LS.IT1S LSM - 62 Living Standards JAN. 1990 Measurement Study Working Paper No. 62 Testing for Significance of Poverty Differences With Application to Cote d'Ivoire Nanak Kakwani 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 Nations 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. 11 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 C6te d'lvoire 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 No. 28 Analysis of Household Expenditures No. 29 The Distribution of Welfare in Cote d'Ivoire in 1985 No. 30 Quality, Quantity, and Spatial Variation of Price: Estimating Price Elasticities from Cross-Sectional Data No. 31 Financing the Health Sector in Peru No. 32 Informal Sector, Labor Markets, and Returns to Education in Peru No. 33 Wage Determinants in Cote d'Ivoire No. 34 Guidelines for Adapting the LSMS Living Standards Questionnaires to Local Conditions No. 35 The Demand for Medical Care in Developing Countries: Quantity Rationing in Rural Cote d'Iwire (List continues on the inside back cover) Testing for Significance of Poverty Differences With Application to C8te d'Ivoire 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 house- hold data collected by statistical offices in developing counties. Its goal is to foster increased use of household data as a basis for policy decsionmaking. Specifically, the LSMS is working to develop new methods to monitor progress in rmising levels of living, to identify the consequences for households of past and proposed gov- ernment policies, and to improve communications between survey statisticians, an- alysts, and policymakers. The ISMS Working Paper series was started to disseminate intermediate prod- ucts from the LSMS. Publications in the senres include critical surveys covering dif- ferent aspects of the LSMS data collection program and reports on improved methodologies for using Living Standards Survey (LSS) data. More recent publica- tions recommend specific survey, questionnaire, and data processing designs, and demonstrate the breadth of policy analysis that can be carried out using LSS data. LSMS Working Paper Number 62 Testing for Significance of Poverty Differences With Application to CMte d'Ivoire Nanak Kakwani The World Bank Washiton, D.C. Copyright © 1990 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 January 1990 This is a working paper 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 findings, interpretations, and conclusions expressed in this paper are entirely those of the author(s) and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they represent. 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The complete backlist of publications from the World Bank is shown in the annual Index of Publications, which contains an alphabetical title list and indexes of subjects, authors, and countries and regions; it is of value principally to libraries and institutional purchasers. The latest edition is available free of charge from the Publications Sales Unit, Department F, The World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A., or from Publications, The World Bank, 66, avenue d'Iena, 75116 Paris, France. Nanak Kakwani is a professor and head of the Department of Econometrics at the University of New South Wales, Australia, and a consultant to the Welfare and Human Resources Division of the World Bank's Population and Human Resources Department. Library of Congress Cataloging-in-Publication Data Kakwani, Nanak. Testing for significance of poverty differences with application to Cote d'Ivoire / Nanak Kakwani. p. cm. - (LSMS working paper, ISSN 0253-4517; no. 62) Includes bibliographical references (p. ). ISBN 0-8213-1426-2 1. Poor-Ivory Coast-Statistical methods. 2. Households-Ivory Coast--Statistical methods. I. Title. II. Series. HC1025.Z9P615 1989 362.5'2'096668-dc2O 89-70647 CIP v ABSTRACT Several poverty indices have been suggested to measure the intensity of poverty suffered by those below the poverty line. Because the studies are estimated on the basis of sample observations, we need to test whether the observed differences in their values are statistically significant. This paper provides distribution free asymptotic confidence interval and statistical inference for several poverty indices. The methodology developed in the paper is applied to analyze poverty in C6te d'Ivoire from the data of the Living Standards Survey, 1985. : - vi -: :: f : ::: : : : : t : : : : : X 0 f : : : : f C8T 0 : : : 7: : :: : V 0 The paper could not; have been completed without the invaluable : computaLtional assistanLce of Kalpana Mehra. Thanks are also due te M^ria Belis for typing and to Brenda0RosaWfor etiting the manuscript:. 0 : : : :; :: 0 t i; 0 : : : : : : u : 0 : X : 0 f C 0 :; j . : - : X :E :S S : : : : : : : : : D : : : : : : :0:: : : . f T: - 0 X 0 f : : : : 000 f 000 0 :::: : : f : : : : k S 0 . R : :: :: f l: :: t: : t: : : : f : : 0 0 f : : - vii - TABLE OF CONTEMTS 1.* Introduction .............. ........................................ 1 2. A Brief Review of Poverty Measures................................3 3. Specific Poverty ....................... . 8 4. Confidence Interval and Hypothesis Testing.........................9 5. Asymptotic Distribution of Poverty Measures......................lI 6. Application to C6te d'Ivoire. ... ........................ * .O..14 7. Breakdown of Aggregate Poverty by Socio-economic and Demographic Household Characteristics.........0.00.0..0 000000....18 ...................C... 36 Referenceso oooooo*ooooeoeeooooooooeooooo39 LIST OF TABLES TABLE 1: Poverty Measures and their Standard Errors: C8te d'Ivoire, 1985 16 TABLE 2: Poverty Comparison by Sex of Household Head: C8te d'Ivoire, 1985 19 TABLE 3: Poverty Comparison by Nationality of Household Head: C8te d'Ivoire, 1985 20 TABLE 4: Poverty Comparison by Size of Household: C8te d'Ivoire, 1985 21 TABLE 5: Statistics for Testing-Significance of Poverty Differences Among Households of Different Size: Cote d'Ivoire, 1985 22 TABLE 6: Poverty Comparison by Regions: C8te d'Ivoire, 1985...S oo...24 TABLE 7: Statistics for Testing Significance of Poverty Differences Among Regions: C8te d'Ivoire, 1985 ooo..25 TABLE 8: Poverty Comparison by Age of Household Head: C6te d'Ivoire, 1985 .... - viii - LIST OF TABLES (Continued) TABLE 9: Statistics for Testing Significance of Poverty Differences Among Households with Different Age of Household Head: C6te d'Ivoire, 1985 ....................25 TABLE 10: Poverty Comparison of Households According to Employer of Household Head: C8te d'Ivoire, 1985..........31. TABLE 11: Statistics for Testing Significance of Poverty Differences According to Employer of Household Head: C8te d'Ivoire,195................................... 3 TABLE 12: Poverty Comparison by Education of Household Head: C6te d'Ivoire, 1985....................... TABLE 13: Statistics for Testing Significance of Poverty Differences Among Households with Different Educational Levels of Household Head: C6te d'Ivoire, 1985. .************.35 1. INTRODUCTION To formulate an adequate program to combat poverty, it is essential to identify the poor and measure the intensity of their poverty. Thus, the measurement of poverty involves two distinct problems: (1) the specification of the poverty line - the threshold below which one is considered to be poor; and (2) once the poverty line is determined, construction of an index to measure the intensity of poverty suffered by those below that line. Since the publication of Sen's (1976) article on the axiomatic approach to the measurement of poverty, several indices of poverty have been developed, which make use of three poverty indicators: - the percentage of poor, - the aggregate poverty gap and - the distribution of income among the poor.l/ These measures differ on the assumptions made about the welfare function implied by them. Because the poverty measures are estimated on the basis of sample observations, we need to test whether the observed differences in their values are statistically significant. No significant tests have been devised for poverty measures because of their complex nature. The paper considers the See for instance Sen (1979), Takayama (1979), Kakwani (1980, 1980a), and Clark, Hemming and Ulph (1981), and Thon (1983). For a review of the literature on poverty indices, see Clark, Hemming and Ulph (1981) and Kakwani (1984). -2- problem of statistical inference with estimated poverty measures. The problem is of considerable importance because we are often interested in knowing if poverty has increased or decreased over time or in comparing poverty differences between countries or various socio-economic groups within the same country. The asymptotic distributions for poverty measures are derived. The results are used to provide distribution free asymptotic confidence interval and statistical inference for poverty measures. The methodology developed in the paper is applied to analyze poverty in C8te d'Ivoire. The data for this purpose were obtained from the 1985 Living Standards Survey in the C6te d'Ivoire. A description of the survey and sampling methodology is given in Ainsworth and Muhioz (1986). 2. A BRIEF REVIEW OF POVERTY MEASURES Suppose income x of an individual is a random variable with the distribution function F(x). Let z denote the poverty line - the threshold income, below which one is considered to be poor. Then F(z) is the proportion of individuals (or families) below the poverty line and has been widely used as a poverty measure. This measure is called the head-count ratio. The head-count is a crude poverty index because it does not take account of the income-gap among the poor. If the degree of misery suffered by an individual is proportional to the income shortfall of that individual from the poverty line, then the sum total of these shortfalls may be considered an adequate measure of poverty. Such a measure is called the poverty gap ratio and can be written as: C = fz g(x)f(x)dx = F(z)[z(!i] (2.1) 0 ~~~~~~z where g(x) = (z-x)/z, f(x) is the density function and U* the mean income of the poor. The measure P will provide adequate information about the intensity of poverty if all the poor are assumed to have exactly the same income, which is less than the poverty level. In practice, the income among the poor is unequally distributed and, therefore, P cannot be an adequate measure of intensity of poverty. More inequality of income among the poor with the mean remaining unchanged should imply greater hardship to the extremely poor in a society, and therefore, the degree of the poverty should be higher. -4- To make G sensitive to the income inequality among the poor Sen (1976) proposed the following poverty measure: S = F(z) [z-p*(1"G*)]/z where V* is the mean income of the poor and G* is the Gini index of the income distribution among the poor. He arrived at this measure on the basis of rank order weighting, which in some way captures the relative deprivation aspect of the poverty. Suppose that the population is divided into m groups according to certain socio-economic and demographic characteristics of households to which individuals belong. Let fi(x) be the density function of the ith group. Further, suppose that due to certain government policies, the density function of the ith group changes from fi(x) to fi *(x) and the distributions of the 1 remaining (m-1) groups have not changed at all. As a consequence, the poverty measure Pi of the ith group has changed to Pi such that Pi > Pi Intuitively then the poverty in the entire population must increase. This property requires that the subgroup and total poverty must move in the same direction. Unfortunately, Sen's povetrty measure violates this simple requirement in certain cases. This violation occurs because Sen's measure is not additive separable. A class of additively separable poverty measures is given by P = JO e(z,x) f(x)dx (2.2) where 0(z,x) is a function of the poverty line z and income x. P is equal to -5 - the head-count measure of poverty when O(z,x) = 1.0. The poverty gap measure in (2.1) is obtained when B(z,x) = (zx) The probability density function f(x) of the entire population may be written as m f(x) = £ B. f.(x) (2.3) i=l 2. 1 where fi(x) is the probability function of the ith subgroup which has m the Xi proportion of individuals such that E X. = 1 or in other words all 2. ~~~~~~~~~i=l1 the subgroups are mutually exclusive. Multiplying both sides of (2.3) by G(z,x) and integrating we obtain m p =z X. P. i=l1 1 where Pi is the poverty measure for the ith subgroup. It implies that total poverty is a weighted average of the subgroup poverty levels, the weights being proportional to the population shares. These poverty measures are called additively decomposable (Foster, Greer and Thorbecke, 1984). Thus, we have proved that all additively separable poverty measures are additively decomposable. The additively decomposable poverty measures are useful because they allow assessment of the effects of changes in subgroup poverty to total poverty. If the population is disaggregated according to some socio-economic and demographic characteristics, it is of interest to know how the poverty in the population is related to each subgroup, that is, how much is the -6- contribution of each subgroup to total poverty. Sen's poverty measure is inadequate to analyze such issues because it is not additively decomposabile. An important attribute of Sen's measure is that it captures the relative deprivation which Sen considers to be central to the notion of poverty. But, in the context of developing countries where the majority of people live below the subsistence level, the idea of relative positions of the poor is not very appealing. Our concern should be with the absolute deprivation rather than with the relative deprivation. To make the poverty measures in (2.2) operational we need to specify O(z,x). First, we consider some general restrictions which may be imposed on this function. It can be easily seen that Sen's monotonicity axiom (which implies that, given other things, a reduction in the income of a poor individual must increase the poverty measure) will be satisfied by (2.2) if e(z,x) is a decreasing function of x; that is, @< 0. Second, we consider Sen's transfer axiom which states that "givein other things, a pure transfer of income from a poor individual to any othLer richer individual must increase the poverty measure". This axiom will be satisfied if O(z,y+a) - O(z,x-6) > 0 2 a30 for y > x or in other words =! > 0. ax - 7 - Kakwani (1980) introduced the transfer sensitivity axiom which states "if a transfer of income takes place from a poor with income x to a poor with income (x+h) then for a given h > 0, the magnitude of increase in poverty measure decreases as x increases". This axiom gives more weight to transfers of income at the lower end of the distribution than at the higher end. If a society is particularly averse to inequality among the poor, the poverty measure must give maximum weight to a transfer from the poorest poor and the weight should decrease with the level of income. This axiom in the case of poverty measures in (2.2) implies that aQ (0, where ax Q = O(z,x * h + 6) - e(z,x - 6). 3 for fixed h > 0 and 6 > 0 or in other words a < 0. ax Finally, we require that doubling all incomes and doubling the poverty line should leave the poverty measure unaltered. This requirement can be met by specifying O(z,x) to be a homogeneous of degree zero in z and x or in other words 0(kz,kx) = O(z,x). 3. SPECIFIC POVERTY MEASURES Foster, Greer and Thorbecke (1984) proposed a class of poverty measures which are additively decomposable. This class of measures is a obtained if we substitute a = (Z x) in (2.2): x a P .f ( s ) f(x)dx (3.1) where a is a parameter to be specified. These measures satisfy Sen's monotonicity axiom for a > 0 and transfer axiom for a > 1. When a > 2, P also satisfies Kakwani's transfer-sensitivity axiom. a In 1968, Watts proposed a poverty measure which can be obtained by substituting e(z,x) = logz - logx: W = .f (logz - logx) f(x)dx (3.2) Although this is an extremely simple poverty measure, at the same time it has all the important attributes: it satisfies Sen's monotonicity and transfer axioms and also Kakwani' s transfer-sensitivity axiom. Finally, we consider the Clark, Hemming and Ulph (1981) poverty measure which can be obtained by substituting O(z,x) = - [1 - (x)B]: Co = Bfz [1 - (x) I f(x)dx (3.3) and clearly satisfies Sen's monotonicity axiom for all B > 0. Both transfer and transfer sensitivity axioms will be satisfied for all B < 1. Thus, B must lie in the range 0 < B < 1. 4. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING Let xl, x2,.,., xn be a random sample of n observations drawn from a population with mean p and variance a . Suppose P given in (2.2) is a poverty measure defined in terms of the population distribution and P is its sample estimate based on n observations. It will be demonstrated below that /n (P-P) is asymptotically normally distributed with zero mean and variance 2* A2I (2ic 2 ^ a (P). If a (P) is a consistent sample estimator of a (P), a6W/n is called the standard error of P, which we denote by SE(P). Then = P-r (4.1) SE(P) is distributed asymptotically normal with zero mean and unit variance. Thus, t can be used to form a distribution free confidence interval for poverty measures. Further, suppose P1 and P2 are estimates of a poverty measure P computed on the basis of two independently drawn random samples of sizes n A2 *2 and n2, respectively. Let a1 and a2 be the sample estimators of the variances A -A of the asymptotic distributors of n-1PI and /nP2, respectively, then the standard error of (P - P2) will be 2 22 SE(P -P ) = and the statistic = A1- A2 (4.2) SE(P1 -P1) - 10 - follows asymptotic normal distribution with zero mean and unit variance. Thus, n can be used to test the null hypothesis that the observed poverty differences in any two samples are statistically insignificant. To calcuLate t and n, we need to derive the asymptotic distributions of various poverty measures which is attempted in the next section. - 11 - 5. ASYMPTOTIC DISTRIBUTION OF POVEBTY MEASURES Suppose that q (5n) is the number of people who have income below the poverty line, then H = q/n is a natural estimator of the head-count ratio F(z). Let Ii =1, xi < z (5.1) = 0, otherwise. Obviously then P [I 1] F(z) and P(I. 0]1 = - F(z) r ir 2 and n E=l i Pr stands for probability. H is a binomial variate with parameters n and F(z). The central limit theorem implies that /n (H - F(z)) follows an asymptotic normal distribution with zero mean and variance F(z) (1 - F(z)] (Cramer, 1946). Thus, the standard error of H will be /I which, in conjunction with (4.1), provides a distribution free statistical inference for the head-count ratio. A sample estimate of the class of additively separable poverty measures P in (2.2) is given by . 1 q P = _z e(zx) (5.2) n i=1 i which when using (5.1) can also be written as - 12 - n 1 (53) P =- M ....... 53 ni=l where Mi = IO.(z,x.) Note that E(M.) = JO 9(z,x) f(x)dx = P 0 which implies that P is an unbiased estimator of P. Because the sample observations xi and Xj are independently distributed, it implies that Mi and M. will also be independently distributed. Applying central limit theorem on (5.3) (Cramer 1946), leads to the result that /n (P - P) is asymptotically normally distributed with zero mean and variance 2 2 = Z2 Z)2 aM = E[M. -P1 = fO e(z,x) f(x)dx - P (5.4) A sample estimate is A 2 1 q 2 ^2 aM = nE £ (z,xi) - P (5.5) n i=l It can be seen, when O(z,x) = 1.0, that P is identical to the head- count ratio and, therefore, a2 becomes F(z) [1 - F(z)] which is in fact the - 13 - variance of i/n H as derived above. Similarly, if we substitute e(z,x) = Z'x, 2 z 7 in (5.4) it gives the variance of /n G, G being the unbiased estimate of the poverty gap ratio given in (2.1). The above formulation allows us to find the asymptotic distribution of all the specific poverty measures discussed in Section 3. Thus, the sample estimates of the variance of these measures are: ~~~2 (1) var (in Pa P2a a A 1 q z-x. where P = - ( £ ) a n i z A =1q2 A2 (2) var (/n W ) n E (logz - logx.) -w 1q where W = - Z (logz - logx.) (3) var (i- A 1 q * A a 2= i= On q X where C= [H - 1 z ( 1)a] s W n i=1 z - 14 - 6. APPLICATION TO COTE D'IVOIRE The methodology developed in this paper is applied to the data obtained from the Cote d'Ivoire Living Standards Survey, conducted by the World Bank's Living Standards Unit and the Direction de la Statistique, Ministere de l'Economie et des Finances of the Republic of C6te d'Ivoire in 1985. To analyze poverty, we need to measure the economic welfare of each individual in the society. Although income is widely used to measure economic welfare, it has many serious drawbacks.2/ In this paper we have used per capita adjusted consumption as a measure of household economic welfare. This measure, constructed by Gleuwe (1987), takes account of the imputed value of owner-occupied dwelling, regional price variation and depreciated value of consumer durables. To take account of the differing needs of various household members, Glewwe dividLed the total household consumption by the number of equivalent adults. In bhis formulation of equivalent adults, children were given smaller weight than adults: children less than seven years old were given a weight of 0.2; between the ages of seven and thirteen a weight of 0.3, and between the ages of thirteen and seventeen a weight of 0.5. When the index of household welfare is constructed, the next step involves the determination of the welfare of the individuals in the household. In this paper individual welfare was derived by assigning every individual in a household a welfare value equal to the consumption per 2/ For a detailed discussion of this issue see Kakwani (1986). - 15 - equivalent adult for that household. The validity of this approach is discussed in Kakwani (1986). Once we have decided upon a suitable index of economic welfare for individuals, the next step is to find a threshold welfare level below which an individual is poor. In this paper we have considered two poverty lines: one with adjusted per capita consumption of 91394 CFAF and another of 162613, CFAF per year. The two poverty lines identify approximately the poorest 10 percent and the poorest 30 percent of the total Ivorian population. As measured in adjusted per capita terms, consumption for the poorest 10 percent of Ivorians is less than 20 percent consumption for the average Ivorian; the poorest 30 percent consume about one third of the national average. The poverty line of 91394 CFAF per year, in our opinion, measures the ultra-poverty situation, below which physical personal maintenance is unstable (Lipton 1988). The numerical values of various poverty measures and their standard errors are presented in Table 1. The t-value in the table is equal to the value of poverty measure divided by its standard error (see equation 4.1). This statistic follows an asymptotic normal distribution with zero mean and unit variance. If t exceeds 1.96, it means that the hypothesis of zero poverty is rejected at 5 level of significance. This method is valid subject to the condition that our sample is large. In practice, it is often difficult to know whether our samples -are so large that these large sample approximations are valid. However, the approximation is usually good for samples larger than 30 (Cramer 1946). Because our analysis of poverty is based on sample sizes larger than 250, the statistical inference based on asymptotic distributions is appropriate. - 16 - TABLE 1: Poverty Measures and their Standard Errors: Cate d'Ivoire, 1985 Poverty line = 162.61 Poverty line = 91.39 Poverty Measures Value Standard Value Standard Z error t-value Z error t-value Head-count Ratio 27.76 1.13 24.57 9.36 0.73 12.82 Poverty gap Ratio 9.34 0.48 19.46 2.42 0.24 10.08B Watts Measure 13.22 0.75 17.63 3.22 0.35 9.20 Foster et Measures a = 2.00 4.42 0.28 15.78 0.98 0.13 7.54 = 3.00 2.43 0.19 12.79 0.49 0.08 6.12 Clark et Measures c = 0.25 12.01 0.66 18.20 2.98 0.32 9.31 0.50 10.98 0.58 18.93 2.77 0.29 9.55 0.75 10.10 0.52 19.42 2.58 0.26 9.912 0.95 9.48 0.48 19.75 2.45 0.25 9.914 The table shows that the values of t are considerably larger than 1.96 (varying from 12.79 to 24.57 for the poverty line 162613 CFAF) which leads to the conclusion that a large degree of poverty exists in Cate d'Ivoire. However, an important observation to be made is that the numerical values of t differ considerably for different poverty measures. The size of t indicates how large the standard error of a poverty measure is relative to its value. Thus, the larger the value of t the greater is the precision with which the poverty measure can be estimated from a given sample. Among all the poverty measures presented in the table, the head-count ratio gives the - 17 - smallest confidence interval relative to its value. But the head-count ratio is a crude measure of poverty because it does not take account of the depth of poverty. The precise estimation of a poverty measure depends on how sensitive the measure is to income transfers among the very poor. For instance, in the case of Foster, Greer and Thorbecke's poverty measures, a is a measure of degree of inequality aversion - the larger the value of a, the greater weight is attached to the poorest poor. The numerical results suggest that the precision of this class of poverty measures is a monotonically decreasing function of a. If our value judgement suggests that the greater weight be attached to income transfers among the most poor, we must select a poverty measure with high value of a. But if we cannot obtain a precise estimate of such a poverty measure from a given sample, its usefulness is limited even if it may have all the desirable properties from the welfare point of view. Should we reject a desirable poverty measure because of its undesirable statistical properties? This is a difficult question to answer particularly when the sample size is small. - 18 - 7. BREAKDOWN OF AGGREGATE POVERTY BY SOCIO-ECONOMIC AND DEMOGRAPHIC HOUSEHOLD CHARACTERISTICS This section focuses on testing for significance of poverty differences between various socio-economic and demographic groups. Table 2 presents poverty comparisons by sex of household head. It is of interest that the mean consumption (adjusted) of female-headed households is about 20 percent higher than those of male-headed households. The difference between the mean consumption of the two household groups is statistically significant at 5 percent level (see Table 2, last row). With the exception of P for a = 3.0, all the remaining poverty measures show that poverty is significantly higher among male-headed households. This is a surprising result because in many developing and also developed countries, female-headed households are often poorer than those headed by males. Some explanation of the situation has been provided by Glewwe (1987) who observed that female- headed households are disproportionately located in Abidjan and other urban areas which are considerably richer than the rural areas. Several nationalities live in C8te d'Ivoire but Ivorians are the most dominant comprising 85.7 percent of the surveyed population. For our poverty comparisons we have placed all other nationalities into one group. The comparisons are provided in Table 3. It is interesting to note that the adjusted per capita consumption is almost identical in the two groups. The difference is insignificant at the 5 percent level as is shown by a value of -0.11 for n given in the last column of the table. Therefore, any significant difference in poverty levels will be due to a difference in within group consumption inequalities. - 19 - TABLE 2: Poverty Comparlson by Sex of Household Head: C8te dlvolre, 1985 Poverty Line a CFAF 162.61 Femaie-Headed Households Male-Headed Households Poverty Measures Value Value of of Poverty Standard Poverty Standard n Measure error t-value Measure error t-value Head-count Ratio 16.96 3.37 5.03 28.46 1.19 23.92 -3.22* Poverty gap Ratio 5.73 1.38 4.15 9.57 0.50 19,14 -2.62* Watts Measure 8.10 2.16 3.75 13.55 0.79 17.15 -2.37* Foster et Measures a = 2.00 2.70 0.81 3.33 4.53 0.30 15.10 -2.12* 3.00 1.49 0.54 2.76 2.49 0.20 12.45 -1.74* Clark et Measures c = 0.25 7.36 1.90 3.87 12.31 0.69 17.84 -2.45* = 0.50 6.74 1.69 3.40 11.25 0.61 18.44 -2.51* = 0.75 6.20 1.52 4.08 10.35 0.55 18.82 -2.57* Mean consumption per person CFAF 406.96 34.21 11.90 337.64 9.47 35.63 1.95 * Poverty differences are significant at 5% level. Table 3 shows that among Ivorians, 28.38 percent of the population is poor as against 24.04 percent among other nationalities. But these differences are statistically insignificant at the 5 percent level. Thus, the hypothesis that the two groups have the same proportion of poor cannot be rejected. The other poverty measures, however, show that poverty among Ivorians is significantly higher than that among other nationalities. These - 20 - TABLE 3: Poverty Comparison by Nationality of Household Head: C8bt d'lvoire, 1965 Poverty Line = CFAF 162.61 Ivorian Others Poverty Measures Value Value of of Poverty Standard t Poverty Standard t Ti Measure error Value Measure error Value Head-count Ratio 28.38 1.25 22.70 24.04 2.60 9.25 1.50 Poverty gap Ratio 9.77 0.54 18.09 6.78 0.92 7.37 2.80* Watts Measure 13.94 0.85 16.40 8.89 1.29 6.89 3.27* Foster et Measures a= 2.00 4.70 0.32 14.69 2.75 0.46 5.98 3.48* = 3.00 2.62 0.22 11.91 1.29 0.26 4.96 3.91i' Clark et Measures c = 0.25 12.63 0.75 16.84 8.26 1.17 7.06 3.14i' = 0.50 11.52 0.66 17.45 7.71 1.08 7.14 3.01' = 0.75 10.58 0.59 17.93 7.22 0.99 7.27 2.92* Mean consumption per person 341.52 10.22 33.42 343.87 19.43 17.70 -0.11 * Poverty differences are significant at 5% level. conflicting conclusions emerge because the head-count ratio is insensitive to the poverty gap as well as the distribution of income among the poor. From these observations, we conclude that the depth of poverty among Ivorians is significantly higher than that among other nationalities. Thus, the poverty analysis based on head-count ratio can lead to the misleading conclusion that the two groups have the same poverty level. TJALE 4: Poerty Comparison by Size of Houseold: C60B d'lvoire, 1985 Poverty Line = CFAF 162.61 Small Households Medium Size Households Large Households Poverty Measures Value Value Value of of of Poverty Standard t Poverty Standard t Poverty Standard t M_ Measure error Value Measure error Value Measure error Value Head-count Ratio 15.20 1.88 8.09 23.40 2.36 9.92 29.75 1.54 19.32 Poverty gap Ratio 5.28 0.81 6.52 7.73 0.96 8.05 10.02 0.65 15.42 Watts Measure 7.93 1.41 5.62 10.69 1.44 7.42 14.17 1.02 13.89 Foster et Measures a = 2.00 2.66 0.52 5.12 3.55 0.54 6.57 4.75 0,39 12.18 = 3.00 1.58 0.39 4.05 1.87 0.34 5.50 2.61 0.26 10.04 Clark et Measures = 0.25 7.05 1.19 5.92 9.79 1.28 7.65 12.88 0.90 14.31 5 0.50 6.34 1.03 6.16 9.01 1.15 7.83 11.78 0.89 14.72 - 0.75 5.76 0.90 6.40 8.33 1.05 7.93 10.83 0.72 15.04 Mean consumption per person 529.69 31.05 17.06 422.62 28.0 15.09 309.43 9.68 31.97 - 22 - TABLE 5: Statistics for Testing Significance of Poverty Differences Among Households of Different Size: C6te d'Ivoire, 1985 Small Households Small Households Medium Householdis Poverty Measures Medium Households Large Households Large Households Head-count Ratio -2.72* -5.99* -2.25* Poverty gap Ratio -1.95* -4.56* -1.98* Watts Measure -1.37 -3*59* -1.97* Foster et Measures a - 2.00 -1.19 -3.22* -1.80 = 3.00 -0.56 -2.20* -1.73 Clark et Measures B = 0.25 -1.57 -3.91* -1.97* = 0.50 -1.73 -4.17* -1.98* = 0.75 -1.86 -4.40* -1.96* Mean consumption per person 2.56* 6.77* 3.82* * Poverty differences are significant at 5% level. The household size is an important demographic variable that has an impact on poverty. A large household has greater needs than a small household. In several studies it has been observed that larger households also tend to have higher income because such households probably have on average a greater number of persons in the work force (Kakwani 1986). The question whether the larger households are better or worse off has important implications because of the closer association between the government poverty reduction programs and the number of dependent persons in the household. - 23 - Table 4 presents the numerical estimates of various poverty measures and their standard errors when the households are classified according to size. The three classifications used are: small households (1 to 4 members); medium size households (5 to 6 members), and large households (7 and more members). All the poverty measures show that small households have the least poverty and large households the highest poverty. In all cases the t values are considerably larger than 1.96 showing that high and significant poverty levels exist in each of the three househoid size classifications. To test if the poverty differences between households of different sizes are statistically significant we computed the values of n for all possible pairs of households classified according to their size. The numerical results are presented in Table 5. All poverty measures presented in Table 5 show that the large households have significantly higher poverty than the small and medium households. The poverty differences between small and medium households are statistically significant only for the head-count ratio and the poverty gap ratio. For the remaining poverty measures, the hypothesis of equal poverty levels in the two groups cannot be rejected at 5 percent significance level. This analysis indicates that the large households are almost certainly more susceptible to poverty than the small and medium sized households. The C8te d'Ivoire may be divided into five regions: Abidjan, Other Urban, West Forest, East Forest and Savannah. The first two regions are the urban areas and the remaining three are the rural areas. About 60 percent of Ivorians live in rural areas. Table 6 presents the poverty estimates and their standard errors according to the geographical location of the "E 6: ty _wJm by _n ak Iixe dISO Poverty Une - CFAF 162.61 Abldjan Other Urban West Forest East Forest Savamah Poerty Iuabz Vale Vabue Value Value Value Of Of Of Of Of __erty Stardard t Poverty Stamdard t Pverty Stardard t Poverty Standard t Poverty Standard t ?haure error Value !¢asure error Value lIhsure error Value Ibasure error Value ?hasure error Value Hmke-t Ratio 5.25 1.22 4.30 11.94 1.78 6.71 18.JO 2.51 7.33 39.13 2.57 15.23 61.62 2.79 22.09 Poerty gap atio 1.26 0.36 3.50 2.68 0.52 5.15 5.30 0.93 5.70 12.52 1.05 11.92 24.38 1.49 16.36 lbtts -lze 1.58 0.47 3.36 3.41 0.72 4.74 7.21 1.36 5.30 17.25 1.64 10.52 36.01 2.52 14.29 hbster et Rasures a 2.00 0.44 0.16 2.75 0.96 0.25 3.84 2.34 0.51 4.59 5.56 0.62 8.97 12.68 1.00 12.68 - 3.00 0.19 0.08 2.38 0.42 0.15 2.80 1.21 0.31 3.90 2.91 0.42 6.93 7.41 0.72 10.29 Clatk et amsuw c - 0.25 1.49 0.44 3.39 3.19 0.65 4.91 6.63 1.23 5.39 15.79 1.44 10.97 32.32 2.17 14.89 - 0.50 IA1 0.41 3.44 3.00 0.60 5.00 6.13 1.11 5.52 14.54 1.28 11.36 29.23 1.89 15.47 - 0.75 1.33 0.38 3.50 2.83 0.56 5.05 5.68 1.01 5.62 13.46 1.16 11.60 26.62 1.67 15.95 PFem e__ 614.39 -M32.11 19.13 392.23 17.25 224 Z13.00 2 244.63 1149 21.29 175.40 8.19 | 21.42 TABlE 7: Statistics for Testing Significance of Poverty Differences Aiong Regions: Cte d'lvoire, 1985 Poverty Line = CFAF 162.61 Other Other West Abidjan Abidjan Abidjan Urban Urban Other Forest West East Poverty Measures Other West East Abidjan West East Urban East Forest Forest Urban Forest Forest Savannah Forest Forest Savannah Forest Savannah Savannah Head-count Ratio -3.10* -4.71* -11.91* -18.51* -2.10* -8.70* -15.01* -5.77* -11.52* -5.93* Poverty gap Ratio -2.25* -4.05* -10.14* -15.08* -2.46* -8.40* -13.75* -5.15* -10.86* -6.51* Watts Measure -2.13* -3.91* -9.19* -13.43* -2.47* -7.73* -12.44* -4.71* -10.06* -6.24* Foster et Measures a = 2.00 -1.75 -3.55* -8.00* -12.09* -2.43* -6.88* -11.37* -4.01* -9.21* -6.05* = 3.00 -1.35 -3.19* -6.36* -9.97* -2.29* -5.58* -9.50* -3.26* -7.91* -5.40* Clark et Measures c = 0.25 -2.17* -3.93* -9.50* -13.92* -2.47* -7.98* -12.86* -4.84* -10.30* -6.35* = 0.50 -2.19* -3*99* -9.77* -14.38* -2.48* -8.16* -13.23* -4.96* -10.54* -6.44* = 0.75 -2.22* -4.03* -9.94* -14.77* -2.47* -8.25* -13.51* -5.06* -10.73* -6.47* Mean consumption per person 6.09* 9.19* 10.84* 13.25* 4.46* 7.12* 11.36 2.96* 7.85* 4.91* * Poverty differences are significant at 5S level. - 26 - household. The empirical results in the table show that poverty varies widely among the regions. For instance, only 5.25 percent of the population is poor in Abidjan whereas in Savannah it is as high as 61.62 percent. All the poverty measures tell the same story: poverty in Savannah is distressingly high whereas in Abidjan it is extremely low. The values of t are considerably larger than 1.96 in all the regions which implies that every region in Cote d'Ivoire has significant poverty. To test whether poverty differences between regions are statistically significant, we computed the value of n given in (4.2) for all possible pairs of regions. The numerical values are presented in Table 7. The last column in the table provides the values of statistics for testing the significance of differences of mean consumption per person (adjusted for size and composition of the household). All the mean consumption differences are significant at the 5 percent level. Thus, the observed differences in mean consumption among the regions are not due to sampling errors. There are some other facts which must be analyzed to explain such wide differences. Almost all poverty measures show significant poverty differences among the regions. One exception is when we compare Abidjan with Other Urban Cities, for which Foster et measures show insignificant differences. The results clearly indicate that poverty in rural areas is significantly higher than that in urban areas. Poverty differences between regions are statistically significant even within rural and urban regions. Thus, the geographical location of a household has a sizeable effect on the poverty level. - 27 - The economic welfare of a household is closely associated with the age of the head. In many countries it has been observed that income per household shows a marked rise, from a low for the under 26 age of head class, to a peak for the 45 to 54 age class, and then a sharp decline to a trough in the 65 and over class (Kuznets 1974). This phenomenon may be explained by skills and experience acquired before a person settles down to a particular field of work. At the age of 65, a sharp decline in income is faced, at retirement from the work force. The age of the head may also have a close relationship to the household size. The size of a household increases with the age of the head as children are born and added to the family. Poverty comparisons by age of household head are presented in Table 8. The last column in the table presents the mean consumption per person. The incidence of poverty is highest among households where the head is over 65 years. This group has the lowest per capita consumption. The age group 46 to 65 also has a fairly high incidence of poverty. The absolute magnitude of t exceeds 1.96 in most cases implying that significant poverty exists in all age groups. Table 9 presents values of n for testing significance of poverty differences among households with different age of household head. The results indicate that poverty differences are insignificant when we make pair comparisons of the age groups (< 26), (26 to 35) and (36 to 45). Poverty in the age group (46 to 65) is significantly higher than that in the three lower age groups. The age group 65 and over has significantly higher poverty than any other age group. Thus, the age of head, when it exceeds 45 years becomes an important determinant of poverty. JaZ 8: rOax oqarfama by, AV of Indxld mal: (te dJImie, 1985 Poverty ULne CFAF 162.61 < 226 26 to 35 36 to 45 46 to 65 > 65 Poverty Measures Valhe Value Value I UaValue Of Of o-f Of jOf Porerty Stardard t Poerty Standird t Poverty Standard t Poverty Standard t Poverty Stardard t M?amure error Value lMasure error Value l-asure error Value Masure error Value l-asure eerror Value IIem-count Ratio 22.13 5.27 4.20 18.59 2.19 8.49 19.22 2.13 9.02 31.50 1.77 17.80 42.40 3.86 11.11 Poverty gap Ratio 5.40 1.67 3.23 5.24 0.76 6.89 4.72 0.68 6.94 10.85 0.77 14.09 18.82 1.98 9.51 Ibtte lure 6.99 2.40 2.91 6.88 1.07 6.43 6.09 0.94 6.48 15.51 1.23 12.61 28.04 3.30 8.50 Foster et lSamires ct - 2.00 2.03 0.88 2.31 2.12 0.39 5.44 1.80 0.33 5.45 5.24 0.47 11.15 9.98 1.29 7.74 - 3.00 0.96 0.53 1.81 1.00 0.22 4.55 0.82 0.19 4.32 2.93 0.32 9.16 5.87 0.92 6.38 Clatk et Maues c - 0.25 6.52 2.17 3.00 6.40 0.98 6.53 5.69 0.86 6.62 14.05 1.08 13.01 25.11 2.85 8.81 - 0.50 6.10 1.98 3.08 5.97 0.90 6.63 5.33 0.79 6.75 12.81 0.95 13.48 22.66 2.49 9.10 - 0.75 5.73 1.82 3.15 5.58 0.83 6.72 5.01 0.73 6.86 11.76 0.85 13.84 20.59 2.21 9.32 ctmq _ __tia_ per person 357.94 36.06 9.93 487.91 27.55 17.71 392.26 23.07 17.00 298.38 10.99 27.15 220.91 15.14 14.59 TABLE 9: Statistics for Testing Significance of Poverty Dtfferences Aenng Households With Different Age of Household Hled: Obte d'Ivoire, 1965 < 26 < 26 < 26 < 26 26 to 35 26 to 35 26 to 35 36 to 45 36 to 45 46 to 65 Poverty Measures 26 to 35 36 to 45 46 to 65 > 65 36 to 45 46 to 65 > 65 46 to 65 > 65 > 65 Head-count Ratio 0.62 0.51 -1.69 -3.18* -0.21 -4,58* -5.48* -4,43* -5.37* -2.68* Poverty gap Ratio 0.09 0.38 -2,96* -5.18* -0.51 -5.19* -6.40* -5.97* -6.74* -3'75* Watts Measure 0.04 0.35 -3.16* -5.16* 0.55 -5.29 -6_ 10 -6.09 -6.40 -3.56 Foster et Measures a = 2.00 -0.09 0.24 -3.22* -5.09* 0.63 -5.11* -5.83* -5,99* -6.14* -3,45* = 3,00 -0.07 0.25 -3.18* -4.62* 0,62 -4.97* -5.15* -5,67* 5,38* -3,02* Clark et Measures 0.25 0.05 0.36 -3.11* -5.19* 0.54 -5.25* -6.21* -6.-06* -6.52* -3.63* - 0.50 0.06 0.36 -3.06* -5.21* 0,53 -5.23* -6.30* -6.05* -6.63* -3.70* 0.75 0.07 0,37 -3aO0 -5.19 0.52 -5.20* -6.36* -6.02* -6.69* -3.73t Mean consumption per person -2.68* -0.80 1.58 3.50' 2.66' 6.39' 8.49' 3.67' 6.21* 4.,14* * Poverty differences are significant at 5% Jevel. - 30 - Tables 10 and 11 present numerical results for poverty comparisons of households classified according to the employer of the household head. Poverty is zero among households whose head is employed by parastatal firms (government-owned corporations). The households whose head is self-employed are most susceptible to poverty. It is interesting to observe that households whose head was not working have lower poverty than those whose head is self- employed. This second group of households has a much lower poverty level than the national average. Unemployment is more common among the non-poor households. Glewwe (1987) points out that some of these households may be entirely composed of retired persons living on pensions or other sources of transfer income. The numerical results in Table 11 show that most of the poverty differences are significant at the 5 percent significance level, suggesting that the employer of the household head is an important factor affecting poverty. Although households whose head is unemployed have significantly higher per capita consumption levels than those whose head is self-employed. All poverty measures do not indicate a significant difference in their poverty levels. Foster et measures show that poverty differences between the two groups are insignificant. Similarly, per capita consumption differences between households whose head is employed by government and parastatal firms are not significant. However, the government employed households have significantly higher levels of poverty than those employed by parastatal firms. This is indicated by all poverty measures presented except the Foster et measures when a = 3.0. TARX 10: poverty arm m of gmgdl&b Acati to aployer af lbntuld Bud: C&e d'volre, 1985 Nome G ertaent Parasttal Private Self-eloyed PoFerty tmre Valhe Valhe Value Valhe Valt_ of of of of of Powrty anaxrd t Poverty MaWard t Poverty Waindard t Poverty Sardard t Poverty 9tandard t M_asure error Value Lasure error Value 1kasure error Value Measure error Value Measure error Value lnad-comt Ratio 21.95 3.49 6.29 3.31 1.34 2.47 0.00 0.00 - 7.07 1.79 3.95 36.54 1.51 24.20 Povrty gap Ratio 8.73 1.57 5.56 0.45 0.20 2.25 0.00 0.00 - 1.59 0.48 3.31 12.35 0.65 19.00 btts eastre 12.25 2.33 5.26 0.49 0.22 2.23 0.00 0.00 - 1.94 0.61 3.18 17.56 1.04 16.88 Foster et mwres e - 2.00 4.24 0.89 4.76 0.07 0.03 2.33 0.00 0.00 - 0.51 0.19 2.68 5.90 0.40 14.75 -3.00 2.27 0.54 4.20 0.01 0.06 0.17 0.00 0.00 - 0.19 0.08 2.38 3.27 0.27 12.11 Clark et ea B - 0.25 11.18 2.09 5.35 0.48 0.21 2.29 0.00 0.00 - 1.84 0.58 3.17 15.93 0.91 17.51 - 0.50 10.25 1.89 5.42 0.47 0.21 2.24 0.00 0.00 - 1.75 0.54 3.24 14.55 0.81 17.96 - 0.75 9.44 1.72 5.49 0.46 0.20 2.30 0.00 0.00 _ 1.67 0.51 3.27 13.37 0.72 18.57 djusted cowuntion per per capita 331.93 21.01 15.80 648.33 45.07 14.38 516.05 60.50 8.53 487.37 30.65 15.90 265.85 8.27 h32.1 TSEM H: Slaetlatics owe Tootieg SIgmf Iscma.4 Of vwly oIffenees Ameurdiag to IEvilowpor a# usebt d Ibad: 0ft. dolwIfr, WSS Sen- 11110- Noo- Wat- Governmant Government Govenwent PARASTATAL ,PARASTATAL PRI VATE Povery Measures Glovernment Parmatatal Privet. Self-emlployed Parastatal' Pri vate Self -employed PRIVATE SELF-EW~LOYED SELF-EWLOYEO How-covat Ratto 4.99' 6.20' 3.79' -3.84' 2.47' -I."6 -6.6 -3.95' -24.20' -P2.58' Plovety gap RastIo 5.23' 5.56' 4.35' -2.13' 2.25' -2.190 -17.50' -3.31' -19.00' -13.32' Mott$ Neemure 5.02' 5.26' 4.281' -2.06' 2.23' -2.24' 1*6 -3.18' -16.88' -12.96' Foster ot easmures 01 2.00 4.68' 4.76' 4.10' -1.70 2.33' -2.29' -14.53' -2.68' -14.75' -12.17' * 3.00 4.16' 4.20' 3.810 16 -0.17 -1.80 -11.79 -2.31' -12.11' -10.94' Clark et measures B=0.25 5.09' 5.35' 4.31' -2.06' 2.29' -2.20' -16.54' -~3.17' -17.51' - 13.06' *0.50 5.14' 5.42' 4.32' -2.09' 2.24' -2.21' -16.65' -3.24* -17.96' -13.1 5 =0.75 5.19' 5.49' 4.33' -2.11' 2.30' -2.210 -17.28' -3.27' -16.57' -13.260 Adjusted consump- tion pe capita -6.360 -2. 87' -4.18' 2.93' 1.75' 2.95' 6.35' 0.42' 4.10' 6.96' 'Pwovrty dlftereaces are slIgnIficant at 5S level. - 33 - In C6te d'Ivoire there were 65 percent of households whose head had no education. This figure varied considerably between regions. For instance, Abidjan had about 36 percent of such households whereas in Savannah the figure was as high as 93 percent. It is possible that significant poverty differences observed earlier between regions are attributed to educational levels of the household head. Tables 12 and 13 present the poverty comparisons of households classified by the education of the household head. As expected, poverty is highest among households whose hea4 had no education. Poverty decreases monotonically with the education level of the household head. Households whose head attended senior high school have zero poverty. But those households whose head had a university education have statistically insignificant poverty level. Poverty differences between these two groups are not significant at the 5 percent level. The numericatl results show that education (up to senior high school) of the household head has an important bearing on poverty. Education even up to elementary school can significantly and substantially reduce poverty. Ik _lb rakyfqmn _IF 1-1:j GE a b h e d'bti, 198b Pawerty Line IFAF 162.61 None EI*taty Selmol Jumior Hlgh Sdhool Senior High School University Fowrty uies Value Value Value Value Value of Of of of of Poverty Stanidr t Powrty Standad t Poverty Sta,Ird t Pverty Standard t Paverty Standard t _ _ _ sure error Vahue Iasure error Value Ihasore error Value tasure error Value astwe error Value Hl&-CMXut Patio 35.62 1.48 24.1 2D.09 2.52 8.00 3.62 1.55 2.30 0.00 o.0o - 1.25 1.51 0.83 Poverty gap Ratio 12.43 0.65 19.10 5.30 0.87 6.10 0.75 0.34 2.20 0.00 0.00 - 0.52 0.63 0.82 ltas be 17.75 1.04 17.10 7.01 1.23 5.70 0.85 0.39 2.20 0.00 0.00 - 0.68 0.82 0.83 Foster et Maasug_s Uf - 2.00 6.00 0.40 15.00 2.19 0.45 4.90 0.17 0.09 1.90 0.00 o.0o - 0.22 0.27 0.81 - 3.00 3.34 0.28 11.90 1.06 0.25 4.20 0.04 0.02 2.00 0.00 0.00 - 0.09 0.11 0.82 Clark et Ihames B - 0.25 16.08 0.91 17.70 6.50 1.12 5.80 0.82 0.38 2.20 0.00 0.00 - 0.64 0.77 0.83 - 0.50 14.67 0.81 18.10 6.06 1.02 5.90 0.80 0.36 2.20 0.00 0.00 - 0.60 0.72 0.83 = 0.75 13.46 0.72 18.70 5.66 0.94 6.00 0.77 0.35 2.20 0.00 0.00 - 0.56 0.68 0.82 1 pea 254.18 6.15 41.31 323.70 13.68 23.70 578.86 40.02 14.50 790.00 68.69 11.50 1285.95 128.86 10.00 TAE 13: Statlstles for T.stii Sifif loes. of I_rty If9 faffasas Ao iaseelds With l1f bfrt EdNetluei Le1is of IbNAsld Heeds Cit dIvolire. 1965 Elementary Elementary Elementary Junior Junior Senlor NO" None Non Nne shool School School High Schcol High School High School Elemeatary Julor 5Selr Junlor Senior Senior Scho Nigh School High School University High School High School Iniversity High School University University Nead-caut Ratlo 5.32' 14.95' 24.10* 16.2P 7.190 8.00' 6.410 2.30* 1.10 -0.63 Poiarty V Ratio 6.54' 16.00' 19.10* 13.09' 4.84* 6.10* 4.43' 2.200 0.32 -0.82 Watts _aure 6.67' 15.22 17.10' 12.93' 4.770 5.70* 4.26' 2.20* 0.19 -0.62 > Foster et _easura us 2.00 6.35' 14.22 15.00 12.040 8.42* 4.90' 3.79* 1.90' -0.16 -0.61 * 3.00 6.16' 11.786 11.900 10.83' 4.25' 4.200 3.73* 2.00' -0.50 -0*62 C e t.t _a 0. 0.25 0.65 15.57' 17.70t 12.97* 4.81' 5.80' 4.31' 2.20 0.21 -0.63 a 0.50 6.62' 15.56' 16.10' 12.91* 4.87* 5.90' 4.370 2.2P0 0.25 -0.63 a 0.75 6.6t1 1566' 16.70* 13.03- 4.89 6.00' 4.40' 2.20* 0.28 -0.62 per garage -4.63' -6.02' -7.60' 4.00 -6.03' -6.6 -7.430 -2.56 -5.240 -3.40' f_vty differences we saplificfat at 5 percent level. - 36 - 8. CONCLUSIONS The main contribution of this paper has been to provide distribution free asymptotic confidence interval and statistical inference for poverty measures. The methodology developed is applied to analyze poverty in C6te d'Ivoire. The empirical results suggest that observed differences in values of poverty measures may lead to misleading conclusions without the statistical tests. Some poverty measures may show significant differences in povert,Y while others may show insignificant differences. This is an important finding which suggests an appropriate measureMshould be selected before embarkinjg on the analysis of poverty differences between populations. The results also suggest that poverty measures which give greater weight to income transfers among the most poor may have larger confidence intervals. This raises a difficult question: should a desirable poverty measure be rejected because of undesirable statistical properties? This issue is of crucial importance when the sample size is small. The paper demonstrates how to use statistical inference to analyze tpoverty. The importance of these statistical tests cannot be overemphasized because the poverty measures are estimated on the basis of sample observations. gowever, these tests-are based on the assumption that samples used are representative of the population they are drawn from. In practice this assuption maybe violated due to non-response errors.31 Moreover, non- _/ The Living Standards Survey data for C6te d'Ivoire, 1985, used in the present paper had a 92 percent response rate, therefore, the possibility of large non-sampling errors is very small. : : \ : \ : :rs r - 37 - sampling errors may be so large that it makes little sense to worry about sampling errors. Greater attention should be paid to the non-sampling errors in future work. - 39 - RFERENCES Ainsworth, Martha and Juan Muntoz, 1986, "The C6te d'Ivoire Living Standards Survey: Design and Implementation", Living Standards Measurement Study Working Paper No. 26, The World Bank, Washington, D.C. Cramer, H., 1946, Mathematical Methods of Statistics, Princeton: Princeton University Press. Clark, S., Richard Hemming and David Ulph, 1981, "On Indices for the Measurement of Poverty", The Economic Journal, Vol. 91, June, pp 515-526. Foster, J., Joel Greer and Eric Thorbecke, 1984, "A Class of Decomposable Poverty Measures", Econometrica, Vol. 52, pp 761-766. Glewwe, Paul, 1987, "The Distribution of Welfare in the Republic of Cote d'Ivoire in 1985", Living Standards Measurement Study Working Paper No. 29, The World Bank, Washington, D.C. Kakwani, N., 1980, Income Inequality and Poverty: Methods of Estimation and Policy Applications, New York: Oxford University Press. Kakwani, N., 1980a, "On a Class of Poverty Measures", Econometrica, Vol. 48. Kakwani, N., 1984, "Issues in Measuring Poverty"i, Advances in Econometrics, Vol. 3. pp 253-282. Kakwani, N., 1986, Analyzing Redistribution Policies: A Study Using Australian Data, New York: Cambridge Univer_ityPre`ss. Kuznets, S., 1974, "Demographic Aspects of the Distribution of Incomes among Families: Recent Trends in the United States", in Willy Sellekaerts (ed.), Econometrics and Economic Theory: Essays in honour of Jan Trinbergen, London: MacMillan Press Ltd., pp. 223-245. Lipton, Michael (1988), "Poverty: Concepts, Thresholds and Equity Conflicts", International Food Policy Research Institute, Washington, D.C. Sen, A., 1976, "Poverty: An Ordinal Approach to Measurement", Econometrica, Vol. 44, pp 219-231. Sen, A., 1979, "Issues in the Measurement of Poverty", Scandinavian Journal of Economics, Vol. 81, pp 285-307. Takayama, N., 1979, "Poverty, Income Inequality and their Measures: Professor Sen's Axiomatic Approach Reconsidered", Econometrica, Vol. 47, May, pp 747-760. Thon, D., 1983, "A Note on a Troublesome Axiom for Poverty Indices", The Economic Journal, Vol. 93, pp 199-200. Watts, H.W., 1968, "An Economic Definition of Poverty", in D.P. Moynihan (ed.), On Understanding Poverty, pp. 316-329, New York$ Basic Books. Distributors of World Bank Publications ARGNTNA PRACE MEXICO SAIN in H ISRL Wom%PuNl$MM I EC MuMP,LimoA 5. G_1~ ~ ovum dib, AodoPF1 22Jl0 3 7 ilS Jlf . 4th Row.Ce.4S/iS 75116 Put lIWOlbp.MeDwO 741Mit IXmmAh RIMANIAIDKLA1RE1PUSUCOF MOROCCO 1 _CEtD06hmgudmaEDa AUSTRALAAuA N1IW CMD UNO.Vtadg t M d Cesed.eCe4391 M133OMOWNLNDR, A. Al 12n omaUt EdM.WAaf tE9a0ma VANUATU. AND WESTEN SAMOA D _ 1 C a DAWo&jowmb SRI LANKA AND liTE IiAlDIVES 11-13551Rod GECE NBTHRANDS hp 3132 KME 0PuK1u b PO E 24 246 , uS liS. Rojlirm P.O.E1Io I , SihteopylamA Gwdtne AIW26.1105 7241ALego~ months Gwidmd CL GUATEIA NUWDAIAND Gobe3l LUtmPladxSa,* 11111sUlxvvy md W SmadesSovim SWEDEN A-lOll CmkoCuihul Plp. fool Pdvabst Fwasr dwar 1i aN6woo.1 Now MuS PRPad&bdwotq .AN GmM a bty Andad R p 12 11Si6 Amodd M. MNG KONC. MACAO NXGEDA PJD. Dm311110 A aDetKM Usivuit NW Ubmit rFraewm.hapim ad Ma1aTw.317 61:t.4PeEdwwd mmiW, GlemowelIdluklgo WmrcW_UIoAll EANJGLADES HoogB Kmgdai S.IQ072S5oddsIhos As Sdym HUNCARY NORWAVY SWITTARLAND Ih.4.ulA es, Nmvm_nlhfmdat CmW Fbwuk*Uid D1b II/Am PD. am1 in BduldNwe vd 12 Ft.P,A I1739 13Udaest42 P.O. hBx 1523 od 4. NOWI ot Coopodi351 RULGIUM INDIA CH1111 CG, 11 Pu*hoIodmNaMon1bb AIRed PbdwhoPiVdbIA. OMAN AV. du Rd 211 Moun Road MEMRB b momSm b. Fwa.hmwdw 10Dnu Madi-WiOW P.D. 1o1412 SubArpmt IJfdohPI Usual SmvimdmAbomo....to BRAZIL Sm.&4bfm Caspo"d3312 PI DaeTemku5omodmal ISJN. Hmodlh MM$ PAKISTAN 5d0(IAmmso U111. BdOu"Ifdl. Mi'. DcAgmo Rum PoWGdoof"9 MO b-YQ ahr.Qsud TANZANIA 014 S. Pmd SP PO. Do N 729 Gdor UrtddtyPew 13/14AsdAllRood L3hoo, P.O. urs 9 CANADA New DeMd- 110 42 DereSdeam CP. IM1)BnuAwyke 17 C _two4. A,mu Edill I IDSroloM THAILAND J4BhM% Qabo C111 4-710 7M2 Aputao 3514 36DCRtmoSm, J035116 Lima 3143cmbRoad JoyndwalbmHosedBuildivi; Bo OIHNA SIb Mob Rod ihlp PID atM Roadal&,uminic Pubiliblg qw4gdor-55i09 NalSlwDook Stme TUDIDAD AITOBAGC, ANTIGUA H. P _011R Aum SARRIDA, BARBADOS4, 514D Fb%DSgJ 36-11205 KKaoi 0a. Road P.D. hO 1934 DOYMD1CAGRE&NADAGUYANA. soft Ilydenuld -S3O7 b*DwoM=ilm JAMAICA, MONTSERAT, ST. KirTua NEVIS, ST. WCXIA. COMROIA PFo_Ps Rh 7A MFloor POLAND ST. VDNT&GRENVINES Ibld. Nw TTbdu:Daw&Nw=e&xm ORPAN S SUnil AP Awa,2 h3170 Ahomdud.30409 PaeK(buyiNsu E9Watbb _DJgolaDS t001 Wa_mwa CGqe COSTA UCA U6AAkMog PORTUGAL UhoMTn4j. Lawknow-21 Uwor t.UGpl* TUREY Cd211.13 Rbu Do CAm701i H0 It4i AS Av. FGaodmGudi INDONESIA 13 Ub No.6lCadddNa49 oJom Pit bu. United Dsqql IL SW R dauo 3 SAUDI ARARIA, QATAR COTED'IVOIUE iJkS Lm J arD.kslm Caowltd' m eede Dfuai PhO.St P.O. hO 3196 UGANDA AthimbI7(CEDA) Rtys"11 Ugm hEodhup (14B. 41 IRELAND PD b n7145 Abtdm0( PlPnis TIDCPubbllm UNdD dmuolomSorvi KEmpSal 12 Nol&h lndut& Sur Bm-t aS2 CYPRUS DoNun I AlAbe. 5rd UNITRO ARAB EMIRATES DERB bd Wuma Sa Al Dss Coo, MEMRB Gul Ca PO. ho Nm9 ITALY PIdSoo P.O rnow Nlta Lm Cmmtormsut Sooo SPA P.O. S17155 .iohoBd_oPmsJLl20/10 It0dil. DENMARK Co_s Fo1*92 UNITrD K0NGOM 5 _Amd,UESdw 31.51n 4FA Ala Duildirg mojoloUd. RA Us 11 Dog lOsd S4rd P.O. a 3 1M190-Pl3Proindn C JAPAN P.O.11= 3S69 Alt. HIvpvInGU342PG DotmBu ookSwvod 01mmn 10- DOMYNCAN RWUNC 374 Hop &3.0snc Budkyo.d 113 slo T A. C.puA Tdkm 33, Mdmm_d Hamm Awed Sb*d URUGUAY _ * a 1aiomelmsbdli CAN" 3to P.O. am SS htOd Nbions! dd Ulo AputdoFPd I 2O W4YA Jeddak SiJaomlill Sfo D _.g AbMalokSwm(RAJIlAd. MootAd.D PD. B1 424 SINGAPORE. TAIWAN, MYANMAR. EL SALVADOR Nali 1RUNRI VINBZUELA PFoi hwamln Pudwmll_ow Ubamdd lou Avodd ual BhotArau,o S3NM KOUREA. ERPUC OF Privt, Kd. ApWd.D.337 EdlhAdoSmA. I.. M Pm Koom Sook Caopordo 0.0 lt F. Pd Indu btl Cwe 100A 5 Sivads Pa a 101, IKwagwhm dg. SEmi 24Nv wldudXt Rd YUGOSLAVIA EGT, ARA" UBMULIC OF stspareow 193jugodovmsusa Kadgo Al Abram KUWAITYUOIlrefRamik AtGa.Skro boomdSo. S SOLTH APAECA BOTSWANA YUlW0WdndT Tlm CAMo P.h5o 5 Frsie4siU ZIUADE COdard tKMweitplnisootur PmOe Zi.b.bd. TheModldo SDbmvw MALAYSIA Ahis. PO o BSF122.%SmokES.. I 01ora.WNWo UIS1dw-qMdeysCaSp1PA hw 1141 Haven Cirol Uookohp, tdwut CyOToM 400 PDILAND xmuuwfw ~ ~ tmatodS y1 PAX am Pn F.O ho 410 ~d 10Joaabu34 LSMS Working Papers (continued) No.36 Labor Market Activity in C6te d'Ivoire and Peru No.37 Health Care Financing and the Demand for Medical Care No.38 Wage Determinants and School Attainment among Men in Peru No.39 The Allocation of Goods within the Household: Adults, Children, and Gender No.40 The Effects of Household and Community Characteristics on the Nutrition of Preschool Children: Evidence from Rural C6te d'lvoire No.41 Public-Private Sector Wage Differentials in Peru, 1985-86 No.42 The Distribution of Welfare in Peru in 1985-86 No.43 Profits from Self-Employment: A Case Study of Cote d'Ivoire No.44 The Living Standards Survey and Price Policy Reform: A Study of Cocoa and Coffee Production in C6te d'Ivoire No.45 Measuring the Willingness to Pay for Social Services in Developing Countries No. 46 Nonagricultural Family Enterprises in Cote d'Ivoire: A Descriptive Analysis No.47 The Poor during Adjustment: A Case Study of C6te d'Ivoire No.48 Confronting Poverty in Developing Countries: Definitions, Information, and Policies No.49 Sample Designs for the Living Standards Surveys in Ghana and Mauritania/Plans de sondage pour les enquetes sur le niveau de vie au Ghana et en Mauritanie No.50 Food Subsidies: A Case Study of Price Reform in Morocco (also in French, 50F) No. 51 Child Anthropometry in COte d'Ivoire: Estimates from Two Surveys, 1985 and 1986 No. 52 Public-Private Sector Wage Comparisons and Moonlighting in Developing Countries: Evidencefrom C6te d'Ivoire and Peru No.53 Socioeconomic Determinants of Fertility in C6te d'Ivoire No.54 The Willingness to Payfor Education in Developing Countries: Evidencefrom Rural Peru No. 55 Rigidite des salaires: Donnees microeconomiques et macroeconomiques sur l'ajustement du marche du travail dans le secteur moderne (in French only) No. 56 The Poor in Latin America during Adjustment: A Case Study of Peru No. 57 The Substitutability of Public and Private Health Care for the Treatment of Children in Pakistan No. 58 Identifying the Poor: Is "Headship" a Useful Concept? No.59 Labor Market Performance as a Determinant of Migration No. 60 The Relative Effectiveness of Private and Public Schools: Evidencefrom Two Developing Countries No. 61 Large Sample Distribution of Several Inequality Measures: With Application to C6te d'Ivoire No. 62 Testing for Significance of Poverty Differences: With Application to C6te d'Ivoire No.63 Poverty and Economic Growth: With Application to C6te d'Ivoire No.64 Education and Earnings in Peru's Informal Nonfarm Family Enterprises No.65 Formal and Informal Sector Wage Determination in Urban Low-Income Neighborhoods in Pakistan No. 66 Testing for Labor Market Duality: The Private Wage Sector in C6te d'Ivoire No. 67 Does Education Pay in the Labor Market? The Labor Force Participation, Occupation, and Earnings of Peruvian Women No.68 The Composition and Distribution of Income in Cote d'Ivoire No. 69 Price Elasticities from Survey Data: Extensions and Indonesian Results The World Bank Headquarters European Office Tokyo Office 1818 H Street, N.W. 66, avenue d'Iena Kokusai Building Washington, D.C. 20433, U.S.A. 75116 Paris, France 1-1, Marunouchi 3-chome Chiyoda-ku, Tokyo 100, Japan Telephone: (202) 477-1234 Telephone: (1) 40.69.30.00 Facsimile: (202) 477-6391 Facsimile: (1) 40.69.30.66 Telephone: (3) 3214-5001 Telex: WUI 64145 WORLDBANK Telex: 640651 Facsimile: (3) 3214-3657 RCA 248423 WORLDBK Telex: 26838 Cable Address: INTBAFRAD WASHINGTONDC