Three essays on a Sri Lanka household survey

LSM - 11 L.5JflS OCT. 1981 Living Standards Measurement Study Working Paper No. 11 Three Essays on a Sri Lanka Household Survey Angus Deaton  LSMS Working Papers No. I Living Standards Surveys in Developing Countries No. 2 Poverty and Living Standards in Asia: An Overview of the Main Results and Lessons of Selected Household Surveys No. 3 Measuring Levels of Living in Latin America: An Overview of Main Problems No. 4 Towards More Effective Measurement of Levels of Living, and Review of Work of the United lNations Statistical Office (UNSO) Related to Statistics of Levels of Living No. 5 Conducting Surveys in Developing Countries: Practical Problems and Experience in Brazil, Malaysia, and the Philippines No. 6 Household Survey Experience in Africa No. 7 Measurement of Welfare: Theory and Practical Guidelines No. 8 Employment Data for the Measurement of Living Standards No. 9 Income and Expenditure Surveys in Developing Countries: Sample Design and Execution No. 10 Reflections on the LSMS Group Meeting No. II Three Essays on a Sri Lanka Household Survey No. 12 The ECIEL Study of Household Income and Consumption in Urban Latin America: An Analytical History No. 13 Nutrition and Health Status Indicators: Suggestions for Surveys of the Standard of Living in Developing Countries No. 14 Child Schooling and the Measurement of Living Standards No. 15 Measuring Health as a Component of Living Standards No. 16 Procedures for Collecting and Analyzing Mortality Data in LSMS No. 17 The Labor Market and Social Accounting: A Framework of Data Presentation No. 18 Time Use Data and the Living Standards Measurement Study No. 19 The Conceptual Basis of Measures of Household Welfare and Their Implied Survey Data Requirements No. 20 Statistical Experimentation for Household Surveys: Two Case Studies of Hong Kong No. 21 The Collection of Price Data for the Measurement of Living Standards No. 22 Household Expenditure Surveys: Some Methodological Issues No. 23 Collecting Panel Data in Developing Countries: Does it Make Sense? No. 24 Measuring and Analyzing Levels of Living in Developing Countries: An Annotated Questionnaire No. 25 The Demand for Urban Housing in the Ivory Coast No. 26 The Cote d'Ivoire Living Standards Survey: Design and Implementation No. 27 The Role of Employment and Earnings in Analyzing Levels of Living: A General Methodology with Applications to Malaysia and Thailand (List continues on the inside back cover)  Three Essays on a Sri Lanka Household Survey   The Living Standards Measurement Study The Living Standards Measurement Study (LSMS) was established by the World Bank in 1980 to explore ways of improving the type and quality of household data collected by Third World statistical offices. Its goal is to foster increased use of household data as a basis for policy decision making. Specifically, the LSMS is working to develop new methods to monitor progress in raising levels of living, to identify the consequences for households of past and proposed government policies, and to improve communications between survey statisticians, analysts, and policy makers. The LSMS Working Paper series was started to disseminate intermediate products from the LSMS. Publications in the series include critical surveys covering different aspects of the LSMS data collection program and reports on improved methodologies for using Living Standards Survey (LSS) data. Future publications will reconmmend specific survey, questionnaire and data processing designs, and demonstrate the breadth of policy analysis that can be carried out using LSS data.   LSMS Working Papers Number 11 Three Essays on a Sri Lanka Household Survey Angus Deaton The World Bank Washington, D.C., U.S.A.  Copyright (C 1981 The International Bank for Reconstruction and Development/THE WORLD BANK 1818 H Street, N.W. Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America First printing October 1981 Second printing July 1985 This is a working document published informally by the World Bank. To present the results of research with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. The publication is supplied at a token charge to defray part of the cost of manufacture and distribution. The World Bank does not accept responsibility for the views expressed herein, which are those of the authors and should not be attributed to the World Bank or to its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates conceming the legal status of any country, territory, city, area, or of its authorities, or concerning the delimitation of its boundaries, or national affiliation. The most recent World Bank publications are described in the annual spring and fall lists; the continuing research program is described in the annual Abstracts of Current Studies. The latest edition of each is available free of charge from the Publications Sales Unit, Department T, The World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A., or from the European Office of the Bank, 66 avenue d'Iena, 75116 Paris, France. When this paper was first published Angus Deaton was professor of Econometrics at the University of Bristol, England. Library of Congress Cataloging in Publication Data Deaton, Angus. Three essays on a Sri Lanka household survey. (LSMS working paper, ISSN 0253-4517; no. 11) "October 1981." Bibliography: p. 1. Cost and standard of living-Sri Lanka. 2. Household surveys-Sri Lanka. 3. Quality of life-Sri Lanka. 4. Food consumption-Sri Lanka. 5. Children- Economic aspects-Sri Lanka. I. Title. II. Series. HDo49.8.D4 1985 339.4'1'095493 85-11535 ISBN 0-8213-0038-5  - vii - THREE ESSAYS ON A SRI LANKA HOUSEHOLD SURVEY TABLE OF CONTENTS Page No. LIST OF TABLES I. ANALYZING THE FOOD SHARES IN A HOUSEHOLD SURVEY viii - ix A. Introduction 1-4 B. Presentation of the Data 4-10 C. The Relationship Between the Food Share and PCE 10-16 D. Demographic Effects and Multivariate Analysis 16-29 E. Equivalence Scales 30-33 APPENDIX 1: ECONOMIC CONSIDERATIONS 34-39 APPENDIX 2: EQUIVALENCE SCALE THEORY 39-40 APPENDIX 3: DATA REQUIREMENTS 41 II. INEQUALITY AND NEEDS: SOME EXPERIMENTAL RESULTS FOR SRI LANKA A. Introduction 42-43 B. Behavioral Models of Equivalence Scales 44-51 C. Equivalence Scales for Sri Lanka 52-58 D. Inequality and Identifying the Poor 58-63 E. Conclusions 63-64 III. ON A METHOD FOR MEASURING THE COSTS OF CHILDREN A. Introduction 65-67 B. The Theoretical Basis of the Rothbarth Procedure 68-74 C. Comparison with the Engel Model 74-78 D. Some Illustrative Calculations 78-83 E. Conclusions 83-84 REFERENCES 85-87  - viii - LIST OF TABLES Table No. Page No. ESSAY I 1. Sectoral Composition of the Sample 5 2. Means and Standard Deviations of Food Shares PCE and lnPCE by Sector (Rupees per month) 9 3. Frequency Distribution (%) of Households. Classified by Foodshare and Sector 11 4. Adult and Child Composition of Sri Lankan Families by Sector (%) 20 5. Regression of Food Share and Family Composition 24 6. F-tests for Age and Sex Effects of Children on the Food Share 27 7. Quadratic and Linear Regressions 29 8. Adult Equivalence Scales for Combinations of #Adults and #Children: I (reference: 2 adults) 32 9. Adult Equivalence Scales for Combinations of #Adults and #Children: II (reference: 2 adults) 32 ESSAY II 1. Parameter Estimates for the Food Share Equation 53 2. Correction Factors for PCE by Numbers of Adults and Childrern, Urban Sector: Sri Lanka 57 3. Proportions of Households in each Decile by PCE and Corrected PCE: Urban Sector 59 4. Percentage of Households Reclassified by Alternative Criteria 60 5. Inequality Measures for Sri Lanka 63  Table No. Page No. ESSAY III 1. Equivalence Scales for Sri Lanka: Urban Sector: Engel Methodology 82 2. Equivalence Scales for Sri Lanka: Urban Sector: Rothbarth Methodology 82  I. ANALYZING THE FOOD SHARES IN A HOUSEHOLD SURVEY A- INTRODUCTION Household surveys from developing countries can be used to illuminate welfare issues in a variety of different ways. This essay explores one possi- bility, the analysis of the share of food in household expenditure. Such studies are of limited interest unless they can be replicated in a number of different countries, even though the details of the analysis will inevitably vary from country to country and from survey to survey. The best approach seems to be to work illustratively, carrying out substantive studies designed in such a way as to be easily replicated elsewhere. Here we report results on one such study, based on the 1969-70 socio-economic survey of Sri Lanka and carried out as part of the World Bank's Living Standards Measurement Study. The food share has been emphasized in studies of household welfare at least since the nineteenth century. Since food is seen as the first necessity, the demand for which rises much less rapidly than do resources, at least once subsistence needs are met, the share of food in total expenditure can be re- garded as an (inverse) indicator of welfare. It is also a very convenient indicator, since its definition as a dimensionless ratio renders it comparable over time periods and between geographical locations, at least if the relative price of food does not vary too much. However, the real interest in the food share is that it may be capable of acting as a better indicator of welfare than measures based on income or expenditure alone. Once again, this is an old idea going back at least to Engel who noticed that larger households had larger food shares than smaller families with the same total outlay and suggested that households with the same food share be regarded as equally well-off irrespective  -2- of their size. This idea will be directly exploited later in the paper, but the principle is of wide potential applicability for measuring factors con- tributing to welfare. In principle it would be more desirable to analyze the complete structure of the household budget rather than focussing on the foodshare alone. For LDC's, however, the food share is typically between 50% and 80%, ratios two to four times higher than those currently existing in the U.S. or the U.K. Hence, other individual categories of consumption, even if quite broadly defined, play a correspondingly limited role. It is also likely that their measurement is subject to much larger proportionate errors. Thus, relatively little of the general information about welfare is likely to be lost by look- ing at food alone. Of course, specific issues are likely to require attention to other items; housing is the obvious example. However, the increase in technical difficulty and presentational complexity in going from one commodity share to many is unlikely to be matched by a corresponding increase in in- formation. The remainder of the paper is divided as follows. Section B discusses the basic presentation of the data and illustrates the type of tabulation which can be used to descry the basic features of the food share in a large data set such as that provided by the Sri Lankan survey. Section C moves from the data to simple bivariate graphical and tabular analysis linking the food share with the most obvious indicator of welfare, household per capita expenditure. A transformation of the data is suggested which generates rough linearity in the relationship, simple bivariate regressions are estimated, and first attempts made at assessing the total expenditure elasticity of food demand as well as the shape of the Engel curve.  -3- Section D turns to the relationship between food consumption and house- hold composition, to the question of how household size and its age and sex composition affect the relationship between food consumption and total outlay. Again, several techniques are illustrated, from analyzing separately house- holds with different compositions, to attempting to combine the various effects into a multivariate regression. In particular, attention is focussed on the sex, age, and numbers of adults, children and old people in the household. For Sri Lanka, and this particular data set, it seems that, in addition to per capita expenditure, only the separation of children and adults contributes very much to the explanation of the variance of the foodshare. Even so, it also appears that there are economies of scale in the costs of maintaining a household, particularly for adults and particularly for better-off families. Section D carries these descriptive results a stage further and uses the results together with Engel's method to calculate behavioral adult equivalence scales for different types of Sri Lankan families. Again, different methodol- ogies are discussed together with their implications for the constructed scales. In this particular study, and in line with the economies of scale already mentioned, it appears that, for a given household composition, better-off families have lower scales. Hence, correction of per capita expenditures to an equivalent per capita basis would have two offsetting effects on measured in- equality; on the one hand, the economies of scale would benefit larger fami- lies more and these typically have lower levels of per capita expenditure, while, on the other hand, such corrections are larger for the better-off house- holds. Finally, there are three appendices. Appendix 1 covers econometric issues, specifically the question of pooling samples from different sectors  - 4 - or regions and also the effects of residual heteroskedasticity on assessing the multivariate regressions reported in the text. Appendix 2 contains the technical mathematical theory supporting the equivalence scale methodology in Section D. It is unnecessary to an understanding of that section but is designed to show that the scales can be supported by the relevant consumer theory. Appendix 3 gives a brief list of the minimal data requirements needed to replicate this study. B. PRESENTATION OF THE DATA 1. Background The 1969-70 socio-economic survey of Sri Lanka is fully described in the two volumes published by the Sri Lanka Department of Census and Statistics (1973). This publication also contains the original questionnaire as well as numerous summary tables and cross-tabulations. A total of 9,694 house- holds were covered by the survey and information was collected, not only on income and households' social, economic and demographic characteristics, including, essentially for present purposes, the age and sex of each member of the household. One-member households were excluded, as were boarding houses and institutions. For the remainder, a two-stage sampling design was adopted with census blocks as primary, and households as secondary sampling units. The island as a whole was stratified into three sectors, urban, rural and estate, with selection probabilities set to favor the inclusion of urban house- holds. Rows 1 and 2 of Table 1 give the total number of households by sector together with those included in the sample. These disproportionate weights, particularly in favor of urban households, must be borne in mind when computing population figures from the sample. However, the three sectors differ so  -5- widely in type and in economic characterization that it is wise, for Sri Lanka, to analyze each stratum or sector separately. Whether or not valid pooling can take place is addressed as a separate issue later in the paper. Table 1 Sectoral Composition of the Sample All Island Urban Rural Estate Total Households 2,372,197 375,042 1,695,610 301,545 In sample 9,694 4,037 3,657 2,000 Tn analysis 9,663 4,022 3,652 1,989 For the current analysis, some 31 households were excluded, leaving an effective data base of 9663 households, the sectoral composition of which is shown in the third row of Table 1. Exclusion was forced when either food or total expenditure data were unusable. Apart from cases of unavailability, the basic requirement that the share lay between zero and unity was checked for each household. More sophisticated editing techniques might well have been worthwhile but were not carried out in the present case. Even so, it is worth emphasizing the importance of this type of checking or editing prior to analy- sis. Even simple statistical analysis is computationally expensive when nearly 10,000 observations are involved and it is extremely costly to repeat calcula- tions when errors are discovered at a late stage in the analysis. However, even the most sophisticated editing techniques cannot detect all errors, and an important second line of defense is the use of robust techniques at early  -6- stages of the analysis. Specifically, graphical analysis, such as scatter diagrams, will reveal outliers while not allowing them to lead to incorrect inference. Regression analysis without graphical or other display can be ex- tremely sensitive and a single nonsensical observation can easily dominate the results even in a regression with many thousands of observations. 2. The Variables The principle variables in the analysis, i.e., food, and total and per capital household expenditure, are largely self-explanatory; nonetheless, there are a number of definitional points. Food is "food and drink," drink cover- ing tea, coffee, milk, etc. but excluding liquor. Tobacco and betel are also excluded. In the survey, food consumption was monitored over a seven-day period, but the figures are grossed up to a monthly basis to match other ex- penditure categories. Expenditure on durable goods was measured on an annual basis and divided by twelve; this at least partially avoids the "bumps" which otherwise would occur in total expenditure if the sample period happened to coincide with the purchase of an expensive durable. During 1969-70, every person over the age of one received a free rice ration (or its equivalent) and the imputed value of these is included in food consumption and hence in total expenditure. Other important imputed elements in total expenditure are the rental value of owner occupied housing as well as the value of free housing, the latter mainly on the estates. Production for own consumption is also valued and added both to food and total expenditure. The use of imputed values in the analysis raises potentially difficult theoretical and practical questions. Pricing non-marketed commodities at market prices implicitly assumes that consumers would have bought those com- modities at the prevailing prices had they not obtained them by other meaLns,  -7- for example, through the free rice ration or free housing. If indeed it is possible for the consumer to sell unwanted rations or home produce, the assump- tion is a reasonable one. For the rice ration, few problems arise. The ration was about half of average consumption in 1969-70 and even very poor households bought rice outside the ration. However, for very poor consumers on the estates (and possibly elsewhere) the imputation of value for free hous- ing may cause distortions in the behavior of the food share. Intuitively, it is reasonable to expect that, for very poor households, a very large fraction of spendable resources will be spent on food and that this fraction will tend to increase as resources decrease. The relationship between the f ood share and outlay would thus be as illustrated by AB in Figure 1. If households near A are allocated free housing, they are likely to wish to sell it or exchange it Food share B 0 Total outlay Figure 1: The effect of imputing value to free housing for very poor consumers  for food. In practice, they cannot do so, so that the shadow price to the recipients is in fact much lower than the market price which is assigned by the survey accountants. Algebraically, if x is spendable resources, r(x) is expenditure on non-food items, and a is the imputed value of housing, the food share, w , is given by w = (x - r(x))/(x + a). (1) For the very poor, r(x) and its rate of change with x are very small, so that w x/(x + a) which tends to zero with x so that the food share, at least initially, is a rising function of outlay. This is illustrated by the curve ODB in Figure 1. Of course, the extreme points near 0 are not observed, but, as will be shown, there is a distinct tendency in the Sri Lankan data for the food share to stop rising and flatten out at low levels of total outlay. Since, on the estates, average imputed income from housing is about 5% of average total income, this phenomenon may be of considerable importance lower in the income distribution and clearly deserves further investigation. Per capita total household expenditure (PCE) is the basic variable used in the study to explain variations in the food share. For reasons of accuracy of measurement, as well as the other issues discussed, for example in Deaton (1980), expenditure is preferred to income as the first approximation to welfare. Similarly, the deflation from total household expenditure to per capita expendi- ture is a first attempt to measure expenditure in relation to needs. More sophisticated corrections will be attempted in Sections C and D below. 3. Univariate Analysis Table 2 lists the means and standard deviations of the food share, per capita expenditure and the logarithm of per capita expenditure. The All-Island figures are weighted averages using the population weights of the three sectors,  - 9 - from Table 1. Note the relative poverty of the rural and estate sectors, parti- cularly the latter, whether assessed on the basis of PCE or of the food share. Dispersion is also less away from the urban sector, both in PCE and in the food share. Much of the positive skewness in the PCE distribution is removed by taking logarithms so that the standard deviations of lnPCE are more useful indicators of dispersion than those of PCE itself, Table 2 Means and Standard Deviations of Food Shares PCE and lnPCE by Sector (Rupees per month) Foodshare PCE lnPCE Mean s.d. mea; .d. .men s.d Urban 0.614 0.138 78.72 54.91 4.1931Y553 Rural 0.662 0.118 55.57 30.40 3.899 0.474 Estate 0.676 0.115 53.64 27.66 3.889 0.414 A-1 Island 0.656 0.122 58.98 36.17 3.944 0.494 Table 3 provides a greater disaggregation of the food share, again by sectors. The model class is a food share from 70-75% of total expenditure in all three sectors. Also in all three sectors, the distributions are slightly negatively skewed. This corresponds to a "tail" of very well-off consumers with low budget shares corresponding to the long upper tail of the PCE distri- bution. This negative skewness is particularly marked in the urban sector corresponding to the greater inequality of PCE as compared with the country and the estates. The higher level of PCE in the urban sector is also apparent from the distribution: 21% of urban households have food expenditures of less than 50% of total expenditure while the corresponding figures for rural and estate are  - 10 - 10% and 8%, respectively. At the other end of the distribution, amongst the very poor, 14% of households on the estates (43,000 households) and 10% in the rural sector (176,000 households) have food shares greater than 80% compared with only 6 1/2% in the urban sector (24,000 households). Even this probably understates relative deprivation on the estates where, with largely free accommodation, the imputation phenomenon discussed above prevents the food share attaining even higher levels. C. THE RELATIONSHIP BETWEEN THE FOOD SHARE AND PCE Figure 2 is a (somewhat rough) sketch of the empirical joint distribution of the food share and per capita expenditure over all the Sri Lankan households in the sample. Ideally, the corresponding diagrams for each sector shou:Ld be examined separately, but as will be seen, the relationship between the share and PCE is sufficiently stable across the three sectors for a single diagram not to be misleading. This sketch is prepared from a standard scatter diagram and the contour lines indicate the density of households falling in the various areas with the inner contours corresponding to the higher densities. The isolated crosses marked are intended to give an idea of the occurrence oiE such isolated observations without faithfully reproducing them on a one for one basis. The steepness of the contours close to the vertical axis reflects the sharp drop in numbers of households with PCE below the mode, but note the very wide range of food shares associated with any given level of PCE, even when the latter takes on extremely low values. Clearly, if the food share turns out to be a good welfare-ranking device, it will give results rather different from those which would be obtained using PCE. Even so, the empirical relationship  Table 3 Frequency Distribution (a) of Households Classified by Foodshare and Sector t ____I_ Frequency v l Cumulative Frequency, . moo share Urban I Rural Estate Urban Rural Estat <.15 0 0 0 0 0 0 < .20 0.2 0 0.1 0.2 0 0.1 S .25 0.4 0.1 0.2 0.6 0.1 0.2 < .30 1.3 0.2 0.2 2.0 0.4 0.4 < .35 2.2 0.8 0.4 4.2 1.1 0.7 < .40 3.7 1.6 0.9 7.8 2.7 1.6 s .45 6.0 2.8 2.4 13.8 5.5 4.0 < .50 7.2 4.8 3.9 21.0 10.3 7.9 < .55 9.8 6.5 6.1 30.8 16.8 14.0 s .60 11.1 10.8 10.0 41.9 27.6 24.0 < .65 13.3 13.4 13.7 55.2 41.0 37.7 < .70 14.2 17.6 15.7 69.4 58.6 53.4 .75 14.2 16.5 17.9 83.6 75.0 71.4 < .80 9.9 14.6 14.5 93.5 89.6 85.8 < .85 4.9 8.0 10.3 98.4 97.6 96.1 < .90 1.5 2.1 3.7 99.9 99.7 99.7 .95 0.1 0.2 0.3 100.0 100.0 100.0  X foodshare 95 90 Figure 2: Foodshare and PCF (All Island) 80 - t 70- 60- 4 50- 04~~~~~~~~~~~~~~~~~' , , .. 40 o 10 20 0 50 100 150 200 250 300 350 400 450, 500 550 600 per cpt xedtr Rupees/month  - 13 - between the food share and PCE is strong and inverse. It also has a consider- able (convex) curvature as might be expected from the strong positive skewness in the marginal distribution of PCE and the slight negative skewness in the marginal distribution of the food share. Much of the non-linearity in Figure 2 can be removed by the use of a simple logarithmic transformation. Figure 3 represents the same joint distri- bution as in Figure 2 but with the horizontal axis on a logarithmic scale. Clearly, the relationship is now much closer to a linear one, although, as will be demonstrated later, there is still some curvature remaining. However, if linearity is taken as a first approximation, Figure 3 suggests a relationship of the form winO0 + lnPCE + u (2) where w is the food share, u is an error, InPCE is the (natural) logarithm of PCE, and $0 and 01 are intercept and slope parameters respectively. This relationship, although here suggested entirely on empirical grounds, is both extremely convenient and of rather distinguished ancestry. It was first used for empirical Engel curve analysis by Holbrook Working (1943) and later recommended by Leser (1963) as a simple functional form which performed well in competition with other specifications. Also, unlike most of the traditional Engel curves, such as those examined by Prais and Houthakker (1955), it is possible for all goods to conform to the Working-Leser specification without violating the constraint that the sum of all budget shares be unity. This is sufficient for the model to be made consistent with the standard theory of consumer behavior with all its attendant apparatus for welfare analysis. Less essentially for present purposes, the model also possesses extremely elegant properties when applied to aggregates  Z foodshare 90 80 - t 70 . 60 I~~~~~~~~~~~I 50~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' 40- 30-I i 20 p Figure 3: Foodshare and_lnPCE 10- 0 per capita expend*- 0 I , Rupeeslmonth 10 20 50 100 200 400 Lpog scale  - 15 - of consumers. For more details and further disctission of the model see Deaton and Muellbauer (1980, Chapters 1, 3 and 5). Equation (2) may be estimated by ordinary least squares to yield:1/ Urban w - 1.3905 - 0.18482 lnPCE 2 (2a) (127.1) C-71.6) R = 0.561 o = .0917 Rural w = 1.2606 - 0.15310 1nPCE 2 (2b) (97.1) (-46.5) R = 0.372 c = .0933 Estates - = 1.2322 - 0.14270 laPCE 2 (2c) (58.2) (-26.4) R = 0.260 v = .0987 where w is the predicted value of w by the regression line, S is the equation standard error (compare with the mean values of w in Table 2) and the numbers in brackets are t-values. The equation standard error is (signi- ficantly) larger on the Estates even though (see.Table 2) the variability of the food share there is less; the combination of these two effects produces the low R2. Clearly, there are other important factors influencing the food share in that sector. By contrast, in the urban sector, the high R2 (compared, say, with the rural sector) is largely a consequence of the greater inequality there and the consequent high variance of the share. 1/ Note that for the predicted food-share to lie between 0 and 1, ln PCE and PCE must lie within a limited range. It may easily be checked that the range given by the estimated equations is very wide and that no household in the sample lies outside it.  - 16 - These results can be used to make first estimates of the total expenditure elasticity of food. From (2), the derivative of lnw with respect to the logarithm of total expenditure is I/w which, in turn, is the elasticity e less unity. Hence, e is calculated from e = a /w + 1 (3) if we use a value of 0.70 for w as (roughly) model for all three sectors, the elasticity estimates are 0.736, 0.781, 0.796 for urban, rural and estates respectively. It should be noted that formula (3) implies that increasing total outlay will cause the elasticity to fall (since < 0 for a necessity which also means that w falls with PCE). Hlowever, irn the present calculations, the same value (0.7) was used for w in (3) for all three sectors. Hence the results suggest that 51 itself may be a declining function of PCE. The next section will confirm this interpretation. D. DEMOGRAPHIC EFFECTS AND MULTIVARIATE ANALYSIS 1. Family Size and Composition In Section B per capita expenditure was used as the main indicator of wel- fare and the variable determining the food share. In this section, rather more sophisticated constructions are considered. Clearly, PCE is likely to be more satisfactory than total household expenditure (THE) in that some allowance is made for household size. However, a crude head count is likely to overstate family needs. In particular, children may have lesser needs than adults, and social customs may indicate unequal allocations among adults, for example, as between men and women. At the same time, there are likely to be economies of scale in the costs of maintaining a household, if only because of the presence of overhead costs independent of family size and which provide facilities shared by all members.  - 17 - Moreover, the presence of several adults and of older children in the household may generate services many of which are not monetized or officially imputed and so do not show up in either THE or PCE. Housemaking services, childminding, and so on are the obvious examples. To the extent that these consequences of larger families generate welfare unrepresented in THE or PCE, the food share may be lower than predicted from PCE alone. Stated another way, the apparent costs associated with larger families are lower than their head counts would suggest. Considering these factors together presents a rather complex picture of the relationship between household size and needs; it is undoubtedly too simple to regard household needs simply as a sum of individual needs, males counting as unity, females as something rather less, and children a fraction of unity depending on their age. One relatively straightforward possibility is to relate the food share to total household expenditure for different family types separately, in the hope that, for a given family type, compositional effects will be held constant. Figure 4 illustrates three (independently estimated) regression lines for three different household types in the urban sector (2 adults and 2 children, 4 adults and 1 child, and 2 adults and 0 children). Ideally, children should be disaggre- gated by age, but this would reduce the numbers of households in each class to unacceptably low figures. Even so, the results shown are rather interesting. All three regressions have very similar slopes, so that although the smaller family has a smaller food share at all levels of THE, most of this can be ascribed to the difference in intercept. The regression lines for the two large family types are very close, suggesting that, for these two groups, PCE is a good enough determinant of the food share, in spite of their differences in composition. Further, if each of those family types has THE increased by a factor of 2.5, so  0.9 --- 2 adu lts and 3 chLldren . . 0.8 | 'ISI C . *1 *. I 0.7. . - - _ _ 0.6. 4 adults and 1 child (128 hou'eholds) 0.5 co-~ f-...--- I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I. { 8 i ~~~~0 chilldren,\X 0.4 _ l _ .(2l7 households) L. - Figure 4: Food shareland inTHE fbr selected - | urban hous'p7ho1d types l . 0.2 - - - -i ,__________________________________________total household expenditure1 log scale 0(1 00 1,!  - ] 9 - that they have the same PCE as the smaller family, the two higher lines are moved down by 0.12 throughout, which brings all three lines very close together. This rather limited evidence, then, suggests that PCE works surprisingly well, at least as a first approximation. However suggestive, it is not really practical to analyze each family type separately, at least in Sri Lanka. In many developed countries, a small number of family types would cover a large proportion of households, but this is not true of LDC's. Table 4 gives the figures for the three sectors of Sri Lanka. Although two adult families are the most common, the dispersion over types is very wide so that in order to fit separate Engel curves for the most important types, a large number of different cases would have to be considered. And even this would take no account of sex or of children's ages. Clearly, a more economical approach must be adopted.  Table 4: Adult and child composition of Sri L.nkan families by sector (%) No. of children 11u1. of children _-0 12 3 4 >5 = 01 2 3 4 >5 1 1. Urban 1 _ 0.3 0.2 0.2 0.1 0.2 1.0 I 0.1 0.1 0.2 0.1 0.3 0.7 Z of households 2 5.4 4.6 4.9 5.2 3.7 4.8 28.6 X of persons 2 1.7 2.2 3.2 4.2 3.6 5.9 20.8 (4022) -25-8)-- -- 3 4.7 3.5 3.3 2.7 2.6 3.0 19.8 (253S8) 3 2.3 2.2 2.6 2.6 2.9 4.3 16.9 No. 4 3.8 3.2 2.9 2.6 1.9 2.7 17.1 No. 4 2.5 2.5 2.8 2.9 2.5 4.2 17.3 of of -- - - adults 5 3.0 2.5 1 2.4 1.6 1.9 13.5 dlt 5 2.4 2.4 2.3 3.1 2.3 3.3 15.8 >6 4.3 4.1 3.3 3.1 2.2 2.8 19.8 >6 4.8 5.2 4.0 5.0 4.0 5.6 28.6 E 21.2 18.2 16.7 16.2 12.1 15.4 100 E 13.7 14.6 15.0 17.9 15.3 23.6 100 No. of children rio. of children 01i- 2 3 4 5 0 I 2 3 4 >5 - 0 I4 > I 1 * 0.4 0.4 0.1 0.3 0.2 1.4 1 * 0.1 0.2 0.1 0.2 0.2 0.8 2. Rural __ - - 2 of households 2 6.4 5.7 6.7 5.8 4.7 4.7 34.0 % of persons 2 2.2 2.9 4.6 5.0 4.8 6.1 25.5 (3652) 3 5.9 3.7 3.3 2.6 2.8 3.6 21.9 (21464) 3 3.0 2.5 2.8 2.7 3.3 5.2 19.6 No. 4 3.5 3.5 3.1 2.2 2.5 2.9 17.7 No. 4 2.4 2.9 3.2 2.6 3.4 4.9 19.4 of 5 2.7 2.3 1.7 1.2 2.1 12.4 5 2.3 2.5 2.8 2.4 1.8 3.6 15.4 adults _-- . ...... ......... adults ____- -. +---- 1-- - - - I -O >6 2.7 2.6 2.7 2.2 1.1 1.3 12.6 >6 3.1 3.4 3.8 3.5 2.3 3.2 19.4 E 21.2 18.3 18.5 14.6 12.6 14.8 100 1 13.0 14.4 17.4 16.2 15.7 23.2 100 No. of chlildru No. of children o | 1 | 2 | 3 1 4 | >5 | z | [ | 0 1 2 3 | >S | 1' 1:.8 0.6 0.3 0.3 0.0 2.0 1 * 0.3 0.3 0.2 0.3 0.0 1.2 3. Estates -- Z of householis 2 11.0 8.1 8.3 6.4 4.0 3.7 41.5 | of persons 2 4.3 4.7 6.5 6.0 4.6 5.3 31.4 (1989) 3 6.6 3.8 3.5 2.8 1.9 1.2 19.8 (10347) 3 3.8 2.9 3.4 3.2 2.5 2.1 18.0 No. 4 4.8 3.0 3.2 2.0 1.4 1.5 15.9 No. 4 3.7 2.9 3.7 2.6 2.1 2.9 18.0 of 5 2.6 2.8 2.1 1.7 1.2 1.0 11.4 of 5 2.5 3.2 2.8 2.6 2.0 2.1 15.4 -.tt t -- t I---- adults| adults 1.5 1.8 1.7 2.0 1.0 1 " '6 I.m Y.h 3.1 4.0 2.2 2.5 1I.2 2 6.5 20,3 19.4 15.2 9.8 8I.8 100 | 1| .1 16. /I19.7 18.6 13.8 15.0 IU0 * Single person households were excluded from the sample. t Adults are persons aged 1.5 or over, children tho:;e aged 0-14.  - 21 - 2. Multivariate Analysis Given the results of Figure 4, it seems sensible to go back to the PCE formulation and modify it by entering the numbers of household members of each type as separate variables. Hence, the basic equation (2) might become: K w S+ allnPCE + nk+u (4) where nk is the number of persons of type k in each household, i.e. number of male and female children of different age groups, number of old people and so on. Note that (4) is not supposed to represent any specific model of how needs are generated in the household; rather it is in the spirit of a "flexible functional form" where the important variables are allowed at least one un- restricted parameter each and which can be thought of as a suitable lineari- zation of whatever is the true (complex) process linking family composition, welfare, and the food share. In practice, (4) was modified still further prior to estimation. First, in order to allow for the remaining curvature in the relationship between the food share and lnPCE, the square of lnPCE was also introduced. Second, it must be noted that the survey was conducted in four rounds, the first in April, May and June of 1969, the third in October, November and December 1969 and the fourth and last in January, February and March 1970. To the extent that there are seasonal patterns in food consumption, the results of different rounds may be different; there are also seasonal fluctuations in prices and availability of some foodstuffs and these too may induce seasonal fluctuations in the food share. Hence, the regression specification used in this section is: K 2 4 v m a + 6 lnPCE+J6k u + y(lnPCE) + J'dk + u (5) 0 1 2 kk 2'-  - 22 - where dk, k - 2,3,4, is a dummy corresponding to rounds 2, 3, and 4. The maximum disaggregation of household members was into eleven classes as follows: