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Determining the prevalence of calorie deficient diets in developing countries by alternative methods of measurement

Shlomo Reutlinger
The World Bank, Washington, D.C., USA

Several recent studies have attempted to assess the seriousness of malnutrition by measuring the extent to which diets of large population groups are deficient in calories. The main advantages of using these calorie-deficiency indicators are that, on a national scale, food consumption data are easier to come by than are nutritional health data, and calorie-deficiency data immediately suggest kinds and magnitudes of interventions that are needed to overcome such deficiencies.

While it would be useful to be able to measure the prevalence and extent of calorie-deficient diets, it must be noted that it is by no means clear that it is possible to do this in an unambiguous way. In this respect, the identification of the nutrition problem is not much different from the identification of, for example, the education or housing problem. It is, of course, possible to define a minimum calorie energy level for the growth and survival of human beings, whereas it is virtually impossible to define a minimum level of education or housing in the same way. But any determination of desired levels of calorie intakes involves judgements about private and social welfare objectives not much different from those under-lying recommendations for education and housing.

Ideally, a determination of the prevalence of calorie-deficient diets should be made on the basis of data describing individuals' caloric intakes and requirements. In reality, such data are not available nor are they likely to become available any time soon for sizeable populations. At present, the only data available in most instances are country average calorie intakes and country average calorie requirements. A very crude way of measuring the prevalence of calorie-deficient diets, therefore, is to construct an index, CR, that shows the extent to which the per capita calorie content of national food consumption meets per capita calorie requirements. Without knowledge about the distribution of calories consumed in the population, such estimates tell us very little about the prevalence of calorie-deficient diets, and even ranking of countries would be meaningful only if we could assume that the distribution of calories is the same for all countries.

Reutlinger and Selowsky (1) refined the measurement of the prevalence and magnitude of calorie-deficient diets by estimating the individual distribution of calorie consumption on the basis of total calories consumed by the population, income distribution data, and extraneous information about the relationship between income and food consumption. Specifically, they estimated per capita calorie intake by each income group (i) with the equations:

(1)

(2)
(3)

where is the per capita income of the i th income group, e is the income elasticity at the country's level of per capita caloric requirements, is the country's average level of calorie requirements, is the country's per capita calorie intake, and W_i is the share of the population in the i th income group. The average calorie deficit in the i th income group, , is defined as when . With this method it is possible to construct an index, CDP, that measures the share of the population whose average calorie intake is below average requirements, and another index, CD, that reflects both the prevalence and the magnitude of calorie deficiency in the population.

A shortcoming of these indices is that no account has been taken of variations in intakes and requirements among individuals in each subgroup. To the extent that, for a variety of reasons, individuals in each subgroup of the population have different intakes and requirements (and there is ample evidence that this is indeed the case), and to the extent that deviations from average intakes and requirements are not perfectly correlated, some individuals in a group that, on average, is calorie-deficient would have calorie-sufficient diets and, similarly, some individuals in a group that, on average, is calorie-sufficient, would have calorie-deficient diets (2).

FIG 1. illustrative Distributions of Individuals in Different Income Groups Experiencing a Calorie Deficit

The new indices of calorie deficiency CD* and CDP* presented in this paper take account of variations in calorie intakes and requirements among individuals. Specifically, it has been assumed that calorie intake and requirements within each income group are distributed normally, with means and and standard deviations and . Hence, for each individual in the i th income group, the calorie deficit is also distributed normally, with mean and standard deviation

(1)

where r is the coefficient of correlation between calorie intakes and requirements. Distributions for three income groups are illustrated in figure 1. The shaded area represents the probability of consuming less calories than required by an individual in the i th income group. It can be seen that even if is an unbiased estimated of , the probability of is sensitive to . Table 1 summarizes the formulae used for calculating CR, CDP, CD, CDP*, and CD*. Estimates of the various indices of calorie deficiency for 41 countries are presented in Table 2.

TABLE 1. Formulae and Definitions Used in Calculating Various Indices of Calorie Deficiency

Index of the prevalence of calorie deficiency	Formula	Definition of terms
CR		and R = country's per capita calorie consumption and requirements
CDP		Wi = proportion of population in income group I average deficit
CD
CDP*		= probability of individual with a calorie deficit in income group i
CD *		= expected calorie deficit of individuals with D > 0 in i th income group

a. is calculated as , where f(0) is the probability distribution and F(0)) is the cumulative probability distribution of Di, evaluated at Di = 0.

TABLE 2. Selected Indices of Calorie Deficiency (Mid-1960s)

For precise definition of variables, see table 1.

CDP is the proportion of the total population belonging to income groups which on average have a calorie deficit.
CDP* is the proportion of the total population having calorie deficits based on a probabilistic appraisal of individual's intakes in relation to requirements.

TABLE 3. Sensitivity of Indices of Calorie Deficiency to Income Elasticity and Calorie Requirements (1964 - 1966;

a. Calorie income elasticity is 0.30 at FAD/WHO calorie requirements.
b. Calorie income elasticity is 0.15 at FAD/WHO calorie requirements.
c. Calorie requirements are 90% of FAD/WHO requirements.

The estimates were derived using country per capita calorie intake data, country per capita requirement data reported by FAO in 1978 (3) (country differences in requirements are the consequences of differences in average body weight, temperature, and the demographic composition of the population), and income distribution data in Reutlinger and Selowsky (1). The income elasticity let the level of the country's requirement) was assumed to be 0.3 for all countries. (Analyses of household survey data in several countries have yielded calorie income elasticities as high as 0.55 [4] . in general, however, elasticities higher than 0.3 yield implausibly low and high levels of calorie intakes at low and high levels of income, when equations 1 through 3 are used to allocate the total known available calorie supply in most countries.) For estimating the new indices CD* and CDP* we assumed that the standard deviation of calorie intakes is 15 per cent of the mean intake of each income group and the standard deviation of requirements is 15 per cent of the country's mean requirement level. In order to assess the maximum error from ignoring inter-individual variations in calorie intakes and requirements, the CDP* and CD* estimates reported in table 2 are based on the assumption that the correlation between intakes and requirements is zero. In reality, it is more plausible to assume that there is a fairly high correlation between intakes and requirements within the same income group. Therefore, and also because the estimates are not seen to be sensitive to the correlation, all CDP* and CD* estimates reported in the remainder of the paper were calculated on the assumption that the correlation coefficient of intakes and requirements is 0.7.

The major noteworthy observation about the data reported in table 2 is that the estimated share of the combined population of all the countres having calorie-deficient diets is not very sensitive to whether or not variability in calorie intakes and requirements is taken into account. On average, estimates of CDP* are slightly lower than those for

CDP. The expected calorie deficit is, however, higher when variations in calorie intakes and requirements among individuals are taken into account. This is as expected, because the total deficit in each group that is, on average, in deficit remains the same by both methods, while CD does not identify a deficit for the groups that, on average, consume more than their calorie requirements and CD* does. (The Spearman Ranking Coefficient is 0.95 for CDP with CDP*, and 0.83 for CD with CD*.)

Next, we may ask how sensitive are national estimates of calorie requirements. In recalculating the indices presented in table 3, the base case is calculated on the assumption that the correlation coefficient between calorie intakes and requirements is 0.7, the calorie income elasticity is 0.3 at the level of each country's requirements, and the level of requirements is the one used by the FAO. For the case of low income elasticity, we assumed that the elasticity is 0.15. For the case of low requirements we have reduced the FAO requirements by 10 per cent.

Estimates of the prevalence of calorie deficient diets turn out to be generally not very sensitive to the calorie income elasticity, whereas, as expected, such estimates are sensitive to the assumed level of requirements. (Similarly, the estimates would also be sensitive to biased estimates of country per capita calorie consumption. Clearly, if, for instance, as some believe, food availability is under-reported, the extent of undernutrition would be significantly less than what is implied by the reported national food statistics. On the other hand, if, as others believe, food consumption is much less than food availability as reported, due to greater losses and spoilage in the marketing channels and in the home, the prevalence of calorie-deficient diets may be higher than the reported estimates.)

The expected calorie deficit is more sensitive to both the calorie income elasticity and the level of calorie requirements. For those countries in which the overall country's average calorie consumption is below average requirements (CR < 1), the lower elasticity of 0.15 increases CDP* as consumption is more equally shared, though CD* is reduced.

TABLE 4. Correlation between Indices Calculated on the Basis of Different Assumptions about Calorie Income Elasticity and Calorie Requirements

Another way of judging the degree of reliability of the estimated index for the purpose of inter-country comparisons is to observe the extent to which different assumptions made in the derivation of the index lead to changes in the ranking of countries, or to changes in relative orders of magnitude. In this regard, the correlation in coefficients reported in table 4 clearly indicates that the indices are quite reliable.

Our assessment of orders of magnitude of the prevalence and extent of calorie deficiency on a national and global scale must be interpreted and used very cautiously. The methods used to obtain estimates of the share of the population who are undernourished has been seen to be fairly reliable with respect to calorie-income elasticities and interpersonal variations in calorie intakes and requirements. The estimates are, as expected, more sensitive to the total calorie availability (or consumption) in each country than to the level of calorie requirements presumed to be critical for particular populations or sub groups in the population. It has not been our purpose to second-guess the quality of reported national food statistics and expert committees' recommendations of calorie requirements, and, therefore, a large element of uncertainty about the estimated extent of undernutrition remains inevitable. However, we can say that, subject to verification of these data, the proportion of undernourishment in the populations of developing countries is high- on the order of 40 to 60 per cent in the mid-1 960s. The expected calorie deficit (CD) usually provides a more sensitive estimate of the calorie-deficiency problem. This index reflects not only the number of people involved but also the severity of their deficit, Estimates of this index clearly show that the total calorie deficit of the deficient diets is generally small relative to total calories available and consumed in the countries, somewhere on the order of 5 to 15 per cent.

For the purpose of evaluating the impact of different income policies and for projections, the estimates derived on the basis of the method used in this study become more sensitive to income elasticities and income distributions. Therefore, while detailed studies of food demand are not needed for the purpose of assessing the extent of calorie-deficient diets at a certain point in time, such studies, even if costly, might be fully justified for the purpose of projections and evaluation of the cost effectiveness of food and income policies. An analysis of food consumption survey data from several countries in a context similar to the one used in this paper is reported by Knudsen and Scandizzo (4).

Similarly, the estimates of the number of undernourished should not be taken to mean that ail are equally undernourished and that there should be no priority target groups within this population, particularly if the capacity or willingness to do something about the problem is limited. We have seen that setting the requirement target lower by only 10 per cent reduces substantially the size of the population defined as undernourished and reduces even more significantly the overall magnitude of the food deficit. As is well known, past efforts at reaching a consensus about what constitutes a correct threshold level of calorie requirements for different populations have not been very successful. Perhaps it would be easier to reach agreement about the marginal value of additional calories at different levels of calorie intake. If the marginal value decreases sharply, it would certainly suggest that, if costs are proportionate, limited resources should be applied to the most undernourished first.

Finally, it should be obvious that estimates of the kind presented in this paper pertain to population averages. They have no predictive value for any sub-group in the population. Some groups may be exposed to more or less than average morbidity, or may require or be predisposed to more or less than average physical exertion. Also, some population groups may have a larger than average proportion of children in their midst. If the distribution of food within households is not in proportion to requirements, and particularly if, as the evidence suggests, young children in many underprivileged populations suffer relatively more deprivation, their households would need to have better distribution as well as higher calories intakes to assure adequate intakes for their children.

REFERENCES

1. S. Reutlinger, and M. Selowsky, Malnutrition and Poverty: Magnitude and Policy Options, World Bank Occasional Paper No, 23 (Johns Hopkins University Press, Baltimore, 1976).

2. J.N. Srinivasan, Malnutrition: Some Measurement and Policy Issues, World Bank Staff Working Paper No. 373 (Washington, D.C., 1980).

3. Food and Agriculture Organization of the United Nations, Fourth World Food Survey ((Rome,, 1978).

4. O. Knudsen and P.L. Scandizzo, Nutrition and Food Needs in Developing Countries, World Bank Staff Working Paper No. 328 (Washington, D.C., 1979).

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