The Implications of Demographics for Measuring Poverty in African Households

Transcription

1 The Implications of emographics for Measuring Poverty in African Households Yele M. Batana, World Bank, John M. Cockburn, Université Laval & PEP Andrew L. abalen, World Bank Keywords: Africa, poverty measurement, equivalence scale, pivot household, demographics, counterfactual distribution, sequential stochastic dominance, sensitivity analysis. Jel Classification: C1, C12, 31, I3, I32, O55 1

2 ABSTRACT The effect of demographics on poverty measurement based on per capita consumption is well known. Many studies have tried to reduce this effect by using equivalence scale approaches. However, the choice of scale is controversial and may lead to problems of comparability between countries due to differences in demographic structures and the choice of the pivot household for establishing the per capita poverty line. How then can we obtain more accurate poverty measures and more appropriate inter-country comparisons? Using the World Bank's African poverty database and the new international poverty line of $1.9, the current study investigates the sensitivity of poverty measurement to the size and the composition of households, and explores several approaches to estimate accurate poverty rates at regional and country levels. The equivalence scales approach is used with the adjustment suggested by eaton (23), which requires the identification of a pivot household. The results are compared with those obtained through an approach of counterfactual distribution based on the joint distribution of size and composition of household for three reference countries. In addition to the reduction of the influence of demographics on poverty, results also show some re-rankings between countries. Finally, a third approach, using the stochastic dominance analysis, shows that most one-dimensional dominance relations based on per capita and equivalence approaches disappear when demographics are taken into account through the sequential stochastic dominance. 2

3 1 INTROUCTION Global monitoring of poverty uses per capita consumption - total household consumption divided by the number of household members - as the core measure of welfare. Thus, all household members are assumed to have the same consumption needs, regardless of age and sex. Moreover, this approach ignores any economies of scale in household consumption. Economies of scale are often enjoyed in the presence of goods, such as housing or consumer durables, that are shared at the household level. As these goods contribute to the welfare of all household members, larger households have smaller per capita consumption needs. These issues are particularly important in Africa, where households tend to be larger and to contain a large share of children. Indeed, per capita poverty rates generally show a strong positive correlation with household size. Most poverty lines are established, based on a reference household with a given size and composition. Thus, when the capita approach is used, poverty may be actually underestimated for households that are smaller or have a larger share of children than the reference household, and overestimated for larger households or households with proportionally less children. Both issues, when addressed, result in changes to the profiles of the poor, and potentially overall poverty estimates (Coulter et al, 1992). To what extent are current measures of poverty in Africa robust to alternatives to per capita measures of consumption? Lanjouw and Ravallion (1995) already found that an efficient adjustment of the household average income by its size and composition is likely to reduce the correlation between poverty estimates and demographics. Many studies address the issue using equivalence scales, with the aim to more adequately measure poverty and its links with the size and the composition of household (inter alia Klasen, 2; Ray, 2; Meenakshi and Ray, 22; White and Masset, 23; Streak et al, 29). The use of equivalence scales is a generic approach to adjusting total household consumption by taking into consideration the size and demographic composition of the household. This requires estimation of two parameters: one which scales each household's composition to a common unit, usually an adult equivalent, and another that accounts for economies of scale in consumption (bulk purchases, sharing of furniture, etc.). Most studies on this issue focus on one or few countries, without addressing the issue from a regional or a global perspective. Recently, Chen and Ravallion (21) presented poverty rate estimates for major regions of the world based on the per capita expenditure approach, and the international (dollar-a-day) poverty line. As emphasized by Batana et al (213), when considering various equivalence scale approaches, the estimates of global poverty rates can significantly vary. They found that, when a conservative estimates of economies of scales and discount factors are used, overall poverty rates fall dramatically and child-adult gaps in the global or regional extreme poverty estimates are much smaller than the one obtained using simply the per capita approach. 3

4 Even if equivalence scales, and discount factors can mitigate these methodological biases, there is no consensus rule to guide the choice of a particular method (Coulter et al, 1992; eaton, 23; eaton and Zaidi, 22). Moreover, even when a method is adopted, the equivalence scales are not easily comparable between countries insofar as there is no certainty that the needs of individual households, in relation with their size and composition, are identical in all countries. Indeed, Lancaster et al. (1999) find that equivalence scales, while varying according to child age groups, also differ according to countries. The same result is obtained by uclos and Mercader-Prats (1999), who compare Spain and United Kingdom. In this situation, some authors (e Vos and Zaidi, 1997; Streak et al, 29) advise considering several definitions of equivalence scales to analyze the sensitivity of poverty measurement. eaton (23), eaton and Zaidi (22), and Ravallion (215) propose the use of a reference household as a pivot such that the poverty measure for people from households with the same characteristics is unchanged regardless of the choice of equivalence scale. In theory, the pivot should be the reference household used to calculate the dollar-a-day poverty line. Moreover, authors like Coulter et al (1992) emphasize, that choosing different equivalence scales may affect not only the level of poverty of a country or a group of individuals, but also the rankings between groups or countries. Bourguignon (1989) suggests a criterion for dominance in social welfare by considering household size, especially since the needs of households may vary with their size and composition. How can we obtain more accurate poverty measures and make more appropriate between-country comparisons? Beyond determining overall poverty rates for a country, a region or in the world, the choice of equivalence scale also alters the identification of the poor (poverty profile) in order to generate appropriate policies. This involves making comparisons between different categories of household or between countries or regions. This study will investigate the sensitivity of poverty measurement to the size and the composition of households, and explore several alternative approaches for estimating more accurate poverty rates at regional and country levels. This, theoretically at least, should minimize the effects of household size and composition when comparing poverty estimates between countries. Using the World Bank's African poverty database, poverty rates are estimated using the new international poverty line of $1.9 defined in terms of 211 purchasing power parity (PPP). The first approach is based on equivalence scales with the use of the adjustment method suggested by eaton (23). Two equivalence scales are considered, namely the FAO/WHO equivalence scales adopted by Batana et al (213), and the square root equivalence scales. The former takes account of the size and composition of households while the latter incorporates only size effects. According to Ray (2) and Meenakshi and Ray (22), the square root method may be suitable for countries where large families comprise relatively many children (for instance developed countries), since the effects of the size and composition of households tend to be linked. It is different for 4

5 most developing countries where, with the existence of extended and polynuclear families, a household may include many adults. The second approach uses a counterfactual distribution based on the joint distribution of size and composition (in terms of average age) of households in three countries (Botswana, Mauritius and South Africa). This makes it possible to derive poverty estimates for African countries under the assumption that they have the same household demographic distribution as the three reference countries. The last approach is the sequential stochastic dominance analysis which allows us to compare poverty between countries or groups of individuals over a full range of poverty lines, sizes of households and average ages of household members. Moreover, theoretically at least, it avoids the controversy over the choice of equivalence scale to yield poverty estimates for countries that are independent of household size and composition profile. The next section describes current demographics in Africa, as well as past and future trends. The third section focuses on poverty profiles estimated using the per capita consumption approach as a function of household demographics. Section four describes the various methods and approaches used to adjust poverty estimates to account for these demographics. The fifth section presents the adjusted poverty estimates, including some sensitivity analyzes. The subsequent section focuses on the results of the sequential stochastic dominance tests. Section seven concludes the paper. 2 EMOGRAPHICS IN AFRICA The study is mainly based on the World Bank's African poverty database. This includes the most recent survey in 35 African countries over the period This sample accounts for around 75% of the total population of Sub-Saharan Africa. The database contains information on household consumption as well as information on other socioeconomic and demographic characteristics of households. Consumption variable is adjusted so as to make it comparable between countries and to derive poverty rates by considering the share of people whose per capita consumption is less than $ 1.9 a day (in 211 international purchasing power parity - PPP). emographics are not homogeneous in Africa since there are significant disparities between countries. There are countries with large household sizes, including Mali, Senegal and Guinea-Bissau with more than 8 household members on average, while countries such as Botswana, Mauritius and South Africa appear to be smallest, with less than 4 members on average (cf. Part A of Figure 1). In all, the average household size varies from 3.5 to 9.5, which matters for the methodological choice for poverty measurement. 5

6 Moreover, the composition of household, as captured by the average adjusted household age 1, seems to vary from one country to another as shown by the Part B of the Figure. The average age of households varies from 12 (Niger) to more than 15 (Botswana, Mauritius and South Africa). In fact, countries with small household sizes tend to have the highest average age, which does not seem to be true for the large household size countries. Figure 1: emographics in African countries A - The average household size B - The average household age 1 16 Average household size Average adjusted household age BWA MUS ZAF NGA COG CMR STP SWZ MWI MOZ RWA CPV NAM ETH LSO UGA CIV MG TZA AGO BEN TGO ZMB LBR MRT SLE TC SN GIN NER SS BFA GNB SEN MLI NER TC SS MLI BFA GIN AGO MOZ UGA MG MWI GNB ETH LBR MRT BEN SEN SN ZMB RWA TGO TZA STP SLE COG CMR CIV SWZ NGA LSO ZAF BWA MUS Countries Countries Source: World Bank's African Poverty atabase. The Figure 2 shows the distribution of households in the sample of 35 African countries according to both the size and the age. The proportion of single adult households represent more than 1% of all households, while the adult households with size less than or equal to 3 represent a bit more than 2% of all households. On the whole, as illustrated by the Figure 1 and 2, there are large variations in household size. On the other hand, there are less but non-negligible variations in age distribution. 1 This is an adjusted average since the ages of all over 18 years old are truncated to 18. In this case when a household is composed only by adults, its adjusted average age will be 18 while its real average should be higher than 18. Then the variation in the adjusted average age is expected to capture the most significant aspect of household composition which is the presence of children in the household. 6

7 Figure 2: Proportion of households by both household size and average age 1. Proportion of households (%) Household size Adjusted average age Source: World Bank Africa Poverty atabase. The demographic transition results in population growth and changes in the age structure of the population. Since people's economic needs and contribution vary depending on the life cycle, demographic change may have effects on economic performance (Bloom and Canning, 24). For instance, large youth and elderly cohorts tend to be associated with slow pace of economic growth unlike large working-age cohorts. Moreover, given the links with poverty measures, demographic change may distort estimates of poverty projections when this dynamic aspect is ignored. Some African countries also seem to be experiencing some demographic transition. As shown in Figure 3, the proportion of individuals under 2 years has increased since the 6s to reach a peak during the 8s and 9s, before experiencing a gradual decline. This decline is mainly due to change in the children under 1. For example, it is expected that the proportion of under five will represent only 14% in 23 against about 18% in 196. This decrease was also observed for the age groups of 5 to 9 years. In contrast, it is rather observed a very slight increase for older children (1 to 19 years). Conversely, the proportion of elderly is expected to rise by more than one percentage point, from less than 2.5% to just over 3.5 between 196 and 23. These trends coincide with an increase in population growth rate since 196, followed by a decline from 198. In total, it is expected that the proportion of working age population (here 2 to 64 age group) will increase from 44% to 47%, which represents a certain demographic dividend. 7

8 Figure 3: emographic changes in Sub-Saharan Africa A - Various children age groups B - Elderly and population growth Proportion (% total population) age group 5-9 age group 1-14 age group age group Years Percentage Source: World Bank: Health Nutrition and population Statistics Proportion of elderly Population growth Years Figure 4: emographic changes in various developing regions A - Under five children B - Elderly 2 15 SSA LAC MENA EAP ECA Proportion (% total population) SSA EAP LAC ECA MENA Years Proportion (% total population) Years SSA: Sub-Saharan Africa; MENA: Middle East and North Africa; LAC: Latin America and Caribbean; EAP: East Asia and Pacific; ECA: Europe and Central Asia. Source: World Bank: Health Nutrition and population Statistics. The comparison with other developing regions shows that the demographic transition in Africa remains relatively low (see Figure 4). SSA will continue to have the highest proportion of under five children in 23. MENA and LAC, that had approximately the same proportion of under five in 196 as SSA (about 18%), will show the proportions of 8.4% and 7.1% respectively in 23, which represents about half that for Africa. The decline in the proportion of under five children was also relatively high in the EAP and ECA regions, with expected levels of around 6% in 23. The opposite scenario is 8

9 observed in the case of elderly whose proportion has increased. As before, the increase will be relatively low in SSA, while MENA, LAC and EAP, where elderly represented less than 4% in 196, will see their proportions increased respectively to 8%, 12% and 14% in 23. The ECA region, which had a proportion of 6%, will end at just under 14%. 3 POVERTY AN EMOGRAPHICS Poverty incidence is estimated in this section using per capita approach and considering the international poverty line of $1.9. The Figure 5 illustrates how demographics (size and age of household) are linked to the poverty incidence in SSA. In fact the poverty incidence varies from 5% for households with a single member to nearly 58% for households with 9 or more members (see Part A of Figure 5). This incidence increases monotonically as the household size increases. An inverse relationship could be observed with household age since the poverty incidence tends to decline when the age increase as shown by the Part B of Figure 5. These correlations may be explained by two main reasons. First, we can expect a trivial correlation between demographics and poverty due to the ability of each individual to generate income depending on age and sex. The second reason is the fact that demographics are involved in the measurement of wellbeing at household and individual levels, as well as in determining the poverty line. The ideal correction would have been to adjust the poverty measure in order to remove this second type of correlation. Figure 5: Poverty incidences by demographics in Sub-Saharan Africa A - Poverty and household size B - Poverty and household age Poverty incidence (%) Poverty incidence (%) member 2 members 3 members 4 members 5 members 6 members 7 members Household size 8 members 9 members 1 members + Source: World Bank's African Poverty atabase Adjusted average age of household (years) The correlations between poverty and demographics may occur at national level since, as shown in Figure 6, demographics vary substantially from country to another. Figure 6 shows to a certain extent the poverty correlation with household size (Part A) and age (Part B). This suggests that comparison between countries should take account of the differences in the demographic structures. 9

10 Figure 6: Poverty incidences by demographics in African countries A - Poverty versus household size B - Poverty versus household age 8 MG 8 MG MWI MOZ ZMB LBR GNB MWI MOZ LBR GNB ZMB 6 RWA LSO 6 RWA LSO Poverty incidence (%) 4 NGA SWZ UGA STP CIV COG CMR ETH BEN TGO TZA AGO SLE TC BFA NER SS GIN SEN MLI Poverty incidence (%) 4 NER BFA MLI SS TC ETH SEN GIN UGA AGO BEN TGO SLE TZA STP CIV COG CMR NGA SWZ 2 BWA ZAF NAM SN 2 NAM SN BWA ZAF CPV MRT CPV MRT MUS MUS National average household size National average household age Poverty rates Fitted poverty rates Poverty rates Fitted poverty rates Source: World Bank's African Poverty atabase. The correlations are finally analyzed by considering jointly the size and the average age. The results are illustrated in the Figure 7. Poverty appeared to be higher for both younger and smaller households. It appears however also higher for large-size adult households. When controlling for the size or for the average age, the trends of poverty are similar to what is observed in the previous Figures. Figure 7: Poverty incidence by both household size and average age 6 Poverty incidence (%) Household size Adjusted average age Source: World Bank's African Poverty atabase. 1

11 4 METHOS OF POVERTY AJUSTMENT 4.1 Equivalence scales Let s consider, for a given household, a general adult equivalent structure computed as follows: N eq θ na nc αi γ j. (1) i= 1 j= 1 = + In this case, i stands for each additional adult in the household, while j represents each child. If there is at least one adult in the household, usually the household head, the weight of the first adult with respect to consumption could be set to one such that: N eq θ nc i γ j (2) i= 1 j= 1 na 1 = 1 + α + The parameters α i and γ j are then the relative costs respectively of an adult i and of a child j of the household as compared to the cost of the first adult. They generally depend on a set of social and demographic characteristics such as the age and the gender of the individual. The variables n a and n c represent respectively the number of adults and the number of children in the household. The parameter θ is the size-elasticity and captures the economies of scale in the household. The per capita approach which is often used for poverty assessment studies in developing countries corresponds to the case in which the parametersα i, γ j and θ are all equal to 1. But in assuming that economies of scale exist in the household, many equivalence scales can be derived from this general formula. Two equivalence methods are considered here, namely the FAO/WHO approach and the square root approach. In the first case, α i and γ j will be provided by the required calories intake for each adult and each child with regard to their age and sex. In the second case, α i and γ j are set to one, while θ is equal to.5. The Equation (1) becomes: [ ].5 eq N na nc = + (3) As suggested by eaton (23), eaton and Zaidi (22) and recently by Ravallion (215), a straightforward way to adjust consumption by the number of adult equivalents is to select a reference household as "pivot", such that poverty in households with the Eq same demographics remains unaffected by changes in the parameters. Let N ref and N ref be respectively the household size and the number of adult equivalents for the reference household, then the consumption per adult equivalent y * for any household could be expressed as follows: 11

12 Eq y Nref y = Eq N N, (4) ref where y is the total household consumption. Then, the consumption per adult equivalent and therefore poverty will remain unchanged for the "pivot" households. A crucial question is determining the demographics of the reference household. Two approaches are used in this study. The first approach is to define the "pivot" as the household whose average caloric requirements are around 2,1 calories 2. The analysis of the distribution in terms of demographics of a sample of households whose caloric needs are around this figure allows to characterize the "pivot" as households typically comprising three members, two adults and one under-five child. The second approach rather considers households whose per capita consumption is around the international poverty line. This time, the distribution analysis leads to defining as "pivot" a households of five members, two adults and three children (one under-five years child, one child between five and nine years, and one over nine years child). To perform sensitivity analyzes, Equation (1) could be written in accordance with the formulation of Cutler and Katz (1992) as follows: ( α ) eq N na n θ c = + (5) In this case, the effect of the household size is captured by θ while the effect of the household composition is captured by a single discount factor α. 4.2 Counterfactual distribution approach The second method is to adopt a counterfactual distribution of demographics based on the joint distribution of household size and age for three countries (Botswana, Mauritius and South Africa). The demographic structure of these three countries corresponds to what we might expect at long term in African countries, after demographic transition. The poverty incidence for each country could be expressed as an additive index as following: P 1 18 Pi, jsi, j i= 1 j= 9 = with S w =, (6) wi, j i= 1 j= 9 i, j i, j The caloric needs of 2,1 calories per person per day appear to be the common figure considered to derive the international poverty line (Ravallion, Chen and Sangraula, 28). 12

13 where wi, jis the weighted population of individuals in households of size i and age j, S i, jis the proportion of population from households of size i and age relative to the total population, and Pi, jthe poverty incidence for group of households of size i and age j. We can then use the S i, j for the three reference countries as being the same for each African country. This method and the previous one are not exclusive and may be advantageously combined. While the equivalence scale adjusts the gap between groups due to differences in demographics, this is not the case for the counterfactual distribution approach. The latter provides simply poverty estimates based on the assumption that all African countries has the same demographics without taking into account the existence of economies of scale. Combining both methods may be helpful to assess the quality of the equivalence scale. The use of equivalence scale should narrow the poverty gap between the initial distribution and the counterfactual distribution. 4.3 Stochastic dominance method Let F A and F B be the cumulative density functions (CFs) of respectively two onedimensional distributions A and B representing two countries, regions or sociodemographic groups. istribution B is said to stochastically dominate distribution A at first order when FA( y) FB( y) for all y in the union of the supports of the two distributions. In the case where y are per capita consumptions and the union of the supports defined as a range of poverty thresholds, this dominance will be in term of poverty 3. The inclusion of an additional dimension such as the size or the age of the household defines the concept of sequential stochastic dominance. Many studies provide the conditions for stochastic dominance in poverty that take account of the differences in household size and composition (Atkinson, 1992; Chambaz and Maurin, 1998; uclos and Makdissi, 25), while other studies focus on applications (uclos, Sahn and Younger, 27; Batana and uclos, 211; Levine, Muwonge and Batana, 214). The first-order stochastic dominance conditions are presented in the Annex 1. The stochastic dominance analysis is not strictly speaking an alternative method of measuring poverty. It remains useful to make robust comparisons between countries regardless the poverty line level and demographics. The statistical inference is done using the approach suggested by avidson and uclos (2), with extension in two dimensions. 3 See Atkinson (1987), Foster and Shorrocks (1988a;1988b) and more recently avidson and uclos (213) for one-dimensional stochastic dominance in poverty. 13

14 5 AJUSTE POVERTY ESTIMATES 5.1 Poverty, demographics and country re-rankings Figure 8 shows the effect of the adjustment based on the approaches of equivalence scales on the correlation between poverty and demographics. Part A of the Figure shows the correlation with the household size while Part B instead shows the correlation with the average age of the household. In both cases, the correction can limit the influence of demographics on poverty measurement. The correlation is less strong with the adjustment as evidenced by the less steep curves observed for the FAO/WHO approach, and especially for the square root approach. Figure 8: Adjusted poverty incidences by demographics in Sub-Saharan Africa A - Household size B - Household age 6 6 Poverty incidence (%) member 2 members 3 members 4 members Initial per capita approach FAO/WHO equivalence scale Square root equivalence scale 5 members 6 members 7 members 8 members 9 members 1 members + Poverty incidence (%) Initial per capita approach FAO/WHO equivalence scale Square root equivalence scale Household size Adjusted average age of household (years) Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. The distribution of poverty incidence both according to the size and the average age of household seems to have lower variability compared to the initial case of the use of the per capita approach. Figure 9 shows this two-dimensional distribution for the FAO/WHO approach (Part A) and the square root approach (Part B). As noted above, the use of these scales equivalence approaches reduces the correlation between poverty and demographics, with a more pronounced reduction for the square root approach. 14

15 Figure 9: Poverty by both household size and average age, using adjusted equivalence approach A - FAO/WHO approach B - Square root approach 6 6 Poverty incidence (%) 4 2 Poverty incidence (%) Household size Adjusted average age Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase Household size Adjusted average age It is possible to enhance the comparability between countries by combining scales equivalence approaches with the counterfactual distribution approach which assumes that all African countries have the same demographic distribution as the three reference countries (Botswana, Mauritius and South Africa). Several scenarios are considered with their results in terms of poverty incidences presented in Table 1. The results suggest that the choice of the pivot influence significantly the poverty incidence. In fact, when the pivot household includes 3 rather than 5 members, the poverty incidence may decrease by 5.4 or 13.4 percentage points depending on whether the FAO/WHO or the square root approach is adopted. Whatever the approach considered (per capita or scales equivalence approaches), the use of the counterfactual distribution approach reduces poverty incidence. For instance, with the per capita approach, this reduction is 7.8 percentage points. Poverty reduction with scales equivalence approaches is much lower, which makes sense in so far as these approaches themselves already minimize the influence of demographics on poverty measurement. The pivot household with 5 members will be considered for further analysis. Table 1: Poverty incidence of African Region (35 countries), The pivot household includes 5 members The pivot household includes 3 members The initial distribution The counterfactual distribution Per capita approach 44.5% 36.7% FAO/WHO equivalence scale 43.1% 39.1% Square root equivalence scale 39.4% 36.8% FAO/WHO equivalence scale 37.7% 34.% Square root equivalence scale 26.% 24.% Source: World Bank's African Poverty atabase. 15

16 The poverty incidences for each country, and using three approaches (FAO/WHO, square root and counterfactual distribution), are compared with the initial per capita approach through the Figure 1. The Figure suggests that the country rankings in terms of poverty incidence change with the alternative approaches. For example, some countries such as Namibia, Senegal, Niger, Burkina Faso, Mali and Guinea-Bissau experience a significant decrease in poverty when the adjustment is done. With the counterfactual distribution approach, apart from the trivial case of the three reference countries that should not know change, most countries experience significant declines in poverty, especially those characterized by household sizes larger than that of the reference. It is clear that countries are re-ranked by these adjustments. The Kendall's rank correlation coefficients between the per capita approach and the 3 alternative approaches (respectively FAO/WHO, square root and counterfactual distribution) are.89,.85 and.84 respectively. However, according to the results of statistical inference, we may not conclude that the rankings derived from these various approaches are different. Figure 1: Adjusting for demographic composition changes a bit the profile of the poor Poverty incidence (%) Initial per capita approach FAO/WHO equivalence scale Square root equivalence scale Use of counterfactual distribution MUS CPV MRT SN ZAF BWA NAM COG CMR AGO CIV STP GIN UGA SEN TC ETH SWZ SS TZA MLI NER SLE BEN NGA TGO BFA LSO RWA ZMB GNB LBR MOZ MWI MG Countries in initial ranking Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. The question may be whether differences in demographics continue to be an issue for poverty measurement when the poverty estimates are already adjusted by scales equivalence approaches. Figure 11 shows that even when demographic differences matter, their influence on poverty measurement is relatively lower compared to the per capita approach. Poverty remains unchanged or slightly changed for a number of countries with relatively low household sizes (Botswana, Cape Verde, Mauritius, Namibia and South Africa). 16

17 Figure 11: Applying equivalence scales to the counterfactual distribution A - FAO/WHO approach B - Square root approach 8 Without counterfactual distribution With counterfactual distribution 8 Without counterfactual distribution With counterfactual distribution 6 6 Poverty incidence (%) 4 Poverty incidence (%) MUS CPV MRT SN ZAF BWA NAM COG CMR AGO CIV STP GIN UGA SEN TC ETH SWZ SS TZA MLI NER SLE BEN NGA TGO BFA LSO RWA ZMB GNB LBR MOZ MWI MG MUS CPV MRT SN ZAF BWA NAM COG CMR AGO CIV STP GIN UGA SEN TC ETH SWZ SS TZA MLI NER SLE BEN NGA TGO BFA LSO RWA ZMB GNB LBR MOZ MWI MG Countries in initial ranking Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. Countries in initial ranking 5.2 Poverty trends Table 2 shows the trends in poverty incidence over the past two decades in four selected African countries (Burkina, Ethiopia, Rwanda, and Uganda). Overall, household size has decreased slightly over this period, which is the result of the demographic transition. In Burkina Faso, the use of the per capita approach shows that poverty decreased by about 28 percentage points between 1994 and 212. When adjusting the poverty estimates by the scales equivalence approaches, this decline becomes 32 and 36 percentage points, respectively for the FAO/WHO and the square root approaches. This means that the poverty reduction for this country may be greater when considering demographics. This result can be explained by the relatively high average size of households for Burkina Faso, with an average number of 6.7 members which is greater than that of the pivot household. For the three other countries whose average household size is around 5 members as for the pivot, the poverty reduction is about 28 percentage points for Ethiopia ( ), 17 percentage points for Rwanda (2-21), and 11 percentage points for Uganda ( ), regardless the approach used. 17

18 Table 2: Poverty incidence trends in some selected African countries, Years Household size Per capita FAO/WHO Square root Household size Per capita FAO/WHO Square root Household size Per capita FAO/WHO Square root Household size Per capita FAO/WHO Square root Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. Burkina Ethiopia Rwanda Uganda What are the demographic characteristics of households that have contributed the most to the reduction of poverty? Figures 12 and 13 illustrate the situation respectively in Burkina Faso and Uganda. In Burkina Faso, with the per capita approach (Part A of Figure 12), the curve of the differences in poverty has an inclined slope down which clearly shows that the greatest reductions in poverty tend to occur in households with relatively small sizes. When adopting the FAO/WHO approach (Part B of Figure 12), the slope of the curve becomes flatter, reflecting a less strong correlation between poverty reduction and demographics. However, regardless the used approach, all categories of households experience a reduction in poverty. In the case of Uganda (see Figure 13), there was an increase in poverty for large size households while poverty has fallen sharply for households with relatively small sizes. Even if the pattern is almost the same for per capita approach (Part A of Figure 13) and FAO/WHO approach (Part B of Figure 13), disparities remain weaker in the second case. Figure 12: ifferences in poverty incidence in Burkina Faso, A - Per capita approach B - FAO/WHO approach ifferences in poverty incidence (%) Household size Adjusted average age Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. ifferences in poverty incidence (%) Household size Adjusted average age 18

19 Figure 13: ifferences in poverty incidence in Uganda, A - Per capita approach B - FAO/WHO approach ifferences in poverty incidence (%) Household size Adjusted average age Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. ifferences in poverty incidence (%) Household size Adjusted average age 5.3 Sensitivity analysis Let consider the adjusted consumption per adult equivalent provided in Equation (4) and the number of adults equivalent formulated in Equation (5). The effect of child discount factor will depend on the composition of household regarding that of the pivot. In fact, if the ratio of adults on children for a household is higher than that of the pivot (which is two-thirds when the pivot is household with 5 members, including 2 adults and 3 children), then its adjusted consumption per adult capita will increase in function of the child discount factor, which will tend to reduce poverty. Otherwise, the correlation between discount factor and consumption will be rather negative, with a consequent increase in poverty. For the whole Africa, the average ratio of adults on children is about 1.2 (higher than two-thirds), which explains why, for a given scale factor, the poverty incidence decreases with the child discount factor (see Table 3). With regard to the scale factor, the correlation with the adjusted consumption is trivially negative for households with sizes larger than pivot and positive for small size households. As shown in Table 3, when the scale factor decreases, which means that the economies of scale become higher, the poverty incidence tends to decrease at any given child discount factor. This result is consistent with the African region which generally includes large households. Table 3: Poverty incidence in Africa, by scale and child discount factors Scale factor (θ) θ =.5 θ =.75 θ = 1 Child discount factor (α) α =.5 41.% 43.9% 47.2% α = % 42.7% 45.7% α = % 41.7% 44.4% Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. 19

20 Figure 14 shows how the choices of scale and child discount factors affect the correlation between poverty and demographics. In the Part A of the Figure, which presents the poverty incidence in function of household size and equivalence factors, one can observe that the child discount factor is important for households with size lower than five, with lower levels resulting in greater poverty. However, it hardly affects poverty for households with size higher than five. On the other side, the scale factor affects poverty for all households. Low levels of θ, corresponding to higher scale factors, result in increases in poverty for households with sizes below 5 and decreases for households with higher sizes. The Part B of the Figure shows rather the correlation with household age. For households whose average age is 11 years or less, poverty is reduced when child discount factor decreases. The situation is reversed for households aged 12 years and over with sometimes quite important differences as in the case of households with average age higher than 15 years. Increasing the scale factor which means the decrease of θ, will result in poverty reduction for all households, except those including adults only. These households will see rather their poverty increased due to the component of equivalence formula using information on the pivot household. Figure 14: Poverty-demographics nexus by scale and child discount factors A - Household size B - Household age Poverty incidence member 2 members 3 members 4 members 5 members 6 members α =.5 & θ =.5 α =.5 & θ =.75 α =.5 & θ = 1. α =.75 & θ =.5 α =.75 & θ =.75 α =.75 & θ =1. α = 1. & θ =.5 α = 1. & θ =.75 α = 1. & θ = 1. 7 members 8 members 9 members 1 members + Poverty incidence α =.5 & θ =.5 α =.5 & θ =.75 α =.5 & θ = 1. α =.75 & θ =.5 α =.75 & θ =.75 α =.75 & θ = 1. α = 1. & θ =.5 α = 1. & θ =.75 α = 1. & θ = Household size Adjusted average age of household (years) Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. Table 4 shows the matrix of Kendall's rank correlation coefficients for understanding how the choice of equivalence factors may affect country rankings in terms of poverty. When a coefficient is equal to one, this means that the rankings induced by a choice of factors is identical to the initial rankings. Compared with the initial rankings based on the per capita approach, consider various scenarios for the scale and the child discount factors may vary the coefficient from.97 to.85, which can represent a quite important re-rankings. 2

21 Table 4: Poverty rank correlation in terms of countries by scale and child discount factors α =.5, θ =.5 α =.5, θ =.75 α =.5, θ = 1. α =.75, θ =.5 α =.75, θ =.75 α =.75, θ = 1. α = 1., θ =.5 α = 1., θ =.75 α = 1., θ = 1. α =.5, θ = α =.5, θ = α =.5, θ = α.75, θ.5 = = α =.75, θ = α.75, θ 1. = = α = 1., θ = α = 1., θ = α = 1., θ = Note: The pivot household is 5 members (2 adults and 3 children) Source: World Bank's African Poverty atabase. 6 STOCHASTIC OMINANCE ANALYSIS The last and less arbitrary approach uses a sequential stochastic dominance which is very suitable to compare poverty between countries or groups of individuals for a full range of poverty lines, sizes of households and average ages of household members. One should be then able, theoretically at least, to yield poverty estimates between countries that are independent of household size and composition. Figure 15: Consumption density curves for the whole Sub-Saharan Africa.3 Per capita approach FAO/WHO equivalence scale Square root equivalence scale ensity function.2.1 $.25 $ 1.9 $ Consumption (PPP US dollars) Source: World Bank's African Poverty atabase. The starting point of this approach is the implementation of standard stochastic dominance tests on one dimension, typically the per capita consumption. To avoid outliers often caused by the extreme values, restricted ranges of consumption levels will be considered. Such a restriction was suggested by avidson and uclos (213) who showed the difficulty or the impossibility to reject the non dominance hypothesis in 21

22 favour of dominance one over the entire supports of continuous distributions. Figure 15 presents the density curve of consumption by per capita and equivalence scale approaches for the whole ASS countries. Based on this Figure, the restricted ranges of consumptions are defined on the interval.25 to 5, since most households (at least 85% of the population) seem to have consumption levels belonging to this interval. The results of one-dimensional stochastic dominance tests are presented in Table B1 in Annex. Given that the sample covers 35 countries while dominance analysis is done for each pair of countries, the tests were performed on 595 possible dominance relations. From these relations, 24, a proportion of 4.3%, were found to be true dominance relations. A country as Mauritius appears to dominate most countries except ten countries. Further, the one-dimensional dominance tests are also performed considering the two approaches of equivalence scales and a per capita approach on only households with size equal 5. The results are compared with the initial per capita approach and presented in Figure 16. The found dominance relations are, in number, 242, 246 and 166 respectively for the FAO/WHO approach, the square root approach and the per capita approach based on the households with size equal 5. Figure 16: One-dimensional stochastic dominance relations by country Number of dominated countries Per capita approach FAO/WHO approach Square root approach Per capita approach (only households with size equal 5) MUS CPV CMR SN ZAF NAM AGO BWA MRT COG UGA TC CIV STP SEN SWZ BEN GIN RWA ETH TZA MLI SLE NGA TGO BFA NER SS MWI LSO ZMB GNB LBR MOZ MG Source: World Bank's African Poverty atabase. ominators countries Taking into account an additional dimension, in this case within the demographics, will allow to perform two-dimensional stochastic dominance analysis. The question here is to know how the consideration of a demographic dimension can affect the dominance relations in comparison to those obtained in the one-dimensional case. When the two considered dimensions are per capita consumption and household size, the results of the tests of stochastic dominance are presented in Table B2 in Annex. This Table contains less proved dominance relations than the first one, with only 23 proved relations out of the 595 possible dominance relations, which represents a proportion of about 3.9%. Table 22

23 B3 in Annex presents the results in the case where household size is replaced by household average age. The number of proved dominance relations is now 52 out of the 595 possible relations (a proportion of 8.7%). The results suggest that most poverty onedimensional dominance relations disappear when demographics are taken into account. Figure 17 compares the one-dimensional stochastic dominance with the sequential or two-dimensional dominance. It is therefore important to keep in mind that, given the role of demographics on poverty measurement, the robust poverty comparisons between countries based on the one-dimensional stochastic dominance do not necessarily mean that poverty is unambiguously higher or lower in one country than in another. To be able to draw such a conclusion, it is necessary to take into account the demographic dimension through two-dimensional sequential stochastic dominance. Figure 17: One versus two-dimensional stochastic dominance relations by country Number of dominated countries One-dimensional dominance (per capita consumption) Two-dimensional dominance (per capita consumption & household size) Two-dimensional dominance (per capita consumption & household age) MUS CPV CMR SN ZAF NAM AGO BWA MRT COG UGA TC CIV STP SEN SWZ BEN GIN RWA ETH TZA MLI SLE NGA TGO BFA NER SS MWI LSO ZMB GNB LBR MOZ MG ominators countries Source: World Bank's African Poverty atabase. 7 CONCLUSION This study shows that demographics matter for poverty measurement. First, poverty remains biased when the demographic characteristics of households are different from that of the reference household. Thus, poverty in a country or region will be higher or lower depending on it demographic structure. The use of equivalence scales in this study, based on the identification of a pivot household, has helped reduce poverty in Sub- Saharan Africa compared with the approach of per capita consumption. It has also shown how poverty may be overestimated in some countries where the size of households are relatively large on average. The same poverty patterns were observed when it was assumed that all African countries had the same demographic structure, corresponding to that which may be expected after the demographic transition. Although the use of equivalence scales may reduce the biases, there is currently no consensual method to ensure that they are totally removed. The reclassifications between countries in terms of 23

24 poverty, and according to the various approaches, do not appear to be statistically significant. The analysis of poverty over time also shows that poverty reduction based on equivalence scales may be greater than that observed with the per capita approach for countries (Burkina Faso for instance) where households are relatively large. Some sensitivity exercises allow us to analyze the role of scale and child discount factors in poverty measurement. If the scale factor affects poverty for all households, the choice of child discount factor appears to affect poverty more importantly for small households (with size lower than five) than for large households. Finally, while the adjustments to poverty measurement help significantly correcting poverty rates in several countries, they turn out to be insufficient to establish robust poverty comparisons between countries that take into account differences in demographics. Indeed, the stochastic dominance analysis shows that most one-dimensional dominance relations based on per capita and equivalence approaches disappear when demographics are taken into account through the sequential stochastic dominance. REFERENCES Atkinson, A. B. (1987), "On the Measurement of Poverty," Economica, 59: Atkinson, A. B. (1992), "Measuring Poverty and ifferences in Family Composition," Econometrica, 55: Batana, Y. M. and J.-Y. uclos (211), "Comparing Multidimensional Poverty with Qualitative Indicators of Well-being," in eutsch, J. and J. Silber (Eds) The Measurement of Individual Well-being and Group Inequalities: Essays in Memory of Z. M. Berrebi, , London: Routeledge. Batana, Y., Bussolo, M. and J. Cockburn (213), "Global Extreme Poverty Rates for Children, Adults and the Elderly," Economics Letters, 12: Bloom,. E. and. Canning (24), "Global emographic Change: imensions and Economic Significance," Working Paper 1817, Cambridge: NBER. Bourguignon, F (1989), "Family size and social utility: Income distribution dominance," Journal of Econometrics, 42: Chambaz, C. and E. Maurin (1998), "Atkinson and Bourguignon's ominance Criteria: Extended and Applied to the Measurement of Poverty in France," Review of Income and Wealth, 44: Chen, S. and M. Ravallion (21), "The eveloping World Is Poorer Than we Thought, but No Less Successful in the Fight Against Poverty," The Quarterly Journal of Economics, 125: