The statistics of hunger

The statistics of hunger

The statistics of hunger Roger W. Hay The critically author commonly used production, market and supply, consumption, absolute offers and...

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The statistics of hunger

Roger W. Hay

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Roger Research House,

W.

Hay Fellow

2 1 St Giles,

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an Queen

Oxford,

Associate Elizabeth UK.

I am grateful for the help and provided by my encouragement supervisors in Oxford, Dr Keith Griffin, Warden of Queen Elizabeth House, Prof J.A.C. Brown, Institute of Economics and Statistics and Prof P. Armitage, Institute of Biomathematics. The work for this article was supported by an ESCOR grant from the UK Ministry of Overseas Development. Significant contributions have come from colleagues with whom I have worked in Africa, particularly in Ethiopia. Despite the help I have received neither Ministry the of Overseas Development nor my colleagues can be held responsible for any conceptual or other errors which may appear in this paper. The views expressed here are not necessarily those of the Ministry of Overseas Development.

’ T.R. Malthus, An Essay on the Principle of Population, Ward Lock & Co, London, 1890. Malthus postulated that there is a ‘constant tendency of all living beings to increase faster than the food supply’. In particular, he suaoested that oooulation tends to increase-% geometrical ratio (1, 2. 4, 8, 16, etc), [and] food in not more than arithmetical (1, 2, 3, 4, 5, 6, etc)‘. He acknowledged the existence of other continuedon page 244

0306-9192/78/040243-l

3 $02.00

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The first question food statistics should answer is not ‘how much food is available? but ‘how many people are hungry? The literature of economic development, and particularly writing relating to food and food supply, reflects two main preoccupations. The first is an attempt to analyze the dynamics of economic growth (as opposed to a static analysis of the state of an economl 1in order to provide a more rational basis for policy decisions. Time series analysis and forecasting have been given added emphasis recently by those who hold the Malthusian view regarding the inevitable consequences of a linear growth in production and an exponential growth in population. l The second preoccupation is with distributional aspects of economic growth arising from the evident failure, in the short term at least, of growth per se to alleviate hunger and poverty. Most observers would agree that some of the so-called ‘developing countries’ have achieved spectacular rates of economic growth in the last two decades, but many would argue that this has not resulted in an acceptable reduction in the number of people who are poor and hungry within those countries .* There is less unanimity about why this should be so and about the extent to which further increases in production will benefit those who are less well off. The debate has produced three main schools of thought. There are those who believe that the desirable and almost inevitable process of economic growth will, and must, continue but that a reduction in poverty is more of a bonus than an objective. They argue that, in any event, some of the poorer are likely to be better off as the benefits of growth ‘trickle down’ to them.3 There are those who believe that the initial period of rapid growth is, of course, accompanied by an increasing disparity between those who have and those who have not, but that a high rate of economic growth is in the best interests of the poor because in the longer term they will benefit as redistribution of the fruits of growth occur. Evidence from the history of economic development in Europe is often quoted to support this argument. It is sometimes known as Kuznet’s hypothesis and it has received considerable publicity in recent times.4 Finally, there are those who believe that poverty and hunger are morally unacceptable and that active, and if necessary, politically unpopular steps should be taken in order to ensure that resources are more evenly distributed both within and between countries.5 Within the general framework provided by this discussion, food has received considerable attention. Opinion is widely divided both as to

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continued from page 243 ‘checks’ on population growth but considered that these would nat be sufficient to avert famine. 2 Keith Griffin and Azizur Rahman Khan; *Poverty in the Third World: ugly facts and fancy models’. WorldDevelopment, Vol6, No 3,1978. 3 Behind this

argument is the usually unspoken corollary that if necessary the poorest may have to 90 to the wall (euphem~sticalj~ called ‘triage’) if this is the unavoidable consequence of achieving stabie potiticai, economic or ecological equilibrium. See for example, Garret Hardin, ‘Living on a lifeboat, Bioscience, October 1974. *See for example, H. Chenery et af, ~e~~stri~~tion with Gruwtb, WorId Bank and University of Sussex Institute of Development Studies, Oxford, 1974. While the hypothesis (that in the long run, growth results in a more equitable distribution of resources) has attracted considerable attention, the theory has its critics. The kterarure is too extensive to review here but a recent appraisal is given in Witfred Beckerman ‘Some reflections on redistribution with growrh’, Wclrld Deveiopment, Voi 5, No 8. 1977. 6 Keith Griffin has written extensively on this topic. See for example, ‘Increasing poverty and changing ideas about development strategies: Deva~e~me~t and Change, Vol8, 1977: and ‘Poverty in the Third World: ugly facts and fancy models’, op tit, Ref 2. In this connection, Atkinson has developed a measure of how much a Society is prepared to lose in order FO carry out a unit transfer from rich FO poor. It is described in A.B. Atkinson, The Economics of Inequality, Clarendon Press, Oxford. 1975. These ideas aw pertinent to basic stratagies for ensuring that people have enough to eat.

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the suficiency of the present world food supply and aiso as to the distribution of the benefits which are likely to accrue from the present trend of fairly substantial increases in agricultural efficiency. Although there is no convincing evidence either way, in the short term at least, the notion that increasing world food production will result in a significant reduction in hunger seems hard to support. However, one’s level of despair about the longer term future depends on the dist~bu~onal theory one adopts and on the type of analysis used to make future projections. Whatever the theory, the statistics commonly used as the basis for estimates and projections are almost invariably ‘per caput’ indices which rest on the assumption that everyone has the same access to food resources. This seems to be quite remarkable in view of the abundant evidence to the contrary. It is at least partially understandable, for two reasons. The first is the relative paucity of available data disaggregated to household or individual level. It must be said, however, that most sample survey data start off at this level but are subsequently subjected to the veritable statistical itch to aggregate them and calculate their ‘mean’. The second reason is that, while simple numerical and graphical techniques exist to display disaggregated data, the speci~cation of the frequency functions they represent is rather complicated and, until quite recently, there was no practical method of inserting these functions in anything but the simplest linear model. Relatively little attention has been paid to more recent computational techniques which are now well established statistical tools. Even more surprisingly, in view of the well publicized inequalities between rich and poor, comparisons between population groups and between countries are often still based on per caput food availability estimates with little or no caveat on the limitations of the methods used or the lack of significance of the results obtained. This article will review the conventional food statistics, to demons~ate their general inadequacy both for the assessment of current household food supply and for forecasting future trends in the prevalence of malnutrition. In the second part of the article, alternative methods of determining food availability will be discussed.

Conventional estimates of current food supply Aggregate estimates of production, market supply, demand, requirements and consumption are commonly used, either singly or in combination, to assess the amount of food available for consumption in a region or a country. These measures are also commonly used to compare country with country, or area with area and to estimate changes in food supply over time. Since the beginning of time the usual way of presenting the results of agricultural surveys has been as estimates of the total production of each crop in one year, for the country as a whole, or, if the design of the survey permits, for each province or region. While an estimate of production is the first essential step in the assessment of food supply this measure is no guide in itself to the availability of food at family level. To be at all useful it is important to know whether allowance has FOOD POLICY November 1978

The statistics 6 In Ethiopia, for example, where actual production is estimated annually, the amount reaching the market is probably less than a quarter of this (personal estimate) so that quite misleading calculations would from a result confusion between ‘production’ and ‘market supply’. ‘See, for example, an excellent and sympathetic review of the subject in: D.G.R. Belshaw Crop production data in Uganda, Development Studies Discussion paper No 7, University of East Anglia, Norwich, November 1975. 8 Two recent FAO documents are sufficient to illustrate the ubiquitous nature of this statistic: National Methods of Collecting Agricultural Statistics, Vol II, FAO, Rome 1975; and Guide to Statistics of Livestock and Livestock Products (provisional), FAO, Rome 1976. However, FAO merely reflects conventional wisdom and should not be held solely responsible !

9 For

example, in a review of current methods of collecting national agricultural statistics which covered a substantial part the developing world, National of Methods of Collectina Aaricultural Statistics, Ibid, attention-was drawn to the important improvements in technique, relevance, flexibility and services which had occurred since the previous review. But no mention was made either of the necessity to assess the relationship between food oroduction and household supply or of the countries which are attempting to do so. The author recognizes that FAO technical staff are deeply concerned about the state of food statistics. However, an opportunity was lost here and elsewhere (for example in the proceedings of the World Food Conference, 1974) to emphasize the misleading nature of per caput production statistics. lo Fourth World Food Survey, FAO, Rome, 1977 for example, presents no information of this nature. ” Full markets, incidentally, can be compatible with a high prevalence of starvation, as was found in Nigeria during the civil war (personal observation). l2 Leonard Joy in Food and Nutrition Planning. IDS Reprint No 10, Institute of Development Studies, University of Sussex, Brighton, 1973. Joy asserted here that people starve because they cannot buy food. See also Shlomo Reutlinger, ‘Malnutrition: a poverty or a food problem’, World Development, Vol 5. No 8,1977. I3In a recent paper, Sen proposed the term ‘exchange entitlement’ as a measure of household purchasing power. In analyzing the causes of starvation during the Bengal famine in 1943 he points out that the chief disturbance was not in supply but in the price of food which rose as a result of aggregate demand factors. The wage rates of the poor failed to keep pace with this rise causing a relative fall in their ‘exchange entitlements’. Sen thus continuedonpage

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been made for field, storage and transport losses which vary enormously with local practices and may amount to more than 50% over the course of the year. It is even more important to know what exactly has been estimated; that is, production or supply to the market.6 Recently considerable criticism has been levelled at the accuracy of field methodology employed in many agricultural surveys.’ While much of this criticism is valid, the difficulties in obtaining statistically reliable data from small holdings, many of which practise mixed cropping, should not be underestimated. In any event our concern here is not with methodological inaccuracies but with conceptual problems. Measures of production are valuable and necessary but aggregate measures of national production by commodity taken alone are all but meaningless for estimating household food supply unless the number of people depending on this production is taken into account and the way in which the production is divided among the people is known. The commonly recommended statistic, production per caput,” takes care of the problem of population but contributes nothing to an estimate of food supply at household level because it assumes that everyone gets an equal share. Traditional agricultural statistical methods simply do not produce the kind of information required for assessing the adequacy of household food supply. Furthermore, institutions which have a responsibility for providing technical guidance to developing countries frequently fail to emphasize the importance of using the information provided by agricultural surveys in this way.’ Measures of market supply Estimates of the amount of food entering the market are usually more difficult to obtain than measures of production and (perhaps for this reason) are published less often. lo While it is relatively easy to estimate imports and the amount of domestic production which enters the market through official channels, it is uncommonly difficult to estimate informal transactions, black market dealings and leaks across the border to a neighbouring state. Despite its problems, the estimation of market supply can be an important indicator of food availability. However, as people who grow their own food do not depend on marketed production, the use of the measure should certainly be restricted to estimating the amount of food available to ‘market-dependent’ groups. Even so, per caput statistics on market supply are no more reliable than estimates of per caput production, as marketed food is not distributed equally to purchasing households.” Measures of demand The measurement of demand for food by households is a relatively recent addition to the tools of the food statistician. Joy,lz among others, drew attention to its importance early in the 1970s. The important distinction between aggregate demand and the purchasing power of an individual household is now generally recognized. Poor people do not significantly influence aggregate demand. Aggregate demand may be estimated, but the way aggregate demand is distributed within the population is more significant. Household demand may be deduced from data on either household income or, more accurately, household expenditure on food.13

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The statistics

of hunger The statistics of household demand invariably demonstrate a skew in the distribution of the individual household’s ability to compete in the market for food. The skew is indicative of one of the chief causes of hunger in urban areas and among the landless rural poor. Measures of household demand are, however, only appropriate for households which buy food. Neither retail food price statistics nor estimates of household demand have any relevance to families which grow or herd their own food supply.

continued from

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distinguishes clearly between aggregate demand for food and an individual household’s purchasing power. See Amartya Sen ‘Starvation and exchange entitlements and its application to the Great Bengal Famine’, Cambridge Journal of Economics, Vol 1, No 1, 1977. 14The term was coined by McLaren in D.S. McLaren: ‘The great protein fiasco’, Lancet. 13 July 1974. This paper caused something of a stir at the time but its message that the importance of protein deficiency had been overestimated is now generally accepted. 15This is the most recent WHO/FAO recommendation referred to, in Howard Rush, ei a/ ‘World food futures’, Food Policy. Vol 3. No 2, 1978. 16See, for example, sources quoted by Howard Rush et al, op tit, Ref 15. I7 However, the dilemma will not be resolved either by recommending that minimum per caput requirements should be met by production (because this assumes that everyone gets an equal share) or by recommending that a notional allowance should be made to cover the skew in consumption. Adding a fixed allowance implies in the first place that the structures and distributional profile of food supply in every country are the same, and second, that an increase in agricultural production will be distributed in a similar manner. There is no evidence distributional that the to suggest configuration of food consumption is the same in all developing countries and we simply do not know how an increase in agricultural production is likely to be distributed in the future. I8 Thomas T. Poleman, ‘World food: myth and reality’, World Development, Vol 5, Nos 5-7, 1977. ISThe assessment of nutritional status reflect the provides indices which food both result of biological and disease. There is consumption therefore no simple linear relationship between the intake of a particular nutrient and an index of nutritional status. ln in measurable changes addition, nutritional status tend to lag behind intake. However in food changes nutritional status data are much easier to collect than food intake data.

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Measures of requirements Man’s requirements for food seems to be of such a fundamental nature that one would have thought that an accurate estimate of minimum energy and protein requirements would have been available by now. Yet the debate on ‘what is enough’ continues. The discussion has been compounded by the understandable caution of early WHO/FAO expert committees not to underestimate minimum requirements. These earlier generous estimates of requirements, which were at least partly responsible for the ‘protein fiasc0’i4 of the 196Os, have diverted attention from the major problem, which is not whether the average daily requirement is 2354’” or 3000 kilocalories but how the available food energy (and protein, vitamins and everything else) is divided among the people of a country. When estimates of minimum food requirements are translated into minimum production requirements strange things begin to happen. Thus, although 20% was added to the minimum production requirements recommended by earlier FAO reports in recognition of the fact that consumption tends to be skewed, it has been interpreted by some to mean that the national production which was recommended was actually enough to feed four times the populations of some countries.16 The fact is that given the distribution of food within some countries, the production of four times the ‘minimum average requirements’ would still not feed everyone.” Measures of consumption The methodology required for estimating individual and household consumption is both costly and time consuming. At least among agricultural statisticians, this measurement has the reputation of being not only high in cost but also low in reliability. If, on the other hand, estimates of food consumed are deduced from estimates of ‘production plus imports minus exports and losses’ the result is merely a ‘residual accumulation of errors’;18 a direct assessment of dietary intake is more desirable.i9 Most food consumption surveys generate estimates of individual dietary intakes. A few content themselves with estimating family consumption. Due, no doubt, to their cost, relatively few national surveys of this kind have been carried out. However, the results have been presented in most cases as frequency histograms so that it is possible to estimate the prevalence of inadequate food consumption in the communities studied. This is the correct method of presentation as any attempt to aggregate data of this kind, and present them as mean values would reduce the usefulness of the survey to zero. Composite and derived measures Per caput estimates have been discussed at length above. These constitute the most commonly derived food supply statistics. It should

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be clear by now that measures of this kind have very little value in assessing the magnitude of food shortage in a community. Commodity estimates are frequently translated into units of energy or protein equivalents. In itself this seems to be a useful means of obtaining a direct comparison between supply and nutrient requirements. The ‘food balance sheet’ is a common method of comparing supply and requirements by expressing both as per caput estimates, usually in terms of energy and protein. This method has very little to offer. First, it relies on the assumption, albeit implicitly, that everyone has an equal share of the available food. Secondly, the ‘balance’ between supply requirements is equivalent to subtracting one large number from another (both full of accumulated errors) to leave a small number in which all the errors reside. The fact that the exercise is tedious is no criticism, because there is no simple way of estimating how many people are hungry, but a tedious method which leads to spurious results would seem to be a waste of scarce resources. It is incorrect, therefore, and unfair to rank countries according to the results of food balance sheet exercises, as is frequently done by international agencies.20

Conventional estimates of future food supply

virtually 2o Furthermore, a identical method is used to extrapolate national results to a global level. In a recent paper, Poleman reviews the results of World Food Budget exercises, World Food Surveys and Food Balance Sheets since 1946. Earlier despondency has given way to cautious optimism about the state of the world food economy on the basis of these estimates. Poleman’s review is rightly critical of their accuracy. He writes: ‘It is common to assert that global supplies are sufficient to feed all. Would matters of that our ignorance on distribution were equally publicized!’ Poleman feels, in general, that the situation is less gloomy than many would suppose. He may be right but this author must remain agnostic on the grounds of insufficient evidence until more is known about who has access to these supplies. See Thomas T. Poleman, op cir, Ref 18. See particularly the 1962 and 1970 World Food Budgets (US Department of Agriculture, Economic Research Service), the World Food Surveys 1946, 1952 and 1963 (FAO), but nor the Fourth World Food Survey of 1977. See also, ‘Food balance sheets and world food supplies’ Nutrition Newsletter, FAO, Rome, AprilJune, 1973; and ‘Assessment of the world food situation, present and future’, Item 8 of the provisional agenda, World Food Conference, 1974. 2’ Howard Rush et al. op cit. Ref 15.

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The conceptual and methodological errors inherent in conventional methods of assessing the status of current food supplies are compounded when future projections are attempted. A review of this subject has been recently undertaken by Howard Rush, Pauline Marstrand and John Gribbin, whose work has been summarized in a recent article.*’ They cover many of the points mentioned here. The new element which enters the equation when attempts are made to forecast the prevalence of hunger in the future is the impossibility of predicting the way the distribution of supply will change as production increases. There is very little information available about the way the supply of any commodity to households has changed in Third World countries during their recent period of explosive economic growth, so that any forecasts of household food supply must necessarily be speculative. If the Kuznet hypothesis is correct, an initial growth in production will result in increasing numbers of people being hungry but eventually better standards of nutrition can be expected for all. Thus, for countries on the downward slope of the ‘U-curve’ the nutritional status of the urban poor and the rural landless are likely to deteriorate in the short term. For countries already on the upward slope an improvement can be expected as the redistribution phase begins. For the reasons given above, information is simply not available to test this hypothesis. The other distributional theories summarized above leave one either consolidating one’s position in the ‘life-boat’ of those who are assured future food supplies, or extremely anxious to ensure that pressure is brought to bear on policy makers and administrators to seek ways of redistributing existing supplies and (perhaps more importantly) the means of production. At least one method of doing this is to ensure that planners know the truth about the extent of the food problem and its causes. This section would not be complete without a reference to the most

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The statistics of hunger ”

FAO,

op cit. Ref

10.

23 The beta type frequency function referred to here and the gamma and lognormal functions mentioned later in the article (Ref 29) are mathematical expressions defining families of curves which might be obtained from histograms showing the frequency with which different levels of household supply are observed in a sample population. In fact the functions mentioned are a few examples from a large array of frequency (or probability density) functions which have been fitted to data of various types. The most common is the so-called normal or Guassian frequency function which is symmetrical and forms the basis of much statistical theory. The point is that the distribution of many welfare indicators including food and income is ‘normally’ neither even nor Guassian. 24This section is in the nature of a preliminary communication. The methods proposed appear to be theoretically sound but have not been fully tested in practice. Further investigation is underway and a more complete technical description is in preparation. The elements of the method described in this section were developed as a result of observing the patent failure of conventional techniques to identify and quantify the magnitude of food shortages which occurred in Ethiopia between 1974 and 1977. During that period the author was technical advisor to a government programme designed to monitor food supply. I am happy to pay tribute to the practical technical and enormous made by my Ethiopian contribution colleagues to the ideas which are summarized in this section. The main parts of this method are being applied by and Nutrition Ethiopian Food the Surveillance Programme although, as further testing and noted, already development are required before its general applicability is confirmed. Further information about the operation of this available from the Programme is Coordinator, PO Box 5686, Addis Ababa. 25 Roger W. Hay, ‘The concept of food supply system -with special reference to the management of famine’, presented to the AAAS Symposium, ‘The Ecology of Famine’, held in Boston, MA, February 1976 (in Ecology of Food and Nutrition, Vol 7, 1978, pages 65-72). The account given here is necessarily brief. In fact the classification by ‘mode of food acquisition’ may be used as the starting point for a systematic analysis of food problems for the design of food monitoring systems and for planning food management methods. 25 Although this classification differs from by method of production a grouping because it focuses on the means of obtaining food, subsistence food supply systems may be subclassified according to their mode of production, eg cropping, contrast, fishing. In herding and households forming a market dependent food supply system may be subclassified continued on page 250

recent World Food Survey. 22 In the preface to this important report, attention is drawn to the recent significant increase in world food production and to the slighter but still significant increase in per caput production. However, to the great credit of FAO, it devotes an entire section to identifying and estimating the number of people who do not have enough to eat. It emphasizes not only the differences in the amount of food available in different countries but also the variations in the amount of food available to different classes of people within countries. In addition, it presents the results of an interesting exercise in which national food supplies (mean per caput estimates) have been ‘distributed’ in the form of beta-type frequency functions23 among the people of a few selected countries. It is this type of approach which will be pursued in the next section.

Alternative approach to food statistics In the first section of this article commonly used methods of assessing food supply have been reviewed. Their chief defects appear to be: 0

0 0

The conceptual problems associated with the use of inappropriate indicators - for example, indicators of market supply and demand for groups who grow their own food. The statistical problems associated with measures which rely on mean values or per caput estimates. The methodological problems of collecting data under difficult conditions.

This section is devoted to describing an analytical approach to the estimation of household level food s~pply.~~ It relies on conventional categories of data and data collecting methods but, throughout the processes of aggregation, maintains emphasis on households and the adequacy of food supply at household level. The method has three components: (a) a classification of households according to their mode of food acquisition; (b) the aggregation of data within these classes to produce an estimate of food supply distribution; and (c) an analysis of food flows within and between these classes of households taking into account exports and imports.

Classification of households People either grow their food, herd it, hunt it or buy it. It would therefore seem to be reasonable to classify households according to the way in which they obtain their food. A group of households which obtain food in a similar manner forms, or depends on, a ‘food supply system’.2S There are two main categories of food supply system: ‘subsistence’ and ‘market-dependent’ although ‘mixed’ systems are often found which combine the production of food for home consumption with regular market exchange.26 The classification of households by food supply system offers a method of selecting the appropriate indicators of their food supply. The main point to note is the choice of method for estimating flows of food to households from the market and from production. Where subsistence food production is common it is a mistake to assume either that total production enters the market or that indicators of

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The statistics o/hunger 2 _

supply and demand have the same relevance to subsistence households as to those which depend on market supply.” market

Frequency function

B

2 0.3 2 z 0.2

Aggregation

0” 8”’ t

I

Product?m 2 pe:holding 56 hmtsl

P

I 1 I 1 123456 ProductIon per holding(umts)

I

L

I

I

-F

1

0.2 04 0.6 0.6 I Rank number stondordtzed for N=I

Figure

Illustration

1.

distribution

functions

food production dependent

of (for

‘A

three

example,

per holding in a crop-

subsistence

food

supply

system).

Figure

2. Order function

food production

representing

per holding in a crop-

dependent subsistence food supply system (p = F -l(R)). Minimum required

level

represented holdings minimum by which

of

by

production

p =

c.

producing required these

Number less

(c)

of than

is r. Total amount

holdings

are deficient

shown by shaded area.

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Although the classification of households by food supply system results in a certain homogeneity of food supply pattern, it does not imply that all households have the same amount of food. In order to determine ‘how many’ households have ‘how much’ food, the data obtained from one food supply should be processed to show the distribution of supply within the system. It can easily be shown that there is not a fixed relationship between the mean value of a variable and a specified fractile of a population, and that the proportion of a sample falling below a specified value can only be deduced from the mean if the parameters governing the distribution of the variable have also been specified. Therefore, in order to determine analytically how many people have how much food, the distribution of food or food-producing factors must be known. Alternatively, the data from a sample survey may be displayed as a histogram. If it is possible to specify the frequency function which fits this histogram best, it can be used for further calculations. The example presented in the FAO World Food Surve_P is based on this method. In this case a beta-type frequency function was used.29 The conventional frequency function flex])) shows the distribution of people but not the distribution of commodities. Thus the true deficit or surplus of food available cannot be calculated directly from this function. A derived frequency function, related to the first moment of the distribution, (xfo), may be used to show the distribution of commodities by households but neither of these functions is particularly amenable to manipulation.30 For these reasons an alternative function is proposed for analyzing data obtained from a food supply system. This is the order function which is constructed by graphing the values of the indicator being considered (say production per holding in a crop-dependent subsistence food supply system) ranked in order of magnitude. Thus suppose, for example, data is obtained on crop production per holding (p) from a sample of n holdings and is plotted on the vertical axis with the rank (R = I to n) on the horizontal axis. The result can be represented by an increasing function of the form shown in Figure 1. The total production from the sample will be represented by the area under the graph. Suppose now that c is the critical minimum level of production required for subsistence by one household. This may be plotted on the same axis as a line whose equation is p = c (see Figure 2). The number of holdings which produce less than amount c can be read off the graph projecting onto the horizontal axis the point where the line p = c intersects the graph of production per household, say at r. The amount produced by the holdings on which production is inadequate is then represented by the area under the graph to the left of r. The amount by which their production falls short of the minimum required for subsistence is represented by the area between the graph and the line, p = c, to the left of r. It can be shown that this function is, in fact, the inverse of the cumulative frequency function F(p) representing the number of

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by occupation, income or another conventional socioeconomic parameter. An alternative, probably better, means of subclassifying food supply systems is by ‘staple food type’. 27This seems to be almost self-evident; and yet it is still thought by some that imported food (calculated no doubt to make up a food balance sheet deficit) will ease a food shortage affecting people whose mode of food acauisition is, for example, subsistence cropping. 28 FAO. OD cit. Ref 10. *¶ Others’might consider the use of a lognormal or gamma function but the imoortant ooint is that each country is likely to have a different distributional profile, making a country by country (indeed, food SUDDIV system bv food supply system) approach preferable.. 30A good summary of conventional techniaues for distributional analvsis is given in H.P Miller, Rich Man, Poor Man (Appendix B), Thomas V. Cromwell Co, 1971. The topic under New York, discussion here is the analysis of the distribution of income but all of the techniques described can be applied to the analysis of the distribution of food. A more technical survey is provided by Cornelius P.A. Bartels in Economic Aspects of Regional Welfare, Income Distribution and Unemolovment. Niihoff. Leiden, 1977. Also, compare the method proposed here with the approach to the analysis of income distribution suggested in J. Pen, Income Distribution, Pelican Books, London, 1976. It seems curious that these well-known economic tools are rarely mentioned in discussions about the analysis of food supply. 31In order to illustrate the flexibility of the the example of data order function, obtained from a hypothetical cropping food supply system has been pursued. However, the method may be applied equally well to data from a livestockdependent food supply system or to the disposal of income from a group Of comprising a markethouseholds dependent food supply system. 32 If, for convenience, the frequency function corresponding to a given order function is required, it may be obtained (given the necessary computing facilities) by transforming the appropriate order function into a cumulative distribution function and differentiating. The example given by no means exhausts the possibilities offered by the order function. In fact there seems to be no reason why it should not be used in models defining the processes involved in food production, distribution and consumption including the effects of policies designed to redistribute food assets more evenly within and between food supply systems.

250

holdings producing less than or equal to each level of output. The order function can therefore be obtained either by direct graphical methods or by inverting the cumulative frequency function and rotating it through 90% about the origin. More formally, if the order function represents a ranking of production (p), where F(j) is the cumulative distribution function, thenp = F-‘(R); and in the example: total production

= 7

F

-I

(R)

or

dR

0

total production

= i

F - ’ CR)

R=l

The number producing less than required can be represented r = F(c) (where c = minimum requirement); and the

x

production

deficit = 3

I

\

production

-1

{C - F- ’

as:

,

or

(R))dR

I

deficit = i

This function is thus useful for expressing both ‘how many’ (people) and ‘how much’ (commodities), the two most important questions concerned with the estimation of food availability at household level. Order functions may be used to show the consecutive components of the food chain of croppers whose food comes partly from their own production and partly from the market (mixed food supply system).31 Although the computational problems have not been thoroughly investigated, theoretically at least, each function shown may be derived from the one before if the technical relationship linking the two can be specified. For example, the following sequence of events might be analyzed using order functions: (a) the distribution of forecasted production per holding from estimated productive area per holding and forecasted yield, the expected yield being itself a function of the size of the holding; (b) the distribution of the disposal of production between consumption, seed and sales, given the appropriate supply and consumption functions; (c) the distribution of income generated by these sales, at a given price; and (d) the distribution of total (grown plus bought, minus losses and seed) food resources per household. Because aggregate production, aggregate market supply, aggregate household income and aggregate household food demand are all simple integrals of the appropriate order functions, the statistics arising from them provide links’between micro- and macro-indicators of food ~upply.~* So far we have considered a classification of households which establishes a certain homogeneity of mode of food acquisition and the aggregation of data from one such food supply system. The final

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of data systems in a country or region.

from

a number

of food supply

The food accounting matrix

33 It is not possible here to describe this useful technique in detail. For a straightforward account see C.C. Greenfield, ‘Social accounting matrices and developing countries’, Statistical News, No 41, May 1975. An example of the way in which SAMs may be applied to planning in a developing economy, in this case Sri Lanka, is given in Graham Pyatt and Erik Thorbecke, Planning for a Better Future, International Labour Organization, Geneva, 1976. Space does not permit a survey of the growing literature and experience of this technique. 34The units of measurement employed can either be units of weight, units of nutritional value (energy and protein) or units of money value. Suitably constructed conversion matrices would allow interchange between these units at will.

The technique of social accounting has become a recognized way of estimating the flows of commodities within an economy.33 A social accounting matrix (SAM) is derived from double entry accounting and display flows of commodities intersecting rows and columns of accounts in which receipts are shown in the rows and expenditures in corresponding columns. A summary of food commodity flows within and between food supply systems may be shown by using a similar technique here called a ‘food accounting matrix’ (FAM). The flows of food within a country are indicated by debiting the account of the producer, seller or donor by the amount of the commodity and crediting a like amount to the account of the recipient. A FAM differs from a conventional social accounting matrix in that its purpose is restricted to showing the flow of food to nutritional demand rather than flow of all commodities to value demand.34 A simplified scheme is shown in Figure 3. In order to clarify the principles involved, a number of important accounts have been omitted from this table and the row accounts have been shown separately from the column accounts. Three food supply systems have been chosen as examples. The first (FSS I) is a subsistence cropping food supply system which has no

F 1

Figure accounting

3a. matrix

accounts

(disposal

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I

2

3

4

5

I

I 6

I

J

food column

a

of food).

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The statistics of hunger

Figure accounting accounts

3b.

Simplified matrix

(receipts

(FAM):

food row

b

of food).

connection with the market so that food flows directly from production to consumption. The second (FSS II) is a mixed subsistence/market-dependent food supply system, and the third (FSS III) depends entirely on the market so that all the food consumed by the households in this food supply system is bought. The accounts in the table are divided into production accounts, appropriation accounts and accumulation accounts, as is conventional with social accounting matrices. The production accounts show the amount and disposal of what is produced. The appropriation accounts show the flow of food commodities through intermediate institutions to households where the food is consumed. In Figure 3 the only appropriation accounts shown are for the market and for households, although in a proper FAM table accounts would be allocated to any institution which serves as a channel for food or a donor of food. (See, for example, the scheme shown in Figure 4.) The accumulation accounts are used to show changes in stock, losses or balances. Considering first the column accounts shown in Figure 3a, it will be seen that the amount produced is entered either in the market row or the household row according to whether it is destined for sale or for home consumption. The addition of an estimate of losses accounts for the disposal of the total food production of the country. The market account shows the amount of food sold to households which, together with the change in traders’ stocks, gives the total food leaving the market during the accounting period. The household column accounts show how much food is consumed by each food supply

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35The array shown in Figure 4 is not intended to represent a particular country. indeed the method is perfectly general and accounts can be allocated to any institution which makes a significant contribution to channelling food toward the households which consume it. The matrix can also be extended to include non-food agricultural production if this provides an important source of revenue for farmers in, say FSS II. If an analysis of expenditure on food is required, the commodity accounts which make up the FAM table may be augmented by the appropriate financial accounts. The most important of these would be household disposable income in a row account and expenditure on food and expenditure on other commodities in a column account. In Figure 4, household accounts have been left open to indicate that they could be used for this purpose. 36 Interesting examples of the usefulness of simulation techniques are described by Thomas J. Manetsch, ‘On the role of systems analysis in aiding countries facing acute food shortages’ Man and Cybernetics SMC-7,4.1977. and M.H. Lorstad. ‘Nutrition planning through gaming’, Food and Nutrition. No 3, FAO, Rome, 1976.

Figure 4. Food accounting

matrix.

Abbreviations: Trans = transactions; Comm = commodities: Biol = biological: Req = required: Prod = production: Exp = export: Dem = demand; Dom = domestic; Nt = nett; Govt = government: Hh = household: Cons = consumption.

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system which, together with an estimate of changes in household stocks, gives the total food flowing to households during the accounting period. Turning now to the row accounts shown in Figure 3b, where the receipts of food are shown, it will be seen that the total of each row account is identical to that of the corresponding column. The amount of food consumed, plus the amount saved from production, gives total food production; the amount entering the market is simply transferred to its corresponding total column, as there are no further additions; and the household row shows the total food received by each food supply system. The total changes in stock for all accounts plus an estimate of losses gives the difference between the amount produced and the amount consumed during the accounting period. A more elaborate array is shown in Figure 4. The same three food supply systems are shown, but in this case the production accounts have been divided between ‘institutions’ and ‘commodities’ to show the production of how much of each commodity is produced by each institution. Food may be produced by food supply systems, by the government on state farms and by commercial food producing enterprises. Each of these ‘productive institutions’ would be allocated an account of its own. The appropriation accounts have also been elaborated to include the government, which may act either as a trader or as a donor, and to include aid organizations and the ‘rest of the world’ so that imports and exports can be shown. Each of these accounts should be subdivided to show the major types of food which flow through them. Household accounts have also been divided into commodity accounts and biological accounts so that food consumed can be shown as a debit on the household commodity accounts, and as a receipt on the household biological accounts. In this way food intakes can be compared with nutritional requirements.35 An array such as Figure 4 shows the possible routes by which food finds its way to the households of each food supply system but it still does not show how much food each household has. However, the amount of food shown in the cells of the household accounts all represent integrals of order functions. Thus if the distributional configuration of the data is known, it is possible to express the cell totals as order statistics and to calculate how food production, supply, and (if financial accounts are used) demand are distributed, and finally how much food households obtain from all sources. A food accounting matrix such as this may be used simply to show the way domestic food production, imports and aid find their way to the people. However, it may also be used as a model of a country’s food economy. The techniques being developed in the field of social accounting are, in theory at least, directly applicable. It should therefore be useful as a basis for the calculation of food import requirements, food aid requirements, the growth in domestic food production required to achieve self-sufficiency and for the simulation of the results of redistributional policies.36 We have now obtained a complete picture of food supply without losing sight of the households where food is required. The data needed is no more than that usually collected during the course of an agricultural survey, a national accounting exercise or a household consumption survey. The method may be integrated with other data collecting and analysis procedures. In addition the final operation, the

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construction of the FAM, lends itself to ‘guestimates’ and other dubious techniques which are sometimes required when data from different sources are collected together and do not tally. In the final analysis, the results of a statistical exercise are only as good as the data which is used. The approach proposed here will not make up for deficiencies in the quality of the data obtained from surveys. It would appear to offer, however, conceptual advantages over other methods which are based on false premises.

Conclusion The evidence suggests that world food production is increasing faster than world population. In this article we have attempted to show that, on the information available, it is not possible to say whether hunger is more or less prevalent now than it was a decade ago. The types of statistics being collected are not, in general, designed to provide this information. An alternative approach to the analysis of food supply data has been proposed, which is designed to identify and estimate the magnitude of food shortages. In his review of global food estimates Poleman states that ‘until there is a modest hue and cry’ nothing will be done about food statistical methods.37 He may be overly pessimistic; winds of change are already beginning to blow. We have noted, for example, the method of estimating the prevalence of hunger suggested by FAO in the Fourth World Survey. He is right, however, in asserting that enormous efforts are required to change the direction of conventional wisdom quickly enough to provide better information, say, by the 1980s. Poleman tends to direct his ‘hue and cry’ towards the establishment in the developed world. Whichever theory of future food distribution one likes to adopt, the forces at work to protect the nutritional status of the rich make food statistics, relatively speaking, a matter of academic interest in developed countries. However, for as long as planners in developing countries have to rely on aggregate production estimates and food balance sheet calculations which define neither the magnitude nor the causes of food shortages, they are being denied a powerful weapon in the war against hunger. Whatever the international inequalities in food supply, the development and management of national food resources will always be the most important method of combating undernutrition.

” Poleman, op cit. Ref 18.

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