Part III: Parallel contributed papers sessions

1. Statistical issues related to improving estimates of distributions for any of the five methods

Fallacies in - and ways of improving - the FAO methodology for estimating prevalence of undernutrition

Peter Svedberg
University of Stockholm
Stockholm, Sweden

This talk is based on the paper by Svedberg (in press) that aimed to scrutinize the FAO method for estimating the prevalence of undernutrition (POU) from selected theoretical and empirical perspectives. On the theory side, it examines the bias in the estimations that follows from FAO’s use of a model relying on a calorie cutoff point. I suggest the application of an alternative model that takes into account the “joint distribution” of calorie requirements and intake across households. This model is better justified theoretically and also empirically defendable.^[27]

The joint-distribution model is more data demanding than the cutoff-point model used by the FAO. In the paper, however, I demonstrate that FAO has indirectly assigned a numerical value to one of the two parameters that are “missing” (the coefficient of variation in household basic calorie requirement). As it turns out, the value of the second missing parameter (the correlation coefficient between intake and basic requirements) is of minuscule importance for the results. The basic requirement is defined as the calorie expenditure necessary to maintain the lowest health-consistent body weight and to pursue light physical (work) activity for household members.

FAO hence claims to have all the data needed for estimating POU in the various countries with the unbiased joint-distribution model, but has refrained from doing this. In the paper, I undertake that exercise while using the FAO “input” data on (1) per capita food supplies, (2) interhousehold distribution of calorie availability and (3) average and minimum per capita calorie requirements for households. With this preferred theoretical model and the FAO input data, the estimated POU becomes implausibly high (about 40 percent higher than the FAO estimates), which casts doubt on these data. I therefore follow up by examining the FAO input data. The main focus is on the two distribution parameters. The first is the coefficient of variation (CVy) for the interhousehold distribution of “available” calories. The values attached by FAO to this parameter imply that for many African and Asian countries, the households in the 5-10 percent lower tail of the distribution have a habitual access to less than 1 000 kcal/person/day. I explore whether such a low access (intake) is biologically feasible in living households and the implied mortality consequences.

The second parameter examined is the in-terhousehold distribution of per capita basic calorie requirements (CVx). FAO’s (implicit) estimate of the CVx takes into consideration that there is a range of health-consistent body weights and a range of “acceptable” physical work intensities. The CVx estimate does not, however, take account of the fact that households’ basic requirements “per person” also vary owing to differences in the size, age and gender composition of households.

Furthermore, several simulation exercises are conducted based on values of the main parameters that are more plausible and/or have a better empirical underpinning than those used by FAO. When inserted into the FAO cutoff-point model, these alternative parameter values generate significantly lower estimates of POU than reported by the organization itself. It is hence concluded that while the model used by FAO induces an underestimation of POU, the chosen values of the input parameters give rise to a bias in the opposite direction, towards overestimation. Inserting the alternative parameter values into the joint-distribution model suggests that on a net basis, FAO has overestimated POU worldwide.

Two caveats are in place. One is that my application of the joint-distribution model is undertaken on the assumption that this distribution is log-normal. It may be that the results are sensitive to this (admittedly rather ambiguous) assumption. Consequently, calculations based on alternative properties of the joint distribution should be conducted as a robustness test. The second caveat is that the empirical foundations for the alternative parameter values are not sufficiently solid to trust the ensuing new POU estimates fully. The main corollary is, nevertheless, that FAO faces an enormous challenge to improve its dataset. This applies to the two distribution parameters, as well as the data on per capita food supplies and on human calorie requirement for basal metabolism (Svedberg, 1999, 2000). An overview of human calorie requirement is now under way (see paper by R. Weisell in this series).

Finally, in the paper by the former chief statistician at FAO, L. Naiken, in this series, it is argued that “under certain assumptions”, the joint-distribution model “reduces” to the cutoff-point model used by FAO. This is theoretically correct. However, the assumptions needed to accomplish this “reduction” are indeed not plausible. These assumptions are (1) that all households who have the lowest per capita basic requirements are undernourished; (2) that all households with “medium high” basic requirements have exactly the intake that meets these requirements; and (3) that all households with a calorie intake above their basic requirements are those with extraordinarily high requirements. For further details on the assumptions needed to reconcile the FAO and the joint-distribution models, see Svedberg (2002).

References

Svedberg, P. 1999. 841 million undernourished? World Dev., 27(12): 2081-2098.

Svedberg, P. 2000. Poverty and undernutrition: theory, measurement, and policy. Oxford, Oxford University Press.

Svedberg, P. 2002. Reconciling the FAO model with the joint-distribution model: the thorny assumptions required. Stockholm University, The Institute for International Economic Studies (mimeo).

Svedberg, P. in press. Undernutrition overestimated. Economic Development and Cultural Change.

Risk-adjusted measures of undernourishment for Sub-Saharan African countries

Silke Gabbert, Jalloh Abu Bakar Sidique and Hans-Peter Weikard
Wageningen University
Wageningen, The Netherlands

Introduction

Cross-country monitoring is a prerequisite for the choice and implementation of effective policies towards food security. For such monitoring, FAO uses two basic measures, the prevalence of undernourishment and the depth of undernourishment (FAO, 1996, 2000). Since these measures implicitly assume access to food to be risk-free, they only allow for an ex post evaluation of food security. However, from an ex ante perspective, access to food is uncertain. The risk of losing access to sufficient food may also affect those who have a sufficient food intake ex post and may aggravate the situation of the undernourished. The existence of risks influences people’s decision-making and their ability to cope with changing living conditions. This will have immediate implications on their food security situation. Therefore, incorporating risk into measures of undernourishment complements and deepens the picture of food security and provides important additional information on the food security status of a region or country. However, this information is not reflected in the measures currently used.

The aim of our paper is twofold. First, we describe a new methodology to measure undernourishment in the face of macroeconomic risk and develop a risk-adjusted measure of the prevalence of undernourishment. Second, we empirically estimate a risk-adjusted measure of the prevalence of undernourishment for Sub-Saharan African countries.

Current state of research

In the past, there has been much controversy surrounding the measurement of undernourishment. In particular, four problems have been addressed: (1) the calculation of the dietary energy supply (DES) (see Svedberg, 1999); (2) the estimation of the coefficient of variation of the distribution of food across a population (Smith, 1998; Svedberg, 1999); (3) the aggregation procedure across undernourished individuals resulting in a measure of undernourishment for an entire population (see Gabbert and Weikard, 2001); and (4) the issue of risk, addressed by Bigman (1993). Bigman’s approach has been developed into the Aggre- gate Household Food Security Index (AHFSI) (FAO, 1994, 1997) and used by the World Food Programme of the United Nations in a framework for assessing food aid needs.

Although the development of the AHFSI is an important step forward, it has its shortcomings. First, the risk component of the AHFSI is based on a cross-section income distribution, which may be independent of the individual income risk. Second, the index does not meet a decomposability requirement, desirable for empirical analysis.

Methodology

The standard measure of prevalence of undernourishment gives information on a current situation, referring to the time period of the data used for estimating the distribution function of dietary energy consumption. Since these data are usually available with a certain time lag, the measures give an ex post assessment of undernourishment. However, from an ex ante perspective, at any point in time, individuals face a certain degree of risk of losing access to sufficient food in the future.

A risk-adjusted measure of undernourishment must be based on the uncertainty of food availability on a macro level, as information on individual access to food is not available. Our approach is based on the standard FAO methodology (FAO, 1996) but includes an adjustment for risk. Hence, we assume a log-normal distribution of food consumption across population. The mean of this distribution is taken to be the DES, which approximates the average food energy consumption in a country. We deviate from the FAO methodology by assuming that the DES is risky. We use time series data to estimate an expected DES value and a standard deviation (SD) for the DES of a country. We then compute an expected value for the prevalence of undernourishment with and without adjustments for risk. The risk-adjusted measure aggregates the prevalence of undernourishment for all possible values of DES using its probability density function for a weighting.

Findings

A comparison of the standard index and the risk-adjusted index for the prevalence of undernourishment, P, shows underestimation of undernourishment in countries with moderate undernourishment. However, we find overestimation in countries with severe undernourishment. Table 1 shows results for a small sample of countries to illustrate the findings. The underestimation effect is stronger if the CV of the distribution across population is smaller. The calculations in Table 1 are based on CV = 0.2. Our findings only capture risks owing to the volatility of the DES. These risks may be only a small part of the overall risk of undernourishment to which the individual is exposed.

References

Bigman, D. 1993. The measurement of food insecurity: chronic undernutrition and temporary food deficiencies. In D. Bigman & P. Berck, eds. Food security and food inventories in developing countries. Wallingford, UK, CAB International.

FAO. 1994. Assessment of the current world food security situation and recent policy developments. CFS: 94/2, Rome.

FAO. 1996. The sixth world food survey. Rome.

FAO. 1997. Assessment of the household food security situation, based on the aggregate household food security index and the sixth world food survey. CFS: 97/4, Suppl. 1, Rome.

FAO. 2000. The state of food insecurity in the world. Rome.

Gabbert, S. & Weikard, H.P. 2001. How widespread is undernourishment? A critique of measurement methods and new empirical results. Food Policy, 26(3): 209-228.

Smith, L.C. 1998. Can FAO’s measure of chronic undernourishment be strengthened? Food Policy, 23(5): 425-445.

Svedberg, P., 1999. 841 million undernourished? World Development, 27(12): 2081-2098.

Estimating undernourishment with household expenditure surveys: a comparison of methods using data from three Sub-Saharan African countries

Dede Aduayom and Lisa C. Smith
International Food Policy Research Institute
Washington, DC, USA

National household expenditure surveys can be used to estimate the proportion of a country’s population that is undernourished - that is, consuming insufficient dietary energy - using data collected on the food quantities acquired by households over a reference period. For each household, the quantity data are translated into energy values using food composition tables. Taking into account household size, total available energy is compared with a requirement. The percentage of households for which the requirement is not met is then the estimated prevalence of undernourishment for the country. This direct method, while simple, relies on large samples of household-level data that require considerable processing and cleaning before use.

The method used by FAO for estimating undernourishment, on the other hand, is distribution-based. It relies on the assumption of a log-normal parametric density function and only two pieces of information, the mean energy availability and its CV, the latter representing the distribution of energy availability across a country’s population. These numbers may be available from sources other than household expenditure surveys, such as food balance sheet data, prior household surveys or surveys from similar countries. A third method, commonly employed by the World Bank to estimate country poverty preva-lences, relies on estimation of a parametric Lorenz curve. A cumulative density function of the percentage share of energy acquired by percentiles of a population is estimated. The information required is percentile means of energy availability, which may be available from survey reports. While these two parametric methods present the advantage of having relatively low data needs, at the same time they may lose some of the accuracy benefits of the direct method.

In this paper, we present a comparison of estimates of undernourishment given by the direct method to those based on parametric methods, using data from the household expenditure surveys of three Sub-Saharan African countries: Malawi (1997), Uganda (1999) and Ghana (1998). The sample sizes are 10 968, 10 685 and 5 927 households, respectively. For all methods, the energy requirement employed is the minimum re- quirement for light activity, approximately 1 800 kcal/day for the average person, the same as that used by FAO for its estimates of undernourishment reported in the State of Food Insecurity in the World (SOFI). For the FAO method, national means are based on average per capita energy availability (PCEA) of the households in the surveys; CVs are based on calculation of the standard deviation of PCEA across households. Lorenz curves are estimated using decile means of PCEA. For calculation of the percentage of people who are undernourished, individuals within households are assumed to have the same status as their household.

The results are reported in Table 1. The estimated prevalence of undernourishment using the direct approach is highest in Malawi (65 percent), followed by Ghana and Uganda. For each country, the estimates given by the three methods are quite close. The greatest difference is between the direct and FAO methods for Malawi, a difference of only four percentage points. Tests for the shape of the density function based on the survey data corroborate the assumption of log-normality.

The last row of Table 1 gives the estimates of undernourishment reported by FAO in SOFI 2001. These estimates tell quite a different story from the expenditure survey-based estimates in terms of both absolute prevalences and relative severities of under- nourishment. While nearly equal for Uganda, the FAO-reported estimates for Malawi and Ghana are far lower than those derived from the FAO method but using household expenditure survey-derived means and CVs; for example, the difference is 34 percentage points in the case of Malawi. In terms of relative severities, the FAO reported estimates indicate that Uganda has almost twice the rate of undernourishment of Ghana. The estimates based on expenditure survey data by contrast indicate a higher rate for Ghana. Given comparable estimates for all three methods when expenditure survey data are used, the obvious source of these large differences is differences in the underlying parameters themselves.

For mean per capita energy availability, FAO uses food balance sheet and population data. A comparison of the means derived from household expenditure survey data with those employed by FAO reveals that the former are much higher for Uganda (2 711 vs. 2 190), and lower for Malawi (1 614 vs. 2 120 kcal) and Ghana (2 429 vs. 2 550 kcal). These differences partially account for the different undernourishment estimates generated using household expenditure survey data. CVs are not reported by FAO for each country, but they are assumed to fall within a range of 0.20-0.35. Estimates generated using the survey data are far outside this range: 0.78, 0.52 and 0.59 for Malawi, Uganda and Ghana, respectively.

In conclusion, the three methods investigated appear to give comparable results when the same underlying household survey data are used. Given a reliable database, the parametric approaches would thus appear to be useful tools for assessing undernourishment. This research finds that estimates based on the FAO probability distribution method but using household expenditure surveys as the database can diverge widely from those actually reported by FAO. The source of these differences is the parameters employed: mean per capita energy availability and degree of variation across countries’ popula- tions, as summarized by the CV. If food quantity data reported directly by households are judged to be the most accurate database for these parameters, the extra costs involved in collecting data from household expenditure or food consumption surveys are warranted. The analysis suggests the following areas for further investigation: (1) appropriate CV ranges and (2) the accuracy of mean energy availability estimates derived from food balance sheet data.

Acknowledgements

The authors wish to thank Ellen Payongayong and Smita Ghosh for their assistance and IFPRI researchers who contributed their comments and suggestions. The efforts of Dave Coady, John Maluccio, Ken Simler and Emmanuel Skoufias to look up additional resources when needed are especially appreciated. We gratefully acknowledge the Ghana Statistical Service, the Malawi National Statistics Office and the Uganda Bureau of Statistics, who conducted the surveys, and the Africa Household Survey Databank of the World Bank for facilitating use of the datasets. This research was conducted under the auspices of the IFPRI-FAO-World Bank project “Improving the Empirical Basis for Assessing Food Insecurity in Developing Countries” and funded by AusAID, CIDA, the World Bank and USDA.

On reliability of estimates of inequality in distributions derived from sample survey data

Arun Kumar Srivastava, Anil Rai and V. Ramasubramanian
Indian Agricultural Statistics Research Institute
New Delhi, India

Introduction

For studying inequalities in populations, the interest often lies in estimating frequency distributions. Several factors of interest, such as income or expenditure, depict highly skewed distributions. The study of economic inequality with respect to such distributions is of common interest, and estimation of frequency distributions is more meaningful in such cases. The sample surveys planned for estimating population parameters such as the mean or total may not adequately capture the distributional properties of the populations needed for estimation of frequency distributions. Among several measures of inequalities, the Lorenz ratio or Gini concentration coefficient (G) is considered as one of the most important measures. Estimation of G involves estimation of frequency distributions as well. It may not be reasonable to estimate these parameters from data collected through sample surveys planned for the estimation of the mean or total. The reliability of such sampling designs as well as estimates of G needs to be investigated. In this paper, the problem of choice of sampling designs for estimation of G as well as frequency distributions is attempted. Since studying the distributional properties of estimators of such complex parameters is not simple, the problem is approached empirically on simulated data.

Simulation of population

For empirical studies, populations with characteristics such as income, expenditure, holding size, etc. having highly skewed distributions have been kept in view. In particular, we consider a population of land holdings in Tamil Nadu State from Agricultural sciences. The population is highly skewed in nature. The parameters of this distribution are taken into account for generating simulated populations. Consider a population of n villages. Let there be M_i households in the ith village. The village size M_i is generated randomly following normal distribution with the mean and variance taken from a real population (for example, mean = 100, variance = 900, i.e. CV= 30 percent). Within each village, M_i values are generated with Gamma (l, m); l and m are determined such that the mean = lm and the variance = lm². The mean and variance of the Gamma distribution are based on real populations (Murthy, 1977). In fact, the mean = 1.25525, and the variance = 2.47430; thus, l = 0.636811 and m = 1.971149. Although populations of various sizes were simulated, for the present illustrations we present the case of n = 100. We also present here only the case of simulation using Gamma distribution. We illustrate the problems in estimation of inequality measures through the simulations of populations based on landholdings, but the approach and the results are likely to hold when looking at income distribution as well, as both are similar in terms of skewness and other distributional properties. Moreover, in rural areas, landholdings are invariably directly related to the household income. The populations generated through this approach have been used for further sampling and investigations relating to calculation of G as well as for estimation of frequency distributions.

Gini Coefficient as a measure of economic inequality

One of the most widely used measures for the extent of inequality is the Gini coefficient. An important feature of this measure is its association with the Lorenz curve in which the proportion of the population arranged from the poorest to the richest are represented on the horizontal x-axis, and the proportion of income held by the bottom x proportion of the population is depicted on the vertical y-axis. The mathematical formulation is as follows: Let the income y (³ 0) have continuous type distributions with density function f(y) with mean:

.

Define

and

F(x) is the proportion of persons with in- come, £ x and F₁(x) is the proportionate share of these persons in the aggregate income of all persons. F(x) and F₁(x) both lie between 0 and 1 for x ranging from 0 to ¥, and F₁ is a monotone increasing function of F. The graph of F₁ against F is called the Lorenz curve or the concentration curve of the given distribution of income.

In general, the Lorenz curve must satisfy the following conditions:

(1) If F = 0, F₁ = 0.
(2) F = 1, F₁ = 1.
(3) F₁ < F.
(4) The slope of the curve increases monotonically.

The area between the Lorenz curve and the egalitarian line is called the area of concentration. The Lorenz ratio, also known as the Gini Coefficient is defined as:

G = 2 × area of concentration
=

= .

The Gini Coefficient (G) may also be represented in several alternative ways. Some of the representations and corresponding interpretations in terms of welfare economics are available in the literature (see e.g. Sen, 1973).

Estimation of Lorenz Ratio or Gini Coeffi cient (G)

For estimation of the Lorenz ratio through a numerical approach, the following procedure is followed.

Let there be K class intervals, p_k the percentage of persons in the kth class (k = 1, 2 ..., K), the average of character x in the kth class, q_k the percentage share of the kth group in the aggregate expenditure, P_k the cumulative p_k (with P_K = 100) and Q_k the cumulative q_k (with Q₀ = 0 and Q_K = 100)

.

For details, please refer Bhattacharya and Coondoo (1992).

Estimation of G, in this method, is essentially based on estimates of p_k and (k = 1, ... K). The role of the sampling design also appears in the estimation of these parameters.

One of the limitations of estimating p_k and in skewed populations could be due to extremes in the distributions, thereby leading towards the proper sampling designs for estimation of frequency distributions. Estimation of the Lorenz curve as well as the fractile graphical analysis (Mahalanobis, 1960) is an attempt in this direction.

In the present investigation, the performance of estimators of G has been examined empirically. The sampling designs considered are as follows:

1. direct sampling of ultimate units:

1.1 simple random sampling without replacement (srswor);

2. sampling of clusters of ultimate units (villages):

2.1 sampling clusters (villages) with srswor;

2.2 sampling clusters (villages with probability proportional to size with replacement (ppswr), size being the number of ultimate units;

3. two-stage sampling:

3.1 both the stages by srswor;
3.2 first stage ppswr and srswor in second stage;

4. stratified sampling:

4.1 selection of clusters by ppswr.

The empirical investigation indicates that the estimates of G have comparatively higher biases in the case of sampling for clusters of villages and also in the case of two-stage sampling as compared with selection of ultimate units by simple random sampling. The selection of villages by probability proportional to size has resulted in larger coefficients of variation for the estimators. The larger biases are perhaps due to the skewed nature of the parent population.

The performance of various sampling designs was also examined for estimating the frequency distribution on the basis of a criterion considered by Murthy (1977). Since estimation of G through grouped data requires estimation of group proportions, it was expected that sampling designs that perform better in estimating frequency distributions should perform well for estimation of G as well. The results were in broad conformity with this expectation.

References

Bhattacharya, N. & Coondoo, D. 1992. Collection and analysis of survey data on income and expenditure, training handbook. Tokyo, SIAP.

Mahalanobis, P.C. 1960. A Method of fractile graphical analysis. Econometrica, 28: 325-351.

Murthy, M.N. 1977. Use of empirical studies in evaluating sample designs for estimating frequency distributions. Proceedings of the meeting of the International Statistical Institute held at New Delhi, India.

Sen, A. 1973. On economic inequality. Oxford, UK, Clarendon Press.

The effect of sampling design on the reliability of estimates of the variance of distributions derived from household survey data: a simulation study

Giuseppe Arbia
“G. d’Annunzio” University
Pescara, Italy

On a regular basis, FAO produces estimates of the prevalence of undernourishment and related measures that require estimates of the frequency distribution of household per capita food consumption, expressed in terms of dietary energy (kilocalories). National sample surveys investigating household income and consumption are the usual source of data for these activities. In using the distribution data from such surveys, it is important to ensure that not only the estimate of the mean but also the variance and the shape of the distribution are sufficiently accurate. Inaccurate estimation of these parameters may lead to serious biases in the evaluation of the prevalence of undernourishment. Most of the sample surveys of household income/expenditure/consumption are generally based on a two-stage sample design with stratification of the primary sample units (usually geographical units) and secondary units represented by households. However, apart from the classical results on the estimation of the mean, in the literature there is no clear evidence that the estimation of the other characteristics (such as variance, skew- ness and kurtosis) is unbiased with respect to this kind of design. This paper presents a simulation study that attempts to address this problem in formal terms.

In the simulation, we start with real data taken from the Mauritius 1996-97 Household Budget Survey. We first simulate a virtual population from a log-normal distribution with expected values, variance and sampling frame derived from the real Mauritius survey data. This will allow much more flexibility and generality of results than simply using the real data. However, the results are connected with a real population and are not just artificially laboratory-generated. In a second phase, the virtual population thus generated is sampled by using various sampling strategies, and the results are compared in terms of the distributional properties of the estimates.

The simulation results suggest that the bias of the estimates of the variance is generally very high in all experimental situations considered. In fact, the relative bias ratio always exceeds the threshold value suggested by Cochrane (1963) as a rule of thumb. The bias is emphasized by the presence of intradis-trict correlation (see Table 1). Conversely, it is not significantly affected by different design effects (DEFF) values (see Table 2). Furthermore, the estimates based on two-stage stratified samples are also seriously affected by a low level of efficiency with respect to estimates based on random sampling, and the efficiency decreases even further by increasing the DEFF. The efficiency of the variance estimates, however, is higher in the two-stage stratified sample in the case of non-zero intradistrict correlations.

The general conclusion is that it is extremely dangerous to try to assess the prevalence of undernourishment by fitting a log-normal distribution to estimates of mean and variance derived from a two-stage stratified sampling design. In real instances, the situation is probably even worse than that depicted here because the empirical distributions may differ dramatically from the log-normal case. In some preliminary experiments (whose results are not reported here for brevity), we have seen that estimates of the skewness and the kurtosis are also biased and highly inefficient if based on two-stage stratified samples.

In a future paper, we will analyse this point further by assuming skewed-normally distributed populations and populations obeying the four-parameter Pearson family. We will study the quality of estimates of the shape parameters (skewness and kurtosis) and of the lower percentiles based on two-stage stratified samples and also possible solutions to improve the precision of these estimates.

Acknowledgements

The author is indebted to J. Mernies, L. Naiken, P. Narain and R. Sibrian of ESSA-FAO, for the many useful comments and suggestions received on previous versions of this paper.

References

Cochrane, W.G. 1963. Sampling techniques. New York, John Wiley.