages occur in both programs, the more effective program appears to be the full-ration, on-site feeding program, in which the child's full calorie intake can 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 would out of income from any other source. However, incomes from all sources are not treated equally as has been demonstrated in studies of consumption behavior in both developing and developed countries. 1/ For consumption decisions, income is regarded as having a permanent and a transitory component. 2/ As originally hypothesized by Friedman, the permanent component reflects income that 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 even though they could have been fully foreseen. The propensities to consume out of these two sources of income are different, with the higher propensity occurring for consumption of permanent income. Transitory income, being temporary in nature or of a "windfall" character, is associated with a low propensity to consume. Consumption is not significantly adjusted upward with increases 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 the implicit income derived from the supplemental food has a higher transitory component 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 than that out of the family's other sources of income and the effect on consumption of the food supplement will be less than that estimated above. Of course, if the opposite situation holds, that is, that a food supplement is considered to be a more permanent source than outside income, then the propensity to consume out of the food transfer will be greater than out of other sources. To resolve which case holds in Tamil Nadu would require investigating the instabilities involved in different sources of the participants' household income and determining the components of transitory and permanent income involved in each income 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. - 12 - 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 the more 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 child would 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 more valuable than its actual market value. To induce higher food intake in the child, this money illusion needs to be consistently,biased upward so that the food 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 participating households, 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 from different 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 children who 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. The former 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 discuss both 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. - 13 - 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 a child that does not require the feeding program. Probability of Type II error (Pr(II)): The probability of excluding a child that requires the feeding program. 2.25 Associated with each of these errors is an expected loss that is equal to the value of the loss times the probability of the error being committed. 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 error depends on the reliability of the measurement criteria, that is, whether age for weight or anthropometric measurements accurately detect malnourishment. In the case of a preventative program, where entry depends on trends in the child's status, an additional probability needs to be accounted for: the probability that the observed trend results in a condition of malnourishment. In other words, with the trend criteria, we have a series of probabilities that contribute to the probability of an entry error. These consist of the probability that the trend is measured correctly and the probability that the trend 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 on a 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 decline over one period might regain normal weight growth in the second period even without the intervention of the feeding. On the other hand, the child might never recover from the initial downward trend in weight and continue to become malnourished. In Figure 1, the various paths are illustrated for two weigh- ing periods in which, for simplicity, it is assumed that a child with two consecutive 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 intervention before malnutrition has set in (the cases illustrated by an asterisk in Figure 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 the Tamil 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. - 15 - 2 P(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: 2 P(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. For example, P(TN) is the probability of a negative trend in weight gain given that the trend was positive the month before and P(TN') is that the trend is negative given that it was negative the month before (the other variables are defined in Figure 1). 2.27 Both of these probabilities P(I/W) and P(0/M) represent errors in the criteria of entry or exclusion. The first, P(I/W) is Type I error; the second, P(0/M), Type II error. For example, assume the following probabil- ities: P(TN) = 0.20 P(TN') = 0.20 P(TP) = 0.80 P(TP') = 0.80 P(y) = 0.10 P(N) = 0.90 P(y') = 0.90 P(N') = 0.10 These probabilities indicate that the child's chances of having a negative weight trend over any one weighing period is 20% and that the chance of a measurement in error is 10%. It also assumes that the probability of having a negative weight trend in one month is independent of the weight trend the previous month; thus, P(TN) equals P(TN') and P(TP) equals P(TP') (later we will 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. That is, under these assumptions, the probability of entering non-malnourished children would be relatively high but the probability of excluding malnourished children would be nearly zero. If our measurement criteria is more inaccurate such that the probability of making an error is 30% then the probabilities of commiting Type I error is 0.55 and Type II error, 0.006. If the accuracy of the measurement is high with only 5% chance of error, then the probability of 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 can be seen from these probabilities, the trend weight measurement as an entry criteria has a high probability of entering into the program children who do not need the supplement and a low probability of passing up a malnourished child, which assumes of course that the malnourished child is brought in for weighing. Returning to our loss function, we would find that the ratio of - 16 - 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 of Measurement Error 10% (a) Probability of Type I Error 0.31 0.38 0.42 0.42 0.39 0.34 (b) Probability of Type II Error 0.0002 0.0007 0.0025 0.0025 0.0036 0.0049 (c) Ratio of Expected Losses 1,710 558 285 170 107 67 Probability of Measurement Error 20% (a) Probability of Type I Error 0.35 0.47 0.48 0.45 0.41 0.34 (b) Probability of Type II Error 0.0007 0.0026 0.0056 0.0095 0.0140 0.0190 (c) Ratio of Expected Losses 536 180 85 48 29 20 Probability of Measurement Error 30% (a) Probability of Type I Error 0.55 0.55 0.53 0.49 0.42 0.35 (b) Probability of Type II Error .0015 0.0056 0.0121 0.0204 0.0304 0.041 (c) Ratio of Expected Losses 374 99 44 24 14 8 Proportion Becoming Malnourished 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 - 17 - probability of continuing on a downward trend in weight in the following period than a child who has previously had adequate weight gain. In Table 4, we present the implications on the probabilities of entry errors of this interaction of weight gains between consecutive periods. We assume in these calculations that, if a child experienced an inadequate weight gain in one period, the probability of having a normal weight gain in the next period is 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 declines substantially 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) increased substantially with this correlation between the weight gains from period to period, going from 3 to 44% to 15 to 66%, over a range of probabilities of inadequate weight gains from 10 to 50%. Table 4: PROBABILITY OF COMMITTING ENTRY ERROR UNDER DIFFERENT CORRELATIONS 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 Malnourishment Correlation 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 the probabilities both of measurement error and the probabilities that a downward trend 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. - 18 - 2.31 Measurement errors occur due to the inaccuracy of the scale, the operator'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 fluids and the quantity of food matter in the stomach and intestines. For example, assume that the fluctuation in daily weight are normally distributed with mean 0 and standard deviation a = Va 2+ a 2. For example, if the standard deviation in the child's weight due to Waily variation is 100 grams and the standard deviation of the measurement is 50 gis, then ac = 112 grams. For this case, we would be able to discern the child's average weight within + 224 grams with 68% accuracy (one standard deviation). This measurement accuracy would be sufficient to determine whether a child is third or second degree malnourished, but, in a weight gain criteria measurement, it would be insuffi- cient to discern in marginal measurements whether adequate or inadequate weight gain has occurred over a period of say, five months. 2.32 Consider the following example of weighing in which actual weight increases 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 weight of W2. The question is for a weight gain criteria rule (for example growth less than L would require entry into the program), what would the actual difference 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 standard deviation 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 gain criteria of 500 grams . 1/ This means that if a weight gain at least of 500 gms is required over the period of measurement for adequate growth then we would need to exclude children from the program who have a measured gain of over 300 gms to commit only an 10% entry due to measurement. Associated with this 300 gm weight gain criteria is the probability of excluding a child who actually needs the program. An example will illustrate. Using the same procedures as above, we calculate the probability that a measured weight gain with a normal distribution of mean 250 gms (the actual weight gain if the scale is unbiased) and standard deviation of 158 grams would be measured as a weight gain of greater than 300 grams. (This mean weight gain of 250 grams would 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 this weighing. Similarly calculated, the probability of excluding a child with 1/ This example is appropriate for a normal child who grows at 167 grams per month, and is weighted to determine weight gain for a three month period. - 19 - no weight gain is only 3%. Clearly in these cases the accuracy of the measurement device and the demarcation rule on entry are critical parameters in determining the effectiveness of the program, in including children who need supplementary feeding, and in excluding children who do not need the program. 1/ 2.35 In an actual feeding program, weighings would be taken on a monthly basis and comparisons in weight gain would be made over various periods to determine the trend in weight. If a child is measured over a three month period and is excluded from the program because weight gain is measured as adequate but in fact is inadequate, the chances are that the child will be discovered 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 not require supplemental feeding as the probability of committing an entry error compounds with the number of weighings. For example if a population has a potential malnutrition rate of 30% (a 0.5 correlation between weight losses) and a measurement technique with 90% accuracy, reference to Table 4 shows that about 25% of the adequately nourished children will enter the program along with nearly all the malnourished children who are weighed, that is, for a 30% malnourishment rate about a third of the children being fed will not require the program. A greater level of measurement error will induce even 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 have less 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 be found to be weighed) almost infallibly, children on the course to malnutri- tion, and an entry criteria that requires moderate levels of malnutrition to set 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 because of pressure from influential people in the community and second, through loss of income originating from a mother or older child foregoing work for at least part 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 these errors. These were simple estimates for illustrative purposes; clearly the probability of each type of measurement error depends on the other, and in turn, both depend on the criteria used. - 20 - 2.38 The first form of leakage results from a child being entered into the program because community leaders or wealthy individuals demand entry of the child and not because of a measurement error of the previously dis- cussed type. Since the food supplement and other activities at the feeding center (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 unintended beneficiaries. This monitoring must be able to measure objectively, at the time of inspection, whether the child indeed should be in the program. If a weight gain criteria for entry is used, on-site inspection will not work as the 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-weight or anthroprometric measures, it can fairly well be determined that the child in the program is in need of feeding. Through this monitoring of the children's status, for instance by personnel from the state or district headquarters, ade- quately nourished children can be removed from the program and this form of leakage to unintended beneficiaries can be minimized. 1/ 2.39 The second form of leakage results from the opportunity costs or the loss in earnings from production activities that an adult or elder child foregoes to bring in for feeding a malnourished child. If the benefits from the feeding program do not exceed these opportunity costs, families will find it to their overall detriment to participate. This benefits versus opportun- ity cost comparison is particularly important to partial feeding programs that require for success inducing the mother through nutrition education to feed more to the malnourished child at home. If the mother finds that the income lost 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 child brought 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 the mother's opportunity costs are low, i.e., when she is unproductive or unable to 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 work opportunities and secondarily by the incidence of malnutrition in her family. 2.40 To illustrate further this point consider the case of a mother who is employed 10 hours a day at a daily wage of 4 rupees. If it takes an hour to bring the child in for feeding, the value of the food supplement must be at 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 income and therefore consumption will decline by participating in the feeding program. If the mother is expected to go to the feeding site the other benefits to the family of participating in the program, such as education or expected 1/ Alternatively, the feeding program could be regarded to have, either by design or unintentionally, a social stigma that assists in keeping out children from upper income families; however, this same stigma might prevent entry of even children from poor families who are also sensitive to this detriment. - 21 - discounted earning of the child if it survives, will need to exceed this dif- ference. If the benefits are insufficient, the feeding center will primarily be occupied by the malnourished children, accompanied by brother and sisters either too young to work or with opportunity costs less than the value of the ration. 2.41 From this analysis of leakages, it appears certain that leakages from 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 the loss of income, the mothers of malnourished children will not participate in the program and the effort to reorient the family's distribution of food toward the malnourished child will be ineffective. In on-site, full feeding programs, 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 as follows: (a) Significant levels of substitution and sharing (the latter in a take-home program) of supplemental food can be expected. To assure effectiveness, ration sizes should be near the full nutrition requirements of the child and the duration of feeding should be short, two to three months. (b) Entry criteria should be an integral part of any feeding program. Without it, the program takes on the character of an income transfer and substitution will be high and effectiveness low. Two types of entry criteria are feasi- ble: one based on the stock condition of the child; the second on the trend in weight of the child. The second criteria is the most difficult to implement and has the greatest probability of committing Type I entry error, where a child who does not require feeding is entered. However, it has the advantage of identifying trends toward malnutrition with almost certainty and thereby avoiding the damage to a child's body and intelligence resulting from malnutrition. (c) The income leakage results from loss of income resulting from foregoing work to take a child to a feeding center. To enhance enrollment and attendance the ration size must be of sufficient value to compensate for the loss in income. As a consequence, the ration size should approach quantities sufficient to meet the entire child's needs and the center should allow for the child staying at the site throughout the day. The first provides an appropriate economic incentive to bring the child in for feeding; the second 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 analysis if the household i8 below the puverty line. However, tefi overall benefits would generally be less the greater are the leakages. - 22 - day to bring the child in for feeding. 1/ Also, the sea- sonal nature-of work opportunities for the mother needs to be accounted for with additional staff required during the harvest and sowing season to assure that children requiring feeding are brought to the center. 2.43 In the next section, we describe an entry criteria based on weight trend that is feasible fo: field operation. III. ENTRY AND EXIT CRITERIA FOR A SUPPLEMENTAL FEEDING PROGRAM 3.01 The purpose of this section is to describe a feasible weight trend criteria that can be used for entering and exiting children from a feeding program. The principal hypothesis of a feeding program using weight gain entry criteria is that a child that is not gaining weight adequately or is losing weight can be identified through a program of monthly weighings and that timely on-site feeding of a supplemental food to this child will (in the majority of cases) result in the child's return to adequate weight gain. As a 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, yet exclude, with a high probability, children that are gaining weight adequately and hence do not require supplemental feeding. Likewise, exit criteria are established that assure that the children entered into the feeding program have returned to adequate weight gain before being permitted to leave the program. Since such a program will be implemented in rural areas these cri- teria must be simple enough that a community nutrition worker can determine that 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 the nutrition worker (to reduce village pressure on the nutrition worker, only the supervisor is permitted to enter a child into the feeding program). As dis- cussed in the previous section, even though these entry and exit criteria will be implemented by trained and supervised personnel, certain measurement errors are inevitable because of the inaccuracy or misreading of the weighing device 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 Harvard standards, a 'normal' child between 6 and 11 months old gains weight at 500 gms per month, between 12 and 14 months old, at 200 gms per month, and between 15 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 educational benefits to the mother are loss and attendance can be unreliable. - 23 - through 3rd degree by a weight-for-age criterion) and gaining weight at 300 gms per month during the 6 to 12 month age period and at 100 gms per month after this period will maintain nutritional status quo. Weight gain less than these magnitudes sustained over many months will eventually result in a deterioration in nutritional status, possibly resulting in 3rd degree malnutrition and a rapidly increasing risk of death. The entry criteria must therefore be designed for the timely identification of children whose weight gain is substandard as well as for those children who maintain and do not improve their nutritional status. These entry criteria must however be balanced against the risk of entering children with adequate weight gain into the program. 3.03 As discussed previously, in implementing entry criteria based on measuring weight gain, three forms of error are possible. The first results from the scale's inaccuracy or miscalibration, or the operator's misreading of the indicated weight. On a balance type scale, this measurement error would have a standard deviation of 50 gms. The second form of error results from the daily and intra-daily fluctuations in the child's weight that results from changes in the body's fluid content or in the quantity of food matter in the stomach 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 the magnitude of this fluctuation in weight. Summary statistics of the results of these weighings are given in Tables 5 and 6. As can be seen from the data in these tables, daily and intra-daily weight changes are substantial. However, the weight change is less between similar times of the day, in particular, in the morning. To minimize the effect of intra-daily fluctuation, a nutrition worker will weigh the children in the mornings before supplemental feeding. With the weighings conducted in the morning, the daily fluctuation in total weight is estimated to have a standard deviation of 100 gms. The third form of error results from weight changes due to interim illnesses or episodes of diarrhea. Diarrhea that results in a semi-solid discharge 4 or 5 times a day can change daily body weight by 5 percent. Diarrhea consisting mostly of liquid and occuring 6 or 7 times a day can result in body weight losses of 7 percent. A child weighing about 10 kg can therefore lose 500 to 700 gns of weight in a single day due to diarrhea. Since this does not necessarily indicate a long term nutritional problem, the entry criteria are designed to exclude a child unless the weight loss persists and adequate weight gain is not reestablished. To do this, a child that has experienced diarrhea within the previous week of the weighing will be reweighed one week after the diar- rhea episode. - 24 - Table 5: MEAN AND STANDARD DEVIATIONS OF WEIGHTS AND MAXIMUM INTRA-DAILY AND INTER-DAILY WEIGHT CHANGES Mean Standard Maximum Intra-Daily (Inter-daily) Change Weight 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 Variations Child Day 1 Day 2 Day 3 Day 4 in Morning Weights Over Five Days 1 100 100 100 100 100 100 2 0 0 100 100 100 100 3 100 100 100 100 100 100 4 100 100 100 100 100 100 5 100 100 100 0 100 100 6 175 175 200 300 200 400 7 300 200 150 150 200 300 8 200 200 0 0 200 700 9 200 100 200 200 200 300 10 200 200 0 100 100 500 11 500 0 100 0 100 500 12 200 500 400 0 300 600 13 100 300 100 100 200 300 14 200 200 200 0 200 300 15 600 0 0 0 600 600 16 400 200 100 300 400 500 17 100 100 100 100 100 200 - 25 - 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 gain will be incorrectly assessed and be excluded from the program. The second is the probability that an adequately growing child will enter the program. As the entry criteria reduce the probability of one form of entry error, it can increase the probability of the other form. To balance the probability of each form of error, the potential costs associated with each error need to be determined 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 ineffectiveness of the program, physical and possibly mental damage, and increased risk of early death. If the second form of error is committed, that is, a child entered into a program who does not need it, then the credibility of the program is reduced and the program's feeding costs are increased. Clearly, in comparing the relative losses, we must consider that the more serious is the loss associated with excluding a malnourished child. As a consequence, the entry criteria are designed to reduce the probability of bypassing a malnourished child but doing so at the cost of an increased probability of entering a child with adequate weight gain. 3.06 Since a child is weighed monthly and therefore up to 30 times between the ages of 6 and 35 months, the probability of bypassing a malnourished child between these ages is nearly zero since the chances are that the malnourished child will be identified at least once in so many weighings. On the other hand, the probability of entering a child gaining adequate weight will be relatively 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 the weighing contributes to an increasing probability of error over the 30 month eligible age period of the child. (It is analogous to rolling a die where the probability of coming up with one dot is small in any one roll but, with many rolls, 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 the ages of 6 to 11 months than from 12 to 35 months, two sets of entry criteria are 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 the previous month; or (ii) Enter a child if its weight gain in two consecutive months has been less than 300 grams in each month. - 26 - This is provided, however, that the child has not had diarrhea in the previous week. If diarrhea has occurred, 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 three months.) (i) Enter a child if its current weight is less than it was three months previously, or (ii) If the average weight change over the previous three months has been less than 300 grams, identify the child as being at risk but do not enter it into the program at that weighing. If, however, on the next monthly weighing the child has still gained less than 300 gms in the previous three month period, enter it into the program provided, that is, an episode of diarrhea has not occurred during the previous week. If diarrhea has occurred conduct a 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 it more probable that the weight change actually indicates a trend of inadequate weight 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 adequate weight gain without bypassing children with long term trends of inadequate weight gains. (a) In Table 7 the probability of bypassing a child aged 6 to 11 months having weight changes from 100 to 500 gms per month are given for the entry criteria l(a) and l(b). As can be seen from the table, the probability of entering into the program a child with adequate weight gain (500 gms/month) is only 0.01 in any one weighing and 0.06 over the five weighings of the child as it ages from 6 to 11 months 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 probability over the five weighings. A child that is not gaining weight at all will be entered with probability 0.33 after the first month of no weight gain and with near certainty, 0.97 probability, after the second month of no weight gain. A child that loses weight enters the program with near certainty the first month that the weight loss occurs. - 27 - 3.09 These weighings occur at a particularly critical stage in the infant's growth when the quantity of breast milk from the mother is declining and the child's calorie needs are increasing. These entry criteria assure that any child with inadequate weight gain in these critical months will be identified and entered into the supplemental feeding program. 3.10 For entry criteria 2(a) and 2(b), Table 8 shows the probability of bypassing a child aged 12 to 35 months having weight changes from 100 to 500 grams over a three month period. As can be seen from this table, a child gaining adequate weight will have only .01 probability of entering the feed- ing program in any one weighing. Within 20.weighings the probability is 0.20 that the child will enter the feeding program at least once. A child gaining weight at an inadequate rate (300 grams over a three month period) but suffi- cient to maintain its nutritional state will enter into the feeding program at 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 0.3 probability within 5 months. A child gaining 100 grams over 3 months will be identified 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 3 months. In summary, children that are gaining weight at an inadequate rate will enter the feeding program with near certainty at least once over their 30 months of eligibility; how quickly they are identified depends on the degree to which weight gain is inadequate. The probabilities of entry indi- cate that those children with marginally inadequate weight gain will not enter for many months while children with very inadequate weight gain or with weight loss will be identified nearly immediately. The system of entry identifies children for the feeding program under an implicit priority ranking with the children with the most likelihood of becoming malnourished, that is, those with the most inadequate weight changes being rapidly identified with the highest probability, while those with marginally inadequate weight changes have a lower probability of being identified early but eventually are identified. The Exit Criterion 3.11 The exit criterion for children who have been in the feeding program for at least three months assures with high probability that a child is gain- ing adequate weight before leaving the program. This criterion is to consider a child recovered and to remove it from the program if it has gained 500 gms over the three months of supplemental feeding. To determine whether a child has actually gained 500 gns, two sets of three weighings are conducted and averaged at entry and exit. Upon entry, the supervisor will average the ini- tial weighing of the nutrition worker, her follow-up weighing, and a weighing on the day of entry to establish the child's initial entry weight. For the exit weight, the child is weighed at least three different days just before the three months of feeding have elapsed. These weighings, conducted in the mornings before feeding, are averaged to establish the final weight of the child. The difference in the everage weights at entry and after three months of feeding must be at least 500 gms for the child to leave the program. If weight gain is less than 500 gms, the child is checked by the health worker for signs of diseases or parasites that might have hindered weight gain. The recommendation of the health worker is used to determine if the child should be retained for continued feeding. - 28 - 3.12 The statistical reason for this procedure is that the multiple weighings at entry and exit reduce the standard deviation of the measurement error by the inverse of the square root of the number of weighings. Hence with three weighings the standard deviation goes down by a factor of 0.6 to about 65 gms. A child in the feeding program who has gained 400 grams over the three months will, by random error, be exited from the feeding program with probability 0.06. The probability of allowing the exit of a child with less than 400 grams weight gain is therefore very slight. The health check-up and the multiple weighings combine to ensure that the children who remain in the feeding program beyond three months are in need of additional feeding and that those children that leave the program are gaining weight adequately. Table 7: PROBABILITY OF BY-PASSING CHILDREN FROM THE AGES 6 to 11 MONTHS WITH WEIGHT CHANGES OF 500 to -100 GRAMS/MONTH Actual Months of Weighing Monthly Growth 1 2 3 4 5 (grams/month) 500 .99 .98 .97 .96 .94 400 .93 .86 .80 .74 .68 300 .74 .54 .40 .24 .22 200 .43 .19 .08 .03 .01 100 .17 .03 .00 .00 .00 0 .04 .00 .00 .00 .00 -100 .01 .00 .00 .00 .00 Table 8: PROBABILITY OF BY-PASSING CHILDREN FROM THE AGES OF 12 to 35 MONTHS WITH WEIGHT GAINS FROM 167 to -33 GRAMS PER MONTH Actual Average Months of Monthly Weighings Three Month Weight Gain 3 4 5 6 7 13 23 (monthly weight gain) 500 (167/mo.) .99 .98 .97 .96 .94 .89 .80 400 (133/mo.) .93 .86 .80 .74 .68 .47 .22 300 (100/mo.) .74 .54 .40 .24 .22 .05 .00 200 (67/mo.) .43 .19 .08 .03 .01 .00 .00 100 (33/mo.) .17 .03 .00 .00 .00 .00 .00 0 (0/mo.) .04 .00 .00 .00 .00 .00 .00 -100 (-33/mo.) .01 .00 .00 .00 .00 .00 .00 - 29 - IV. THE COSTS OF SUPPLEMENTAL FEEDING AND THE QUANTITY OF FOOD REQUIRED 4.01 In a supplemental feeding program, the number of children that will actually be fed a supplement will depend to a large extent on external factors, including the price of food and its general availability, income levels and its distribution, the quality of the water supply, the birth rate and the season of the year, which determine to a large extent the degree of malnutrition that can be expected in any village or region. The number of children actually fed out of the total number malnourished and eligible depends on the incentives to potential beneficiaries to participate, which are related to factors such as the size of the food supplement and its perceived value, the opportunity cost to the mother or older sibling of bringing the child in for feeding, the effectiveness of the nutrition worker in reaching children to weigh them, and the perceived benefits to be obtained from the education and nutritional services. The number of children that remain in the program after the intended days of feeding depends on the effectiveness of the nutrition worker in inducing the family to feed the child more at home and the calorie content of the ration given at the feeding center (the larger the ration, the more independent to the amount fed at home is the program's success in rehabilitating malnourished children). Since some of the children being 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 month will also depend on the relapse rate, which in turn is determined by the external factors described above. As a consequence of these influences on the number of children being fed, the estimates of a program's beneficiaries are complicated and largely dependent on these environmental factors. 4.02 To begin, we will construct a mathematical model, which illustrates the parameters that influence a feeding program. We will then present a simulation model to do estimates of the number of beneficiaries and food costs under 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 one month and leaving the program. Once having recovered, the child enters a high relapse group and is closely monitored for a reoccurrence of malnutrition. If successful in passing through this high relapse group, the child has the same or perhaps a somewhat lesser risk of becoming malnourished and reentering the program then children who have never been malnourished. 2/ 1/ For those non-mathematically inclined this section can be skipped in favor 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, then the selection process of having been malnourished once before would mean that the probability would be greater than for other children. - 30 4.04 To calculate the influences on costs of parameters of the feeding program, 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 high k relapse group = proportion of target population N entering the program 1 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: T F. Z X (14) L J.1-1 The number of children entering the program consists of new entries, e Na and 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 T y. pi'x (17) J-1 - 31 - 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 Substituting (18) into (19) we get TR-1 R 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 T F. = ~ 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 manageable expression for the number being fed (using this expression, a simple computer simulation has been constructed which allows one to determine actual numbers being 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 children being fed recover. That is, assume that p 1 while P. = 0 for all i 0 T Also assume that the probability of relapsing is equal in any month and that the target population is large in comparison to the number being fed in the relapse group. That is, assume that PR. = PR. - PR for all i and j J 1. - 32 - 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-l R. PR(1-PR) (26) 1 kik-0 The probability of relapsing in TR months TR-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. - 33 - A Simulation Model of Supplemental Feeding 4.06 A simulation model has been constructed to estimate beneficiary flows and the quantity of food required. 1/ The model is applied to the conditions in Tamil Nadu and a supplemental feeding program of the following characteristics: 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 35 months. Ration Size : Children from 6-23 months old, 145 calories per day (40 gis/day). Children from 24-35 months old 290 calories per day (80 gms/day). Third degree malnourished children receive double the above rations. Minimum Duration of Feeding Three months. 4.07 The model is designed to estimate beneficiary flows by age group for two categories of children: those that are not third degree malnourished and 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 specific assumptions are described in the following paragraphs. A Simulation Model 4.08 The simulation model estimates beneficiary flows and costs as a function of the rate of malnutrition, rate of relapse, and a feeding program's efficiency in returning children to adequate weight gain or adequate nutri- tional status. As shown in Figure 2, the model consists of three principal components: one that simulates entry into the feeding program, one that describes the feeding and the monthly probabilities of returning to adequate weight gain, and one that consists of the monthly probabilities of relapse through 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 with each age group is a monthly probability of becoming eligible for the program that depends on whether the child has been malnourished previously, whether the child is third degree malnourished and whether the child has been in the feeding 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 the ages of 6 months and 3 years only. The model is of course expandable to other age groups. - 34 - Figure 2: Model of Entry and Exit from Supplemental Feeding Program 1/ Children Children Who Have Who Have Never Been Been in the Malnourished Program and By R ereed Age Group / Monthly \ / Monthly Probability - Probability of Becoming of Becoming Ianourished Malnourished Feeding Program Initial N Prntiln 7 Months /PProportionroail_ Relapsingl Within. First SxMnths After \ \ Rcovery/\ \ / ~~~~~~Probability \ of Recovery After N + i High Risk . _ ~~~~Relapse Group (6Months) Pobability of Passing Through High Risk I/ The model is repeated for each age group: 6 to 11 months, 12 to 23 months and 24 to 35 months and for three groups of children; those coming from households with inadequate caloric availability, those from households with adequate caloric availability, and third degree malnourished children. - 35 - have a high risk of relapse. These three categories for each age group cons- titute the population that can enter the feeding program. The probabilities associated with each category and age group can diminish or increase over time thereby simulating the trends in malnutrition rates or the effects of a 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 of feeding. The ratio of the number of children who recover (who return to an adequate growth path within 3 months) to the total number of children being fed is called the recovery rate. This rate is estimated to vary between 10 and 40% of the children being fed. 4.11 The third component of the simulation takes into account the higher probabilities of relapse that exist in the months just after feeding and recovery. In the model, after recovery the child enters a high risk relapse group 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 at nearly 6 months a return to a lower probability. This high risk relapse group is assumed to have a relapse rate of between 10 and 40%. Once leaving the feeding 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 never been 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 demographics of the model and the impact of feeding on life span of the population. The mortality rates are based upon the Narangwal intervention in the Punjab, an experiment conducted from 1968 to 1973 by the Indian Council of Medical Research and the John Hopkins Department of International Health. It was a reasonably large study in which control villages were used to differentiate the impact of medical and nutrition interventions. Although this experiment was conducted in the Punjab, the measurements correspond to infant morbidity and mortality rates of Tamil Nadu. 4.13 The mortality rates associated with the third degree malnourished children are based on a Bangladesh study of mortality among children of dif- ferent degrees of malnutrition. This study found that third degree children have a 3 to 5 times greater mortality rate than adequately or even moderately malnourished children. For the purposes of the simulation a mortality rate of 3 times that of other children is used for the third degree malnourished children. Although reduced mortality rates from feeding tend to increase the number of children in each age group, other factors operate to decrease birth rates. Since the existence of a feeding program increases the probability of a 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 are high in terms of social prestige, labor and income losses, and potential support to the parents in their old age while the losses of a larger family size are relatively less in terms of increased food expenditures and other costs, the tendency will be for parents to have a greater than desired number of children. This bias towards a larger family size will increase with the - 36 - Table 9: 8UMHARY OF ASSUMPTIONS OF SUPPLEMENTAL FEEDING MODEL 6-11 MoB 12-23 Mos 24-35 Moe I. Proportion of participants becoming eligible by weight gain a. No previous Malnourishment 0.50 0.20 0.15 group b. Previously malnourished group 0.65 0.28 0.22 II. Probability 1/ of recovery after 0.8 0.8 0.8 feeding III. Probability of relapse / after 0.1-0.4 0.1-0.4 0.1-0.4 6 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 Moe Lee than 6 moo Over 6 Mos 104 26 12 6 1,000 1,000 1,000 1,000 Infant Mortality 130 1,000 VIII. Fifth year mortality rates 64 16 8 5 1,000 1,000 1,000 1,000 30 1,000 IX. Initial participation rates 602 70X 702 Increment per year 05X 052 05S Maximum participation rater; 902 902 902 X. Initial third degree 10 152 152 malnutrition r2te XI. Third degree participation rate 602 602 70% XII. Proportion of children becoming 102 10% 102 third degree after program XIII. Proportion of recovered third degree 15X 152 152 children relapsing into third degree after 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 .99 2/ 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. The relapse probabilities during those 6 months arei Month 1 2 3 4 5 6 .015 .0S', .062 .099 .091 .060 y 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. - 37 - risk of not having the desired number of children. As the risk of mortality is lowered for children, the bias will decrease and as a consequence fewer births will be required and family sizes will decline. With the project reducing the risk of early mortality, it can be expected that birth rates will also fall. It is conservatively assumed here that birth rates will decline from 30/1000 to 28/1000 over 5 years. 4.14 The final factor that needs to be accounted for is the participation rates 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 and 70% 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 is also 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 children eligible for feeding. The malnutrition rates of the children that are weighed establishes the number actually entering the feeding program. 4.15 In Tables 10 and 11, the beneficiary flows and quantity of food required to feed malnourished children from a 100,000 population are presented for relapse rates of 10 to 40%. The non-third degree malnourished are entered by weight-for-age. 4.16 Before entry is permitted for those entering by weight gain, several months of weighing must pass, while, for third degree malnourished, entry occurs immediately upon discovery of sufficiently low weight-for-age. Ini- tially then the feeding of weight gain children begins slowly, increasing as occurrences of insufficient weight gain are found, and as participation in the weighing 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 initial sweep is completed then only new occurrences of malnutrition are treated along with the third degree malnourished children from newly participating popula- tions. As a result, the number of children being fed who are not third degree malnourished increases in a gradual trend while the number of third degree has this initial increase, a falling off as the historical stock of malnourished are fed, and then a gradual increase as participation expands. Except ini- tially (due to this sweep), the number of children being fed who are third degree malnourished will be about 25 percent of all children being fed. For a 20% relapse rate on both third degree and non-third degree malnourished, the centers will be feeding approximately 1,400 children daily out of a total population of 100,000 with about 6,500 eligible children. Therefore, about 20% of all eligible children will be fed at any one time, given the conditions existing 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 eligible for feeding, this quantity of food would provide 1,200 calories for about 13 1/ The first year consists of establishing the feeding centers and providing the initial investments; feeding begins in the second year. This makes the timing of feeding costs consistent with the cost-benefit analysis of Section V. - 38 - Table 10: AVERAGE BENEFICIARIES PER DAY AS A FUNCTION OF SIX-MONTH-RELAPSE-RATE - PARTIAL FEEDING 1/ 2/ I. Average Beneficiaries per day per 100,000 population 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 2. Relapse rate - 20% (a) 6-11 months - 198 290 303 314 (b) 11-23 months - 214 374 416 434 (c) 24-35 months - 157 290 338 360 Total - 569 954 1,057 1,108 3. Relapse rate - 30% (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 1. Relapse rate * 10% (a) 6-11 months - 60 57 61 65 (b) 11-23 months - 126 109 118 125 (c) 24-35 months - 138 116 125 132 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 3. Relapse rate * 30% (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 4. Relapse rate * 40% (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. - 39 - days. If full feeding is used instead of partial feeding and the duration of feeding is reduced from 90 to 60 days then the total quantity of food required would 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 is economically viable will be examined in the next section on benefits and costs. Table 11: QUANTITY OF FOOD REQUIRED AS A FUNCTION OF SIX-MONTH-RELAPSE RATES - PARTIAL FEEDING Year 1 Year 2 Year 3 Year 4 Year 5 I. Total Quantity of Food Required per 100,000 Population (tons/year) A. Non-3rd Degree Malnourished 1. Rate of Relapse = 10% - 10.22 16.71 18.74 19.69 2. Rate of Relapse = 20% - 10.44 17.90 20.90 21.13 3. Rate of Relapse = 30% - 10.67 19.23 21.63 22.78 4. Rate of Relapse = 40% - 10.90 20.69 23.41 24.69 B. 3rd Degree Malnourished 1. Rate of Relapse = 10% - 13.27 11.46 12.36 13.09 2. Rate of Relapse = 20% - 13.96 12.33 13.31 14.10 3. Rate of Relapse = 30% - 14.66 13.34 14.41 15.27 4. Rate of Relapse = 40% - 15.36 14.50 15.69 16.64 V. THE BENEFITS AND COSTS OF SUPPLEMENTAL FEEDING OF CHILDREN AND PREGNANT AND LACTATING WOMEN 5.01 The purpose of this section is to quantify both the efficiency and social benefits of supplemental feeding of children and pregnant and lactating women. 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 reduced childhood malnutrition and mortality. The social benefits result from income in the form of food being distributed to the poor and from a basic needs commodity being supplied to those in need. The analysis of these social benefits is based on the Squire and van der Tak methodology of social benefit analysis 1/ and the Scandizzo-Knudsen approach to the evaluation of the benefits of basic needs program. 2/ 1/ Lyn Squire and Herman G. van der Tak, Economic Analysis of Projects, A World 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. - 40 - The Project 5.02 To illustrate how these methodologies apply to the evaluating of nutrition projects, we determine the benefits and costs of a proposed feeding and nutrition education project in six districts of Tamil Nadu, covering a population of about 14 million. These districts are to be phased in over a five year period with a supplemental ration being fed to eligible children, 6 to 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 gain criteria while pregnant women would be selected by rural health workers. The children's ration would be relatively small, from 80 grams (240 calories) to 160 grams (480 calories) depending on the child's condition, and would be fed for a minimum of ninety days. The pregnant women would receive a single ration of 240 calories for the last trimester of pregnancy and for four months during lactation. Mothers would be educated to improved child feeding prac- tices at community nutrition centers and through a communication campaign which provides wall posters, radio advertisements, short films, etc. A moni- toring and evaluation component would monitor the progress of the project and a 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 of the supplemental feeding of preschool chil- dren and pregnant lactating women. The pro- ject includes an education-communication component, along with widescale deworming and diarrhea management education. About 8,000 community nutrition centers would de- liver nutrition services and food. Location : Six districts in Tamil Nadu with a rural population of about 14 million including about 1.5 million children in the eligible age groups. Feeding A ration consisting of a 240 calorie biscuit given to children entered in the program by weight gain criteria and a double ration of 480 calories given to third degree malnou- rished children. A single ration of 240 calories would be provided to pregnant and lactating women. Duration of Feeding Feeding at the centers would be for a mini- mum of 90 days for children and for 7 months for women, 3 months while pregnant followed by 4 months when lactating. - 41 - Entry Criteria For children: based upon weight gain criteria for most children (see section III for details) and by weight-for-age criteria to determine third degree malnourishment. For women: se- lection by health worker according to need. Exit Criteria : 90 days of feeding or until adequate weight gain is achieved. 5.03 The project proposes a substantial supervisory infrastructure, from state headquarters down through block, taluk, and village levels. At the village each 10 nutrition workers would be supervised by one nutrition super- visor. One step up the hierarchy, each 5 nutrition supervisors would have an instructress 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 the supplemental food. 1/ Over the five years of project implementation, nutri- tion delivery cost including salaries and equipment will be US$21 million while 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 these costs? 5.04 Clearly, the food delivery costs do not simply justify the amount of food that is being delivered. Even India's public food distribution sys- tem with its inefficiencies and its ration shop structure is able to deliver food to the target group with an overhead of 20 percent, 2/ including leak- ages to unintended beneficiaries. Nor could the project be justified solely on its income redistributive effects. Subsidizing consumption of the poor or taxing the rich could deliver or take away income much more efficiently than such an elaborate structure of delivery. Instead, the benefits of the project must occur because of some multiplier effect, whereby the small amount of food acts as a catalyst for improved nutrition, through inducing more equitable distribution of food within the family or improved food pre- paration and utilization. We therefore must begin with the assumption that the "educating" aspects of the project bring about this multiplier effect. Otherwise, we can end the analysis at this point, since alternative forms of food delivery to the household are more efficient and net benefits can only be claimed to the extent that they are greater than that of the next best alternative. 5.05 The next major question is how well will the system function. Will it achieve lower mortality of preschool children? Will it be able to avoid 1/ A less costly organization would be to combine the health and nutrition infrastructure into one unit in which the village worker deliver both nutrition and health services. As such, the project should not be con- sidered an ideal model of a nutrition delivery system. Likewise, the administrative costs should not be regarded as typical. 2/ See P. Scandizzo and J. Graves, "Alleviation of Malnutrition; Impact and Cost Effectiveness of Official Programs." AGREP Working Paper No. 9, 1979. - 42 - large amounts of intra-family substitution? Will a large portion of the mal- nourished children participate in the feeding? Clearly, the benefits that the project will realize depend on these outcomes, which are at the present unknown without a pilot project. The performance of the project therefore is a parameter of the analysis to which the sensitivity of the benefits will be tested. The procedure then for the benefit analysis is to assume some reasonable performance parameters, calculate the costs and benefits under these values, and test their sensitivities. 5.06 We begin by estimating the efficiency benefits, that is, those benefits that are manifested in high earnings from extended working years and more productivity. We then determine the social or redistributive bene- fits, or those benefits accruing because society values income to the poor greater than that to the rich. We complete the analysis by adding on the benefits 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 preschool mortality and extended working years and the productivity gains as an adult, resulting from avoiding malnourishment as an infant or preschool child. We begin with the mortality reduction and extended working years. 1/ 5.08 Because the project is directed primarily to the poor and the risk of early death is different for the rich and poor, we divide the population into those households with adequate calorie availability (the "rich") and those without adequate calories (the "poor") and calculate the probability of death for children from each group. In Figure 3, we give a diagram for the 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 probability of being rich or poor through to the probability of surviving through the first year of life. 3/ During the second and third years of life, a surviving child can become malnourished with a probability that depends on whether it comes 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 the probability of surviving for children of the rich and poor through the first three years of life. 1/ Studies in Bangladesh indicate that mortality rates between adequately nourished children and 1st and 2nd degree malnourished children do not differ significantly. However, the mortality rate for 3rd degree mal- nourished children is 3 to 5 times that of the above group. Hence, in these mortality calculations, we have the project only influencing the mortality 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 mortality rate differences between castes (artisans, merchants versus agricultural laborers) from the Narangwal study. Figure 1: Ptobability of Surviving With and Without Project 2 Life Years After 3 Years ( 981) S W/O (.810) x (.610) x (.980) = .480 of Age S .98 \Poor/Not M)jnourished (.610 19) With(.858) x (.870) x (.981) = .732 50 W .6~~~~~~~~~~~~~~~~~~~6 (.85 3 9 0 (.910) W /O (.810) x (.390) x (.900) - .280 .832 0.38 -1/ G ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~/40 poor38 .190 (.090) With(.858) x (.130) x (.910) - .102 0.62 1/ Life Years vrich (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 60 0 005) ~~~~~~~~~~~~~.904 \ \ (.982) S g .914 \ (.081) \ S .980 W/O (.910) x (.080) x (.980) = .071 D \ .090 D.018 Rich/Malnourished With(.919) x (.050) x (.982) = .045 50 S - Survive D = Death W = Adequately nourished M = Malnourished (Third Degree) W/0 = Without project W - With project poor = Children from households below the FAO/WHO calorie requirement rich = 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. - 44 - 5.09 After the first three years of life, we assume for simplicity that the life span is a fixed number of years, the specific number being dependent on whether the household has adequate calories available and whether the child was ever third degree malnourished. 1/ Depending on which category an individual falls, an expected earnings stream is accrued, with the higher earnings going to the rich and never malnourished and the lower earnings to the poor and malnourished. The specific earnings are summarized in Table 13. They assume that the difference in earnings of those who have been third degree malnourished and those who have not is 25% (centered about the average unskilled laborer's wage). We also assume a 50% unemployment rate and a de- clining percentage of households with calorie availability below the FAO/WHO requirement. 2/ 5.10 As illustrated in Table 13 and Figure 1, the project is expected to (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 and if a reduction in birth rates does not occur, the population in each age group expands. As a consequence of this population expansion, eventually more people will be working, and GNP will increase. If we measure benefits of the project in part by its contributions to GNP, we are incorporating the effect of this increased population. Should a larger population in the country already over-populated be considered a benefit? Although we have other productivity benefits from the project, people working for longer periods 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 movement from rich to poor or vice versa. We do provide, however, for the number of poor to decline over time; essentially then we assume that the child's birth status, rich or poor, determines the probability of surviving the first three years of life and the life span thereafter. 2/ The projection is based upon calculations in Odin Knudsen and Pasquale Scandizzo, Nutrition and Food Needs in Developing Countries, World Bank Staff Working Paper No. 328, May 1979. - 45 - 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 old mortality rates: a. Third degree malnourished: - 100/1000 20/1000 b. Non-third degree mal- nourished: - 20/1000 5/1000 3. Probability of becoming third degree malnourished: 0.15 /a 0.39 0.08 4. Lifetime after surviving first three years of life: a. Third degree malnourished: - 40 50 b. 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 old mortality rates: a. Third degree malnourished: - 90/1000 18/1000 (-10%) (-10%) b. Non-third degree mal- - 19/1000 5/1000 nourished: (-5%) (0%) 3. Probability of becoming third degree malnourished: 0.15 /a 0.13 0.05 (-67%) (-40%) 4. Lifetime after surviving first three years of life: a. Third degree malnourished: - 40 50 b. 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). - 46 - 5.11 There are several ways of handling the expansion in population in the analysis. First, we could assume that the increased production, despite the larger population, is a net benefit, that is, not deduct the social costs of the population increase. 1/ Second, we could assume that the increased population carries a social cost equal to the additional expenditures on social services induced by the larger population. Third, we could do the calculations 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 from population pressure on prices of scarce commodities and count this loss as the costs of expanded population. A fifth procedure would be to deduct from their earnings the consumption of the increased population, essentially counting only their savings as a benefit. A sixth procedure would be to value the benefits as the willingness-to-pay for reduced children's mortality as 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 to reduce the economic rate of return to the opportunity cost to capital. Then we repeat the calculation assuming a compensating reduction in birth rates so that population remains constant. Reference to Figure 4 will illustrate. 5.13 In panel A of Figure 4, we depict a case where project costs are accrued 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 as the life saved reaches working age, and continues until death at age 53. In panel B, we assume that an exactly compensating birth rate reduction occurs the year after the lives are saved. Without the birth rate reduction, these new births would have reached working age in year 14 and continued on working until 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 occurs in 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. In diagram C, we depict a more realistic case in which the birth rate reduction is more gradual. 5.14 Under what circumstances would we find such a gradual compensating effect? Consider a case where families target the number of children: a family continues to have children until a targetted number of children have lived to an age when the probability of early death is low, after five years old. Under this circumstance, a child surviving to be five years old results in 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 unemployed will not increase because of the larger population. For the population increase that we are discussing here - around 300,000 - this is a rea- sonable approximation. - 47 - 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 years Project _+ 1 r Costs B. Earnings From Lives Saved With Exactly Compensating Birth Rate Reduction One Year Later. +Ne 53 54 _ 13 14 x years _ ProJect . X C. Earnings From Lives Saved With Lagged Birth Rate Reduction. + Net Benefitt 13 7/years Project 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 been the case with lower survival rates for children. This additional benefit of accelerated earnings is depicted in panel C of Figure 4. 5.15 In summary, the mortality rate reduction occurs because the project changes the age composition and size of the population. These changes result in an accelerated and larger earnings stream that, in calculating the net benefits of a mortality rate reduction, is reduced by a social cost stream resulting from a larger population. We now explore the third element in the efficiency 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, Selowsky reviews the empirical evidence on the relation between malnutrition during the preschool years and productivity as an adult. 1/ He observes that an increasing number of studies have shown that preschool children of the poor have substantially lower scores on tests of cognitive development than higher- income groups. Furthermore, studies on earnings functions show an independent effect on early ability of future earnings. Also, the evidence indicates a complementarity between schooling and ability, with the marginal productivity of 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 earnings function where wages, W, are related to years of schooling, S, preschool ability, 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 represented by aS/aA. That is, additional increments of preschool ability are assumed to result in additional years of schooling. 5.19 By assuming a diminishing rate of return to additional years of schooling 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 Economic Significance of Complementarities at Early Ages". Present at the Sixth World 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 increase in schooling costs for each additional year of schooling. 5.20 From a series of empirical studies of developing countries, Selowsky derives ranges for the coefficients in (32) and (34). From these studies, he selects values for c, b, d and 0, such that, c = 0.05, b = 0.18, d = 0.06 and 0 = 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 coming directly from ability increases (operating through c with dS/dA = 0) and the remaining 22.5% coming from induced additional years of schooling. 5.22 What magnitude of improvement in ability, dA, can be expected from reducing malnutrition in early ages? Selowsky sites two studies: one from Columbia, the other from Chile. The Columbia study found that children with mild to moderate malnutrition (90 to 79 percent of weight and height for age norms) could increase their ability scores at 43 months of age by one stan- dard deviation if nutrition is improved. The Chile study found that severely malnourished children, less than 70 percent of the norm, could have improved preschool ability scores by two standard deviations if early malnutrition had been avoided (from multiple regression results). 5.23 Although these studies are not necessarily representative of results achievable in other parts of the developing world, they indicate the magni- tude of results that are conceivable. The results are summarized in the table below: - 50 - Table 14: INCREMENTAL INCREASE IN EARNINGS FROM IMPROVEMENT IN COGNI- TIVE DEVELOPMENT AS MEASURED BY PRESCHOOL ABILITY SCORES Due to Direct Effect of Increased Due to Increase Cognitive Development in Schooling Overall /a Severely Malnourished 10% 45% 55% Children Moderately to Mildly Malnourished Chil- 5% 22.5% 27.5% dren /a Note that the major part of the productivity increase comes from increased schooling. If schooling is unavailable, then the productivity increase will be substantially less. 5.24 Using an average daily wage in rural areas for an unskilled worker of Rs 5 and an employment rate of 50% for 300 working days, we derive an annual 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 assume a 15% premium above average wages, while for those who have experienced mal- nutrition, we assume a 15% deduction from the average. Furthermore, we assume that a child that has become malnourished and recovered will exper- ience as an adult a 25% productivity increase above that of someone who was malnourished. For those children from households with adequate calorie avail- ability, we-assume that average adult earnings would be about three times that of an unskilled worker. We also assume similar proportional deficits in earnings if the person was malnourished as a child. Differences in the length of working life are also assumed between the categories of rich, poor, malnourished, etc., however, when translated to earnings these differences if 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 factor above 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% of earnings 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 improving feeding practices: 1. Increased productivity from avoiding the detrimental effects of malnutrition in the preschool years. 2. Increased populations in certain participant age groups com- pensated for by reduced populations in younger age group as birth rates decline. 3. And as a consequence, accelerated earnings in the early years with 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, we have divided the beneficiaries into two groups - the third degree malnourished - 52 - children and those children entered by the weight gain criteria. Four types of benefits accrue to those in the third degree malnourished category - reduced mortality, increased productivity, accelerated earnings, and extended working years. For those in the weight gain category, we attribute as bene- fits only productivity increases as studies have shown only minor differences in mortality rates between mildly to moderatily malnourished and adequately nourished children. VI. A BENEFIT AND COST ANALYSIS OF A SUPPLEMENTAL 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 of the feeding program in regards to participation, recovery and relapse in Section IV. (Those assumptions are summarized in Section IV, Table 9.) To summarize briefly, we have assumed increasing participation rates during the years of the project from 60% to 90% of the eligible chidren, recovery rates from 70 to 80%, and relapse rates of 30 and 20%, varied by the age of the child and the degree of malnourishment. In addition, we assume that the feeding program will operate in any one location for 15 years. Since the project 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 district phasing have been used to calculate the costs and quantity of supplemental food and the beneficiaries flows of the project. To calculate benefits, we have assumed that 90 percent of the children that enter the feeding program would have become malnourished to an extent that would have resulted in productivity declines. We further assume that the program is 80% successful in avoiding these productivity declines in those who participate in the program. Later, we will test the sensitivity of the benefits and costs to these performance parameters. In the meantime, we will evaluate the efficiency benefits and costs at the assumed values. 6.03 The effect of the project is to save children's lives and extend their life as adults. As a consequence, during the project years, population increases as more children are alive, and again much later, when death would have occurred, adults continue to live on due to their improved childhood nutrition (here we assume no effect on birth rates). This additional popu- lation reaches a steady state in year 20 when the project ends, maintains this level for a period, and then again increases (relative to the size it would have been without the project) when death would have normally occurred. Figure 5 illustrates by tracing the population in an age group affected by the 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 40 onward. But because of the project, a larger population age group B survives and lives longer. The difference between these populations A and B is the increased population alive in any year in that age group. The summation of these incremental populations in each age group is the increase in population 1/ Implicitly we are assuming that the reduced levels of malnutrition by 1995 to 2000 will not justify the cost of the feeding centers. - 53 - Figure 5: The Project's Effect on the Population Population Cohort / ~~~~Population B\ Population A 10 20 30 40 50 years Incremental Population (B-A) 10 20 30 40 50 yearl' - 54 - induced by the project, if no reduction in birth rate occurs. This increase is given in Table 16. 6.04 Without a birth rate effect, the project results in an increased population in year 20 of about 140,000 and reaches a maximum of around 310,000 in year 48. This projection assumes no effects on birth rates and disregards the additional population resulting from those surviving having children. We have then in Table 16, the minimum population increase given no birth rate reduction. If we account for the additional children of survivors, we can conservatively double these population projections in the later years. Efficiency Benefits and Costs Attributing Zero Social Cost to Population Expansion 6.05 In the analysis that follows, we calculate the efficiency benefits and costs of the project under the assumption that the expansion in popula- tion is without social cost and that it achieves mortality rate reductions comparable to those of the Narangwal experiment. This will produce the upper limits on the benefits of the project assuming that birth rates are unaffec- ted by reduced infant and preschool mortality. 1/ We will then test the sensitivity of the economic rate of return to the performance parameters of the 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 consumption whcih is converted at the factor for foodgrains of 1.1. 2/ The food transfer has been treated as an income transfer where food consumption for the household increases 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 the standard conversion factor weight. Otherwise costs and benefits are handled without 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 block is initiated and operation begins in year 3). The benefits do not begin until year 14 when the beneficiaries reach working age. 3/ 1/ In the Narangwal experiment, a twice daily ration was fed any child in the village throughout the year. If both feedings were taken, the supple- ment provided 400 calories. Since the project in Tamil Nadu provides 240 calories to most children for a minimum of ninety days, the Narangwal results are only indicative and probably represent an upper "bound" on this project's performance. 2/ The conversion factor is the ratio of the shadow price to the domestic price. See Squire and van der Tak, Economic Analysis of Projects for a detailed discussion. 3/ In reality, children work before age 13. However, this is probably of minor economic significance; for simplicity, we assume it to be zero. - 55 - Table 16: INCREASE IN POPULATION DUE TO PROJECT ASSUMING NO CHANGE IN BIRTH RATE: NARANGWAL ASSUMPTIONS Additional Additional Population Population Total from 'Poor' from 'Rich' Additional Perlods Households Households Population I 0.00 0.00 0,00 2 75.62 32.18 107.80 3 2408.12 1163.58 3571.70 4 5552.12 2736.58 8288.70 5 10330.20 5274.39 15604.59 6 16595.10 8795.65 25390.75 7 21510.37 11462.82 32973.19 8 26766.88 14316.53 41083.41 9 32362.04 17355.68 49717.73 10 38217.76 20542.32 58760.08 11 44262.94 23840.29 68103.23 12 50405.10 27197.95 77603.05 13 56547,26 30555.61 87102.87 14 62689.42 33913.26 96602.69 15 68831.58 37270.92 106102.51 16 74973.74 40628.58 115602.32 17 81069.66 43966.56 125036.22 18 85759.59 46621.34 132380.93 19 89169,82 48625.27 137795,09 20-32 909i5.58 49699.68 140615.26 33 91136.65 49699.68 140836.33 34 97955.55 49699.68 147655.22 35 107146,79 49699.68 156846.47 36 121115.16 49699.68 170814.84 37 139430.16 49699.68 189129.84 38 153799.61 49699.68 203499.29 39 169166.62 49699,68 218866.30 40 185523.69 49699.68 235223.37 41 202642.46 49699.68 252342.14 42 220315,09 49699.68 270014.77 43 237974.56 49745.91 287720.48 44 246779.34 51371.65 298150.99 45 252400.27 53631.94 306032.21 46 251609.99 57278.58 308888.57 47 244986.25 62338.36 307324.61 48 243522.50 66170.89 309693.39 49 236609.65 70271.45 306881.10 50 224626.98 74638.48 299265.46 51 206756.10 79217,44 285973.55 52 183038.29 83956.38 266994.67 S3 158939.97 68702.67 247642.63 54 134841.64 90770.23 225611.86 55 110743.31 91761.64 202504.95 56 86644.98 90401.89 177046.86 57 62546.65 e6645.55 149192.2b 58 38629.76 84942.28 123572,04 59 20229,16 81802.72 102031.88 60- 6849.37 77276.04 84125.41 61 0.00 71054.28 71054.28 62 0.00 63017.38 63017.38 63 0.00 54835.02 54835.02 64 0.00 46652.66 46652.66 65 0.00 30470.30 38470.30 66 o0oo 30287.94 30287.94 67 0.00 22105.58 12105.58 as 0.00 13971.17 13971,17 69 0.00 7501.68 7501,68 70 o0oO 2618.26 2618.25 71-100 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 000 4i1442414414i2 444404 400040 CCCCCCCCCCCooooooo....................... 0000.040-4004040.0400 .0000000000 .....0 ....00000000000.0.0....0000000000 000 444040 4 . .. .. .... . 0 44. 0.II. . I 0 .04 IO C .0'04 0 4.00 C ~ 00 . 4 5 4 2 0 IOr>o_ rI_r o 0 00 O o oooo ooooooooooooooooooooooooooo O00000 g 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0. 0 000.00002440 0'0....C .. ... ... .. ... .. ... ... ..0 o... I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t 0 n. 0 -420.. ..-... .. e- 04.000so 4-LOOOOOOOOOOOOOOOOOOO=OOOOO I .00Q .-.0...(.0.0.00 0 0 0 0 0 . . a . -40004-0 0-40.04000.000.- - - - 0 c--4. .0 ------- o-- -- ° C.. | e^¢o>$$$$$$$$s$$- 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 o 00.00. C0.000 040000400404404404004044004-40.40020000 00 00004-ooo88000 000 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 _n0 G °- 0 0 0L 0 0 0 0 0< oNN eGG QU - 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 for productivity gains. Because the earnings potential of the rich is much greater than that of the poor, even the slight reductions in the rich's mortality 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 feeding program and the relatively substantial 25% productivity increase. At an opportunity cost of capital of 10%, the net present values are presented in Table 18 along with their individual sensitivities. The project produces an anticipated economic rate of return of 14.5%. 6.09 In Table 19, we analyze the sensitivity of the economic rate of return to the performance parameters of the project. The rate of return remains above the opportunity cost of capital except under some worst case assumptions: 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 the success rate in avoiding malnutrition is 60%, and if productivity gains are 10% for the non-third degree participants. A reduction in participation rates to 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 the non-third degree malnourished participants is zero but the other performance parameters are maintained, then the rate of return approaches the opportunity cost 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 cost per capita, beginning at birth, needs to be to reduce the rate of return to equal 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 zero since the rate of return is below 10%, the opportunity costs of capital. For the assumed parameters, the social cost is $100 per capita - or about equal to the consumption of an individual at the poverty line. If the project has 75% less participation to 67% of eligible children at full implementation, but the other performance parameters remain as assumed, then the annual social costs must be no more than $83 per capita. Recall that this disregards the costs of subsequent population increases, that is, the social costs of the beneficiaries' children. 6.11 But what if birth rates subsequently compensated for the increased population after a five year lag'- that is, population remains as it would have without the project but with a five year adjustment lag. This would produce 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 a rate of return of 12.5% and, at the "worst case" assumptions of row 12 in Table 19, a 6.3% rate of return. By disregarding social costs, we have them giving the project an additional 2 percentage points of rate of return. 6.12 There remains one more issue in this regard. Is it actually indeed the "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 DISCOUNT RATE 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 DISCOUNT RATE 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=== DISCOUNT RATE 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 RATE RATE 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 - Rich B.PRWGP - Social Benefits of Productivity Gains - Children Entered by Weight Gain Criteria C.FD - Economic Costs of Food Transferred C.NPD - Economic Costs of Non-Food Consumption C.NUTRDELR - Economic Costs of Nutrition Delivery and Administration C.C0MNR - Economic Costs of Cousmunication Component C.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 Percentage Percentage Reduction in I to Percentaes Reduction Percentage Reduction Full Tmplementatiop Success Rate Resulting Reduction in 2 Year Old Kartality in 1 to 2 Year Old in Third Degree Percentage In Avoiding Productivity Economic Rate Sensitivity Infant Mortalitv Not Malnourished Mortalitv - Malnourished Malnutrition Rates Participation Rate Malnutrition Gain of Return Parameter(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 and Malnutrition Rates (10) (5) 5 0 10 10 (10) (10) 90 80 25 12.3% o Malnutrition KaCes and Infant Mortality and 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 and Malnutrition Rate plus success Rate plus Recovery Rate (10) (5) 5 0 10 10 (10) (10) 90 (60) (10) 8.8% Mormality Rat" and Parttcipation 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 considering potential levels of substitution? Consider if we triple food costs - that is have a full feeding where moderately malnourished children receive nearly a 1,000 calorie ration, if third degree malnourished, nearly 1,500 calories or as much as they could eat, and where pregnant and lactating women received an intake nearly equal to 50% of their daily requirements. Other secondary effects would possibly result: more rapid recovery, shorter duration of feeding, more consistent attendance at the center, and perhaps some addi- tional administration costs. Could, at assumed performance, the project be justified? Reference to Table 18 gives an indication. If food costs in- creased by nearly 600%, the rate or return would decline to the opportunity cost of capital. A rough estimate indicates that at triple the appraised food costs, the economic rate of return would fall to about 12 to 13%, an insignificant decline, especially considering the additional guarantees that this would ensure in project performance. The Social Benefit Analysis 6.13 We now examine the benefits and costs when both the efficiency and social gains are taken into account. The social benefit analysis places an additional benefit to income that accrues to the poor. Even if supplemental feeding 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 have economic value, households and individuals that participate in the project receive a real increase in income. In the social benefit analysis, the transfer of these services to the poor results in a benefit that is greater than the market value of the food and services. To calculate this benefit, social parameters that yield income specific weights are used along with estimate of the disbursement among income groups of the project's commodities and services. The social parameters used to weight these disbursements are from 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 distributional weights are disbursed among income classes in a manner given by the parameter n = 1. 1/ This particular value for n means that the distributional weight for 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 poor produces 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 more detail on this social analysis. Essentially, weights are assigned to income classes with the larger weights going to the poorer groups by means of a specific utility function. These weights increase the value of income or other transfers going to the poor and decrease them to the rich in calculating benefits. - 61 - Table 20: ESTIMATES OF NATIONAL PARAMETERS FOR PROJECT ANALYSIS: INDIA (Summary) Conversion Factors: Standard Conversion Factor 0.80 Consumption 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 1.10 Opportunity 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 to average consumption (v) 1.54 Consumption Distribution Parameter (n) 1.00 Critical Consumption Level (as a percent of national per capita income) 60% Accounting Rate of Interest 9%-10% 6.14 The other social parameter in the Social Benefit Analysis is the conversion 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, this conversion 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 in the feeding program, the conversion factor is 1.10. 6.15 Using these social parameters, benefits are calculated from the income weights and the estimated disbursement of food and services. Since the nutrition component attempts to reach the malnourished preschool child (an individual who is particularly poor even in comparison to the others in its household), individual specific weights are appropriate. To convert household weights on income to those for individuals, we need to derive indi- vidual real income levels. Since real income data by individuals are nearly impossible to come by, an approximate procedure has been used. This proce- dure assumes, except for food, household income is equitably distributed according to need. In the Tamil Nadu Nutrition project communication and educational components have been included that attempt to improve the intra- family distribution in favor of these preschool children. Hence, in the benefit analysis, we take into account this group's income relative to that of other 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, real consumption of non-food items is shared equitably (as measured by need) but that 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 relative calorie intake of an individual c0 to his requirement, rO divided by the relative calorie intake of the household c°, to its aggregate requirement, r°. Letting cf represent average household per capital food expenditure and ci average household per capital consumption expenditures, the relative con- sumption position of an individual j, cj, in household i can be written as the summation 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 that of the household i. If in this equation a equals 1, consumption of individual j is equal to that of the average per capital consumption of the household and an additional distributional weight above that given to the household is un- necessary. However, if a is less than 1 (indicating that in terms of food consumption) the individual is relatively worse off than others in the house- hold, then the distributional weight for this individual will be greater than that 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 are able to account for the particularly acute nutritional situation of children and pregnant and lactating women by placing a greater benefit to food that goes to them versus food that goes to other relatively better off members of the household. We additionally estimate distributional weights specific by the age of the child and hence account for the social benefits of feeding particularly malnourished younger children within the family. We therefore set distributional weights by households according to average income levels and by individuals in the household according to age, consumption level, and reproductive 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 of the Rs 24 to 75 per month expenditure groups and in particular to the 1 year old.. At very low expenditure levels, calories are distributed relatively equitably. As expenditure levels rise, the distribution to children becomes more inequitable with the 1 year olds' conaumption remaining nearly constant until an expenditure of about Rs 55 per month is reached whereupon consump- tion begins to rise again but remaining inequitable. As a consequence of this distributional pattern the benefit weights for food going to the children, in particular the 1 year olds, are higher than for the household in general. - 63 - Table 21: PERCENTAGE OF INDIVIDUAL CALORIE NEED FULFILLED BY AGE /a Percentage of Caloric Needs Met:Household Percentage Calorie Needs Met:Individuals 1 Year Old 2 Year Old 3 Year Old 60% 57 56 58 70% 65 65 66 80% 65 72 74 90% 68 84 86 100% 71 93 98 110% 78 98 104 /a Source: Tamil Nadu Nutrition Study. 6.19 A similar procedure is used to set the distributional weights for pregnant and lactating women. The Tamil Nadu Nutrition Study found that these women are relatively more deprived in respect to calorie needs than other 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 found that only 73% of needs are met and for lactating women, only 64%. Therefore, commodities and services for these women receive a greater distributional weight than for other household members. 6.20 Besides these distributional weights, food transferred to those in basic needs deficit received a basic needs weight that shadow prices food above its private value. This basis needs weight originates because India places priority on the fulfillment of basic needs. 1/ An increase in the consumption of the malnourished is considered a social externality originating because society attaches value to the fulfillment of basic needs. As applied to food, this externality results in a shadow price for food which is greater the more widespread is malnutrition. Taking the FAO calorie requirements adjusted for individual variability and accounting for losses within the family, 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 if an increase in food consumption results. 6.21 The direct benefits from the supplemental feeding originate with the increased calorie intakes of the child and of the household (the latter 1/ The concept behind these basic needs weights is given in P. Scandizzo and 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 account is taken of weight and age and sex distribution of the population. For this calculation see 0. Knudsen and P. Scandizzo, Nutrition and Food Needs in Developing Countries, World Bank Staff Working Paper No. 328, May 1979, Appendix 4. - 64 - from leakages) and the increased consumption of other commodities that results from the income implicit in the value of the food supplement. The food supplement acts as an income transfer to the household even when it is fed on-site, directly to the child. Since the household can refrain from buying as much food as it normally would and use the additional income on other consumer goods, the value of the food supplement to the household is measured by the value of the consumption that the household can now direct according to its preferences. The value of the food operating through the propensity to consume thus determines the increase in the household's food consumption. The part that goes to the child depends, in part, on the effectiveness of the education and communication components of the project in convincing the household of the child's nutritional needs. If these components are effective then the leakage to others in the household will be minimal and the child will receive most of the benefits of the supplement. If these components are ineffective, then the child will be fed the supplement on-site but at home will receive less food, in effect a substitution for supplemental food. Although this substitution results in the program being less effective in reducing malnutrition of children, it is not without benefit to other house- hold members who are poor. But since the distributional weight for additional consumption of the child is greater than that of the general household, a portion of the total benefits of the food supplement is lost, the amount being equal to the difference in the distributional weights multiplied by the value of the food that goes to other household members. If the leakages to other household members increase, the benefits of the project are reduced but are not entirely lost since others in the household are also below the critical levels of consumption and hence have distributional weights greater than 1. Also, since the food that goes to the other household members results in increased food consumption, transfers to the child and leakages to other household 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 but not a basic needs weight. The social benefits given to the value of the food transferred to the household, therefore, depends on how much of the addi- tional food is consumed by the intended beneficiary, how much is consumed by others in the household, and how much is directed to purchase non-food items. Note that all these leakages away from the intended beneficiaries can occur without reselling the food; what is required is merely that food formerly purchased not be purchased. 6.23 Another benefit of the project results from the reallocation of food within the family, which is induced by the education and communication components. In many households, the mother and other adults in the household do not recognize the full nutritional needs of the preschool child and infant. Through education and communication on the child's needs, the household will direct small quantities of food away from other household members to the children most in need. Since the distributional weight of these children's consumption is greater than that of the household, a benefit results that is equal to the value of the increased consumption multiplied times the diffe- rence in the distributional weights between that of the children and that of the household. However, this benefit can only be achieved in households where there exists the potential to redistribute food away from members in relative surplus and in households where the caloric needs of the child are - 65 - not being met. As a consequence, this redistribution primarily occurs in the moderately low to moderately high expenditure groups. 6.24 Another benefit of the project results from the more efficient utilization 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 and parasites. By shortening the duration and reducing the frequency of diarrhea through health care, education and oral rehydration, the effective calorie intake of the child will be increased. Likewise by reducing worm infestation the child's body will utilize available food more effectively. As a result of these measures, we estimated that effective calorie intake will increase by 15% for the children under 3 years old. 1/ This increase in calorie intake will occur primarily for children in households that have average per capita expenditures from Rs 24 to 75 each month as those below the lower level will be difficult to reach and those above the upper level will be less in need of these 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 social and basic needs benefit are given. In Table 22, the calorie consumption and food expenditures by expenditure group are present as calculated from the 1974 National Sample Survey for rural Tamil Nadu. As shown in the table, the poorest 33% of the population consume 25% of the calories while the richest 33% consume about 38% of the calories. About 50% of the households have an average 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 distributional weights, di, are shown by expenditure group for children, women by repro- ductive status, and the households. As demonstrated in the table by the consumption 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 receiving distributional weights greater than that for household. 6.27 In Table 24, the disbursement of the food supplement is given by expenditure group. In this disbursement, it is assumed that the third degree malnourished children are distributed among households proportional to the household's average per capita calorie deficit from 1,800 calories. This results in about 37% of the third degrees being in the poorest 6% of the households. The children that enter the supplemental feeding program by the 1/ Depending on the severity of the infestation, nutrient utilization can be increased from 3 to 25Z. See for more detail, L. Latham, M. Latham and S. Basta, "The Nutritional and Economic Implications of Ascaris Infection in Kenya", World Bank Staff Working Paper No. 271, September 1977. 2/ The distributional weights are weighted by the population proportions in each expenditure group. - 66 - weight gain criteria will most probably come from households that are slightly better off than those with third degree malnourished children. Also, since weight changes that qualify children for entry in the program occur even in households with only minor calorie deficits, it is assumed that the dis- tribution of these children will be proportional to the household's calorie gap from the FAO/WHO calorie requirement of 2,100 calories. In regards to pregnant and lactating women participating in the supplemental feeding, it is assumed that they will come from the poorest households, those that tend to produce third degree malnourished children (the entry criteria allows entry of only 30% of the pregnant and lactating women). 6.28 In Table 25 a summary of other specific parameters used in the benefit 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 for 1 to 2 year olds, 2.6 for 2 to 3 year olds, 2.3 for pregnant women and 2.7 for lactating women. The propensity to consume food is 0.83; the value of the food supplement is 3,800 Rs/ton; the value of at-home consumption is 2,500 Rs/ton. It is also assumed that 30% of the households will react to the educational and communication component by increasing the calorie intake of the under 3 year olds by 20%. The participation rate in diarrhea control and deworming is assumed at 50% and the resulting efficiency gain is 15% of current calorie intake levels. 6.29 The results of the social cost-benefit analysis without basic needs weight 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 M and a social rate or return of 21.5%. This compares to a net present value of Rs 416 M and an economic rate of return of 14.5% if only the efficiency benefits and costs are taken into account. 6.30 In Table 27, the rates of return for the efficiency and social benefit-cost analysis are compared for the case of the assumed parameters and for some of the worst case assumptions and under the case where social costs of increase population size are considered to be zero. As shown, if the worst case assumptions become reality, then the accounting for social benefits raises the rate of return from below (7.7%) to slightly above (11.5%) the opportunity cost of capital. If, in addition, the basic needs benefits are included then the rate of return slightly improves to 12.2%. 6.31 If account is taken of an initial population increase followed by a reduction in birth rates five years later then the rates of returns decline by about 2% points, such that, under the worst case assumptions the rate of return fails slightly below the opportunity cost of capital. 6.32 In Table 28, the minimum social costs per additional population that would drive the economic and social rate of returns to the opportunity cost 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 assumed parameters. At the worst case values the permissible social costs are nega- tive, indicating that essentially any social cost to increased population will result in a rate of return below the opportunity cost of capital. - 67 - 6.33 Finally, the rate of return is relatively insensitive to an increase in the amount or costs of food. In the social benefit analysis, an increase in food costs of 900% is possible before the rate of return falls below the opportunity costs of capital. Indeed, if the ration size or value in increased, and the food remains targetted to the poor, the social benefits would increase with the amount of food delivered, the result being that the rate 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 improvements in mortality rates and a relatively substantial increase in productivity, is economically justifiable, especially if account 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 performance parameter and to many parameters if varied in tantum. (c) The addition of social benefit analysis contributes about 7 percentage points to the rate of return under the assumed performance. Under the worst case assumptions, the addi- tion of social benefits raises the rate of return from below to above the opportunity cost of capital. (d) However, if social costs are attached to population increases than these results become less favorable. In particular if the social cost of a population increase is at nearly the annual 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 into account. With social benefits included, then the annual social cost of an additional person can be as high as Rs 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 return falling about 2 percentage points. Hence, if indeed families target for a desired number of children and no social costs are taken into account for interim population increases then the project remains viable over a broad range of performance. (f) Finally, the issue remains if successful performance can be expected when the ration is as small as in this project. Clearly a small ration increases project risks considerably while a larger, more costly ration could easily be tolerated without the rate of return declining to below the opportunity cost of capital. In other words, there is considerable room for increases in feeding cost before the project becomes in- viable. The project benefits and costs analysis points to increasing the ration to reduce the risk of poor project performance. Table 22: CONSUMPTION DATA FOR RURAL TAMIL NADU BASED ON NSS SURVEY ESTIMATES: 1974 Rural Tamil Nadu % share Household Expenditure 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 Intake r';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 d Group Distributed By Expenditure Class Basic Needs Distributional Weights 4/ (a i/ - B,) Entered By Pregnant Lactating 3rd Degree 1/ Weight Gain 2/ Women 3/ Household 1 Year Old 2 Year Old 3 Year Old Women Women Children 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 1800 calories 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/WHO caloric 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. - 71 - Table 25: ASSUMPTIONS OF BENEFIT ANALYSIS Household Propensity to Consume 0.83 Average Distributional Weight Very poor : 2.48 Less poor : 2.14 Others : 1.37 Basic Need Weight : 1.25 6-11 Months Old Children 3rd Degree Malnourished Average Distributional Weight = 2.56 Substitution Rate = 25% Non-3rd Degree Average Distributional Weight = 2.29 Substitution Rate = 25% Others Average Consumption per 6 mos = 0.032 tons grain equivalents Average Distributional Weight = 1.63 Average Increase in Consumption = 10% Efficiency Gain = 10% 12-23 Months Old Children 3rd Degree Malnourished Average Distributional Weight 2.69 Substitution Rate = 50% Non-3rd Degree Average Distributional Weight = 2.36 Substitution Rate = 50% Others Average Consumption per Year - 0.081 tons grain equivalents Average Distributional Weights = 1.53 Average Increase in Consumption = 10% Efficiency Gain = 10% - 72 - Table 25 (cont.) 25-35 Months Old Children 3rd Degree Malnourished Average Distributional Weight 2.56 Substitution Rate = 50% Non-3rd Degree Average Distributional Weight 3 2.28 Substitution Rate 50% Others Average Consumption per Year - 0.97 tons/year Average Distributional Weight = 1.52 Average Increse in Consumption 10% Efficiency Gain 3 10% Lactating Women Participants Average Distributional Weight G 2.69 Substitution Rate 50% Others Average Consumption per Year - 0.213 tons/year Average Distributional Weight 1.52 Average Increase in Consumption 6% Pregnant Women Participants Average Distributional Weight - 2.56 Substitution Rate - 80X Others Average Consumption per Year - 0.201 tons/year Average Disributional Weight - 1.53 Average Increase in Consumption - 6X General Basic Needs Weight - 1.25 Value of Food Transferred - 3,800 Rs/year Value of Increased Consumption - 2,200 Rs/year - 73 - Table 25 (cont.) Average Distributional Weight for Earnings 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 DISCOlINT RAIT 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 DISCOUNT RATE C.NUTRTkELR C.COhtMR C.CMERR 10.00 209637492.8 33022C31.9 5564760.0 SWITCHING VALUES - WeT P't"^^ '-' DISCOUNT RATE 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 DISCOUNT RATE C.NUTRI'ELR C.COMMR C.ChERR _ _ _ _ _ _- _ -_ _ _ _ -- - - - - -_ - - - - - - - -_ _ _ __-- - 10.00 904075399.1 727460738.2 700002666.3 PERCENTAGE CHANGE DISCOUNT RATE 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 DISCOUNT RATE 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-orwing C.FD - Economic Costs of Food Transferred C.11FD - Economic Costs of Non Food Consumption C.HNLrRDEIJ . Economic Costs of Nutrition Delivery and Administration C.COM?H - Econowic Costa of Cowmmnicstion Component C.CHERS. - Economic Costa of lIbtertu ad Uvslustio - 75 - Table 27: ECONOMIC AND SOCIAL RATE OF RETURN AND NET PRESENT VALUE UNDER DIFFERENT ASSUMPTIONS ON BIRTH RATE CHANGE I. Condition A: No Birth Rate Change; No Social Costs of Additional Population Economic Rate Social Rate of Return Of Return a. Narangwal Assumptions 14.5 21.5 b. Worst case with appraisal participa- tion rates Ia 8.8 13.5 c. Appraisal values with 75% less participation rates 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 with appraisal participa- tion rates /a 6.3 11.8 c. Narangwal Assumptions with 75% less participation /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%. - 76 - Table 28: ANNUAL SOCIAL COSTS PER DEATH AVERTED NECESSARY TO HAVE A RATE OF RETURN EQUAL TO 10% Economic Rate Social Rate of Return Of Return ----Rs/Year/Additional Life---- 1. Narangwal Assumptions 802 1,247 ($100) ($156) 2. Worst case with high participation rates Negative /a 559 ($70) 3. At Narangwal values 663 1,148 with 75% less partici- ($83) ($144) pation 4. At worst case values Negative /a Negative /a with 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 malnourished children : leakages, costs, PJB HG3881.5.W57 W67 no.451 Knudsen, Odin K. Economics of supplemental feeding of malnourished children :