Policy, Research, and External Affairs WORKING PAPERS Development Economics Office of the Vice President The World Bank May 1991 WPS 684 The Value of Intra-household Survey Data for Age-based Nutritional Targeting Lawrence Haddad and Ravi Kanbur The design of niutritioni intervenltionis can be very' susceptible to the level of aggregation of available informationi. I hc Poc y, Research, aid lxieia! Af Ifirs Coin( lcx dsLinhuics IPR F 9Aorking l'arcrv ti, di-emiate the Lic nditng Of s of rk in progrcss aid to crncourag OiC exchaige o0f ideds amiong lidlik stalf diad all others intCersted in docsloprnenr issues Ihese parvirs san) the lieiics of the authors, reflect ofII dicir % icA ss dnd shr.u:d he ustd and cit,d according!) Ihc rfidndigs. iInerpre-'1t1oli. ald ciulsirns ate! tlCe authors own. Ihc) should not he anthtecd to dhc World lanIk. its Bfoard of Diretors itr aninaptuert- r ans of its niembhr coomriic. Policy, Research, and External Affairs Development Economics WPS 684 This paper - a product of thc Rescarch Advisory Staff, Office of the Vicc Prcsidcnt, Devclopmncit Economics - is part of a larger effort in PRE to understand the dcsign of povcrty alleviation policies. Copies are available free from the World Bark, 1818 H- Street NW, Washinlgton, DC 2(A33. Plcase contaict Janc Sweeney, room S3-026. extension 31021 (29 pages, with figures and tables ). Age is a good indicator f( identifying at-risk * How useful is it to kinow thc caloric reallo- population groups for intervenitions that focus on cation outcome if age is used as a targeting prevention rather than cure. But whait is the ideal instrumcint ? upper age limit for tar-geting intcrvcintionls to minimize undernutrition>? Age proved to be a good indicator of under- nutrition wheni researchers had data on individual Within the framework of upper-limit indica- nutrition and on the intra-lhouschold allocation of tor targeting, Haddad and Kanlbur addrcssed calories. certain questions: Age was apparently less uselul aIs a targetinig * How far wrong can one go using only instrument when only houseihold-level dala on household-level data on nutrition? calorie adequacy were used. TIlhc cnors in age- based targeting were theefoire significanit. * How valuable is thc extra infotmnation one gets from costlier intra-household surveys on Food sharing rcndered age trulY less useful nutrition? as a targeting instrumcnt because oflecakaige within thc houseihold. Calories tarmted to the * How far wrong can one go by neglecting the younger household members cnd up reaching the intra-houschold repercussions of nutritionazl older individuals. interventions - for example, supplemeints to a child being nullified by equivalent reductions in food to the chiild in the home? The PRE Working Paper Series disseminates ihc findings of work under As\iT in the Bank's Polii-, Research. and Emtemal AffairsConiplex. Anobjectiveofthe series is .Iog.ttlicscfind ingsoutquickl\.cv cn ifprescntation, are lesc than. fully p1\lished. The nindings, intcrpretatiorts, and conclusions in ihcse papers do not necessa.rily represcrit official Bank polic'y. I'ro(luced by the PRE l)icssmination Center TABLE OF CONTENTS 1. Introduction.. . . . . . .. .. . . . . . . 1 2. Upper-Limit Indicator Targeting: Theory . . . . . . . . . . . 3 3. Optimal Age Cut Offs for Nutritional Targeting: An Application to Philippine Data . . . . . . . . . . . . . . 7 4. The Value of Intra-Household Information . . . . . . . . . . . 9 5. Intra-Household Allocation, Leakage and the Implications for Targeting . . . . . . . .. . . 11 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 14 * The authors would like to thank the International Food Policy Research Institute for access to the data, and Pete Mitchell for hf programming assistance. 1. INTF-JCTION Nutritional interventions exist in many developing countries. They are of course to be found as emergency relief programs after disasters or famines, but regular supplementary feeding programs are also widespread. A key question for these programs is targeting. Since resources are limited, some method has to be adopted of making sure that nutritional supplements are given to those who need it most. The most effective method is to evaluate the nutrient shortfall from a given standard for each individual and to supply exactly this amount of supplement and no more. But such fine targeting is not possible on the ground, and practitioners rely on more easily observable indicators. Examples of such methods are levels and trends in anthropometric indicators such as weight-for-height, weight-for-age, and upper arm circumference. However, if the intervention is fccussed specifically on prevention rather than cure, age is acknowledged to be one of the better ways of identifying at-ri:k population groups (Kennedy and Alderman 1986).' Accepting that age may fulfill the role of a useful targeting indicator, this still leaves open the exact nature of its use. In many cases programs use an upper ae Jimnit for eligibility (Pfeffermann and Griffin 1989, Beaton and Ghassemi 1982, Timmons et. 1 How easy is it to assess an individual's age in cultures not dominated by calendars? Enumerators concerned with accurate age measurements under these circumstances are trained to construct a detailed calendar of local events based on, for example, climatic auid crop cycle highlights (UN 1986). -2- al. 1983).2 What should this upper age lint be, if the objective is to minimize undernutrition with given resources for the provision of nutritional supplements? It will be recognized that the above question is part of the general class of indicator targeting problems, as developed by Akerlof (1978). We refer to it as the problem of unoer-liMit indicatgr irgiUtng. The first objective of this paper is thus to develop a framework for upper-limit indicator targeting, and to illustrate it for the case of age-based nutritional interventions using individual level, intra- household survey data from the Philippines. Although the data used provide only an approximation to individual nutritional achievements within the household, most surveys in developing countries do not provide even this information. How far wrong can one go with only household level data on nutrition? The second objective of this paper is therefore to provide a quantitative estimate of the value of the extra information that the costlier intra-household survey provides, when the objective is to design optimally targeted nutritional interventions. There is, however, a recognition in the nutrition literature that such interventions cannot be seen independently of the nature of the intrahousehold nutritional allocaticn, since a supplement to a child can be nullified by an equivalent reduction in 2 Infants in the age range 6-36 months are especially highly targeted as (1) they are vulnerable to undernutrition (low energy density weaning foods for example), and infection (the move from breast feeding to weaning foods, and increased toddler mobility for example) and (2) the functional consequences of poor health are more severe for this age group. .3- feeding at home (Alderman 1990). The third objective of the paper is therefore to provide a quantitative assessment of how far wrong one goes by neglecting the intrahousehold repercussions of a nutritional intervention. We start, howevpr, with some basic theory on indicator targeting. 2. UPPER-LINIT INDICATOR TARGETING: THEORY Let 0 denote a measure of nutritional adequacy (for example, the calorie adequacy ratio for an individual) and t the age of an individual. Let f(0,t) be the Joint density of the two variables in the population. If z measures a normatively given "adequate level for 0, (e.g. z - 1 for calorie adequacy), then a measure of the extent of undernutrition in the population is given by P. = f AA'f(t )dot (1) 00 z It will be recognized that this measure of undernutrition is analogous to the measure of poverty put forward by Foster, Greer, and Thorbecke (1984). Variants of it have been discussed in the context of undernutrition by Kakwani (1989) and Ravallion (1990). This will be the workhorse of our analysis of nutritional targeting-the object of policy will be to reduce the value of Pa as given by (l). The magnitude of a reflects value judgements on the view taken about the depth of undernutrition. When e - 0 this depth is ignored and the PO -4- essentially miasures the fraction of population that is underno"rished. When a - 1, P1 is the aggregate nutrition gap, suitably normalized. As a increases above 1, P. gives greater and greater weight to those with lowest nutritional achievement. Most of our empirical analysis will concentrate on the values a - 09 1 and 2 as capturing this range of value judgements. Before introducing policy, notice that P. can be rewritten using the fact that f(,,t) = a(*It) h(t) (2) where a(0 I t) is the conditional density of 0 given t and h(t) is the marginal density of t in the population. Using (2), (') becomes Ps f (f -ZAv a(*tt)d#3 h(t)dt 0 0 (3) co f Ps (t) h(t) dt 0 In other words, total undernutrition is simply the sum of undernutrition at each age level, weighted by the proportioit of population at that age level. We sappose that the policy maker has a total amount of nutritional supplement B to dispense. If each individual 0 could be -5- observed costlessly the policy program would be easy-simply find those for whom 0 is less than z and administer the right amount of y supplement. But on the ground this is impos.'Nle to do and other criteria are used. One such criterion is an tpper age limit T such that only those with age less than or equal to T receive the supplement. If there exists a household survey that allows us to estimate the bivariate density f(o,t), this could be used to choose the optimal value of T, such that Pe is minimized for the given amount of rasources B. But how? We have to specify how the supplement is distributed to those who meet the criterion. The simplest model, and also the most practicable method, is to distribute the supplement equally among those 'let through the door" on the criterion that their age be less than or equal to T. There are H(T) individuals of age less than or equal to T where H(-) is the cumulative distribution of the density h(.). Thus each individual who satisfies the criterion gets an amount B/H(T) and the new level of undernutrition is given by T z-B/H(t) P, (B,T) * f [Z -, a(* ! t)] h(t)dt (4) as z f | f Zt a (4 1 t) Ih (t) dt -6- The central question is what happens to Pe (B,T) when T changes for given B. Differentiating (4) with respect to T we get: d.6(BT) a , Bh(T) f P- B(,T I t)h(t)dt d-r Z [H(T) ]2 (5 + [ Pe(B,T I t) - P, (O,T I T) ]h(t) The two terms on the right hand side of (5) capture the conflicting effects on undernutrition when the upper age limit is increased at the margin, so that more people are drawn into the net. These new people get a supplement so their nutrition improves-this is the second term on the right hand side of (5). But with the new people there is less to go around, anJ those already in the net lose out. This intra- marginal' effect is captured by the first term on the right hand side of (5). As shown in Kanbur (1987), the impact of a small decrease in transfer on Pi is proportional to P,.1 and this term consists precisely of expressions of this type. Further insight into (5) can be derived by specializing to the case of a - 1. Then (5) becomes T dPj1 (B, T) _ 2. Bh (T) T~ BrIthtd 6 dT z (H(T) 2 o (6) + [P1 (B,T I T) - P1 (O,T I T)lh(T) Further manipulation on P, (B,T I T) and P, (O,T I T) leads to -7- dPj (B,T) 1 .B * h(T) lp (B,T I t sT) - Po (B,T I T)| dT zH (T)0 z (7) h fT a z3 t !) do z_B/H (T) ) From (7), the impact of a change in T on undernutrition as measured by P, de .)nds on two factors. First, there is the extent to which the incidence of undernutrition for those with age less than or equal to T exceeds or falls below the incidence of undernutritien for those at age T. Second, there is the extent of original undernutrition of those of age T who stop being undernourished with the intervention. While the second term is somewhat convoluted, the first term is intuitive--it is the difference between the marginal and the infra- marginal incidence of undernutrition for given T. The optimal value of the age cut-off occurs when (5) is zero. Denote this by T*. But it can be seen that this leads to a complex equation for T that cannot be solved in closed form. A numerical analysis is required, and we now turn to that in the context of a specific data set. 3. OPTIMAL AGE CUT OFFS FOR NUTRITIONAL TARGETING: AN APPLICATION TO PHILIPPINE DATA The data set used here comes from a household survey in the Philippines. The data and methods of collection are descriued fully in Bouls and Haddad (1990). The data contain information on nutrition among 448 households in the southern Philippine province of Bukidnon, .80 collected and averaged over four rounds to account for seasonality and other fluctuations. The distinctive feature of the data Is that the food intake of each individual in the household was obtained. The 24- hour recall method was used (for an evaluation of this method, see Bouis and Haddad, 1990). This intake can be converted into calories using standard conversion factors. !n addition, we can calculate the calorie requirement for each individual baWed on 32 age-gender- pregnancy status categories. For this reason, the data are to he viewed as illustrative rather than definitive measures nf individual- level nutrient adequacy.3 The calorie adequacy ratio, the ratio of intake to requirement, is our measure of undernutrition in this application, and we use a calorie adequacy ratio of one as our benchmark (i.e. z - 1, in terms of the formulae in the previous section). We will refer to this as a "poverty line", although it is clear that in our application it is an 'adequate nutrition line". The food energy deficit in our sample, namely the sum of the individual difference between intake and requirement, is 1,048,631 calories for the 2880 individuals in the 448 households.4 As in the previous section, let 0 be an individual's calorie adequacy ratio. If we did not have individual level data, we would be forced to assign a households calorie adequacy ratio to each individual in that household. Donate this variable by 4 . Figure 1 shows that the mean 3 For a finer analysis, individual energy requirements would in addition be based on body weight and activity patterns. '4 All programmes for Tables 1, 2, 4 and Figures 1-7 were written in Microsoft Fortran version 3.1. -9- of 0 in an age group Increases, by and large, with age, but that the mear of 4 , does not. This insensitivity of * to age is also brought out by figure 2. Here poverty indices as given by equation (1' are calculated for each age grouping based on 0 and Pl. P'ain, age is a sensitive predictor of P,(O) but not Pi( 4 ). This insensitivity of 4 and its transforms drives many of our results in the following section. The sensitivity of X to age may suggest a prima facie case for an upper age limit to calorie supplements through feeding programs and the like. But what is the optimal age cut off? Figure 3 shows the behavior of P^ (B, T) as a functiz*. of T for various values of B with a set at 1. The top line is for B * 0, which obviously shows no effect on P. of changes in T. The lowest line is when 8 - 1 million calories, Just abou. the amount necessary to eliminAte the energy deficit if it could be targeted only to those with deficits. But when this is not possible, the curve shows the best that can be achieved with age-bas!d targeting. As the upper age limit of eligibility increases, from low values of T, undernutrition falls. Thus the marginal effect of bringing more people into the net dominates the infra-marginal effect of spreading resources more thinly over the existing beneficiaries. However, as figure 3 shows, eventually this balance is reversed, and there is an optimal T. We call this our scenario 1. How does the optimal T, T, depend on a and B, the parameters of the problem? Table I presents values of the optimal upper age eligibility for various values of a and B and figure 4 plots this surface. It is seen that, by and large, T* increases in a and in B. -10- The fact that T increases in B is intuitive - when there are more resources, mors people can be optimally brought into the net. The fact that T* increases in a is related to a greater depth of undernutrition at the mdargin rather than infra-marginally. At lower age eligibilities there are so few who qualify for supplement that those within the net are pushed far above the poverty line, therefore there is no inframarginal undernutrition, and as a increases, undernutrition at the margin is weighed more heavily, and the optimal T is reached at higher ages. 4. THE VALUE OF INTRA-HOUSEHOLD INFORMATION The analysis of the previous section is based on a survey that collects information on individual nutrition within the household. Bt;t most surveys available to planners in developing countries collect food consumption information only at the household level. The usual method of proceeding is ths;i to calculate a measure of household calorie ade uacy, and to attribute this to each individual in the household. Intra-household inequality is therefore ignored. Intra-household information on nutrition is costly to collect and it would be useful to know the benefits from its collection. In particular, how useful is it in targeting? With our data set, we can provide an answer to this question. As before, let O be the true individual calorie adequacy ratio and denote by $ the individual calorie consumption adequacy ratio when each individual is simply allocated the household's calorie adequacy ratio. Without information on individual intakes, we would be forced to use the bivariate -11- distribution of $ and t, to calculate the optimal upper age eligibility. We call this our scenario 2. Denote the optimal value of T as t . Thus all those with age less than V will get nutrition supplement B/H( ' ). Undernutrition with this supplement is given by expression (4) with T - Figure 5 compares the behavior of Po(B,T) and P.s(B,T) as a function of T for 2 values of B at a - l. It is clear that TI and V can be very different. In general, the Ps* curves are flatter and lower than the P, curves. Intuitively, the flatness is a reflection of the flatness of the $ and Pm# lines evaluated within each age group (see figures 1 and 2). The suppression of intrahousehold inequality as represented by $ results in age being a much poorer correlate with observed undernutrition and hence a poorer targeting instrument. The marginal undernutrition reduction effect dominates the inframarginal effect until much higher levels of T are reached. In addition, the lowness of the Pg4 curve reflects the shallowness of observed poverty, at all age groups, once intrahousehold inequality is suppressed. The difference between P. (B,T) and P* (B, ) is the difference in undernutrition when the wrong infonmation is used. A measure of this difference in calorie terms can be derived as follows. If B. is the solution of the following equation: P64#(B,T) (B,l -12- the difference between B. and B represents the extra calories (or equivalent gain5)that would be needed to achieve the same level of undernutrition reduction with the 'wrong' age cutoff, t! , as was achieved with the correct age cutoff, T'. Table 2 presents equivalent gains for various values of B and a. The costs to not having accurate individual level calorie adequacy information upon which to identify r, when expressed as percentages of the original interventions, can exceed 30%. The calorie costs are substantial precisely because actual calorie adequacy is strongly associated with age, and suppression of intrahousehold calorie information deprives us of a useful targeting instrument. 5. INTRA-HOUSEHOLD ALLOCATION. LEAKAGE AND THE INPLICATIONS FOR TARGETING The analysis so far has assumed zero sharing of the calorie intervention that the eligible individual brings into the household. Either because the intervention is divided within the household, or through reductions in non-intervention calorie intake of the eligible member, it is highly unlikely that intervention calories add, one-for one, to the total calories consumed by the eligible individual. What are the implications for the age-based targeting of calorie leakage from the eligible individual to his or her fellow household members? Does it still make sense? In general, this depends on the extent to which there is intrahousehold calorie allocation away from the 5 For a related use of the equivalent gain concept, see Ravallion (1989). -13- targeted group (TG), i.e. children. These tradeoffs are represented in Table 3. Case numbers 4 and 3 represent scenarios 1 and 2 respectively, and case 8 represents the third scenario, food sharing. If within- household food sharing is substantial but intrahousehold food allocations are skewed away from those with the lowest calorie adequacies, age-based targeting is not feasible. Calories directed to the younger housahold members end up in the hands of the older individuals. Specifically, our data set allows us to provide an answer to the question 'how useful is it to know the calorie reallocation outcome if age is used as a targeting instrument?'. As before, let O be the true calorie adequacy ratio, and let each eligible individual receive B/H(T) calories. Now, however, the individual shares the calories with the other household members. The arbitrary rule imposed here is that the ith individual's pre-intervention share of household calories, w,, is unaffected by the intervention.6 Thu the ith individual in the household receives (B/H(T)).w, calories. The upper age eligibility at which undernutrition in the entire sample is minimized is denoted by T;. Figure 6 shows the behavior of P#oc(B,T) as a function of T for various values of B with a set at 1. As with previous figures, the marginal/inframarginal relationship exists although it is not as smooth. In the previous scenarios individuals 6 This rule can be justified, however, by reference to certain principles of bargaining theory; see Selten (1978). For an analysis of intra-household bargaining over nutritional and other resources, see Haddad and Kanbur (1990b). -14- could only receive less calories as the net widened. In this scenario, however, individuals already in the intervention can receive Mu calories as the eligibility age is increased (if, for example, their households contain two children quite close in age). Thus P,O,(B,T), the undernutrition index, can go up and then down. Figure 7 compares the behavior of Po+(B,T), Pa,(B,T) and P#(B,T) as a function of T at B-i and a-I. It is clear that T , can be very different from T and t . When the three functions are compared on the same vertical scale, we can see that P0C (B,T) is the flattest and lowest of the th,ee lines. The fLnt_M is because the original sampling design required each rural household in the Philippines survey contain at least one preschooler. Each household immediately receives calories even when the upper age eligibility is only 2. Therefore age is only a good targeting instrument if poor households contain more young children and intrahousehold allocations are not skewed away from them. The same analysis with a more demographically representative sample containing older, richer households with no children would produce a more curved PO(B,T). The 1qLpilin of the line results from (1) the objective function we have chosen to minimize: undernutrition across all individuals in the sample, and (2) the large absolute calorie interventions that are reaching adults who are close to the poverty line compared to smaller calorie interventions reaching children who are far below the poverty line. If we had placed larger weights in -15- the objective function on the alleviation of infant undernutrition, the curve would be higher. The difference between P#O(B,Tc) and P.4k(B,T') is the cost in foregone undernutrition-reduction when no food sharing is assumed in the calculation of upper age eligibility, even though food sharing does indeed take place. Again, if B. is the solution of the following equation: Poc(B,T*) - aoc(Bej the difference between B. and B is a measure of the cost of making the wrong assumption on food sharing. Table 4 presents equivalent gains for various values of B and a. As can be seen, this cost is virtually zero since age is no longer closely associated with the delivery of calories to those who need them most. 6. CONCLUSION The object of this paper has been, first to develop a framework for upper-limit indicator targeting, and to illustrate it for age based targeting of nutrition interventions using data from the Philippines. Second, we have provided quantitative estimates of the value of individual level information and of knowledge of the intra- household allocation of calories. For our sample, age proved to be a good indicator of undernutrition. However, this proved not to be the case with household level calorie adequacy which rendered age a0argnt]x less useful as a targeting instrument, at an often -16- considerable calorie cost. Food sharing, on the other hand, trulv rendered age impotent as a targeting instrument because of within- household leakage. This effect was strengthened because each household contained at least one preschooler. Therefore, getting the age 'wrong' here had few consequences in terms of calorie foregone. We conclude that the design of nutrition interventions can be very susceptible to the level of aggregation of available information. This is consistent with our findings in Haddad and Kanbur (1990a), that while poverty or undernutrition rankings of groups defined on household level characteristics were not sensitive to the level of aggregation, the rankings of groups defined on individual characteristics were very sensitive. Possibly the costs of collection of these intra-household data outweigh the benefits, but the experiments in this paper begin to answer questions about the costs of M collecting them. igure 1: Man calorie adequacy within each age group for 0 and Ohat 1.4 1.3 - 1.2- roan calorie 1 adequac~~~~~~~~~j ~~~~ ~nean within age *-,. X * *.* n''""'at 9.6 9.5 1 11 21 31 41 51 61 age group (irs) -18- ,4 - Om~~~~~~~C o .-~12S¶4*.. . . La S.. U,~~~~~~~~~............. w S..~~~~~~~~~~........ P4 ~ ~ ~ ~ ~ ~ ~ .P ......... i. ' 0r) 00 4'~~~~~~~~~~~~~~~~~~~~~~~~~~~~- 1 '4p4~~~~~~~~~~~~~~~c ZI. I 2~~~~~~ V u Figure 3: Undernutrition levels, ac=l, for different upper age cutoffs and calorie interventions (B=nillions of calories) 8.2 8.18 -P1, B=O 8.16 8 11 [ \--- -------'|---1,-= 25|N ft 8.1:2 ,.--.-P1a . =8 .S 8.14 lPl, B=O._5 6.16 &, ,M,,.,c.-a~~~~~ - -m P 1, EB8.715 8.88 . 8 .E; . ~~~~~~~~~~~P 1, Bt=1 2 7 12 17 22 27 32 37 42 47 52 58 65 upper age eligibilitg (ygears) -20- Figure 4: Surfaces of undernutrition-minimizing upper age eligibilities for different calorie interventions at different sensitivies to undernutrition N 14.9 21.21\ : OotRm 14.9 / / I // I\ /\ Optimal upper age ell ibility 84///\, JIf 2.3 -~/t 0.7 ~ ~ ~ . 0.1 Sensitivity to depth of undernutrition Caorie intervention (B)() Cl (millions) Figure 5: Undernutrition, =1, individual (0) versus household (Ohat) level data 6.16_ _ _ _ _ _ _ _ _ _ 0.14 -P1i, B=0.5 P1P, B=1 l P8 .12 ftE. . _-_ -- -- e… - n ee…-… ---- P10hat, B=1 o.86 Plhat, B=8.5 2 7 12 17 22 27 32 37 42 47 52 58 65 upper age eligibilitg (years) Figure 6: Undernutrition, a=2: intra-household calorie shares naintained 0.813 …~~~~~~~~~~~~~~ 0.8125 -** , , l 0.012 - - P0c(m=2,b=1.00) 0.0115 \\ _.\ ~ . - - --- P0c(m=2,b=B.25) - = ~-oo P0c(K=2,b=0.50) 0.811 0.E*185 I**I2 * * , * *t* *t t ' ' 2 7 12 17 22 2 32 37 42 47 52 58 65 upper age eligibility (years) Figure 7: Undernutrition, 0K=1, for individual level (0) household level (Ohat), both no leakage, and individual level and leakage (0c) 6.18 8.16 _ 8.14 IB 1 6.1 Pa - P0hat(M=1,b=1.00) 8.88 P0c(K=1 ,b=1 .88) 8.84- 8.6 food sharing 8. 2 7 1217 22 27323742 4752 5865 upper age eligibility (gears) -24- Table 1--Optimal age cutoffs (T) for various values of a and calorie intervention Intervention (millions of calories) a values 0.1 0.5 1 0 2.30 6.00 11.60 1 5.00 13.30 17.50 2 5.40 14.30 21.20 -25- Table 2--The equivalent cost (in calories) of not having individual-level data with which to target -- -- , -- -- -- - -- - - -- -- -- -- -- -- -- - -- -- -- - . - , -- -- - a calorie T (X) T ( 4 ) P (T (T)) P (T( 4 )) difference equivalent intervention (yrs) (yrs) V(1) (2) (2)-(1) gain (cals) 0 100000 2.3 3.5 0.66736 0.67500 0.00764 20200 0 200000 3.7 5.1 0.63090 0.64028 0.00938 18300 0 300000 4.8 6.2 0.59688 0.60972 0.01284 23500 0 400000 5.8 8.3 0.56285 0.58576 0.02291 55500 0 500000 6.0 9.1 0.53125 0.54757 0.01632 39800 0 600000 7.0 10.5 0.50104 0.51910 0.01806 51100 0 700000 8.8 11.4 0.46840 0.49236 0.02396 60700 0 800000 - 9.4 13.4 0.43368 0.46944 0.03576 96900 0 900000 10.5 15.7 0.40799 0.44549 0.03750 100000 0 1000000 11.6 18.7 0.38194 0.42014 0.03820 109800 1 100000 5.0 9.1 0.16722 0.16865 0.00143 2500 1 200000 7.3 11.5 0.15112 0.15270 0.00158 3700 1 300000 8.5 14.2 0.13661 0.13809 0.00148 3200 1 400000 11.8 18.8 0.12289 0.12589 0.00300 14600 1 500000 13.3 55.0 0.11008 0.12735 0.01727 153500 1 600000 14.2 65.4 0.09803 0.11679 0.01876 176900 1 700000 14.2 65.4 0.08729 0.10655 0.01926 192800 1 800000 17.5 65.4 0.07745 0.09683 0.01938 205700 1 900000 17.5 65.4 0.06835 0.08764 0.01929 217500 1 1000000 17.5 65.4 0.06047 0.07893 0.01846 221700 2 100000 5.4 11.9 0.05681 0.05748 0.00067 0 2 200000 11.4 18.3 0.04882 0.05013 0.00131 4000 2 300000 11.9 54.9 0.04173 0.04878 0.00705 113400 2 400000 14.2 54.9 0.03560 0.04341 0.00781 140700 2 500000 14.3 65.4 0.03044 0.03860 0.00816 163800 2 600000 17.5 65.4 0.02617 0.03410 0.00793 175000 2 700000 17.5 65.4 0.02230 0.03000 0.00770 187800 2 800000 19.8 65.4 0.01904 0.02627 0.00723 194500 2 900000 21.2 65.4 0.01622 0.02291 0.00669 198300 2 1000000 21.2 65.4 0.01387 0.01988 0.00601 195600 Note: the tolerance for (2)-(l) is 0.001, with increments of 1000 calories. -26- Table 3-Targstins idividals: Dsribiltity ad feaibility DOsirable Feasble to"e (1) (2) (3 (4) t5) (6) Are _uia9Inee Doe TO a is themr is there Any masured Does It tke snse to target lnterventfmw Scerlo of failuro to lowr utrient su*stnftil signif leant Intre- at an ndividlO scenarlo level? ant sutrisnt adeACy? houhold food Intrahouseld houshold admcy afW ss*stitutimn ftrient IneqaslIty? eer for TO activity? inqality ay I Ye yu no no no desirable, feasible 2 ye yes no no we desiroble. fesfble, wreng ag 3 yes yes no ye no desirable, feasible, e 2 4 Yu Yes no yeu yae desirable, feasible I S Ys Ye Ys no n dfirable, feaible 6 VWa we we no Ye desirable, Mntlx lnfesiblet 7 s we VWe wes no desirable, inruntz fnfmaible. wru age a we we ws dsirabte. not Infeasble 3 Notes: I ot would agree that the, wer to qetion (1) is ywe'. Na micro data sets find lowr calorie adeqacies for prechoolers sugtin that the ser to (2) Is also swe'. The tatter result coutd be true or false. Faiseness could cme from mesurnt errors on the Intake side (hae prescholers been fully weaed? do they exhibit sacking behavior?) or the reqflrnts sfde. On the other hwd, the results could be a true reflectiln of a lak of a reference rorm for a health presooler. 2. O(M) Is dilficult to aer, but a stron posibility exists for sherirg of a presd oler's food increment, or a reictlon In replar food to preschooler If the increment Is dlltd-epecif Ic. 3. 0(4): Research with this date set sugsts that inerality exists, slthough asomnt pblm men that althoug the nser to (S) Is "ye'. the answer to (4) could be 'no'. 4 0(6): The uwr to this qustion depnds an a ohole host of logistic and ost varables that w he cenw iently abstrated from, but &lSeIS mfLm. how does the anser to this qLmstion depnd on the swes to qtlens 1-5? .27- Table 4--The equivalent cost (in calories) of assuming no leakage when computing optimal upper age eligibilities . .. ... O. *.............................. O. ........... @. . . .......................... .......... .... a calorie T*e(O) T (0) P *O(T. (0)) P(T*(0)) difference equivalent interv (yrs) (yrs) (if (2) (2)-(l) gain (cals) …-- - - - - - - - - - - . - - . - - - - - -. 0 100000 5.3 2.3 0.67535 0.68160 0.00625 1000 0 200000 11.0 3.7 0.65382 0.65903 0.00521 1000 0 300000 13.1 4.8 0.63194 0.63889 0.00695 1000 0 400000 3.8 5.8 0.61042 0.61979 0.00937 1000 0 500000 4.5 6.0 0.58611 0.59167 0.00556 1000 0 600000 4.8 7.0 0.56424 0.57257 0.00833 1000 0 700000 4.4 8.8 0.54410 0.55035 0.G0625 1000 0 800000 7.3 9.4 0.52431 0.52674 0.00243 1000 0 900000 8.0 10.5 0.50382 0.50868 0.00486 1000 0 1000000 9.0 11.6 0.48403 0.48993 0.00590 1000 1 100000 12.1 5.0 0.17562 0.17630 0.00068 0 1 200000 13.9 7.3 0.15535 0.16607 0.00072 0 1 300000 13.9 8.5 0.15550 0.15652 0.00102 1000 1 400000 13.9 11.8 0.14608 0.14662 0.00054 0 1 500000 18.4 13.3 0.13702 0.13734 0.00032 0 1 600000 18.4 14.2 0.12835 0.12860 0.00025 0 1 700000 20.4 14.2 0.12010 0.12045 0.00035 0 1 800000 20.4 17.5 0.11221 0.11252 0.00031 0 1 900000 20.4 17.5 0.10470 0.10504 0.00034 0 1 1000000 20.4 17.5 0.09758 0.09793 0.00035 0 2 100000 13.9 5.4 0.06236 0.06296 0.00060 0 2 200000 18.4 11.4 0.05750 0.05762 0.00012 0 2 300000 18.4 11.9 0.05297 0.05305 0.00008 0 2 400000 18.4 14.2 0.04876 0.04886 0.00010 0 2 500000 18.4 14.3 0.04485 0.04499 0.00014 0 2 600000 18.4 17.5 0.04123 0.04131 0.00008 0 2 700000 18.4 17.5 0.03787 0.03796 0.00009 0 2 800000 18.4 19.8 0.03477 0.03487 0.00010 0 2 900000 18.4 21.2 0.03190 0.03200 0.00010 0 2 1000000 18.4 21.2 0.02927 0.02935 0.00008 0 Note: the tolerance for (2)-(l) is 0.001, with increments of 1000 calories. -28- REFERENCES Akerlof, G. (1978). "The Economics of 'Tagging' as Applied to the Optimal Income Tax, Welfare Programs, and Manpower Planning". American Economic Review, Vol. 25. Alderman, H. (1990). "Food Subsidies and the Poor". Chapter in Essays in Poverty. Equity and Growth, Eds. Lal, D. and Myint, H. Washington, D.C.: Washington, D.C.: World Bank. Beaton, G. and Ghassemi, H. (1982). "Supplementary Feeding Programs for Young Children in Developing Countries". American Journal of Cl-inical Nutrition, No. 34 (supplement). Bouis, H. and Haddad, L. (1990). Agricultural Commercialization Nutrition and the Rural Poor. Boulder, CO: Lynne Rienner Press. Foster, J., Greer, J. and Thorbecke, E. (1984). "A Class of Decomposable Poverty Measures". Econometrica, vol. 52 (3). Haddad, L. and Kanbur, R. (1990a). "How Serious is the Neglect of Intrahousehold Inequality". Economic Journal vol. 100. September. Haddad, L. and Kanbur, R. (1990b). "Are Better Off Households More Unequal or Less Unequal?". PRE Working Paper No. 373, The World Bank. Kakwani, N. (1989). "On Measuring Undernutrition". Oxford Economic Papers. Kanbur, R. (1987). "Measurement and Alleviation of Poverty". IE Staff Papr. Kennedy, E. and Alderman, H. (1987). "Comparative Analyses of Nutritional Effectiveness of Food Subsidies and other Food-Related Interventions". IFPRI-WHO-UNICEF. Washington, D.C.: International Food Policy Research Institute. Pfefferman, G. and Griffin, C. (1989). Nutrition and Health Programs in Latin America; Targeting Social ExRenditures. Washington, D.C.: World Bank. -29- Ravallion, M. (1989). "Land-contingent Poverty Alleviation Schemes*. Worel DeveloDmmnt. Vol. 17. Ravallion, M. (1990). 'Does Undernutrition Respond to Income and Prices?'. World Bank, processed. Selten, R. (1978). "The Equity Principle in Economic Behaviour*. In Dcision Ther and Social Ethics, eds H.W. Gottinger and W. Leinfellner, Dordrecht: D. Reidel. Timmons, R., Miller, R. and Drake, W. (1983). 'Targeting: A Means to Better Intervention." Report submitted to the U.S. Agency for International Development. Ann Arbour, Michigan: Conmunity Systems Foundation. United Nations (1986). "How to Weigh and Measure Children'. New York: National Household Survey Capability Programme. PRE Working Paer Series Contact MeL Author DLe for p2aper WPS662 Trends in Social Indicators and Jacques van der Gaag May 1991 B. Rosa Social Sector Financing Elene Makonnen 33751 Pierre Englebert WPS663 Bank Holdirng Companies: A Better Samuel I-. Tal.ey May 1991 7 Seguis Structure for Conducting Universal 37665 Banking? WPS664 Should Employee Participation Be Barbara W. Lee May 1991 G Oriaca-Tetteh Part of Privatization? 37646 WPS665 Microeconomic Distortions: Static Ramon Lopez May 1991 WDR Office Losses and their Effect on the 31393 Efficiency of Investment WPS666 Agriculture and the Transition to the Karen M. Brooks May 1991 C. Spooner Market Jose Luis Guasch 30464 Avishay Braverman Csaba Csaki WPS667 VERs Under Imperfect Competition Jaime de Melo May 1991 D. Ballantyne and Foreign Direct Investment David Tarr 337947 A Case Study of the U.S.-Japan Auto VER WPS668 Inflation Tax and Deficit Financing Hinh T. Dinh May 1991 L. Santano in Egypt Marcelo Giugale 80553 WPS669 Are High Real Interest Rates Bad for Nemat Shafik May 1991 M Divino World Economic Growlh Jalaleddin Jalali 33739 WPS670 Inflation Adjustments of Financial Yaaqov Goldschmidt May 1991 C. Spooner Statements: Application of Jacob Yaron 30464 International Accounting Standard 29 WPS671 Lessons from the Heterodox Miguel A Kiguel May 1991 E.